0.01/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.01/0.12 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM 0.13/0.33 % Computer : n026.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 1920 0.13/0.33 % WCLimit : 240 0.13/0.33 % DateTime : Wed Jul 30 02:15:04 EDT 2025 0.13/0.33 % CPUTime : 0.20/0.47 Running higher-order theorem proving 0.20/0.53 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=240 /export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p 2.01/0.96 # Version: 3.0.0-ho 2.01/0.96 # Preprocessing class: HSLMSLSSLLLCHFA. 2.01/0.96 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 2.01/0.96 # Starting ehoh_best5 with 240s (1) cores 2.01/0.96 # Starting almost_fo_3_lam with 240s (1) cores 2.01/0.96 # Starting new_bool_5 with 240s (1) cores 2.01/0.96 # Starting pre_casc_3 with 240s (1) cores 2.01/0.96 # Starting ho_unfolding_8 with 240s (1) cores 2.01/0.96 # Starting new_ho_10_cnf2 with 240s (1) cores 2.01/0.96 # Starting new_bool_3 with 240s (1) cores 2.01/0.96 # Starting new_ho_5 with 240s (1) cores 2.01/0.96 # new_bool_5 with pid 755 completed with status 0 2.01/0.96 # Result found by new_bool_5 2.01/0.96 # Preprocessing class: HSLMSLSSLLLCHFA. 2.01/0.96 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 2.01/0.96 # Starting ehoh_best5 with 240s (1) cores 2.01/0.96 # Starting almost_fo_3_lam with 240s (1) cores 2.01/0.96 # Starting new_bool_5 with 240s (1) cores 2.01/0.96 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 2.01/0.96 # Search class: HGHSM-FSLM32-MHFMMSBN 2.01/0.96 # Scheduled 10 strats onto 1 cores with 240 seconds (240 total) 2.01/0.96 # Starting ho_unfolding_8 with 44s (1) cores 2.01/0.96 # ho_unfolding_8 with pid 774 completed with status 0 2.01/0.96 # Result found by ho_unfolding_8 2.01/0.96 # Preprocessing class: HSLMSLSSLLLCHFA. 2.01/0.96 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 2.01/0.96 # Starting ehoh_best5 with 240s (1) cores 2.01/0.96 # Starting almost_fo_3_lam with 240s (1) cores 2.01/0.96 # Starting new_bool_5 with 240s (1) cores 2.01/0.96 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 2.01/0.96 # Search class: HGHSM-FSLM32-MHFMMSBN 2.01/0.96 # Scheduled 10 strats onto 1 cores with 240 seconds (240 total) 2.01/0.96 # Starting ho_unfolding_8 with 44s (1) cores 2.01/0.96 # Preprocessing time : 0.049 s 2.01/0.96 # Presaturation interreduction done 2.01/0.96 2.01/0.96 # Proof found! 2.01/0.96 # SZS status Theorem 2.01/0.96 # SZS output start CNFRefutation 2.01/0.96 thf(decl_23, type, in: $i > $i > $o). 2.01/0.96 thf(decl_24, type, exu: ($i > $o) > $o). 2.01/0.96 thf(decl_25, type, setextAx: $o). 2.01/0.96 thf(decl_26, type, emptyset: $i). 2.01/0.96 thf(decl_27, type, emptysetAx: $o). 2.01/0.96 thf(decl_28, type, setadjoin: $i > $i > $i). 2.01/0.96 thf(decl_29, type, setadjoinAx: $o). 2.01/0.96 thf(decl_30, type, powerset: $i > $i). 2.01/0.96 thf(decl_31, type, powersetAx: $o). 2.01/0.96 thf(decl_32, type, setunion: $i > $i). 2.01/0.96 thf(decl_33, type, setunionAx: $o). 2.01/0.96 thf(decl_34, type, omega: $i). 2.01/0.96 thf(decl_35, type, omega0Ax: $o). 2.01/0.96 thf(decl_36, type, omegaSAx: $o). 2.01/0.96 thf(decl_37, type, omegaIndAx: $o). 2.01/0.96 thf(decl_38, type, replAx: $o). 2.01/0.96 thf(decl_39, type, foundationAx: $o). 2.01/0.96 thf(decl_40, type, wellorderingAx: $o). 2.01/0.96 thf(decl_41, type, descr: ($i > $o) > $i). 2.01/0.96 thf(decl_42, type, descrp: $o). 2.01/0.96 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 2.01/0.96 thf(decl_44, type, dsetconstrI: $o). 2.01/0.96 thf(decl_45, type, dsetconstrEL: $o). 2.01/0.96 thf(decl_46, type, dsetconstrER: $o). 2.01/0.96 thf(decl_47, type, exuE1: $o). 2.01/0.96 thf(decl_48, type, prop2set: $o > $i). 2.01/0.96 thf(decl_49, type, prop2setE: $o). 2.01/0.96 thf(decl_50, type, emptysetE: $o). 2.01/0.96 thf(decl_51, type, emptysetimpfalse: $o). 2.01/0.96 thf(decl_52, type, notinemptyset: $o). 2.01/0.96 thf(decl_53, type, exuE3e: $o). 2.01/0.96 thf(decl_54, type, setext: $o). 2.01/0.96 thf(decl_55, type, emptyI: $o). 2.01/0.96 thf(decl_56, type, noeltsimpempty: $o). 2.01/0.96 thf(decl_57, type, setbeta: $o). 2.01/0.96 thf(decl_58, type, nonempty: $i > $o). 2.01/0.96 thf(decl_59, type, nonemptyE1: $o). 2.01/0.96 thf(decl_60, type, nonemptyI: $o). 2.01/0.96 thf(decl_61, type, nonemptyI1: $o). 2.01/0.96 thf(decl_62, type, setadjoinIL: $o). 2.01/0.96 thf(decl_63, type, emptyinunitempty: $o). 2.01/0.96 thf(decl_64, type, setadjoinIR: $o). 2.01/0.96 thf(decl_65, type, setadjoinE: $o). 2.01/0.96 thf(decl_66, type, setadjoinOr: $o). 2.01/0.96 thf(decl_67, type, setoftrueEq: $o). 2.01/0.96 thf(decl_68, type, powersetI: $o). 2.01/0.96 thf(decl_69, type, emptyinPowerset: $o). 2.01/0.96 thf(decl_70, type, emptyInPowerset: $o). 2.01/0.96 thf(decl_71, type, powersetE: $o). 2.01/0.96 thf(decl_72, type, setunionI: $o). 2.01/0.96 thf(decl_73, type, setunionE: $o). 2.01/0.96 thf(decl_74, type, subPowSU: $o). 2.01/0.96 thf(decl_75, type, exuE2: $o). 2.01/0.96 thf(decl_76, type, nonemptyImpWitness: $o). 2.01/0.96 thf(decl_77, type, uniqinunit: $o). 2.01/0.96 thf(decl_78, type, notinsingleton: $o). 2.01/0.96 thf(decl_79, type, eqinunit: $o). 2.01/0.96 thf(decl_80, type, singletonsswitch: $o). 2.01/0.96 thf(decl_81, type, upairsetE: $o). 2.01/0.96 thf(decl_82, type, upairsetIL: $o). 2.01/0.96 thf(decl_83, type, upairsetIR: $o). 2.01/0.96 thf(decl_84, type, emptyE1: $o). 2.01/0.96 thf(decl_85, type, vacuousDall: $o). 2.01/0.96 thf(decl_86, type, quantDeMorgan1: $o). 2.01/0.96 thf(decl_87, type, quantDeMorgan2: $o). 2.01/0.96 thf(decl_88, type, quantDeMorgan3: $o). 2.01/0.96 thf(decl_89, type, quantDeMorgan4: $o). 2.01/0.96 thf(decl_90, type, prop2setI: $o). 2.01/0.96 thf(decl_92, type, prop2set2propI: $o). 2.01/0.96 thf(decl_93, type, notdexE: $o). 2.01/0.96 thf(decl_94, type, notdallE: $o). 2.01/0.96 thf(decl_95, type, exuI1: $o). 2.01/0.96 thf(decl_96, type, exuI3: $o). 2.01/0.96 thf(decl_97, type, exuI2: $o). 2.01/0.96 thf(decl_98, type, inCongP: $o). 2.01/0.96 thf(decl_99, type, in__Cong: $o). 2.01/0.96 thf(decl_100, type, exuE3u: $o). 2.01/0.96 thf(decl_101, type, exu__Cong: $o). 2.01/0.96 thf(decl_102, type, emptyset__Cong: $o). 2.01/0.96 thf(decl_103, type, setadjoin__Cong: $o). 2.01/0.96 thf(decl_104, type, powerset__Cong: $o). 2.01/0.96 thf(decl_105, type, setunion__Cong: $o). 2.01/0.96 thf(decl_106, type, omega__Cong: $o). 2.01/0.96 thf(decl_107, type, exuEu: $o). 2.01/0.96 thf(decl_108, type, descr__Cong: $o). 2.01/0.96 thf(decl_109, type, dsetconstr__Cong: $o). 2.01/0.96 thf(decl_110, type, subset: $i > $i > $o). 2.01/0.96 thf(decl_113, type, subsetI1: $o). 2.01/0.96 thf(decl_114, type, eqimpsubset2: $o). 2.01/0.96 thf(decl_115, type, eqimpsubset1: $o). 2.01/0.96 thf(decl_116, type, subsetI2: $o). 2.01/0.96 thf(decl_117, type, emptysetsubset: $o). 2.01/0.96 thf(decl_118, type, subsetE: $o). 2.01/0.96 thf(decl_119, type, subsetE2: $o). 2.01/0.96 thf(decl_120, type, notsubsetI: $o). 2.01/0.96 thf(decl_121, type, notequalI1: $o). 2.01/0.96 thf(decl_122, type, notequalI2: $o). 2.01/0.96 thf(decl_123, type, subsetRefl: $o). 2.01/0.96 thf(decl_124, type, subsetTrans: $o). 2.01/0.96 thf(decl_125, type, setadjoinSub: $o). 2.01/0.96 thf(decl_126, type, setadjoinSub2: $o). 2.01/0.96 thf(decl_127, type, subset2powerset: $o). 2.01/0.96 thf(decl_128, type, setextsub: $o). 2.01/0.96 thf(decl_129, type, subsetemptysetimpeq: $o). 2.01/0.96 thf(decl_130, type, powersetI1: $o). 2.01/0.96 thf(decl_131, type, powersetE1: $o). 2.01/0.96 thf(decl_132, type, inPowerset: $o). 2.01/0.96 thf(decl_133, type, powersetsubset: $o). 2.01/0.96 thf(decl_134, type, sepInPowerset: $o). 2.01/0.96 thf(decl_135, type, sepSubset: $o). 2.01/0.96 thf(decl_136, type, binunion: $i > $i > $i). 2.01/0.96 thf(decl_137, type, binunionIL: $o). 2.01/0.96 thf(decl_138, type, upairset2IR: $o). 2.01/0.96 thf(decl_139, type, binunionIR: $o). 2.01/0.96 thf(decl_140, type, binunionEcases: $o). 2.01/0.96 thf(decl_141, type, binunionE: $o). 2.01/0.96 thf(decl_142, type, binunionLsub: $o). 2.01/0.96 thf(decl_143, type, binunionRsub: $o). 2.01/0.96 thf(decl_144, type, binintersect: $i > $i > $i). 2.01/0.96 thf(decl_145, type, binintersectI: $o). 2.01/0.96 thf(decl_146, type, binintersectSubset5: $o). 2.01/0.96 thf(decl_147, type, binintersectEL: $o). 2.01/0.96 thf(decl_148, type, binintersectLsub: $o). 2.01/0.96 thf(decl_149, type, binintersectSubset2: $o). 2.01/0.96 thf(decl_150, type, binintersectSubset3: $o). 2.01/0.96 thf(decl_151, type, binintersectER: $o). 2.01/0.96 thf(decl_152, type, disjointsetsI1: $o). 2.01/0.96 thf(decl_153, type, binintersectRsub: $o). 2.01/0.96 thf(decl_154, type, binintersectSubset4: $o). 2.01/0.96 thf(decl_155, type, binintersectSubset1: $o). 2.01/0.96 thf(decl_156, type, bs114d: $o). 2.01/0.96 thf(decl_158, type, setminus: $i > $i > $i). 2.01/0.96 thf(decl_159, type, setminusI: $o). 2.01/0.96 thf(decl_160, type, setminusEL: $o). 2.01/0.96 thf(decl_161, type, setminusER: $o). 2.01/0.96 thf(decl_162, type, setminusSubset2: $o). 2.01/0.96 thf(decl_163, type, setminusERneg: $o). 2.01/0.96 thf(decl_164, type, setminusELneg: $o). 2.01/0.96 thf(decl_165, type, setminusILneg: $o). 2.01/0.96 thf(decl_166, type, setminusIRneg: $o). 2.01/0.96 thf(decl_167, type, setminusLsub: $o). 2.01/0.96 thf(decl_168, type, setminusSubset1: $o). 2.01/0.96 thf(decl_169, type, symdiff: $i > $i > $i). 2.01/0.96 thf(decl_170, type, symdiffE: $o). 2.01/0.96 thf(decl_171, type, symdiffI1: $o). 2.01/0.96 thf(decl_172, type, symdiffI2: $o). 2.01/0.96 thf(decl_173, type, symdiffIneg1: $o). 2.01/0.96 thf(decl_174, type, symdiffIneg2: $o). 2.01/0.96 thf(decl_175, type, iskpair: $i > $o). 2.01/0.96 thf(decl_176, type, secondinupair: $o). 2.01/0.96 thf(decl_177, type, setukpairIL: $o). 2.01/0.96 thf(decl_178, type, setukpairIR: $o). 2.01/0.96 thf(decl_179, type, kpairiskpair: $o). 2.01/0.96 thf(decl_180, type, kpair: $i > $i > $i). 2.01/0.96 thf(decl_181, type, kpairp: $o). 2.01/0.96 thf(decl_182, type, cartprod: $i > $i > $i). 2.01/0.96 thf(decl_183, type, singletonsubset: $o). 2.01/0.96 thf(decl_184, type, singletoninpowerset: $o). 2.01/0.96 thf(decl_185, type, singletoninpowunion: $o). 2.01/0.96 thf(decl_186, type, upairset2E: $o). 2.01/0.96 thf(decl_187, type, upairsubunion: $o). 2.01/0.96 thf(decl_188, type, upairinpowunion: $o). 2.01/0.96 thf(decl_189, type, ubforcartprodlem1: $o). 2.01/0.96 thf(decl_190, type, ubforcartprodlem2: $o). 2.01/0.96 thf(decl_191, type, ubforcartprodlem3: $o). 2.01/0.96 thf(decl_192, type, cartprodpairin: $o). 2.01/0.96 thf(decl_193, type, cartprodmempair1: $o). 2.01/0.96 thf(decl_194, type, cartprodmempair: $o). 2.01/0.96 thf(decl_195, type, setunionE2: $o). 2.01/0.96 thf(decl_196, type, setunionsingleton1: $o). 2.01/0.96 thf(decl_197, type, setunionsingleton2: $o). 2.01/0.96 thf(decl_198, type, setunionsingleton: $o). 2.01/0.96 thf(decl_199, type, singleton: $i > $o). 2.01/0.96 thf(decl_200, type, singletonprop: $o). 2.01/0.96 thf(decl_201, type, ex1: $i > ($i > $o) > $o). 2.01/0.96 thf(decl_202, type, ex1E1: $o). 2.01/0.96 thf(decl_203, type, ex1I: $o). 2.01/0.96 thf(decl_204, type, ex1I2: $o). 2.01/0.96 thf(decl_205, type, singletonsuniq: $o). 2.01/0.96 thf(decl_210, type, setukpairinjL1: $o). 2.01/0.96 thf(decl_211, type, kfstsingleton: $o). 2.01/0.96 thf(decl_212, type, theprop: $o). 2.01/0.96 thf(decl_213, type, kfst: $i > $i). 2.01/0.96 thf(decl_214, type, kfstpairEq: $o). 2.01/0.96 thf(decl_215, type, cartprodfstin: $o). 2.01/0.96 thf(decl_216, type, setukpairinjL2: $o). 2.01/0.96 thf(decl_217, type, setukpairinjL: $o). 2.01/0.96 thf(decl_218, type, setukpairinjR11: $o). 2.01/0.96 thf(decl_219, type, setukpairinjR12: $o). 2.01/0.96 thf(decl_220, type, setukpairinjR1: $o). 2.01/0.96 thf(decl_221, type, upairequniteq: $o). 2.01/0.96 thf(decl_222, type, setukpairinjR2: $o). 2.01/0.96 thf(decl_223, type, setukpairinjR: $o). 2.01/0.96 thf(decl_224, type, ksndsingleton: $o). 2.01/0.96 thf(decl_225, type, ksnd: $i > $i). 2.01/0.96 thf(decl_226, type, ksndpairEq: $o). 2.01/0.96 thf(decl_227, type, kpairsurjEq: $o). 2.01/0.96 thf(decl_228, type, cartprodsndin: $o). 2.01/0.96 thf(decl_229, type, cartprodpairmemEL: $o). 2.01/0.96 thf(decl_230, type, cartprodpairmemER: $o). 2.01/0.96 thf(decl_231, type, cartprodmempaircEq: $o). 2.01/0.96 thf(decl_232, type, cartprodfstpairEq: $o). 2.01/0.96 thf(decl_233, type, cartprodsndpairEq: $o). 2.01/0.96 thf(decl_234, type, cartprodpairsurjEq: $o). 2.01/0.96 thf(decl_235, type, breln: $i > $i > $i > $o). 2.01/0.96 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 2.01/0.96 thf(decl_237, type, dpsetconstrI: $o). 2.01/0.96 thf(decl_238, type, dpsetconstrSub: $o). 2.01/0.96 thf(decl_239, type, setOfPairsIsBReln: $o). 2.01/0.96 thf(decl_240, type, dpsetconstrERa: $o). 2.01/0.96 thf(decl_241, type, dpsetconstrEL1: $o). 2.01/0.96 thf(decl_242, type, dpsetconstrEL2: $o). 2.01/0.96 thf(decl_243, type, dpsetconstrER: $o). 2.01/0.96 thf(decl_244, type, func: $i > $i > $i > $o). 2.01/0.96 thf(decl_245, type, funcSet: $i > $i > $i). 2.01/0.96 thf(decl_246, type, funcImageSingleton: $o). 2.01/0.96 thf(decl_247, type, apProp: $o). 2.01/0.96 thf(decl_248, type, ap: $i > $i > $i > $i > $i). 2.01/0.96 thf(decl_249, type, app: $o). 2.01/0.96 thf(decl_250, type, infuncsetfunc: $o). 2.01/0.96 thf(decl_251, type, ap2p: $o). 2.01/0.96 thf(decl_252, type, funcinfuncset: $o). 2.01/0.96 thf(decl_253, type, lamProp: $o). 2.01/0.96 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i). 2.01/0.96 thf(decl_255, type, lamp: $o). 2.01/0.96 thf(decl_256, type, lam2p: $o). 2.01/0.96 thf(decl_257, type, brelnall1: $o). 2.01/0.96 thf(decl_258, type, brelnall2: $o). 2.01/0.96 thf(decl_259, type, ex1E2: $o). 2.01/0.96 thf(decl_260, type, funcGraphProp1: $o). 2.01/0.96 thf(decl_261, type, funcGraphProp3: $o). 2.01/0.96 thf(decl_262, type, funcGraphProp2: $o). 2.01/0.96 thf(decl_263, type, funcextLem: $o). 2.01/0.96 thf(decl_264, type, funcGraphProp4: $o). 2.01/0.96 thf(decl_265, type, subbreln: $o). 2.01/0.96 thf(decl_266, type, eqbreln: $o). 2.01/0.96 thf(decl_267, type, funcext: $o). 2.01/0.96 thf(decl_268, type, funcext2: $o). 2.01/0.96 thf(decl_269, type, ap2apEq1: $o). 2.01/0.96 thf(decl_270, type, ap2apEq2: $o). 2.01/0.96 thf(decl_271, type, beta1: $o). 2.01/0.96 thf(decl_272, type, eta1: $o). 2.01/0.96 thf(decl_273, type, lam2lamEq: $o). 2.01/0.96 thf(decl_274, type, beta2: $o). 2.01/0.96 thf(decl_275, type, eta2: $o). 2.01/0.96 thf(decl_276, type, iffalseProp1: $o). 2.01/0.96 thf(decl_277, type, iffalseProp2: $o). 2.01/0.96 thf(decl_278, type, iftrueProp1: $o). 2.01/0.96 thf(decl_279, type, iftrueProp2: $o). 2.01/0.96 thf(decl_280, type, ifSingleton: $o). 2.01/0.96 thf(decl_281, type, if: $i > $o > $i > $i > $i). 2.01/0.96 thf(decl_282, type, ifp: $o). 2.01/0.96 thf(decl_283, type, theeq: $o). 2.01/0.96 thf(decl_284, type, iftrue: $o). 2.01/0.96 thf(decl_285, type, iffalse: $o). 2.01/0.96 thf(decl_286, type, iftrueorfalse: $o). 2.01/0.96 thf(decl_287, type, binintersectT_lem: $o). 2.01/0.96 thf(decl_288, type, binunionT_lem: $o). 2.01/0.96 thf(decl_289, type, powersetT_lem: $o). 2.01/0.96 thf(decl_290, type, setminusT_lem: $o). 2.01/0.96 thf(decl_291, type, complementT_lem: $o). 2.01/0.96 thf(decl_292, type, setextT: $o). 2.01/0.96 thf(decl_293, type, subsetTI: $o). 2.01/0.96 thf(decl_294, type, powersetTI1: $o). 2.01/0.96 thf(decl_295, type, powersetTE1: $o). 2.01/0.96 thf(decl_296, type, complementTI1: $o). 2.01/0.96 thf(decl_297, type, complementTE1: $o). 2.01/0.96 thf(decl_298, type, binintersectTELcontra: $o). 2.01/0.96 thf(decl_299, type, binintersectTERcontra: $o). 2.01/0.96 thf(decl_300, type, contrasubsetT: $o). 2.01/0.96 thf(decl_301, type, contrasubsetT1: $o). 2.01/0.96 thf(decl_302, type, contrasubsetT2: $o). 2.01/0.96 thf(decl_303, type, contrasubsetT3: $o). 2.01/0.96 thf(decl_304, type, doubleComplementI1: $o). 2.01/0.96 thf(decl_305, type, doubleComplementE1: $o). 2.01/0.96 thf(decl_306, type, doubleComplementSub1: $o). 2.01/0.96 thf(decl_307, type, doubleComplementSub2: $o). 2.01/0.96 thf(decl_308, type, doubleComplementEq: $o). 2.01/0.96 thf(decl_309, type, complementTnotintersectT: $o). 2.01/0.96 thf(decl_310, type, complementImpComplementIntersect: $o). 2.01/0.96 thf(decl_311, type, complementSubsetComplementIntersect: $o). 2.01/0.96 thf(decl_312, type, complementInPowersetComplementIntersect: $o). 2.01/0.96 thf(decl_313, type, contraSubsetComplement: $o). 2.01/0.96 thf(decl_314, type, complementTcontraSubset: $o). 2.01/0.96 thf(decl_315, type, binunionTILcontra: $o). 2.01/0.96 thf(decl_316, type, binunionTIRcontra: $o). 2.01/0.96 thf(decl_317, type, inIntersectImpInUnion: $o). 2.01/0.96 thf(decl_318, type, inIntersectImpInUnion2: $o). 2.01/0.96 thf(decl_319, type, inIntersectImpInIntersectUnions: $o). 2.01/0.96 thf(decl_320, type, intersectInPowersetIntersectUnions: $o). 2.01/0.96 thf(decl_321, type, inComplementUnionImpNotIn1: $o). 2.01/0.96 thf(decl_322, type, inComplementUnionImpInComplement1: $o). 2.01/0.96 thf(decl_323, type, binunionTE: $o). 2.01/0.96 thf(decl_324, type, binunionTEcontra: $o). 2.01/0.96 thf(decl_325, type, demorgan2a1: $o). 2.01/0.96 thf(decl_326, type, complementUnionInPowersetComplement: $o). 2.01/0.96 thf(decl_327, type, demorgan2a2: $o). 2.01/0.96 thf(decl_328, type, demorgan1a: $o). 2.01/0.96 thf(decl_329, type, demorgan1b: $o). 2.01/0.96 thf(decl_330, type, demorgan1: $o). 2.01/0.96 thf(decl_331, type, epred1_0: $o). 2.01/0.96 thf(decl_332, type, esk1_2: $i > $i > $i). 2.01/0.96 thf(decl_333, type, esk2_2: $i > $i > $i). 2.01/0.96 thf(decl_334, type, esk3_2: $i > $i > $i). 2.01/0.96 thf(decl_335, type, esk4_1: $i > $i). 2.01/0.96 thf(decl_336, type, esk5_2: ($i > $i > $o) > $i > $i). 2.01/0.96 thf(decl_337, type, esk6_2: ($i > $i > $o) > $i > $i). 2.01/0.96 thf(decl_338, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 2.01/0.96 thf(decl_339, type, esk8_1: $i > $i). 2.01/0.96 thf(decl_340, type, esk9_1: ($i > $o) > $i). 2.01/0.96 thf(decl_341, type, esk10_1: ($i > $o) > $i). 2.01/0.96 thf(decl_342, type, esk11_2: $i > $i > $i). 2.01/0.96 thf(decl_343, type, esk12_2: $i > $i > $i). 2.01/0.96 thf(decl_344, type, esk13_1: $i > $i). 2.01/0.96 thf(decl_345, type, esk14_1: $i > $i). 2.01/0.96 thf(decl_346, type, esk15_1: $i > $i). 2.01/0.96 thf(decl_347, type, esk16_2: $i > $i > $i). 2.01/0.96 thf(decl_348, type, esk17_3: $i > $i > $o > $i). 2.01/0.96 thf(decl_349, type, esk18_1: ($i > $o) > $i). 2.01/0.96 thf(decl_350, type, esk19_1: $i > $i). 2.01/0.96 thf(decl_351, type, esk20_2: $i > ($i > $o) > $i). 2.01/0.96 thf(decl_352, type, esk21_2: $i > ($i > $o) > $i). 2.01/0.96 thf(decl_353, type, esk22_2: $i > ($i > $o) > $i). 2.01/0.96 thf(decl_354, type, esk23_2: $i > ($i > $o) > $i). 2.01/0.96 thf(decl_355, type, esk24_2: $i > ($i > $o) > $i). 2.01/0.96 thf(decl_356, type, esk25_2: $i > ($i > $o) > $i). 2.01/0.96 thf(decl_357, type, esk26_2: ($i > $o) > $i > $i). 2.01/0.96 thf(decl_358, type, esk27_1: ($i > $o) > $i). 2.01/0.96 thf(decl_359, type, esk28_1: ($i > $o) > $i). 2.01/0.96 thf(decl_360, type, esk29_2: ($i > $o) > $i > $i). 2.01/0.96 thf(decl_361, type, esk30_2: ($i > $o) > ($i > $o) > $i). 2.01/0.96 thf(decl_362, type, esk31_2: ($i > $o) > ($i > $o) > $i). 2.01/0.96 thf(decl_363, type, esk32_2: ($i > $o) > ($i > $o) > $i). 2.01/0.96 thf(decl_364, type, esk33_2: ($i > $o) > ($i > $o) > $i). 2.01/0.96 thf(decl_365, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 2.01/0.96 thf(decl_366, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 2.01/0.96 thf(decl_367, type, esk36_2: $i > $i > $i). 2.01/0.96 thf(decl_368, type, esk37_2: $i > $i > $i). 2.01/0.96 thf(decl_369, type, esk38_2: $i > $i > $i). 2.01/0.96 thf(decl_370, type, esk39_3: $i > $i > $i > $i). 2.01/0.96 thf(decl_371, type, esk40_3: $i > $i > $i > $i). 2.01/0.96 thf(decl_372, type, esk41_2: $i > $i > $i). 2.01/0.96 thf(decl_373, type, esk42_2: $i > ($i > $o) > $i). 2.01/0.96 thf(decl_374, type, esk43_2: $i > ($i > $o) > $i). 2.01/0.96 thf(decl_375, type, esk44_2: $i > ($i > $o) > $i). 2.01/0.96 thf(decl_376, type, esk45_3: $i > ($i > $o) > $i > $i). 2.01/0.96 thf(decl_377, type, esk46_2: $i > ($i > $o) > $i). 2.01/0.96 thf(decl_378, type, esk47_2: $i > ($i > $o) > $i). 2.01/0.96 thf(decl_379, type, esk48_3: $i > $i > ($i > $i) > $i). 2.01/0.96 thf(decl_380, type, esk49_3: $i > $i > ($i > $i) > $i). 2.01/0.96 thf(decl_381, type, esk50_3: $i > $i > ($i > $i) > $i). 2.01/0.96 thf(decl_382, type, esk51_4: $i > $i > $i > ($i > $o) > $i). 2.01/0.96 thf(decl_383, type, esk52_4: $i > $i > $i > ($i > $o) > $i). 2.01/0.96 thf(decl_384, type, esk53_4: $i > $i > $i > ($i > $o) > $i). 2.01/0.96 thf(decl_385, type, esk54_4: $i > $i > $i > ($i > $o) > $i). 2.01/0.96 thf(decl_386, type, esk55_4: $i > $i > $i > $i > $i). 2.01/0.96 thf(decl_387, type, esk56_4: $i > $i > $i > $i > $i). 2.01/0.96 thf(decl_388, type, esk57_4: $i > $i > $i > $i > $i). 2.01/0.96 thf(decl_389, type, esk58_4: $i > $i > $i > $i > $i). 2.01/0.96 thf(decl_390, type, esk59_4: $i > $i > $i > $i > $i). 2.01/0.96 thf(decl_391, type, esk60_4: $i > $i > $i > $i > $i). 2.01/0.96 thf(decl_392, type, esk61_4: $i > $i > $i > $i > $i). 2.01/0.96 thf(decl_393, type, esk62_4: $i > $i > $i > $i > $i). 2.01/0.96 thf(decl_394, type, esk63_4: $i > $i > $i > $i > $i). 2.01/0.96 thf(decl_395, type, esk64_3: $i > $i > ($i > $i) > $i). 2.01/0.96 thf(decl_396, type, esk65_3: $i > $i > ($i > $i) > $i). 2.01/0.96 thf(decl_397, type, esk66_3: $i > $i > ($i > $i) > $i). 2.01/0.96 thf(decl_398, type, esk67_3: $i > $i > $i > $i). 2.01/0.96 thf(decl_399, type, esk68_3: $i > $i > $i > $i). 2.01/0.96 thf(decl_400, type, esk69_3: $i > $i > $i > $i). 2.01/0.96 thf(decl_401, type, esk70_3: $i > $i > $i > $i). 2.01/0.96 thf(decl_402, type, esk71_0: $i). 2.01/0.96 thf(decl_403, type, esk72_0: $i). 2.01/0.96 thf(decl_404, type, esk73_0: $i). 2.01/0.96 thf(decl_405, type, esk74_0: $i). 2.01/0.96 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', sepInPowerset)). 2.01/0.96 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', descr__Cong)). 2.01/0.96 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', exu__Cong)). 2.01/0.96 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', exuI2)). 2.01/0.96 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', exuI3)). 2.01/0.96 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', emptyE1)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', ksndsingleton)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', exuE2)). 2.01/0.96 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setoftrueEq)). 2.01/0.96 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', nonemptyI)). 2.01/0.96 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setbeta)). 2.01/0.96 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', dsetconstrER)). 2.01/0.96 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', dsetconstrEL)). 2.01/0.96 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', dsetconstrI)). 2.01/0.96 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', ex1E1)). 2.01/0.96 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', replAx)). 2.01/0.96 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', ex1I)). 2.01/0.96 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', ex1I2)). 2.01/0.96 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', kfstsingleton)). 2.01/0.96 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setOfPairsIsBReln)). 2.01/0.96 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', dpsetconstrEL1)). 2.01/0.96 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', dpsetconstrER)). 2.01/0.96 thf(apProp, axiom, ((apProp)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', apProp)). 2.01/0.96 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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', lamp)). 2.01/0.96 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', lam2p)). 2.01/0.96 thf(beta1, axiom, ((beta1)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', beta1)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', eta1)). 2.01/0.96 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', iftrueProp2)). 2.01/0.96 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', ifSingleton)). 2.01/0.96 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', iftrueProp1)). 2.01/0.96 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', iffalseProp2)). 2.01/0.96 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', iffalseProp1)). 2.01/0.96 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', eta2)). 2.01/0.96 thf(beta2, axiom, ((beta2)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', beta2)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', lam2lamEq)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', ex1E2)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', lamProp)). 2.01/0.96 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', funcImageSingleton)). 2.01/0.96 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', dpsetconstrEL2)). 2.01/0.96 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', dpsetconstrERa)). 2.01/0.96 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', dpsetconstrSub)). 2.01/0.96 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', dpsetconstrI)). 2.01/0.96 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', singletonprop)). 2.01/0.96 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', sepSubset)). 2.01/0.96 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', dsetconstr__Cong)). 2.01/0.96 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', exuEu)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', exuE3u)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', exuI1)). 2.01/0.96 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', exuE3e)). 2.01/0.96 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', exuE1)). 2.01/0.96 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', descrp)). 2.01/0.96 thf(demorgan2a, conjecture, ((setextAx)=>(((((setunionAx)=>((((omegaIndAx)=>((((wellorderingAx)=>((descrp)=>(((((exuE1)=>((prop2setE)=>(((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>(((((nonemptyE1)=>((((setadjoinIL)=>((emptyinunitempty)=>((((setadjoinOr)=>(((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>(((setunionI)=>(((subPowSU)=>((((uniqinunit)=>((notinsingleton)=>(((singletonsswitch)=>((upairsetE)=>(((upairsetIR)=>(((((quantDeMorgan2)=>(((quantDeMorgan4)=>((prop2setI)=>(((notdexE)=>(((exuI1)=>((((inCongP)=>(((exuE3u)=>(((emptyset__Cong)=>((((setunion__Cong)=>((omega__Cong)=>((exuEu)=>(((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>(((((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>(((subset2powerset)=>((setextsub)=>(((powersetI1)=>((powersetE1)=>(((((sepSubset)=>((binunionIL)=>((((((binunionLsub)=>(((binintersectI)=>((binintersectSubset5)=>((((((binintersectER)=>((disjointsetsI1)=>(((binintersectSubset4)=>((binintersectSubset1)=>(((setminusI)=>((setminusEL)=>(((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((((((symdiffE)=>((((((secondinupair)=>(((setukpairIR)=>((kpairiskpair)=>(((singletonsubset)=>(((singletoninpowunion)=>(((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>(((setunionE2)=>((((((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>(((kfstsingleton)=>(((kfstpairEq)=>(((setukpairinjL2)=>((((setukpairinjR12)=>(((((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>(((cartprodsndpairEq)=>(((((setOfPairsIsBReln)=>(((dpsetconstrEL1)=>(((dpsetconstrER)=>(((apProp)=>(((((((lamp)=>((lam2p)=>(((((((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>(((funcext)=>((((ap2apEq2)=>((beta1)=>((eta1)=>((((((((iftrueProp2)=>(((((iftrue)=>(((iftrueorfalse)=>((((((((((((((binintersectTERcontra)=>((contrasubsetT)=>(((((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>(((((complementSubsetComplementIntersect)=>(((contraSubsetComplement)=>((((binunionTIRcontra)=>(((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>(((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>(((((demorgan1b)=>(![X4:$i, X21:$i]:((![X48:$i]:((![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))<=(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))<=(in @ X48 @ (powerset @ X4))))<=(in @ X21 @ (powerset @ X4))))<=(demorgan1)))<=(demorgan1a))<=(demorgan2a2))<=(complementUnionInPowersetComplement)))))<=(inComplementUnionImpInComplement1))))))<=(inIntersectImpInUnion)))<=(binunionTILcontra))<=(complementTcontraSubset)))<=(complementInPowersetComplementIntersect)))<=(complementImpComplementIntersect))<=(complementTnotintersectT))<=(doubleComplementEq))))))<=(contrasubsetT3))<=(contrasubsetT2))<=(contrasubsetT1))))<=(binintersectTELcontra))<=(complementTE1))<=(complementTI1))<=(powersetTE1))<=(powersetTI1))<=(subsetTI))<=(setextT))<=(complementT_lem))<=(setminusT_lem))<=(powersetT_lem))<=(binunionT_lem))<=(binintersectT_lem)))<=(iffalse)))<=(theeq))<=(ifp))<=(ifSingleton)))<=(iftrueProp1))<=(iffalseProp2))<=(iffalseProp1))<=(eta2))<=(beta2))<=(lam2lamEq)))))<=(ap2apEq1))<=(funcext2)))<=(eqbreln))))))<=(funcGraphProp3))<=(funcGraphProp1))<=(ex1E2))<=(brelnall2))<=(brelnall1))))<=(lamProp))<=(funcinfuncset))<=(ap2p))<=(infuncsetfunc))<=(app)))<=(funcImageSingleton)))<=(dpsetconstrEL2)))<=(dpsetconstrERa)))<=(dpsetconstrSub))<=(dpsetconstrI))<=(cartprodpairsurjEq)))<=(cartprodfstpairEq))))))))))<=(setukpairinjR2))<=(upairequniteq))<=(setukpairinjR1)))<=(setukpairinjR11))<=(setukpairinjL)))<=(cartprodfstin)))<=(theprop)))<=(setukpairinjL1))))))<=(singletonprop))<=(setunionsingleton))<=(setunionsingleton2))<=(setunionsingleton1)))<=(cartprodmempair)))))))))<=(upairset2E)))<=(singletoninpowerset)))<=(kpairp))))<=(setukpairIL)))<=(symdiffIneg2))<=(symdiffIneg1))<=(symdiffI2))<=(symdiffI1)))<=(setminusSubset1))<=(setminusLsub))<=(setminusIRneg))<=(setminusILneg)))))<=(setminusER))))<=(bs114d))))<=(binintersectRsub))))<=(binintersectSubset3))<=(binintersectSubset2))<=(binintersectLsub))<=(binintersectEL))))<=(binunionRsub)))<=(binunionE))<=(binunionEcases))<=(binunionIR))<=(upairset2IR))))<=(sepInPowerset))<=(powersetsubset))<=(inPowerset))))<=(subsetemptysetimpeq))))<=(setadjoinSub2))))))))<=(subsetE2))<=(subsetE))<=(emptysetsubset)))))))<=(descr__Cong)))))<=(powerset__Cong))<=(setadjoin__Cong)))<=(exu__Cong)))<=(in__Cong)))<=(exuI2))<=(exuI3)))<=(notdallE)))<=(prop2set2propI))))<=(quantDeMorgan3)))<=(quantDeMorgan1))<=(vacuousDall))<=(emptyE1)))<=(upairsetIL))))<=(eqinunit))))<=(nonemptyImpWitness))<=(exuE2)))<=(setunionE)))<=(powersetE)))))<=(setoftrueEq)))<=(setadjoinE))<=(setadjoinIR))))<=(nonemptyI1))<=(nonemptyI)))<=(setbeta))<=(noeltsimpempty))<=(emptyI))))))<=(emptysetE))))<=(dsetconstrER))<=(dsetconstrEL))<=(dsetconstrI))))<=(foundationAx))<=(replAx)))<=(omegaSAx))<=(omega0Ax)))<=(powersetAx))<=(setadjoinAx))<=(emptysetAx))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', demorgan2a)). 2.01/0.96 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', emptysetAx)). 2.01/0.96 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setminusSubset2)). 2.01/0.96 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', powersetsubset)). 2.01/0.96 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', secondinupair)). 2.01/0.96 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', inPowerset)). 2.01/0.96 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', subsetemptysetimpeq)). 2.01/0.96 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setadjoinSub2)). 2.01/0.96 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setukpairIR)). 2.01/0.96 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', subsetE2)). 2.01/0.96 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', subsetE)). 2.01/0.96 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', kpairiskpair)). 2.01/0.96 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', emptysetsubset)). 2.01/0.96 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', powerset__Cong)). 2.01/0.96 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', singletonsubset)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', setadjoin__Cong)). 2.01/0.96 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', singletoninpowunion)). 2.01/0.96 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', in__Cong)). 2.01/0.96 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', notdallE)). 2.01/0.96 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', upairsubunion)). 2.01/0.96 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', quantDeMorgan3)). 2.01/0.96 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', quantDeMorgan1)). 2.01/0.96 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', upairinpowunion)). 2.01/0.96 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', vacuousDall)). 2.01/0.96 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', upairsetIL)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', ubforcartprodlem1)). 2.01/0.96 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', eqinunit)). 2.01/0.96 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setminusERneg)). 2.01/0.96 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', nonemptyImpWitness)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', ubforcartprodlem2)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', setunionE)). 2.01/0.96 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', powersetE)). 2.01/0.96 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setadjoinE)). 2.01/0.96 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', ubforcartprodlem3)). 2.01/0.96 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setadjoinIR)). 2.01/0.96 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', nonemptyI1)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', cartprodpairin)). 2.01/0.96 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', noeltsimpempty)). 2.01/0.96 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', cartprodmempair1)). 2.01/0.96 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', emptyI)). 2.01/0.96 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', emptysetE)). 2.01/0.96 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setunionE2)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', foundationAx)). 2.01/0.96 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', omegaSAx)). 2.01/0.96 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', omega0Ax)). 2.01/0.96 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', powersetAx)). 2.01/0.96 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setadjoinAx)). 2.01/0.96 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setminusELneg)). 2.01/0.96 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', singletonsuniq)). 2.01/0.96 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', kfstpairEq)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', setukpairinjL2)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', setukpairinjR12)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', setukpairinjR)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', contraSubsetComplement)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', binunionTIRcontra)). 2.01/0.96 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', ksndpairEq)). 2.01/0.96 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', kpairsurjEq)). 2.01/0.96 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', cartprodsndin)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', cartprodpairmemEL)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', cartprodpairmemER)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', cartprodmempaircEq)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', cartprodsndpairEq)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', symdiffE)). 2.01/0.96 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', funcGraphProp2)). 2.01/0.96 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', funcextLem)). 2.01/0.96 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', funcGraphProp4)). 2.01/0.96 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', subbreln)). 2.01/0.96 thf(funcext, axiom, ((funcext)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', funcext)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', ap2apEq2)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', iftrue)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', iftrueorfalse)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', binintersectTERcontra)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', contrasubsetT)). 2.01/0.96 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', doubleComplementI1)). 2.01/0.96 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', doubleComplementE1)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', doubleComplementSub1)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', doubleComplementSub2)). 2.01/0.96 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', complementSubsetComplementIntersect)). 2.01/0.96 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binintersectSubset2)). 2.01/0.96 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binintersectLsub)). 2.01/0.96 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binintersectEL)). 2.01/0.96 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binunionRsub)). 2.01/0.96 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binunionE)). 2.01/0.96 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binunionEcases)). 2.01/0.96 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binunionIR)). 2.01/0.96 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', upairset2IR)). 2.01/0.96 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', inIntersectImpInUnion2)). 2.01/0.96 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', inIntersectImpInIntersectUnions)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', intersectInPowersetIntersectUnions)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', inComplementUnionImpNotIn1)). 2.01/0.96 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binunionTE)). 2.01/0.96 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binunionTEcontra)). 2.01/0.96 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', demorgan2a1)). 2.01/0.96 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', demorgan1b)). 2.01/0.96 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', demorgan1)). 2.01/0.96 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', demorgan1a)). 2.01/0.96 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', demorgan2a2)). 2.01/0.96 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', complementUnionInPowersetComplement)). 2.01/0.96 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', inComplementUnionImpInComplement1)). 2.01/0.96 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', inIntersectImpInUnion)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', binunionTILcontra)). 2.01/0.96 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', complementTcontraSubset)). 2.01/0.96 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', complementInPowersetComplementIntersect)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', complementImpComplementIntersect)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', complementTnotintersectT)). 2.01/0.96 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', doubleComplementEq)). 2.01/0.96 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', contrasubsetT3)). 2.01/0.96 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', contrasubsetT2)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', contrasubsetT1)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', binintersectTELcontra)). 2.01/0.96 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', complementTE1)). 2.01/0.96 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', complementTI1)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', powersetTE1)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', powersetTI1)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', subsetTI)). 2.01/0.96 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setextT)). 2.01/0.96 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', complementT_lem)). 2.01/0.96 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', setminusT_lem)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', powersetT_lem)). 2.01/0.96 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binunionT_lem)). 2.01/0.96 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', binintersectT_lem)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', iffalse)). 2.01/0.96 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', theeq)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', ifp)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', ap2apEq1)). 2.01/0.96 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', funcext2)). 2.01/0.96 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', eqbreln)). 2.01/0.96 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', funcGraphProp3)). 2.01/0.96 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', funcGraphProp1)). 2.01/0.96 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', brelnall2)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', brelnall1)). 2.01/0.96 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', funcinfuncset)). 2.01/0.96 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', ap2p)). 2.01/0.96 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', infuncsetfunc)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', app)). 2.01/0.96 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', cartprodpairsurjEq)). 2.01/0.96 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', cartprodfstpairEq)). 2.01/0.96 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setukpairinjR2)). 2.01/0.96 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', upairequniteq)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', setukpairinjR1)). 2.01/0.96 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setukpairinjR11)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', setukpairinjL)). 2.01/0.96 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', cartprodfstin)). 2.01/0.96 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', theprop)). 2.01/0.96 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setukpairinjL1)). 2.01/0.96 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setunionsingleton)). 2.01/0.96 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setunionsingleton2)). 2.01/0.96 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setunionsingleton1)). 2.01/0.96 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', cartprodmempair)). 2.01/0.96 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', upairset2E)). 2.01/0.96 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', singletoninpowerset)). 2.01/0.96 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', kpairp)). 2.01/0.96 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.Lnjexvu4wz/E---3.1_664.p', setukpairIL)). 2.01/0.96 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', symdiffIneg2)). 2.01/0.96 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', symdiffIneg1)). 2.01/0.96 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', symdiffI2)). 2.01/0.96 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', symdiffI1)). 2.01/0.96 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setminusSubset1)). 2.01/0.96 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setminusLsub)). 2.01/0.96 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setminusIRneg)). 2.01/0.96 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setminusILneg)). 2.01/0.96 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setminusER)). 2.01/0.96 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', bs114d)). 2.01/0.96 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binintersectRsub)). 2.01/0.96 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binintersectSubset3)). 2.01/0.96 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setminusEL)). 2.01/0.96 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setminusI)). 2.01/0.96 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binintersectSubset1)). 2.01/0.96 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binintersectSubset4)). 2.01/0.96 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', disjointsetsI1)). 2.01/0.96 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binintersectER)). 2.01/0.96 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binintersectSubset5)). 2.01/0.96 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binintersectI)). 2.01/0.96 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binunionLsub)). 2.01/0.96 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', binunionIL)). 2.01/0.96 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', powersetE1)). 2.01/0.96 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', powersetI1)). 2.01/0.96 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setextsub)). 2.01/0.96 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', subset2powerset)). 2.01/0.96 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setadjoinSub)). 2.01/0.96 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', subsetTrans)). 2.01/0.96 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', subsetRefl)). 2.01/0.96 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', notequalI2)). 2.01/0.96 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', notequalI1)). 2.01/0.96 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', notsubsetI)). 2.01/0.96 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', subsetI2)). 2.01/0.96 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', eqimpsubset1)). 2.01/0.96 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', eqimpsubset2)). 2.01/0.96 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', subsetI1)). 2.01/0.96 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', omega__Cong)). 2.01/0.96 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setunion__Cong)). 2.01/0.96 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', emptyset__Cong)). 2.01/0.96 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', inCongP)). 2.01/0.96 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', notdexE)). 2.01/0.96 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', prop2setI)). 2.01/0.96 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', quantDeMorgan4)). 2.01/0.96 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', quantDeMorgan2)). 2.01/0.96 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', upairsetIR)). 2.01/0.96 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', upairsetE)). 2.01/0.96 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', singletonsswitch)). 2.01/0.96 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', notinsingleton)). 2.01/0.96 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', uniqinunit)). 2.01/0.96 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', subPowSU)). 2.01/0.96 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setunionI)). 2.01/0.96 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', emptyInPowerset)). 2.01/0.96 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', emptyinPowerset)). 2.01/0.96 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', powersetI)). 2.01/0.96 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setadjoinOr)). 2.01/0.96 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', emptyinunitempty)). 2.01/0.96 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setadjoinIL)). 2.01/0.96 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', nonemptyE1)). 2.01/0.96 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setext)). 2.01/0.96 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', notinemptyset)). 2.01/0.96 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', emptysetimpfalse)). 2.01/0.96 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', prop2setE)). 2.01/0.96 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', wellorderingAx)). 2.01/0.96 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.Lnjexvu4wz/E---3.1_664.p', omegaIndAx)). 2.01/0.96 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setunionAx)). 2.01/0.96 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.Lnjexvu4wz/E---3.1_664.p', setextAx)). 2.01/0.96 thf(c_0_270, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 2.01/0.96 thf(c_0_271, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 2.01/0.96 thf(c_0_272, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 2.01/0.96 thf(c_0_273, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 2.01/0.96 thf(c_0_274, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 2.01/0.96 thf(c_0_275, plain, ((emptyE1)<=>![X4:$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])). 2.01/0.96 thf(c_0_276, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 2.01/0.96 thf(c_0_277, 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])). 2.01/0.96 thf(c_0_278, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 2.01/0.96 thf(c_0_279, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 2.01/0.96 thf(c_0_280, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 2.01/0.96 thf(c_0_281, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 2.01/0.96 thf(c_0_282, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 2.01/0.96 thf(c_0_283, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 2.01/0.96 thf(c_0_284, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 2.01/0.96 thf(c_0_285, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 2.01/0.96 thf(c_0_286, plain, ((ex1I)<=>![X4:$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])). 2.01/0.96 thf(c_0_287, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 2.01/0.96 thf(c_0_288, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 2.01/0.96 thf(c_0_289, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 2.01/0.96 thf(c_0_290, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 2.01/0.96 thf(c_0_291, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 2.01/0.96 thf(c_0_292, plain, ((apProp)<=>![X4:$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])). 2.01/0.96 thf(c_0_293, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 2.01/0.96 thf(c_0_294, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 2.01/0.96 thf(c_0_295, plain, ((beta1)<=>![X4:$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])). 2.01/0.96 thf(c_0_296, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 248 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])). 2.01/0.96 thf(c_0_297, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])). 2.01/0.96 thf(c_0_298, plain, ((ifSingleton)<=>![X4:$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])). 2.01/0.96 thf(c_0_299, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 2.01/0.96 thf(c_0_300, plain, ((iffalseProp2)<=>![X4:$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])). 2.01/0.96 thf(c_0_301, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 2.01/0.96 thf(c_0_302, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 248 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 2.01/0.96 thf(c_0_303, plain, ((beta2)<=>![X4:$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])). 2.01/0.96 thf(c_0_304, 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])). 2.01/0.96 thf(c_0_305, 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])). 2.01/0.96 thf(c_0_306, 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])). 2.01/0.96 thf(c_0_307, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 2.01/0.96 thf(c_0_308, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 2.01/0.96 thf(c_0_309, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 2.01/0.96 thf(c_0_310, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 2.01/0.96 thf(c_0_311, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 2.01/0.96 thf(c_0_312, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 2.01/0.96 thf(c_0_313, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 2.01/0.96 thf(c_0_314, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 2.01/0.96 thf(c_0_315, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 2.01/0.96 thf(c_0_316, 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])). 2.01/0.96 thf(c_0_317, 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])). 2.01/0.96 thf(c_0_318, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 2.01/0.96 thf(c_0_319, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 2.01/0.96 thf(c_0_320, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 2.01/0.96 thf(c_0_321, plain, ((epred1_0)<=>![X916:$i]:(?[X917:$i]:((((![X918:$i]:(((in @ X918 @ X917)=>![X919:$i]:(((in @ X919 @ X918)=>(in @ X919 @ X916)))))&![X920:$i, X921:$i]:((((in @ X920 @ X916)&(in @ X921 @ X916))=>(![X922:$i]:(((in @ X922 @ X917)=>((in @ X920 @ X922)<=>(in @ X921 @ X922))))=>((X920)=(X921))))))&![X923:$i, X924:$i]:((((in @ X923 @ X917)&(in @ X924 @ X917))=>(![X925:$i]:(((in @ X925 @ X923)=>(in @ X925 @ X924)))|![X926:$i]:(((in @ X926 @ X924)=>(in @ X926 @ X923)))))))&![X927:$i]:(((![X928:$i]:(((in @ X928 @ X927)=>(in @ X928 @ X916)))&?[X929:$i]:((in @ X929 @ X927)))=>?[X930:$i, X931:$i]:(((((in @ X930 @ X917)&(in @ X931 @ X927))&~(?[X932:$i]:(((in @ X932 @ X930)&(in @ X932 @ X927)))))&![X933:$i]:(((in @ X933 @ X917)=>(![X934:$i]:(((in @ X934 @ X933)=>(in @ X934 @ X930)))|(in @ X931 @ X933)))))))))))), introduced(definition)). 2.01/0.96 thf(c_0_322, negated_conjecture, ~((![X907:$i, X908:$i]:((![X909:$i]:(((in @ X909 @ X907)<=>(in @ X909 @ X908)))=>((X907)=(X908))))=>(![X1758:$i]:(~(in @ X1758 @ emptyset))=>(![X1755:$i, X1756:$i, X1757:$i]:(((in @ X1757 @ (setadjoin @ X1755 @ X1756))<=>(((X1757)=(X1755))|(in @ X1757 @ X1756))))=>(![X1752:$i, X1753:$i]:(((in @ X1753 @ (powerset @ X1752))<=>![X1754:$i]:(((in @ X1754 @ X1753)=>(in @ X1754 @ X1752)))))=>(![X910:$i, X911:$i]:(((in @ X911 @ (setunion @ X910))<=>?[X912:$i]:(((in @ X911 @ X912)&(in @ X912 @ X910)))))=>((in @ emptyset @ omega)=>(![X1751:$i]:(((in @ X1751 @ omega)=>(in @ (setadjoin @ X1751 @ X1751) @ omega)))=>(![X913:$i]:((((in @ emptyset @ X913)&![X914:$i]:((((in @ X914 @ omega)&(in @ X914 @ X913))=>(in @ (setadjoin @ X914 @ X914) @ X913))))=>![X915:$i]:(((in @ X915 @ omega)=>(in @ X915 @ X913)))))=>(![X1745:$i > $i > $o, X1746:$i]:((![X1747:$i]:(((in @ X1747 @ X1746)=>(exu @ (X1745 @ X1747))))=>?[X1748:$i]:(![X1749:$i]:(((in @ X1749 @ X1748)<=>?[X1750:$i]:(((in @ X1750 @ X1746)&(X1745 @ X1750 @ X1749))))))))=>(![X1741:$i]:((?[X1742:$i]:((in @ X1742 @ X1741))=>?[X1743:$i]:(((in @ X1743 @ X1741)&~(?[X1744:$i]:(((in @ X1744 @ X1743)&(in @ X1744 @ X1741))))))))=>((epred1_0)=>(![X935:$i > $o]:(((exu @ X935)=>(X935 @ (descr @ (^[Z0/* 17 */:$i]:(X935 @ Z0))))))=>(![X1738:$i, X1739:$i > $o, X1740:$i]:(((in @ X1740 @ X1738)=>((X1739 @ X1740)=>(in @ X1740 @ (dsetconstr @ X1738 @ X1739)))))=>(![X1735:$i, X1736:$i > $o, X1737:$i]:(((in @ X1737 @ (dsetconstr @ X1735 @ X1736))=>(in @ X1737 @ X1735)))=>(![X1732:$i, X1733:$i > $o, X1734:$i]:(((in @ X1734 @ (dsetconstr @ X1732 @ X1733))=>(X1733 @ X1734)))=>(![X936:$i > $o]:(((exu @ X936)=>?[X937:$i]:(((X936 @ X937)&![X938:$i]:(((X936 @ X938)=>((X937)=(X938))))))))=>(![X939:$o, X940:$i]:(((in @ X940 @ (prop2set @ ((X939))))=>(X939)))=>(![X1730:$i]:(((in @ X1730 @ emptyset)=>![X1731:$o]:((X1731))))=>(![X941:$i]:(((in @ X941 @ emptyset)=>~($true)))=>(![X942:$i]:(~(in @ X942 @ emptyset))=>(![X943:$i > $o]:(((exu @ X943)=>?[X944:$i]:((X943 @ X944))))=>(![X945:$i, X946:$i]:((![X947:$i]:(((in @ X947 @ X945)=>(in @ X947 @ X946)))=>(![X948:$i]:(((in @ X948 @ X946)=>(in @ X948 @ X945)))=>((X945)=(X946)))))=>(![X1728:$i]:((![X1729:$i]:(~(in @ X1729 @ X1728))=>((X1728)=(emptyset))))=>(![X1726:$i]:((![X1727:$i]:(~(in @ X1727 @ X1726))=>((X1726)=(emptyset))))=>(![X1723:$i, X1724:$i > $o, X1725:$i]:(((in @ X1725 @ X1723)=>((in @ X1725 @ (dsetconstr @ X1723 @ X1724))<=>(X1724 @ X1725))))=>(![X949:$i]:(((nonempty @ X949)=>?[X950:$i]:((in @ X950 @ X949))))=>(![X1720:$i, X1721:$i > $o, X1722:$i]:(((in @ X1722 @ X1720)=>((X1721 @ X1722)=>(nonempty @ (dsetconstr @ X1720 @ X1721)))))=>(![X1718:$i]:((?[X1719:$i]:((in @ X1719 @ X1718))=>(nonempty @ X1718)))=>(![X951:$i, X952:$i]:((in @ X951 @ (setadjoin @ X951 @ X952)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1715:$i, X1716:$i, X1717:$i]:(((in @ X1717 @ X1716)=>(in @ X1717 @ (setadjoin @ X1715 @ X1716))))=>(![X1711:$i, X1712:$i, X1713:$i]:(((in @ X1713 @ (setadjoin @ X1711 @ X1712))=>![X1714:$o]:(((((X1713)=(X1711))=>(X1714))=>(((in @ X1713 @ X1712)=>(X1714))=>(X1714))))))=>(![X953:$i, X954:$i, X955:$i]:(((in @ X955 @ (setadjoin @ X953 @ X954))=>(((X955)=(X953))|(in @ X955 @ X954))))=>(![X1710:$i]:(((dsetconstr @ X1710 @ (^[Z0/* 1 */:$i]:($true)))=(X1710)))=>(![X956:$i, X957:$i]:((![X958:$i]:(((in @ X958 @ X957)=>(in @ X958 @ X956)))=>(in @ X957 @ (powerset @ X956))))=>(![X959:$i]:((in @ emptyset @ (powerset @ X959)))=>(![X960:$i]:((in @ emptyset @ (powerset @ X960)))=>(![X1707:$i, X1708:$i, X1709:$i]:(((in @ X1708 @ (powerset @ X1707))=>((in @ X1709 @ X1708)=>(in @ X1709 @ X1707))))=>(![X961:$i, X962:$i, X963:$i]:(((in @ X962 @ X963)=>((in @ X963 @ X961)=>(in @ X962 @ (setunion @ X961)))))=>(![X1703:$i, X1704:$i]:(((in @ X1704 @ (setunion @ X1703))=>![X1705:$o]:((![X1706:$i]:(((in @ X1704 @ X1706)=>((in @ X1706 @ X1703)=>(X1705))))=>(X1705)))))=>(![X964:$i, X965:$i]:(((in @ X965 @ X964)=>(in @ X965 @ (powerset @ (setunion @ X964)))))=>(![X1700:$i > $o]:(((exu @ X1700)=>?[X1701:$i]:(![X1702:$i]:(((X1700 @ X1702)<=>((X1702)=(X1701)))))))=>(![X1698:$i]:(((nonempty @ X1698)=>?[X1699:$i]:(((in @ X1699 @ X1698)&$true))))=>(![X966:$i, X967:$i]:(((in @ X966 @ (setadjoin @ X967 @ emptyset))=>((X966)=(X967))))=>(![X968:$i, X969:$i]:((((X968)!=(X969))=>~(in @ X969 @ (setadjoin @ X968 @ emptyset))))=>(![X1696:$i, X1697:$i]:((((X1696)=(X1697))=>(in @ X1696 @ (setadjoin @ X1697 @ emptyset))))=>(![X970:$i, X971:$i]:(((in @ X970 @ (setadjoin @ X971 @ emptyset))=>(in @ X971 @ (setadjoin @ X970 @ emptyset))))=>(![X972:$i, X973:$i, X974:$i]:(((in @ X974 @ (setadjoin @ X972 @ (setadjoin @ X973 @ emptyset)))=>(((X974)=(X972))|((X974)=(X973)))))=>(![X1694:$i, X1695:$i]:((in @ X1694 @ (setadjoin @ X1694 @ (setadjoin @ X1695 @ emptyset))))=>(![X975:$i, X976:$i]:((in @ X976 @ (setadjoin @ X975 @ (setadjoin @ X976 @ emptyset))))=>(![X1691:$i, X1692:$i > $o]:((?[X1693:$i]:(((in @ X1693 @ X1691)&(X1692 @ X1693)))=>(((dsetconstr @ X1691 @ X1692)=(emptyset))=>~($true))))=>(![X1689:$i > $o, X1690:$i]:(((in @ X1690 @ emptyset)=>(X1689 @ X1690)))=>(![X1685:$i, X1686:$i > $o]:((~(![X1687:$i]:(((in @ X1687 @ X1685)=>(X1686 @ X1687))))=>?[X1688:$i]:(((in @ X1688 @ X1685)&~((X1686 @ X1688))))))=>(![X977:$i, X978:$i > $o]:((![X979:$i]:(((in @ X979 @ X977)=>~((X978 @ X979))))=>~(?[X980:$i]:(((in @ X980 @ X977)&(X978 @ X980))))))=>(![X1681:$i, X1682:$i > $o]:((~(?[X1683:$i]:(((in @ X1683 @ X1681)&(X1682 @ X1683))))=>![X1684:$i]:(((in @ X1684 @ X1681)=>~((X1682 @ X1684))))))=>(![X981:$i, X982:$i > $o]:((?[X983:$i]:(((in @ X983 @ X981)&~((X982 @ X983))))=>~(![X984:$i]:(((in @ X984 @ X981)=>(X982 @ X984))))))=>(![X985:$o]:(((X985)=>(in @ emptyset @ (prop2set @ ((X985))))))=>((prop2set2propI)=>(![X986:$i, X987:$i > $o]:((~(?[X988:$i]:(((in @ X988 @ X986)&(X987 @ X988))))=>![X989:$i]:(((in @ X989 @ X986)=>~((X987 @ X989))))))=>(![X1677:$i, X1678:$i > $o]:((~(![X1679:$i]:(((in @ X1679 @ X1677)=>(X1678 @ X1679))))=>?[X1680:$i]:(((in @ X1680 @ X1677)&~((X1678 @ X1680))))))=>(![X990:$i > $o]:((?[X991:$i]:(((X990 @ X991)&![X992:$i]:(((X990 @ X992)=>((X991)=(X992))))))=>(exu @ X990)))=>(![X1673:$i > $o]:((?[X1674:$i]:((X1673 @ X1674))=>(![X1675:$i, X1676:$i]:(((X1673 @ X1675)=>((X1673 @ X1676)=>((X1675)=(X1676)))))=>(exu @ X1673))))=>(![X1670:$i > $o]:((?[X1671:$i]:(![X1672:$i]:(((X1670 @ X1672)<=>((X1672)=(X1671)))))=>(exu @ X1670)))=>(![X993:$i, X994:$i]:((((X993)=(X994))=>![X995:$i, X996:$i]:((((X995)=(X996))=>((in @ X995 @ X993)=>(in @ X996 @ X994))))))=>(![X1666:$i, X1667:$i]:((((X1666)=(X1667))=>![X1668:$i, X1669:$i]:((((X1668)=(X1669))=>((in @ X1668 @ X1666)<=>(in @ X1669 @ X1667))))))=>(![X997:$i > $o]:(((exu @ X997)=>![X998:$i, X999:$i]:(((X997 @ X998)=>((X997 @ X999)=>((X998)=(X999)))))))=>(![X1662:$i > $o, X1663:$i > $o]:((![X1664:$i, X1665:$i]:((((X1664)=(X1665))=>((X1662 @ X1664)<=>(X1663 @ X1665))))=>((exu @ X1662)<=>(exu @ X1663))))=>(((emptyset)=(emptyset))=>(![X1658:$i, X1659:$i]:((((X1658)=(X1659))=>![X1660:$i, X1661:$i]:((((X1660)=(X1661))=>((setadjoin @ X1658 @ X1660)=(setadjoin @ X1659 @ X1661))))))=>(![X1656:$i, X1657:$i]:((((X1656)=(X1657))=>((powerset @ X1656)=(powerset @ X1657))))=>(![X1000:$i, X1001:$i]:((((X1000)=(X1001))=>((setunion @ X1000)=(setunion @ X1001))))=>(((omega)=(omega))=>(![X1002:$i > $o]:(((exu @ X1002)=>![X1003:$i, X1004:$i]:(((X1002 @ X1003)=>((X1002 @ X1004)=>((X1003)=(X1004)))))))=>(![X1652:$i > $o, X1653:$i > $o]:((![X1654:$i, X1655:$i]:((((X1654)=(X1655))=>((X1652 @ X1654)<=>(X1653 @ X1655))))=>((exu @ X1652)=>((exu @ X1653)=>((descr @ X1652)=(descr @ X1653))))))=>(![X1005:$i, X1006:$i]:((((X1005)=(X1006))=>![X1007:$i > $o, X1008:$i > $o]:((![X1009:$i]:(((in @ X1009 @ X1005)=>![X1010:$i]:(((in @ X1010 @ X1006)=>(((X1009)=(X1010))=>((X1007 @ X1009)<=>(X1008 @ X1010)))))))=>((dsetconstr @ X1005 @ X1007)=(dsetconstr @ X1006 @ X1008))))))=>(![X1011:$i, X1012:$i]:((![X1013:$i]:(((in @ X1013 @ X1011)=>(in @ X1013 @ X1012)))=>(subset @ X1011 @ X1012)))=>(![X1014:$i, X1015:$i]:((((X1014)=(X1015))=>(subset @ X1015 @ X1014)))=>(![X1016:$i, X1017:$i]:((((X1016)=(X1017))=>(subset @ X1016 @ X1017)))=>(![X1018:$i, X1019:$i]:((![X1020:$i]:(((in @ X1020 @ X1018)=>(in @ X1020 @ X1019)))=>(subset @ X1018 @ X1019)))=>(![X1651:$i]:((subset @ emptyset @ X1651))=>(![X1648:$i, X1649:$i, X1650:$i]:(((subset @ X1648 @ X1649)=>((in @ X1650 @ X1648)=>(in @ X1650 @ X1649))))=>(![X1645:$i, X1646:$i, X1647:$i]:(((subset @ X1645 @ X1646)=>(~(in @ X1647 @ X1646)=>~(in @ X1647 @ X1645))))=>(![X1021:$i, X1022:$i, X1023:$i]:(((in @ X1023 @ X1021)=>(~(in @ X1023 @ X1022)=>~(subset @ X1021 @ X1022))))=>(![X1024:$i, X1025:$i]:((~(subset @ X1024 @ X1025)=>((X1024)!=(X1025))))=>(![X1026:$i, X1027:$i, X1028:$i]:(((in @ X1028 @ X1026)=>(~(in @ X1028 @ X1027)=>((X1026)!=(X1027)))))=>(![X1029:$i]:((subset @ X1029 @ X1029))=>(![X1030:$i, X1031:$i, X1032:$i]:(((subset @ X1030 @ X1031)=>((subset @ X1031 @ X1032)=>(subset @ X1030 @ X1032))))=>(![X1033:$i, X1034:$i]:((subset @ X1034 @ (setadjoin @ X1033 @ X1034)))=>(![X1642:$i, X1643:$i, X1644:$i]:(((subset @ X1642 @ X1644)=>(subset @ X1642 @ (setadjoin @ X1643 @ X1644))))=>(![X1035:$i, X1036:$i]:(((subset @ X1035 @ X1036)=>(in @ X1035 @ (powerset @ X1036))))=>(![X1037:$i, X1038:$i]:(((subset @ X1037 @ X1038)=>((subset @ X1038 @ X1037)=>((X1037)=(X1038)))))=>(![X1641:$i]:(((subset @ X1641 @ emptyset)=>((X1641)=(emptyset))))=>(![X1039:$i, X1040:$i]:(((subset @ X1040 @ X1039)=>(in @ X1040 @ (powerset @ X1039))))=>(![X1041:$i, X1042:$i]:(((in @ X1042 @ (powerset @ X1041))=>(subset @ X1042 @ X1041)))=>(![X1640:$i]:((in @ X1640 @ (powerset @ X1640)))=>(![X1638:$i, X1639:$i]:(((subset @ X1638 @ X1639)=>(subset @ (powerset @ X1638) @ (powerset @ X1639))))=>(![X1636:$i, X1637:$i > $o]:((in @ (dsetconstr @ X1636 @ X1637) @ (powerset @ X1636)))=>(![X1043:$i, X1044:$i > $o]:((subset @ (dsetconstr @ X1043 @ X1044) @ X1043))=>(![X1045:$i, X1046:$i, X1047:$i]:(((in @ X1047 @ X1045)=>(in @ X1047 @ (binunion @ X1045 @ X1046))))=>(![X1634:$i, X1635:$i]:((in @ X1635 @ (setadjoin @ X1634 @ (setadjoin @ X1635 @ emptyset))))=>(![X1631:$i, X1632:$i, X1633:$i]:(((in @ X1633 @ X1632)=>(in @ X1633 @ (binunion @ X1631 @ X1632))))=>(![X1627:$i, X1628:$i, X1629:$i, X1630:$o]:(((in @ X1629 @ (binunion @ X1627 @ X1628))=>(((in @ X1629 @ X1627)=>(X1630))=>(((in @ X1629 @ X1628)=>(X1630))=>(X1630)))))=>(![X1624:$i, X1625:$i, X1626:$i]:(((in @ X1626 @ (binunion @ X1624 @ X1625))=>((in @ X1626 @ X1624)|(in @ X1626 @ X1625))))=>(![X1048:$i, X1049:$i]:((subset @ X1048 @ (binunion @ X1048 @ X1049)))=>(![X1622:$i, X1623:$i]:((subset @ X1623 @ (binunion @ X1622 @ X1623)))=>(![X1050:$i, X1051:$i, X1052:$i]:(((in @ X1052 @ X1050)=>((in @ X1052 @ X1051)=>(in @ X1052 @ (binintersect @ X1050 @ X1051)))))=>(![X1053:$i, X1054:$i, X1055:$i]:(((subset @ X1055 @ X1053)=>((subset @ X1055 @ X1054)=>(subset @ X1055 @ (binintersect @ X1053 @ X1054)))))=>(![X1619:$i, X1620:$i, X1621:$i]:(((in @ X1621 @ (binintersect @ X1619 @ X1620))=>(in @ X1621 @ X1619)))=>(![X1617:$i, X1618:$i]:((subset @ (binintersect @ X1617 @ X1618) @ X1617))=>(![X1615:$i, X1616:$i]:(((subset @ X1615 @ X1616)=>((binintersect @ X1615 @ X1616)=(X1615))))=>(![X1613:$i, X1614:$i]:((((binintersect @ X1613 @ X1614)=(X1614))=>(subset @ X1614 @ X1613)))=>(![X1056:$i, X1057:$i, X1058:$i]:(((in @ X1058 @ (binintersect @ X1056 @ X1057))=>(in @ X1058 @ X1057)))=>(![X1059:$i, X1060:$i]:((~(?[X1061:$i]:(((in @ X1061 @ X1059)&(in @ X1061 @ X1060))))=>((binintersect @ X1059 @ X1060)=(emptyset))))=>(![X1611:$i, X1612:$i]:((subset @ (binintersect @ X1611 @ X1612) @ X1612))=>(![X1062:$i, X1063:$i]:(((subset @ X1063 @ X1062)=>((binintersect @ X1062 @ X1063)=(X1063))))=>(![X1064:$i, X1065:$i]:((((binintersect @ X1064 @ X1065)=(X1064))=>(subset @ X1064 @ X1065)))=>(![X1608:$i, X1609:$i, X1610:$i]:(((binintersect @ X1608 @ (binunion @ X1609 @ X1610))=(binunion @ (binintersect @ X1608 @ X1609) @ (binintersect @ X1608 @ X1610))))=>(![X1066:$i, X1067:$i, X1068:$i]:(((in @ X1068 @ X1066)=>(~(in @ X1068 @ X1067)=>(in @ X1068 @ (setminus @ X1066 @ X1067)))))=>(![X1069:$i, X1070:$i, X1071:$i]:(((in @ X1071 @ (setminus @ X1069 @ X1070))=>(in @ X1071 @ X1069)))=>(![X1605:$i, X1606:$i, X1607:$i]:(((in @ X1607 @ (setminus @ X1605 @ X1606))=>~(in @ X1607 @ X1606)))=>(![X1072:$i, X1073:$i]:(((subset @ X1072 @ X1073)=>((setminus @ X1072 @ X1073)=(emptyset))))=>(![X1074:$i, X1075:$i, X1076:$i]:((~(in @ X1076 @ (setminus @ X1074 @ X1075))=>((in @ X1076 @ X1074)=>(in @ X1076 @ X1075))))=>(![X1077:$i, X1078:$i, X1079:$i]:((~(in @ X1079 @ (setminus @ X1077 @ X1078))=>(~(in @ X1079 @ X1078)=>~(in @ X1079 @ X1077))))=>(![X1602:$i, X1603:$i, X1604:$i]:((~(in @ X1604 @ X1602)=>~(in @ X1604 @ (setminus @ X1602 @ 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def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emptysetAx]), c_0_270]), setminusSubset2]), powersetsubset]), secondinupair]), inPowerset]), subsetemptysetimpeq]), setadjoinSub2]), setukpairIR]), subsetE2]), subsetE]), kpairiskpair]), emptysetsubset]), c_0_271]), powerset__Cong]), singletonsubset]), setadjoin__Cong]), c_0_272]), singletoninpowunion]), in__Cong]), c_0_273]), c_0_274]), notdallE]), upairsubunion]), quantDeMorgan3]), quantDeMorgan1]), upairinpowunion]), vacuousDall]), c_0_275]), c_0_276]), upairsetIL]), ubforcartprodlem1]), eqinunit]), setminusERneg]), nonemptyImpWitness]), c_0_277]), ubforcartprodlem2]), setunionE]), powersetE]), c_0_278]), setadjoinE]), ubforcartprodlem3]), setadjoinIR]), nonemptyI1]), cartprodpairin]), c_0_279]), c_0_280]), noeltsimpempty]), cartprodmempair1]), emptyI]), emptysetE]), setunionE2]), c_0_281]), c_0_282]), c_0_283]), c_0_284]), foundationAx]), c_0_285]), c_0_286]), omegaSAx]), omega0Ax]), powersetAx]), c_0_287]), setadjoinAx]), setminusELneg]), singletonsuniq]), c_0_288]), kfstpairEq]), setukpairinjL2]), setukpairinjR12]), setukpairinjR]), contraSubsetComplement]), binunionTIRcontra]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodsndpairEq]), c_0_289]), symdiffE]), c_0_290]), c_0_291]), c_0_292]), c_0_293]), c_0_294]), funcGraphProp2]), funcextLem]), funcGraphProp4]), subbreln]), funcext]), ap2apEq2]), c_0_295]), c_0_296]), c_0_297]), iftrue]), iftrueorfalse]), binintersectTERcontra]), contrasubsetT]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), complementSubsetComplementIntersect]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binunionRsub]), binunionE]), binunionEcases]), binunionIR]), upairset2IR]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), binunionTE]), binunionTEcontra]), demorgan2a1]), demorgan1b]), demorgan1]), demorgan1a]), demorgan2a2]), complementUnionInPowersetComplement]), inComplementUnionImpInComplement1]), inIntersectImpInUnion]), binunionTILcontra]), complementTcontraSubset]), complementInPowersetComplementIntersect]), complementImpComplementIntersect]), complementTnotintersectT]), doubleComplementEq]), contrasubsetT3]), contrasubsetT2]), contrasubsetT1]), binintersectTELcontra]), complementTE1]), complementTI1]), powersetTE1]), powersetTI1]), subsetTI]), setextT]), complementT_lem]), setminusT_lem]), powersetT_lem]), binunionT_lem]), binintersectT_lem]), iffalse]), theeq]), ifp]), c_0_298]), c_0_299]), c_0_300]), c_0_301]), c_0_302]), c_0_303]), c_0_304]), ap2apEq1]), funcext2]), eqbreln]), funcGraphProp3]), funcGraphProp1]), c_0_305]), brelnall2]), brelnall1]), c_0_306]), funcinfuncset]), ap2p]), infuncsetfunc]), app]), c_0_307]), c_0_308]), c_0_309]), c_0_310]), c_0_311]), cartprodpairsurjEq]), cartprodfstpairEq]), setukpairinjR2]), upairequniteq]), setukpairinjR1]), setukpairinjR11]), setukpairinjL]), cartprodfstin]), theprop]), setukpairinjL1]), c_0_312]), setunionsingleton]), setunionsingleton2]), setunionsingleton1]), cartprodmempair]), upairset2E]), singletoninpowerset]), kpairp]), setukpairIL]), symdiffIneg2]), symdiffIneg1]), symdiffI2]), symdiffI1]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusILneg]), setminusER]), bs114d]), binintersectRsub]), binintersectSubset3]), setminusEL]), setminusI]), binintersectSubset1]), binintersectSubset4]), disjointsetsI1]), binintersectER]), binintersectSubset5]), binintersectI]), binunionLsub]), binunionIL]), c_0_313]), powersetE1]), powersetI1]), setextsub]), subset2powerset]), setadjoinSub]), subsetTrans]), subsetRefl]), notequalI2]), notequalI1]), notsubsetI]), subsetI2]), eqimpsubset1]), eqimpsubset2]), subsetI1]), c_0_314]), c_0_315]), omega__Cong]), setunion__Cong]), emptyset__Cong]), c_0_316]), inCongP]), c_0_317]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan2]), upairsetIR]), upairsetE]), singletonsswitch]), notinsingleton]), uniqinunit]), subPowSU]), setunionI]), emptyInPowerset]), emptyinPowerset]), powersetI]), setadjoinOr]), emptyinunitempty]), setadjoinIL]), nonemptyE1]), setext]), c_0_318]), notinemptyset]), emptysetimpfalse]), prop2setE]), c_0_319]), c_0_320]), wellorderingAx]), omegaIndAx]), setunionAx]), setextAx])])]), c_0_321])). 2.01/0.96 thf(c_0_323, negated_conjecture, ![X1759:$i, X1760:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1772:$i, X1773:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1781:$i, X1782:$i > $i > $o, X1783:$i, X1786:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1793:$i, X1794:$i > $o, X1795:$i, X1796:$i > $o, X1797:$i, X1798:$i, X1799:$i > $o, X1800:$i, X1801:$i, X1802:$i > $o, X1803:$i, X1804:$i > $o, X1806:$i, X1807:$o, X1808:$i, X1809:$i, X1810:$o, X1811:$i, X1812:$i, X1813:$i > $o, X1815:$i, X1816:$i, X1819:$i, X1821:$i, X1823:$i, X1824:$i > $o, X1825:$i, X1826:$i, X1828:$i, X1829:$i > $o, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$o, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$o, X1861:$i, X1862:$i, X1863:$i > $o, X1865:$i, X1866:$i, X1867:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i > $o, X1886:$i, X1887:$i > $o, X1888:$i, X1889:$i, X1890:$i > $o, X1891:$i, X1893:$i, X1894:$i > $o, X1896:$i, X1897:$i, X1898:$i > $o, X1900:$i, X1901:$i, X1902:$i > $o, X1903:$i, X1905:$o, X1906:$i, X1907:$i > $o, X1909:$i, X1910:$i, X1911:$i > $o, X1912:$i, X1914:$i > $o, X1915:$i, X1917:$i > $o, X1918:$i, X1921:$i > $o, X1922:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i > $o, X1933:$i, X1934:$i, X1935:$i > $o, X1936:$i > $o, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i > $o, X1948:$i, X1949:$i, X1950:$i > $o, X1951:$i > $o, X1954:$i, X1955:$i, X1956:$i > $o, X1957:$i > $o, X1960:$i, X1961:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i > $o, X2008:$i, X2009:$i > $o, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$o, X2022:$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, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$o, 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, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i > $o, X2164:$i, X2165:$i, X2166:$i > $o, X2168:$i, X2169:$i > $o, X2170:$i, X2172:$i, X2173:$i > $o, X2176:$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:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, 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X2464) @ X2464)|(subset @ X2463 @ X2464)|~(in @ X2464 @ (powerset @ X2462))|~(in @ X2463 @ (powerset @ X2462)))))&((((in @ (esk70_3 @ X2466 @ X2467 @ X2468) @ X2466)|(in @ X2467 @ (powerset @ X2468))|~(in @ X2468 @ (powerset @ X2466))|~(in @ X2467 @ (powerset @ X2466)))&(((in @ (esk70_3 @ X2466 @ X2467 @ X2468) @ X2467)|(in @ X2467 @ (powerset @ X2468))|~(in @ X2468 @ (powerset @ X2466))|~(in @ X2467 @ (powerset @ X2466)))&(~(in @ (esk70_3 @ X2466 @ X2467 @ X2468) @ X2468)|(in @ X2467 @ (powerset @ X2468))|~(in @ X2468 @ (powerset @ X2466))|~(in @ X2467 @ (powerset @ X2466)))))&((~(in @ X2471 @ (powerset @ X2470))|(~(in @ X2472 @ (powerset @ X2470))|(~(in @ X2473 @ X2470)|(~(in @ X2471 @ (powerset @ X2472))|(~(in @ X2473 @ X2471)|(in @ X2473 @ X2472))))))&((~(in @ X2475 @ (powerset @ X2474))|(~(in @ X2476 @ X2474)|(~(in @ X2476 @ X2475)|~(in @ X2476 @ (setminus @ X2474 @ X2475)))))&((~(in @ X2478 @ (powerset @ X2477))|(~(in @ X2479 @ X2477)|((in @ X2479 @ (setminus @ X2477 @ X2478))|(in @ X2479 @ X2478))))&((~(in @ X2481 @ (powerset @ X2480))|(~(in @ X2482 @ (powerset @ X2480))|(~(in @ X2483 @ X2480)|((in @ X2483 @ X2481)|~(in @ X2483 @ (binintersect @ X2481 @ X2482))))))&((~(in @ X2485 @ (powerset @ X2484))|(~(in @ X2486 @ (powerset @ X2484))|(~(in @ X2487 @ X2484)|((in @ X2487 @ X2486)|~(in @ X2487 @ (binintersect @ X2485 @ X2486))))))&((~(in @ X2489 @ (powerset @ X2488))|(~(in @ X2490 @ (powerset @ X2488))|(~(in @ X2491 @ X2488)|(~(subset @ X2489 @ (setminus @ X2488 @ X2490))|(~(in @ X2491 @ X2490)|~(in @ X2491 @ X2489))))))&((~(in @ X2493 @ (powerset @ X2492))|(~(in @ X2494 @ (powerset @ X2492))|(~(in @ X2495 @ X2492)|(~(subset @ X2493 @ X2494)|((in @ X2495 @ X2494)|~(in @ X2495 @ X2493))))))&((~(in @ X2497 @ (powerset @ X2496))|(~(in @ X2498 @ (powerset @ X2496))|(~(subset @ X2497 @ X2498)|(subset @ (setminus @ X2496 @ X2498) @ (setminus @ X2496 @ X2497)))))&((~(in @ X2500 @ (powerset @ X2499))|(~(in @ X2501 @ (powerset @ X2499))|(~(subset @ (setminus @ X2499 @ X2501) @ (setminus @ X2499 @ X2500))|(subset @ X2500 @ X2501))))&((~(in @ X2503 @ (powerset @ X2502))|(~(in @ X2504 @ X2502)|(~(in @ X2504 @ X2503)|(in @ X2504 @ (setminus @ X2502 @ (setminus @ X2502 @ X2503))))))&((~(in @ X2506 @ (powerset @ X2505))|(~(in @ X2507 @ X2505)|(~(in @ X2507 @ (setminus @ X2505 @ (setminus @ X2505 @ X2506)))|(in @ X2507 @ X2506))))&((~(in @ X2509 @ (powerset @ X2508))|(subset @ X2509 @ (setminus @ X2508 @ (setminus @ X2508 @ X2509))))&((~(in @ X2511 @ (powerset @ X2510))|(subset @ (setminus @ X2510 @ (setminus @ X2510 @ X2511)) @ X2511))&((~(in @ X2513 @ (powerset @ X2512))|((X2513)=(setminus @ X2512 @ (setminus @ X2512 @ X2513))))&((~(in @ X2515 @ (powerset @ X2514))|(~(in @ X2516 @ (powerset @ X2514))|(~(in @ X2517 @ X2514)|(~(in @ X2517 @ (setminus @ X2514 @ X2515))|~(in @ X2517 @ (binintersect @ X2515 @ X2516))))))&((~(in @ X2519 @ (powerset @ X2518))|(~(in @ X2520 @ (powerset @ X2518))|(~(in @ X2521 @ X2518)|(~(in @ X2521 @ (setminus @ X2518 @ X2519))|(in @ X2521 @ (setminus @ X2518 @ (binintersect @ X2519 @ X2520)))))))&((~(in @ X2523 @ (powerset @ X2522))|(~(in @ X2524 @ (powerset @ X2522))|(subset @ (setminus @ X2522 @ X2523) @ (setminus @ X2522 @ (binintersect @ X2523 @ X2524)))))&((~(in @ X2526 @ (powerset @ X2525))|(~(in @ X2527 @ (powerset @ X2525))|(in @ (setminus @ X2525 @ X2526) @ (powerset @ (setminus @ X2525 @ (binintersect @ X2526 @ X2527))))))&((~(in @ X2529 @ (powerset @ X2528))|(~(in @ X2530 @ (powerset @ X2528))|(~(subset @ X2529 @ (setminus @ X2528 @ X2530))|(~(in @ X2531 @ X2528)|(~(in @ X2531 @ X2530)|(in @ X2531 @ (setminus @ X2528 @ X2529)))))))&((~(in @ X2533 @ (powerset @ X2532))|(~(in @ X2534 @ (powerset @ X2532))|(~(subset @ X2533 @ (setminus @ X2532 @ X2534))|(subset @ X2534 @ (setminus @ X2532 @ X2533)))))&((~(in @ X2536 @ (powerset @ X2535))|(~(in @ X2537 @ (powerset @ X2535))|(~(in @ X2538 @ X2535)|((in @ X2538 @ (binunion @ X2536 @ X2537))|~(in @ X2538 @ X2536)))))&((~(in @ X2540 @ (powerset @ X2539))|(~(in @ X2541 @ (powerset @ X2539))|(~(in @ X2542 @ X2539)|((in @ X2542 @ (binunion @ X2540 @ X2541))|~(in @ X2542 @ X2541)))))&((~(in @ X2544 @ (powerset @ X2543))|(~(in @ X2545 @ (powerset @ X2543))|(~(in @ X2546 @ (powerset @ X2543))|(~(in @ X2547 @ X2543)|(~(in @ X2547 @ (binintersect @ X2544 @ X2545))|(in @ X2547 @ (binunion @ X2544 @ X2546)))))))&((~(in @ X2549 @ (powerset @ X2548))|(~(in @ X2550 @ (powerset @ X2548))|(~(in @ X2551 @ (powerset @ X2548))|(~(in @ X2552 @ X2548)|(~(in @ X2552 @ (binintersect @ X2549 @ X2550))|(in @ X2552 @ (binunion @ X2550 @ X2551)))))))&((~(in @ X2554 @ (powerset @ X2553))|(~(in @ X2555 @ (powerset @ X2553))|(~(in @ X2556 @ (powerset @ X2553))|(~(in @ X2557 @ X2553)|(~(in @ X2557 @ (binintersect @ X2554 @ X2555))|(in @ X2557 @ (binintersect @ (binunion @ X2554 @ X2556) @ (binunion @ X2555 @ X2556))))))))&((~(in @ X2559 @ (powerset @ X2558))|(~(in @ X2560 @ (powerset @ X2558))|(~(in @ X2561 @ (powerset @ X2558))|(in @ (binintersect @ X2559 @ X2560) @ (powerset @ (binintersect @ (binunion @ X2559 @ X2561) @ (binunion @ X2560 @ X2561)))))))&((~(in @ X2563 @ (powerset @ X2562))|(~(in @ X2564 @ (powerset @ X2562))|(~(in @ X2565 @ X2562)|(~(in @ X2565 @ (setminus @ X2562 @ (binunion @ X2563 @ X2564)))|~(in @ X2565 @ X2563)))))&((~(in @ X2567 @ (powerset @ X2566))|(~(in @ X2568 @ (powerset @ X2566))|(~(in @ X2569 @ X2566)|(~(in @ X2569 @ (setminus @ X2566 @ (binunion @ X2567 @ X2568)))|(in @ X2569 @ (setminus @ X2566 @ X2567))))))&(((((in @ X2574 @ X2572)|(X2573)|(in @ X2574 @ X2571)|~(in @ X2574 @ (binunion @ X2571 @ X2572))|~(in @ X2574 @ X2570)|~(in @ X2572 @ (powerset @ X2570))|~(in @ X2571 @ (powerset @ X2570)))&(~(X2573)|(X2573)|(in @ X2574 @ X2571)|~(in @ X2574 @ (binunion @ X2571 @ X2572))|~(in @ X2574 @ X2570)|~(in @ X2572 @ (powerset @ X2570))|~(in @ X2571 @ (powerset @ X2570))))&(((in @ X2574 @ X2572)|(X2573)|~(X2573)|~(in @ X2574 @ (binunion @ X2571 @ X2572))|~(in @ X2574 @ X2570)|~(in @ X2572 @ (powerset @ X2570))|~(in @ X2571 @ (powerset @ X2570)))&(~(X2573)|(X2573)|~(X2573)|~(in @ X2574 @ (binunion @ X2571 @ X2572))|~(in @ X2574 @ X2570)|~(in @ X2572 @ (powerset @ X2570))|~(in @ X2571 @ (powerset @ X2570)))))&((~(in @ X2576 @ (powerset @ X2575))|(~(in @ X2577 @ (powerset @ X2575))|(~(in @ X2578 @ X2575)|((in @ X2578 @ X2576)|((in @ X2578 @ X2577)|~(in @ X2578 @ (binunion @ X2576 @ X2577)))))))&((~(in @ X2580 @ (powerset @ X2579))|(~(in @ X2581 @ (powerset @ X2579))|(~(in @ X2582 @ X2579)|(~(in @ X2582 @ (setminus @ X2579 @ (binunion @ X2580 @ X2581)))|(in @ X2582 @ (setminus @ X2579 @ X2580))))))&((~(in @ X2584 @ (powerset @ X2583))|(~(in @ X2585 @ (powerset @ X2583))|(in @ (setminus @ X2583 @ (binunion @ X2584 @ X2585)) @ (powerset @ (setminus @ X2583 @ X2584)))))&((~(in @ X2587 @ (powerset @ X2586))|(~(in @ X2588 @ (powerset @ X2586))|(~(in @ X2589 @ X2586)|(~(in @ X2589 @ (setminus @ X2586 @ (binunion @ X2587 @ X2588)))|(in @ X2589 @ (setminus @ X2586 @ X2588))))))&((~(in @ X2591 @ (powerset @ X2590))|(~(in @ X2592 @ (powerset @ X2590))|(~(in @ X2593 @ X2590)|(~(in @ X2593 @ (setminus @ X2590 @ (binintersect @ X2591 @ X2592)))|(in @ X2593 @ (binunion @ (setminus @ X2590 @ X2591) @ (setminus @ X2590 @ X2592)))))))&((~(in @ X2595 @ (powerset @ X2594))|(~(in @ X2596 @ (powerset @ X2594))|(~(in @ X2597 @ X2594)|(~(in @ X2597 @ (binunion @ (setminus @ X2594 @ X2595) @ (setminus @ X2594 @ X2596)))|(in @ X2597 @ (setminus @ X2594 @ (binintersect @ X2595 @ X2596)))))))&((~(in @ X2599 @ (powerset @ X2598))|(~(in @ X2600 @ (powerset @ X2598))|((setminus @ X2598 @ (binintersect @ X2599 @ X2600))=(binunion @ (setminus @ X2598 @ X2599) @ (setminus @ X2598 @ X2600)))))&((in @ esk72_0 @ (powerset @ esk71_0))&((in @ esk73_0 @ (powerset @ esk71_0))&((in @ esk74_0 @ esk71_0)&((in @ esk74_0 @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0)))&~(in @ esk74_0 @ (binintersect @ (setminus @ esk71_0 @ esk72_0) @ (setminus @ esk71_0 @ esk73_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_322])])])])])])])). 2.01/0.96 thf(c_0_324, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_323])). 2.01/0.96 thf(c_0_325, negated_conjecture, (in @ esk74_0 @ (setminus @ esk71_0 @ (binunion @ esk72_0 @ esk73_0))), inference(split_conjunct,[status(thm)],[c_0_323])). 2.01/0.96 thf(c_0_326, negated_conjecture, ~((in @ esk74_0 @ (binintersect @ (setminus @ esk71_0 @ esk72_0) @ (setminus @ esk71_0 @ esk73_0)))), inference(split_conjunct,[status(thm)],[c_0_323])). 2.01/0.96 thf(c_0_327, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ (binintersect @ X3 @ X4))|~((in @ X2 @ X3))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_323])). 2.01/0.96 thf(c_0_328, negated_conjecture, ~((in @ esk74_0 @ (binunion @ esk72_0 @ esk73_0))), inference(spm,[status(thm)],[c_0_324, c_0_325])). 2.01/0.96 thf(c_0_329, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X4 @ X3))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_323])). 2.01/0.96 thf(c_0_330, negated_conjecture, (~((in @ esk74_0 @ (setminus @ esk71_0 @ esk73_0)))|~((in @ esk74_0 @ (setminus @ esk71_0 @ esk72_0)))), inference(spm,[status(thm)],[c_0_326, c_0_327])). 2.01/0.96 thf(c_0_331, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ X4))|(in @ X2 @ X4)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_323])). 2.01/0.96 thf(c_0_332, negated_conjecture, (in @ esk74_0 @ esk71_0), inference(split_conjunct,[status(thm)],[c_0_323])). 2.01/0.96 thf(c_0_333, negated_conjecture, ~((in @ esk74_0 @ esk73_0)), inference(spm,[status(thm)],[c_0_328, c_0_329])). 2.01/0.96 thf(c_0_334, negated_conjecture, ![X3:$i, X5:$i, X4:$i, X2:$i]:((~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3)))|~((in @ X5 @ X3))|~((in @ X5 @ (setminus @ X3 @ (binunion @ X2 @ X4))))|~((in @ X5 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_323])). 2.01/0.96 thf(c_0_335, negated_conjecture, (in @ esk73_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_323])). 2.01/0.96 thf(c_0_336, negated_conjecture, (in @ esk72_0 @ (powerset @ esk71_0)), inference(split_conjunct,[status(thm)],[c_0_323])). 2.01/0.96 thf(c_0_337, negated_conjecture, ~((in @ esk74_0 @ (setminus @ esk71_0 @ esk72_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_330, c_0_331]), c_0_332])]), c_0_333])). 2.01/0.96 thf(c_0_338, negated_conjecture, ~((in @ esk74_0 @ esk72_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_334, c_0_325]), c_0_335]), c_0_336]), c_0_332])])). 2.01/0.96 thf(c_0_339, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_337, c_0_331]), c_0_332])]), c_0_338]), ['proof']). 2.01/0.96 # SZS output end CNFRefutation 2.01/0.96 # Parsed axioms : 583 2.01/0.96 # Removed by relevancy pruning/SinE : 313 2.01/0.96 # Initial clauses : 435 2.01/0.96 # Removed in clause preprocessing : 37 2.01/0.96 # Initial clauses in saturation : 398 2.01/0.96 # Processed clauses : 782 2.01/0.96 # ...of these trivial : 11 2.01/0.96 # ...subsumed : 45 2.01/0.96 # ...remaining for further processing : 726 2.01/0.96 # Other redundant clauses eliminated : 54 2.01/0.96 # Clauses deleted for lack of memory : 0 2.01/0.96 # Backward-subsumed : 1 2.01/0.96 # Backward-rewritten : 3 2.01/0.96 # Generated clauses : 8198 2.01/0.96 # ...of the previous two non-redundant : 7954 2.01/0.96 # ...aggressively subsumed : 0 2.01/0.96 # Contextual simplify-reflections : 9 2.01/0.96 # Paramodulations : 8109 2.01/0.96 # Factorizations : 2 2.01/0.96 # NegExts : 0 2.01/0.96 # Equation resolutions : 61 2.01/0.96 # Disequality decompositions : 0 2.01/0.96 # Total rewrite steps : 212 2.01/0.96 # ...of those cached : 140 2.01/0.96 # Propositional unsat checks : 0 2.01/0.96 # Propositional check models : 0 2.01/0.96 # Propositional check unsatisfiable : 0 2.01/0.96 # Propositional clauses : 0 2.01/0.96 # Propositional clauses after purity: 0 2.01/0.96 # Propositional unsat core size : 0 2.01/0.96 # Propositional preprocessing time : 0.000 2.01/0.96 # Propositional encoding time : 0.000 2.01/0.96 # Propositional solver time : 0.000 2.01/0.96 # Success case prop preproc time : 0.000 2.01/0.96 # Success case prop encoding time : 0.000 2.01/0.96 # Success case prop solver time : 0.000 2.01/0.96 # Current number of processed clauses : 360 2.01/0.96 # Positive orientable unit clauses : 45 2.01/0.96 # Positive unorientable unit clauses: 0 2.01/0.96 # Negative unit clauses : 9 2.01/0.96 # Non-unit-clauses : 306 2.01/0.96 # Current number of unprocessed clauses: 7911 2.01/0.96 # ...number of literals in the above : 34004 2.01/0.96 # Current number of archived formulas : 0 2.01/0.96 # Current number of archived clauses : 350 2.01/0.96 # Clause-clause subsumption calls (NU) : 60171 2.01/0.96 # Rec. Clause-clause subsumption calls : 25932 2.01/0.96 # Non-unit clause-clause subsumptions : 45 2.01/0.96 # Unit Clause-clause subsumption calls : 909 2.01/0.96 # Rewrite failures with RHS unbound : 0 2.01/0.96 # BW rewrite match attempts : 33 2.01/0.96 # BW rewrite match successes : 3 2.01/0.96 # Condensation attempts : 0 2.01/0.96 # Condensation successes : 0 2.01/0.96 # Termbank termtop insertions : 212278 2.01/0.96 # Search garbage collected termcells : 27554 2.01/0.96 2.01/0.96 # ------------------------------------------------- 2.01/0.96 # User time : 0.348 s 2.01/0.96 # System time : 0.022 s 2.01/0.96 # Total time : 0.370 s 2.01/0.96 # Maximum resident set size: 8732 pages 2.01/0.96 2.01/0.96 # ------------------------------------------------- 2.01/0.96 # User time : 0.364 s 2.01/0.96 # System time : 0.026 s 2.01/0.96 # Total time : 0.390 s 2.01/0.96 # Maximum resident set size: 2760 pages 2.01/0.96 % E exiting 2.01/0.97 % E exiting 2.01/0.97 EOF