0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.12 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM 0.11/0.33 % Computer : n016.cluster.edu 0.11/0.33 % Model : x86_64 x86_64 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.33 % Memory : 8042.1875MB 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.33 % CPULimit : 1920 0.11/0.33 % WCLimit : 240 0.11/0.33 % DateTime : Wed Jul 30 03:39:04 EDT 2025 0.11/0.34 % CPUTime : 0.20/0.48 Running higher-order theorem proving 0.38/0.54 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p 25.96/3.85 # Version: 3.0.0-ho 25.96/3.85 # Preprocessing class: HSLMSLSSLLLCHFA. 25.96/3.85 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 25.96/3.85 # Starting ehoh_best5 with 240s (1) cores 25.96/3.85 # Starting almost_fo_3_lam with 240s (1) cores 25.96/3.85 # Starting new_bool_5 with 240s (1) cores 25.96/3.85 # Starting pre_casc_3 with 240s (1) cores 25.96/3.85 # Starting ho_unfolding_8 with 240s (1) cores 25.96/3.85 # Starting new_ho_10_cnf2 with 240s (1) cores 25.96/3.85 # Starting new_bool_3 with 240s (1) cores 25.96/3.85 # Starting new_ho_5 with 240s (1) cores 25.96/3.85 # ho_unfolding_8 with pid 13851 completed with status 0 25.96/3.85 # Result found by ho_unfolding_8 25.96/3.85 # Preprocessing class: HSLMSLSSLLLCHFA. 25.96/3.85 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 25.96/3.85 # Starting ehoh_best5 with 240s (1) cores 25.96/3.85 # Starting almost_fo_3_lam with 240s (1) cores 25.96/3.85 # Starting new_bool_5 with 240s (1) cores 25.96/3.85 # Starting pre_casc_3 with 240s (1) cores 25.96/3.85 # Starting ho_unfolding_8 with 240s (1) cores 25.96/3.85 # No SInE strategy applied 25.96/3.85 # Search class: HGHSM-FSLM32-MHFMMSBN 25.96/3.85 # Scheduled 9 strats onto 1 cores with 240 seconds (240 total) 25.96/3.85 # Starting ho_unfolding_8 with 49s (1) cores 25.96/3.85 # ho_unfolding_8 with pid 13859 completed with status 0 25.96/3.85 # Result found by ho_unfolding_8 25.96/3.85 # Preprocessing class: HSLMSLSSLLLCHFA. 25.96/3.85 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 25.96/3.85 # Starting ehoh_best5 with 240s (1) cores 25.96/3.85 # Starting almost_fo_3_lam with 240s (1) cores 25.96/3.85 # Starting new_bool_5 with 240s (1) cores 25.96/3.85 # Starting pre_casc_3 with 240s (1) cores 25.96/3.85 # Starting ho_unfolding_8 with 240s (1) cores 25.96/3.85 # No SInE strategy applied 25.96/3.85 # Search class: HGHSM-FSLM32-MHFMMSBN 25.96/3.85 # Scheduled 9 strats onto 1 cores with 240 seconds (240 total) 25.96/3.85 # Starting ho_unfolding_8 with 49s (1) cores 25.96/3.85 # Preprocessing time : 0.090 s 25.96/3.85 # Presaturation interreduction done 25.96/3.85 25.96/3.85 # Proof found! 25.96/3.85 # SZS status Theorem 25.96/3.85 # SZS output start CNFRefutation 25.96/3.85 thf(decl_23, type, in: $i > $i > $o). 25.96/3.85 thf(decl_24, type, exu: ($i > $o) > $o). 25.96/3.85 thf(decl_25, type, setextAx: $o). 25.96/3.85 thf(decl_26, type, emptyset: $i). 25.96/3.85 thf(decl_27, type, emptysetAx: $o). 25.96/3.85 thf(decl_28, type, setadjoin: $i > $i > $i). 25.96/3.85 thf(decl_29, type, setadjoinAx: $o). 25.96/3.85 thf(decl_30, type, powerset: $i > $i). 25.96/3.85 thf(decl_31, type, powersetAx: $o). 25.96/3.85 thf(decl_32, type, setunion: $i > $i). 25.96/3.85 thf(decl_33, type, setunionAx: $o). 25.96/3.85 thf(decl_34, type, omega: $i). 25.96/3.85 thf(decl_35, type, omega0Ax: $o). 25.96/3.85 thf(decl_36, type, omegaSAx: $o). 25.96/3.85 thf(decl_37, type, omegaIndAx: $o). 25.96/3.85 thf(decl_38, type, replAx: $o). 25.96/3.85 thf(decl_39, type, foundationAx: $o). 25.96/3.85 thf(decl_40, type, wellorderingAx: $o). 25.96/3.85 thf(decl_41, type, descr: ($i > $o) > $i). 25.96/3.85 thf(decl_42, type, descrp: $o). 25.96/3.85 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 25.96/3.85 thf(decl_44, type, dsetconstrI: $o). 25.96/3.85 thf(decl_45, type, dsetconstrEL: $o). 25.96/3.85 thf(decl_46, type, dsetconstrER: $o). 25.96/3.85 thf(decl_47, type, exuE1: $o). 25.96/3.85 thf(decl_48, type, prop2set: $o > $i). 25.96/3.85 thf(decl_49, type, prop2setE: $o). 25.96/3.85 thf(decl_50, type, emptysetE: $o). 25.96/3.85 thf(decl_51, type, emptysetimpfalse: $o). 25.96/3.85 thf(decl_52, type, notinemptyset: $o). 25.96/3.85 thf(decl_53, type, exuE3e: $o). 25.96/3.85 thf(decl_54, type, setext: $o). 25.96/3.85 thf(decl_55, type, emptyI: $o). 25.96/3.85 thf(decl_56, type, noeltsimpempty: $o). 25.96/3.85 thf(decl_57, type, setbeta: $o). 25.96/3.85 thf(decl_58, type, nonempty: $i > $o). 25.96/3.85 thf(decl_59, type, nonemptyE1: $o). 25.96/3.85 thf(decl_60, type, nonemptyI: $o). 25.96/3.85 thf(decl_61, type, nonemptyI1: $o). 25.96/3.85 thf(decl_62, type, setadjoinIL: $o). 25.96/3.85 thf(decl_63, type, emptyinunitempty: $o). 25.96/3.85 thf(decl_64, type, setadjoinIR: $o). 25.96/3.85 thf(decl_65, type, setadjoinE: $o). 25.96/3.85 thf(decl_66, type, setadjoinOr: $o). 25.96/3.85 thf(decl_67, type, setoftrueEq: $o). 25.96/3.85 thf(decl_68, type, powersetI: $o). 25.96/3.85 thf(decl_69, type, emptyinPowerset: $o). 25.96/3.85 thf(decl_70, type, emptyInPowerset: $o). 25.96/3.85 thf(decl_71, type, powersetE: $o). 25.96/3.85 thf(decl_72, type, setunionI: $o). 25.96/3.85 thf(decl_73, type, setunionE: $o). 25.96/3.85 thf(decl_74, type, subPowSU: $o). 25.96/3.85 thf(decl_75, type, exuE2: $o). 25.96/3.85 thf(decl_76, type, nonemptyImpWitness: $o). 25.96/3.85 thf(decl_77, type, uniqinunit: $o). 25.96/3.85 thf(decl_78, type, notinsingleton: $o). 25.96/3.85 thf(decl_79, type, eqinunit: $o). 25.96/3.85 thf(decl_80, type, singletonsswitch: $o). 25.96/3.85 thf(decl_81, type, upairsetE: $o). 25.96/3.85 thf(decl_82, type, upairsetIL: $o). 25.96/3.85 thf(decl_83, type, upairsetIR: $o). 25.96/3.85 thf(decl_84, type, emptyE1: $o). 25.96/3.85 thf(decl_85, type, vacuousDall: $o). 25.96/3.85 thf(decl_86, type, quantDeMorgan1: $o). 25.96/3.85 thf(decl_87, type, quantDeMorgan2: $o). 25.96/3.85 thf(decl_88, type, quantDeMorgan3: $o). 25.96/3.85 thf(decl_89, type, quantDeMorgan4: $o). 25.96/3.85 thf(decl_90, type, prop2setI: $o). 25.96/3.85 thf(decl_91, type, set2prop: $i > $o). 25.96/3.85 thf(decl_92, type, prop2set2propI: $o). 25.96/3.85 thf(decl_93, type, notdexE: $o). 25.96/3.85 thf(decl_94, type, notdallE: $o). 25.96/3.85 thf(decl_95, type, exuI1: $o). 25.96/3.85 thf(decl_96, type, exuI3: $o). 25.96/3.85 thf(decl_97, type, exuI2: $o). 25.96/3.85 thf(decl_98, type, inCongP: $o). 25.96/3.85 thf(decl_99, type, in__Cong: $o). 25.96/3.85 thf(decl_100, type, exuE3u: $o). 25.96/3.85 thf(decl_101, type, exu__Cong: $o). 25.96/3.85 thf(decl_102, type, emptyset__Cong: $o). 25.96/3.85 thf(decl_103, type, setadjoin__Cong: $o). 25.96/3.85 thf(decl_104, type, powerset__Cong: $o). 25.96/3.85 thf(decl_105, type, setunion__Cong: $o). 25.96/3.85 thf(decl_106, type, omega__Cong: $o). 25.96/3.85 thf(decl_107, type, exuEu: $o). 25.96/3.85 thf(decl_108, type, descr__Cong: $o). 25.96/3.85 thf(decl_109, type, dsetconstr__Cong: $o). 25.96/3.85 thf(decl_110, type, subset: $i > $i > $o). 25.96/3.85 thf(decl_113, type, subsetI1: $o). 25.96/3.85 thf(decl_114, type, eqimpsubset2: $o). 25.96/3.85 thf(decl_115, type, eqimpsubset1: $o). 25.96/3.85 thf(decl_116, type, subsetI2: $o). 25.96/3.85 thf(decl_117, type, emptysetsubset: $o). 25.96/3.85 thf(decl_118, type, subsetE: $o). 25.96/3.85 thf(decl_119, type, subsetE2: $o). 25.96/3.85 thf(decl_120, type, notsubsetI: $o). 25.96/3.85 thf(decl_121, type, notequalI1: $o). 25.96/3.85 thf(decl_122, type, notequalI2: $o). 25.96/3.85 thf(decl_123, type, subsetRefl: $o). 25.96/3.85 thf(decl_124, type, subsetTrans: $o). 25.96/3.85 thf(decl_125, type, setadjoinSub: $o). 25.96/3.85 thf(decl_126, type, setadjoinSub2: $o). 25.96/3.85 thf(decl_127, type, subset2powerset: $o). 25.96/3.85 thf(decl_128, type, setextsub: $o). 25.96/3.85 thf(decl_129, type, subsetemptysetimpeq: $o). 25.96/3.85 thf(decl_130, type, powersetI1: $o). 25.96/3.85 thf(decl_131, type, powersetE1: $o). 25.96/3.85 thf(decl_132, type, inPowerset: $o). 25.96/3.85 thf(decl_133, type, powersetsubset: $o). 25.96/3.85 thf(decl_134, type, sepInPowerset: $o). 25.96/3.85 thf(decl_135, type, sepSubset: $o). 25.96/3.85 thf(decl_136, type, binunion: $i > $i > $i). 25.96/3.85 thf(decl_137, type, binunionIL: $o). 25.96/3.85 thf(decl_138, type, upairset2IR: $o). 25.96/3.85 thf(decl_139, type, binunionIR: $o). 25.96/3.85 thf(decl_140, type, binunionEcases: $o). 25.96/3.85 thf(decl_141, type, binunionE: $o). 25.96/3.85 thf(decl_142, type, binunionLsub: $o). 25.96/3.85 thf(decl_143, type, binunionRsub: $o). 25.96/3.85 thf(decl_144, type, binintersect: $i > $i > $i). 25.96/3.85 thf(decl_145, type, binintersectI: $o). 25.96/3.85 thf(decl_146, type, binintersectSubset5: $o). 25.96/3.85 thf(decl_147, type, binintersectEL: $o). 25.96/3.85 thf(decl_148, type, binintersectLsub: $o). 25.96/3.85 thf(decl_149, type, binintersectSubset2: $o). 25.96/3.85 thf(decl_150, type, binintersectSubset3: $o). 25.96/3.85 thf(decl_151, type, binintersectER: $o). 25.96/3.85 thf(decl_152, type, disjointsetsI1: $o). 25.96/3.85 thf(decl_153, type, binintersectRsub: $o). 25.96/3.85 thf(decl_154, type, binintersectSubset4: $o). 25.96/3.85 thf(decl_155, type, binintersectSubset1: $o). 25.96/3.85 thf(decl_156, type, bs114d: $o). 25.96/3.85 thf(decl_158, type, setminus: $i > $i > $i). 25.96/3.85 thf(decl_159, type, setminusI: $o). 25.96/3.85 thf(decl_160, type, setminusEL: $o). 25.96/3.85 thf(decl_161, type, setminusER: $o). 25.96/3.85 thf(decl_162, type, setminusSubset2: $o). 25.96/3.85 thf(decl_163, type, setminusERneg: $o). 25.96/3.85 thf(decl_164, type, setminusELneg: $o). 25.96/3.85 thf(decl_165, type, setminusILneg: $o). 25.96/3.85 thf(decl_166, type, setminusIRneg: $o). 25.96/3.85 thf(decl_167, type, setminusLsub: $o). 25.96/3.85 thf(decl_168, type, setminusSubset1: $o). 25.96/3.85 thf(decl_169, type, symdiff: $i > $i > $i). 25.96/3.85 thf(decl_170, type, symdiffE: $o). 25.96/3.85 thf(decl_171, type, symdiffI1: $o). 25.96/3.85 thf(decl_172, type, symdiffI2: $o). 25.96/3.85 thf(decl_173, type, symdiffIneg1: $o). 25.96/3.85 thf(decl_174, type, symdiffIneg2: $o). 25.96/3.85 thf(decl_175, type, iskpair: $i > $o). 25.96/3.85 thf(decl_176, type, secondinupair: $o). 25.96/3.85 thf(decl_177, type, setukpairIL: $o). 25.96/3.85 thf(decl_178, type, setukpairIR: $o). 25.96/3.85 thf(decl_179, type, kpairiskpair: $o). 25.96/3.85 thf(decl_180, type, kpair: $i > $i > $i). 25.96/3.85 thf(decl_181, type, kpairp: $o). 25.96/3.85 thf(decl_182, type, cartprod: $i > $i > $i). 25.96/3.85 thf(decl_183, type, singletonsubset: $o). 25.96/3.85 thf(decl_184, type, singletoninpowerset: $o). 25.96/3.85 thf(decl_185, type, singletoninpowunion: $o). 25.96/3.85 thf(decl_186, type, upairset2E: $o). 25.96/3.85 thf(decl_187, type, upairsubunion: $o). 25.96/3.85 thf(decl_188, type, upairinpowunion: $o). 25.96/3.85 thf(decl_189, type, ubforcartprodlem1: $o). 25.96/3.85 thf(decl_190, type, ubforcartprodlem2: $o). 25.96/3.85 thf(decl_191, type, ubforcartprodlem3: $o). 25.96/3.85 thf(decl_192, type, cartprodpairin: $o). 25.96/3.85 thf(decl_193, type, cartprodmempair1: $o). 25.96/3.85 thf(decl_194, type, cartprodmempair: $o). 25.96/3.85 thf(decl_195, type, setunionE2: $o). 25.96/3.85 thf(decl_196, type, setunionsingleton1: $o). 25.96/3.85 thf(decl_197, type, setunionsingleton2: $o). 25.96/3.85 thf(decl_198, type, setunionsingleton: $o). 25.96/3.85 thf(decl_199, type, singleton: $i > $o). 25.96/3.85 thf(decl_200, type, singletonprop: $o). 25.96/3.85 thf(decl_201, type, ex1: $i > ($i > $o) > $o). 25.96/3.85 thf(decl_202, type, ex1E1: $o). 25.96/3.85 thf(decl_203, type, ex1I: $o). 25.96/3.85 thf(decl_204, type, ex1I2: $o). 25.96/3.85 thf(decl_205, type, singletonsuniq: $o). 25.96/3.85 thf(decl_210, type, setukpairinjL1: $o). 25.96/3.85 thf(decl_211, type, kfstsingleton: $o). 25.96/3.85 thf(decl_212, type, theprop: $o). 25.96/3.85 thf(decl_213, type, kfst: $i > $i). 25.96/3.85 thf(decl_214, type, kfstpairEq: $o). 25.96/3.85 thf(decl_215, type, cartprodfstin: $o). 25.96/3.85 thf(decl_216, type, setukpairinjL2: $o). 25.96/3.85 thf(decl_217, type, setukpairinjL: $o). 25.96/3.85 thf(decl_218, type, setukpairinjR11: $o). 25.96/3.85 thf(decl_219, type, setukpairinjR12: $o). 25.96/3.85 thf(decl_220, type, setukpairinjR1: $o). 25.96/3.85 thf(decl_221, type, upairequniteq: $o). 25.96/3.85 thf(decl_222, type, setukpairinjR2: $o). 25.96/3.85 thf(decl_223, type, setukpairinjR: $o). 25.96/3.85 thf(decl_224, type, ksndsingleton: $o). 25.96/3.85 thf(decl_225, type, ksnd: $i > $i). 25.96/3.85 thf(decl_226, type, ksndpairEq: $o). 25.96/3.85 thf(decl_227, type, kpairsurjEq: $o). 25.96/3.85 thf(decl_228, type, cartprodsndin: $o). 25.96/3.85 thf(decl_229, type, cartprodpairmemEL: $o). 25.96/3.85 thf(decl_230, type, cartprodpairmemER: $o). 25.96/3.85 thf(decl_231, type, cartprodmempaircEq: $o). 25.96/3.85 thf(decl_232, type, cartprodfstpairEq: $o). 25.96/3.85 thf(decl_233, type, cartprodsndpairEq: $o). 25.96/3.85 thf(decl_234, type, cartprodpairsurjEq: $o). 25.96/3.85 thf(decl_235, type, breln: $i > $i > $i > $o). 25.96/3.85 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 25.96/3.85 thf(decl_237, type, dpsetconstrI: $o). 25.96/3.85 thf(decl_238, type, dpsetconstrSub: $o). 25.96/3.85 thf(decl_239, type, setOfPairsIsBReln: $o). 25.96/3.85 thf(decl_240, type, dpsetconstrERa: $o). 25.96/3.85 thf(decl_241, type, dpsetconstrEL1: $o). 25.96/3.85 thf(decl_242, type, dpsetconstrEL2: $o). 25.96/3.85 thf(decl_243, type, dpsetconstrER: $o). 25.96/3.85 thf(decl_244, type, func: $i > $i > $i > $o). 25.96/3.85 thf(decl_245, type, funcSet: $i > $i > $i). 25.96/3.85 thf(decl_246, type, funcImageSingleton: $o). 25.96/3.85 thf(decl_247, type, apProp: $o). 25.96/3.85 thf(decl_248, type, ap: $i > $i > $i > $i > $i). 25.96/3.85 thf(decl_249, type, app: $o). 25.96/3.85 thf(decl_250, type, infuncsetfunc: $o). 25.96/3.85 thf(decl_251, type, ap2p: $o). 25.96/3.85 thf(decl_252, type, funcinfuncset: $o). 25.96/3.85 thf(decl_253, type, lamProp: $o). 25.96/3.85 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i). 25.96/3.85 thf(decl_255, type, lamp: $o). 25.96/3.85 thf(decl_256, type, lam2p: $o). 25.96/3.85 thf(decl_257, type, brelnall1: $o). 25.96/3.85 thf(decl_258, type, brelnall2: $o). 25.96/3.85 thf(decl_259, type, ex1E2: $o). 25.96/3.85 thf(decl_260, type, funcGraphProp1: $o). 25.96/3.85 thf(decl_261, type, funcGraphProp3: $o). 25.96/3.85 thf(decl_262, type, funcGraphProp2: $o). 25.96/3.85 thf(decl_263, type, funcextLem: $o). 25.96/3.85 thf(decl_264, type, funcGraphProp4: $o). 25.96/3.85 thf(decl_265, type, subbreln: $o). 25.96/3.85 thf(decl_266, type, eqbreln: $o). 25.96/3.85 thf(decl_267, type, funcext: $o). 25.96/3.85 thf(decl_268, type, funcext2: $o). 25.96/3.85 thf(decl_269, type, ap2apEq1: $o). 25.96/3.85 thf(decl_270, type, ap2apEq2: $o). 25.96/3.85 thf(decl_271, type, beta1: $o). 25.96/3.85 thf(decl_272, type, eta1: $o). 25.96/3.85 thf(decl_273, type, lam2lamEq: $o). 25.96/3.85 thf(decl_274, type, beta2: $o). 25.96/3.85 thf(decl_275, type, eta2: $o). 25.96/3.85 thf(decl_276, type, iffalseProp1: $o). 25.96/3.85 thf(decl_277, type, iffalseProp2: $o). 25.96/3.85 thf(decl_278, type, iftrueProp1: $o). 25.96/3.85 thf(decl_279, type, iftrueProp2: $o). 25.96/3.85 thf(decl_280, type, ifSingleton: $o). 25.96/3.85 thf(decl_281, type, if: $i > $o > $i > $i > $i). 25.96/3.85 thf(decl_282, type, ifp: $o). 25.96/3.85 thf(decl_283, type, theeq: $o). 25.96/3.85 thf(decl_284, type, iftrue: $o). 25.96/3.85 thf(decl_285, type, iffalse: $o). 25.96/3.85 thf(decl_286, type, iftrueorfalse: $o). 25.96/3.85 thf(decl_287, type, binintersectT_lem: $o). 25.96/3.85 thf(decl_288, type, binunionT_lem: $o). 25.96/3.85 thf(decl_289, type, powersetT_lem: $o). 25.96/3.85 thf(decl_290, type, setminusT_lem: $o). 25.96/3.85 thf(decl_291, type, complementT_lem: $o). 25.96/3.85 thf(decl_292, type, setextT: $o). 25.96/3.85 thf(decl_293, type, subsetTI: $o). 25.96/3.85 thf(decl_294, type, powersetTI1: $o). 25.96/3.85 thf(decl_295, type, powersetTE1: $o). 25.96/3.85 thf(decl_296, type, complementTI1: $o). 25.96/3.85 thf(decl_297, type, complementTE1: $o). 25.96/3.85 thf(decl_298, type, binintersectTELcontra: $o). 25.96/3.85 thf(decl_299, type, binintersectTERcontra: $o). 25.96/3.85 thf(decl_300, type, contrasubsetT: $o). 25.96/3.85 thf(decl_301, type, contrasubsetT1: $o). 25.96/3.85 thf(decl_302, type, contrasubsetT2: $o). 25.96/3.85 thf(decl_303, type, contrasubsetT3: $o). 25.96/3.85 thf(decl_304, type, doubleComplementI1: $o). 25.96/3.85 thf(decl_305, type, doubleComplementE1: $o). 25.96/3.85 thf(decl_306, type, doubleComplementSub1: $o). 25.96/3.85 thf(decl_307, type, doubleComplementSub2: $o). 25.96/3.85 thf(decl_308, type, doubleComplementEq: $o). 25.96/3.85 thf(decl_309, type, complementTnotintersectT: $o). 25.96/3.85 thf(decl_310, type, complementImpComplementIntersect: $o). 25.96/3.85 thf(decl_311, type, complementSubsetComplementIntersect: $o). 25.96/3.85 thf(decl_312, type, complementInPowersetComplementIntersect: $o). 25.96/3.85 thf(decl_313, type, contraSubsetComplement: $o). 25.96/3.85 thf(decl_314, type, complementTcontraSubset: $o). 25.96/3.85 thf(decl_315, type, binunionTILcontra: $o). 25.96/3.85 thf(decl_316, type, binunionTIRcontra: $o). 25.96/3.85 thf(decl_317, type, inIntersectImpInUnion: $o). 25.96/3.85 thf(decl_318, type, inIntersectImpInUnion2: $o). 25.96/3.85 thf(decl_319, type, inIntersectImpInIntersectUnions: $o). 25.96/3.85 thf(decl_320, type, intersectInPowersetIntersectUnions: $o). 25.96/3.85 thf(decl_321, type, inComplementUnionImpNotIn1: $o). 25.96/3.85 thf(decl_322, type, inComplementUnionImpInComplement1: $o). 25.96/3.85 thf(decl_323, type, binunionTE: $o). 25.96/3.85 thf(decl_324, type, binunionTEcontra: $o). 25.96/3.85 thf(decl_325, type, demorgan2a1: $o). 25.96/3.85 thf(decl_326, type, complementUnionInPowersetComplement: $o). 25.96/3.85 thf(decl_327, type, demorgan2a2: $o). 25.96/3.85 thf(decl_328, type, demorgan1a: $o). 25.96/3.85 thf(decl_329, type, epred1_0: $o). 25.96/3.85 thf(decl_330, type, esk1_2: $i > $i > $i). 25.96/3.85 thf(decl_331, type, esk2_2: $i > $i > $i). 25.96/3.85 thf(decl_332, type, esk3_2: $i > $i > $i). 25.96/3.85 thf(decl_333, type, esk4_1: $i > $i). 25.96/3.85 thf(decl_334, type, esk5_2: ($i > $i > $o) > $i > $i). 25.96/3.85 thf(decl_335, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 25.96/3.85 thf(decl_336, type, esk7_2: ($i > $i > $o) > $i > $i). 25.96/3.85 thf(decl_337, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 25.96/3.85 thf(decl_338, type, esk9_1: $i > $i). 25.96/3.85 thf(decl_339, type, esk10_2: ($i > $o) > $i > $i). 25.96/3.85 thf(decl_340, type, esk11_2: ($i > $o) > $i > $i). 25.96/3.85 thf(decl_341, type, esk12_1: ($i > $o) > $i). 25.96/3.85 thf(decl_342, type, esk13_2: ($i > $o) > $i > $i). 25.96/3.85 thf(decl_343, type, esk14_1: ($i > $o) > $i). 25.96/3.86 thf(decl_344, type, esk15_2: $i > $i > $i). 25.96/3.86 thf(decl_345, type, esk16_2: $i > $i > $i). 25.96/3.86 thf(decl_346, type, esk17_1: $i > $i). 25.96/3.86 thf(decl_347, type, esk18_1: $i > $i). 25.96/3.86 thf(decl_348, type, esk19_1: $i > $i). 25.96/3.86 thf(decl_349, type, esk20_2: $i > $i > $i). 25.96/3.86 thf(decl_350, type, esk21_3: $i > $i > $o > $i). 25.96/3.86 thf(decl_351, type, esk22_2: ($i > $o) > $i > $i). 25.96/3.86 thf(decl_352, type, esk23_1: ($i > $o) > $i). 25.96/3.86 thf(decl_353, type, esk24_1: $i > $i). 25.96/3.86 thf(decl_354, type, esk25_2: $i > ($i > $o) > $i). 25.96/3.86 thf(decl_355, type, esk26_2: $i > ($i > $o) > $i). 25.96/3.86 thf(decl_356, type, esk27_2: $i > ($i > $o) > $i). 25.96/3.86 thf(decl_357, type, esk28_2: $i > ($i > $o) > $i). 25.96/3.86 thf(decl_358, type, esk29_2: $i > ($i > $o) > $i). 25.96/3.86 thf(decl_359, type, esk30_2: $i > ($i > $o) > $i). 25.96/3.86 thf(decl_360, type, esk31_2: ($i > $o) > $i > $i). 25.96/3.86 thf(decl_361, type, esk32_1: ($i > $o) > $i). 25.96/3.86 thf(decl_362, type, esk33_1: ($i > $o) > $i). 25.96/3.86 thf(decl_363, type, esk34_1: ($i > $o) > $i). 25.96/3.86 thf(decl_364, type, esk35_1: ($i > $o) > $i). 25.96/3.86 thf(decl_365, type, esk36_2: ($i > $o) > $i > $i). 25.96/3.86 thf(decl_366, type, esk37_1: ($i > $o) > $i). 25.96/3.86 thf(decl_367, type, esk38_2: ($i > $o) > $i > $i). 25.96/3.86 thf(decl_368, type, esk39_2: ($i > $o) > ($i > $o) > $i). 25.96/3.86 thf(decl_369, type, esk40_2: ($i > $o) > ($i > $o) > $i). 25.96/3.86 thf(decl_370, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 25.96/3.86 thf(decl_371, type, esk42_2: ($i > $o) > ($i > $o) > $i). 25.96/3.86 thf(decl_372, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 25.96/3.86 thf(decl_373, type, esk44_2: ($i > $o) > ($i > $o) > $i). 25.96/3.86 thf(decl_374, type, esk45_2: ($i > $o) > $i > $i). 25.96/3.86 thf(decl_375, type, esk46_2: ($i > $o) > ($i > $o) > $i). 25.96/3.86 thf(decl_376, type, esk47_2: ($i > $o) > ($i > $o) > $i). 25.96/3.86 thf(decl_377, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 25.96/3.86 thf(decl_378, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 25.96/3.86 thf(decl_379, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 25.96/3.86 thf(decl_380, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 25.96/3.86 thf(decl_381, type, esk52_2: $i > $i > $i). 25.96/3.86 thf(decl_382, type, esk53_2: $i > $i > $i). 25.96/3.86 thf(decl_383, type, esk54_2: $i > $i > $i). 25.96/3.86 thf(decl_384, type, esk55_3: $i > $i > $i > $i). 25.96/3.86 thf(decl_385, type, esk56_3: $i > $i > $i > $i). 25.96/3.86 thf(decl_386, type, esk57_2: $i > $i > $i). 25.96/3.86 thf(decl_387, type, esk58_2: $i > ($i > $o) > $i). 25.96/3.86 thf(decl_388, type, esk59_2: $i > ($i > $o) > $i). 25.96/3.86 thf(decl_389, type, esk60_2: $i > ($i > $o) > $i). 25.96/3.86 thf(decl_390, type, esk61_3: $i > ($i > $o) > $i > $i). 25.96/3.86 thf(decl_391, type, esk62_2: $i > ($i > $o) > $i). 25.96/3.86 thf(decl_392, type, esk63_2: $i > ($i > $o) > $i). 25.96/3.86 thf(decl_393, type, esk64_3: $i > $i > ($i > $i) > $i). 25.96/3.86 thf(decl_394, type, esk65_3: $i > $i > ($i > $i) > $i). 25.96/3.86 thf(decl_395, type, esk66_3: $i > $i > ($i > $i) > $i). 25.96/3.86 thf(decl_396, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 25.96/3.86 thf(decl_397, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 25.96/3.86 thf(decl_398, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 25.96/3.86 thf(decl_399, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 25.96/3.86 thf(decl_400, type, esk71_4: $i > $i > $i > $i > $i). 25.96/3.86 thf(decl_401, type, esk72_4: $i > $i > $i > $i > $i). 25.96/3.86 thf(decl_402, type, esk73_4: $i > $i > $i > $i > $i). 25.96/3.86 thf(decl_403, type, esk74_4: $i > $i > $i > $i > $i). 25.96/3.86 thf(decl_404, type, esk75_4: $i > $i > $i > $i > $i). 25.96/3.86 thf(decl_405, type, esk76_4: $i > $i > $i > $i > $i). 25.96/3.86 thf(decl_406, type, esk77_4: $i > $i > $i > $i > $i). 25.96/3.86 thf(decl_407, type, esk78_4: $i > $i > $i > $i > $i). 25.96/3.86 thf(decl_408, type, esk79_4: $i > $i > $i > $i > $i). 25.96/3.86 thf(decl_409, type, esk80_3: $i > $i > ($i > $i) > $i). 25.96/3.86 thf(decl_410, type, esk81_3: $i > $i > ($i > $i) > $i). 25.96/3.86 thf(decl_411, type, esk82_3: $i > $i > ($i > $i) > $i). 25.96/3.86 thf(decl_412, type, esk83_3: $i > $i > $i > $i). 25.96/3.86 thf(decl_413, type, esk84_3: $i > $i > $i > $i). 25.96/3.86 thf(decl_414, type, esk85_3: $i > $i > $i > $i). 25.96/3.86 thf(decl_415, type, esk86_3: $i > $i > $i > $i). 25.96/3.86 thf(decl_416, type, esk87_0: $i). 25.96/3.86 thf(decl_417, type, esk88_0: $i). 25.96/3.86 thf(decl_418, type, esk89_0: $i). 25.96/3.86 thf(decl_419, type, esk90_0: $i). 25.96/3.86 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', replAx)). 25.96/3.86 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', exu)). 25.96/3.86 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', descrp)). 25.96/3.86 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', exuE1)). 25.96/3.86 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', exuE3e)). 25.96/3.86 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', nonempty)). 25.96/3.86 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', nonemptyI)). 25.96/3.86 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', exuE2)). 25.96/3.86 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', exuI1)). 25.96/3.86 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', exuI3)). 25.96/3.86 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', exuI2)). 25.96/3.86 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', exuE3u)). 25.96/3.86 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', exu__Cong)). 25.96/3.86 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', exuEu)). 25.96/3.86 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', descr__Cong)). 25.96/3.86 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', ex1E1)). 25.96/3.86 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', ex1)). 25.96/3.86 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', ex1I)). 25.96/3.86 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', ex1I2)). 25.96/3.86 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setOfPairsIsBReln)). 25.96/3.86 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', breln)). 25.96/3.86 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', ex1E2)). 25.96/3.86 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', dsetconstrI)). 25.96/3.86 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', dsetconstrEL)). 25.96/3.86 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', dsetconstrER)). 25.96/3.86 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setbeta)). 25.96/3.86 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', nonemptyE1)). 25.96/3.86 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', nonemptyI1)). 25.96/3.86 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setoftrueEq)). 25.96/3.86 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', nonemptyImpWitness)). 25.96/3.86 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', emptyE1)). 25.96/3.86 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', dsetconstr__Cong)). 25.96/3.86 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', sepInPowerset)). 25.96/3.86 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', sepSubset)). 25.96/3.86 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', singletonprop)). 25.96/3.86 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', kfstsingleton)). 25.96/3.86 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', ksndsingleton)). 25.96/3.86 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', dpsetconstrI)). 25.96/3.86 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', dpsetconstrSub)). 25.96/3.86 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', dpsetconstrERa)). 25.96/3.86 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', dpsetconstrEL1)). 25.96/3.86 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', dpsetconstrEL2)). 25.96/3.86 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', dpsetconstrER)). 25.96/3.86 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', funcImageSingleton)). 25.96/3.86 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', apProp)). 25.96/3.86 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', lamProp)). 25.96/3.86 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', lamp)). 25.96/3.86 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', lam2p)). 25.96/3.86 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', brelnall1)). 25.96/3.86 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', brelnall2)). 25.96/3.86 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', subbreln)). 25.96/3.86 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', eqbreln)). 25.96/3.86 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', beta1)). 25.96/3.86 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', eta1)). 25.96/3.86 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', lam2lamEq)). 25.96/3.86 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', beta2)). 25.96/3.86 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', eta2)). 25.96/3.86 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', iffalseProp1)). 25.96/3.86 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', iffalseProp2)). 25.96/3.86 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', iftrueProp1)). 25.96/3.86 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', iftrueProp2)). 25.96/3.86 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', ifSingleton)). 25.96/3.86 thf(demorgan1b, conjecture, ((setextAx)=>(((((setunionAx)=>(((((((((dsetconstrI)=>(((dsetconstrER)=>((((emptysetE)=>((((exuE3e)=>((setext)=>(((noeltsimpempty)=>(((nonemptyE1)=>((nonemptyI)=>(((setadjoinIL)=>((emptyinunitempty)=>((((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((((powersetE)=>(((setunionE)=>((subPowSU)=>((exuE2)=>(((((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((((vacuousDall)=>((quantDeMorgan1)=>((((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>(((exuI1)=>((exuI3)=>((exuI2)=>((((exuE3u)=>((exu__Cong)=>(((((setunion__Cong)=>(((((dsetconstr__Cong)=>(((eqimpsubset2)=>((((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((((((powersetE1)=>(((((((upairset2IR)=>((binunionIR)=>((((binunionLsub)=>((((binintersectSubset5)=>((binintersectEL)=>(((binintersectSubset2)=>(((binintersectER)=>(((((binintersectSubset1)=>((((((setminusSubset2)=>(((setminusELneg)=>((setminusILneg)=>(((setminusLsub)=>((setminusSubset1)=>((((symdiffI2)=>(((symdiffIneg2)=>(((setukpairIL)=>((setukpairIR)=>(((kpairp)=>(((singletoninpowerset)=>((singletoninpowunion)=>(((upairsubunion)=>(((((ubforcartprodlem3)=>(((cartprodmempair1)=>(((setunionE2)=>(((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>(((ex1I)=>(((singletonsuniq)=>((setukpairinjL1)=>(((theprop)=>(((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((((upairequniteq)=>((setukpairinjR2)=>(((ksndsingleton)=>(((kpairsurjEq)=>((cartprodsndin)=>((((cartprodmempaircEq)=>((((cartprodpairsurjEq)=>(((dpsetconstrSub)=>((setOfPairsIsBReln)=>((((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((((infuncsetfunc)=>(((((lamp)=>((lam2p)=>(((brelnall2)=>((ex1E2)=>((((funcGraphProp2)=>((funcextLem)=>(((((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>(((beta2)=>(((((((ifSingleton)=>((((iftrue)=>(((iftrueorfalse)=>((binintersectT_lem)=>(((powersetT_lem)=>(((complementT_lem)=>(((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((((binintersectTERcontra)=>(((contrasubsetT1)=>(((contrasubsetT3)=>(((doubleComplementE1)=>(((doubleComplementSub2)=>(((((complementSubsetComplementIntersect)=>(((contraSubsetComplement)=>(((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((((((inComplementUnionImpInComplement1)=>((binunionTE)=>(((((demorgan2a2)=>((demorgan1a)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:((![X2:$i]:((((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))<=(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))<=(in @ X2 @ X4)))<=(in @ X48 @ (powerset @ X4))))))))<=(complementUnionInPowersetComplement))<=(demorgan2a1))<=(binunionTEcontra))))<=(inComplementUnionImpNotIn1))<=(intersectInPowersetIntersectUnions))<=(inIntersectImpInIntersectUnions))<=(inIntersectImpInUnion2)))))<=(complementTcontraSubset)))<=(complementInPowersetComplementIntersect)))<=(complementImpComplementIntersect))<=(complementTnotintersectT))<=(doubleComplementEq)))<=(doubleComplementSub1)))<=(doubleComplementI1)))<=(contrasubsetT2)))<=(contrasubsetT)))<=(binintersectTELcontra))<=(complementTE1))))))<=(setextT)))<=(setminusT_lem)))<=(binunionT_lem))))<=(iffalse)))<=(theeq))<=(ifp)))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2))<=(iffalseProp1))<=(eta2)))<=(lam2lamEq))))))))<=(eqbreln))<=(subbreln))<=(funcGraphProp4))))<=(funcGraphProp3))<=(funcGraphProp1))))<=(brelnall1))))<=(lamProp))<=(funcinfuncset))<=(ap2p)))<=(app))<=(apProp)))))<=(dpsetconstrEL1))<=(dpsetconstrERa))))<=(dpsetconstrI)))<=(cartprodsndpairEq))<=(cartprodfstpairEq)))<=(cartprodpairmemER))<=(cartprodpairmemEL))))<=(ksndpairEq)))<=(setukpairinjR))))<=(setukpairinjR1))<=(setukpairinjR12))))))<=(kfstpairEq)))<=(kfstsingleton))))<=(ex1I2)))<=(ex1E1)))))<=(setunionsingleton1)))<=(cartprodmempair)))<=(cartprodpairin)))<=(ubforcartprodlem2))<=(ubforcartprodlem1))<=(upairinpowunion)))<=(upairset2E))))<=(singletonsubset)))<=(kpairiskpair))))<=(secondinupair)))<=(symdiffIneg1)))<=(symdiffI1))<=(symdiffE))))<=(setminusIRneg))))<=(setminusERneg)))<=(setminusER))<=(setminusEL))<=(setminusI))<=(bs114d)))<=(binintersectSubset4))<=(binintersectRsub))<=(disjointsetsI1)))<=(binintersectSubset3)))<=(binintersectLsub))))<=(binintersectI))<=(binunionRsub)))<=(binunionE))<=(binunionEcases))))<=(binunionIL))<=(sepSubset))<=(sepInPowerset))<=(powersetsubset))<=(inPowerset)))<=(powersetI1))<=(subsetemptysetimpeq))<=(setextsub))<=(subset2powerset)))))<=(subsetRefl))<=(notequalI2)))))))<=(subsetI2))<=(eqimpsubset1)))<=(subsetI1)))<=(descr__Cong))<=(exuEu))<=(omega__Cong)))<=(powerset__Cong))<=(setadjoin__Cong))<=(emptyset__Cong))))<=(in__Cong))<=(inCongP)))))<=(notdallE))))))<=(quantDeMorgan3))<=(quantDeMorgan2))))<=(emptyE1))<=(upairsetIR))))))<=(notinsingleton))<=(uniqinunit))<=(nonemptyImpWitness)))))<=(setunionI)))<=(emptyInPowerset))<=(emptyinPowerset)))))<=(setadjoinE))<=(setadjoinIR))))<=(nonemptyI1))))<=(setbeta)))<=(emptyI))))<=(notinemptyset))<=(emptysetimpfalse)))<=(prop2setE))<=(exuE1)))<=(dsetconstrEL)))<=(descrp))<=(wellorderingAx))<=(foundationAx))<=(replAx))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax)))<=(powersetAx))<=(setadjoinAx))<=(emptysetAx))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', demorgan1b)). 25.96/3.86 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setextAx)). 25.96/3.86 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', emptysetAx)). 25.96/3.86 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setadjoinAx)). 25.96/3.86 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', powersetAx)). 25.96/3.86 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setunionAx)). 25.96/3.86 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', omega0Ax)). 25.96/3.86 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', omegaSAx)). 25.96/3.86 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', omegaIndAx)). 25.96/3.86 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', foundationAx)). 25.96/3.86 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', wellorderingAx)). 25.96/3.86 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', prop2setE)). 25.96/3.86 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', emptysetE)). 25.96/3.86 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', emptysetimpfalse)). 25.96/3.86 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', notinemptyset)). 25.96/3.86 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setext)). 25.96/3.86 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', emptyI)). 25.96/3.86 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', noeltsimpempty)). 25.96/3.86 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setadjoinIL)). 25.96/3.86 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', emptyinunitempty)). 25.96/3.86 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setadjoinIR)). 25.96/3.86 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setadjoinE)). 25.96/3.86 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setadjoinOr)). 25.96/3.86 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', powersetI)). 25.96/3.86 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', emptyinPowerset)). 25.96/3.86 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', emptyInPowerset)). 25.96/3.86 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', powersetE)). 25.96/3.86 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setunionI)). 25.96/3.86 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setunionE)). 25.96/3.86 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', subPowSU)). 25.96/3.86 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', uniqinunit)). 25.96/3.86 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', notinsingleton)). 25.96/3.86 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', eqinunit)). 25.96/3.86 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', singletonsswitch)). 25.96/3.86 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', upairsetE)). 25.96/3.86 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', upairsetIL)). 25.96/3.86 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', upairsetIR)). 25.96/3.86 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', vacuousDall)). 25.96/3.86 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', quantDeMorgan1)). 25.96/3.86 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', quantDeMorgan2)). 25.96/3.86 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', quantDeMorgan3)). 25.96/3.86 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', quantDeMorgan4)). 25.96/3.86 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', prop2setI)). 25.96/3.86 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', prop2set2propI)). 25.96/3.86 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', notdexE)). 25.96/3.86 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', notdallE)). 25.96/3.86 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', inCongP)). 25.96/3.86 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', in__Cong)). 25.96/3.86 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', emptyset__Cong)). 25.96/3.86 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setadjoin__Cong)). 25.96/3.86 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', powerset__Cong)). 25.96/3.86 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setunion__Cong)). 25.96/3.86 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', omega__Cong)). 25.96/3.86 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', subsetI1)). 25.96/3.86 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', eqimpsubset2)). 25.96/3.86 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', eqimpsubset1)). 25.96/3.86 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', subsetI2)). 25.96/3.86 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', emptysetsubset)). 25.96/3.86 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', subsetE)). 25.96/3.86 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', subsetE2)). 25.96/3.86 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', notsubsetI)). 25.96/3.86 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', notequalI1)). 25.96/3.86 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', notequalI2)). 25.96/3.86 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', subsetRefl)). 25.96/3.86 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', subsetTrans)). 25.96/3.86 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setadjoinSub)). 25.96/3.86 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setadjoinSub2)). 25.96/3.86 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', subset2powerset)). 25.96/3.86 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setextsub)). 25.96/3.86 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', subsetemptysetimpeq)). 25.96/3.86 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', powersetI1)). 25.96/3.86 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', powersetE1)). 25.96/3.86 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', inPowerset)). 25.96/3.86 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', powersetsubset)). 25.96/3.86 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binunionIL)). 25.96/3.86 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', upairset2IR)). 25.96/3.86 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binunionIR)). 25.96/3.86 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binunionEcases)). 25.96/3.86 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binunionE)). 25.96/3.86 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binunionLsub)). 25.96/3.86 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binunionRsub)). 25.96/3.86 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binintersectI)). 25.96/3.86 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binintersectSubset5)). 25.96/3.86 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binintersectEL)). 25.96/3.86 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binintersectLsub)). 25.96/3.86 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binintersectSubset2)). 25.96/3.86 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binintersectSubset3)). 25.96/3.86 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binintersectER)). 25.96/3.86 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', disjointsetsI1)). 25.96/3.86 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binintersectRsub)). 25.96/3.86 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binintersectSubset4)). 25.96/3.86 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binintersectSubset1)). 25.96/3.86 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', bs114d)). 25.96/3.86 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setminusI)). 25.96/3.86 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setminusEL)). 25.96/3.86 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setminusER)). 25.96/3.86 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setminusSubset2)). 25.96/3.86 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setminusERneg)). 25.96/3.86 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setminusELneg)). 25.96/3.86 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setminusILneg)). 25.96/3.86 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setminusIRneg)). 25.96/3.86 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setminusLsub)). 25.96/3.86 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setminusSubset1)). 25.96/3.86 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', symdiffE)). 25.96/3.86 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', symdiffI1)). 25.96/3.86 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', symdiffI2)). 25.96/3.86 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', symdiffIneg1)). 25.96/3.86 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', symdiffIneg2)). 25.96/3.86 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', secondinupair)). 25.96/3.86 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setukpairIL)). 25.96/3.86 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setukpairIR)). 25.96/3.86 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', kpairiskpair)). 25.96/3.86 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', kpairp)). 25.96/3.86 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', singletonsubset)). 25.96/3.86 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', singletoninpowerset)). 25.96/3.86 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', singletoninpowunion)). 25.96/3.86 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', upairset2E)). 25.96/3.86 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', upairsubunion)). 25.96/3.86 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', upairinpowunion)). 25.96/3.86 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', ubforcartprodlem1)). 25.96/3.86 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', ubforcartprodlem2)). 25.96/3.86 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', ubforcartprodlem3)). 25.96/3.86 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', cartprodpairin)). 25.96/3.86 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', cartprodmempair1)). 25.96/3.86 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', cartprodmempair)). 25.96/3.86 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setunionE2)). 25.96/3.86 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setunionsingleton1)). 25.96/3.86 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setunionsingleton2)). 25.96/3.86 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setunionsingleton)). 25.96/3.86 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', singletonsuniq)). 25.96/3.86 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setukpairinjL1)). 25.96/3.86 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', theprop)). 25.96/3.86 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', kfstpairEq)). 25.96/3.86 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', cartprodfstin)). 25.96/3.86 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setukpairinjL2)). 25.96/3.86 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setukpairinjL)). 25.96/3.86 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setukpairinjR11)). 25.96/3.86 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setukpairinjR12)). 25.96/3.86 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setukpairinjR1)). 25.96/3.86 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', upairequniteq)). 25.96/3.86 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setukpairinjR2)). 25.96/3.86 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setukpairinjR)). 25.96/3.86 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', ksndpairEq)). 25.96/3.86 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', kpairsurjEq)). 25.96/3.86 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', cartprodsndin)). 25.96/3.86 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', cartprodpairmemEL)). 25.96/3.86 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', cartprodpairmemER)). 25.96/3.86 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', cartprodmempaircEq)). 25.96/3.86 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', cartprodfstpairEq)). 25.96/3.86 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', cartprodsndpairEq)). 25.96/3.86 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', cartprodpairsurjEq)). 25.96/3.86 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', app)). 25.96/3.86 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', infuncsetfunc)). 25.96/3.86 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', ap2p)). 25.96/3.86 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', funcinfuncset)). 25.96/3.86 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', funcGraphProp1)). 25.96/3.86 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', funcGraphProp3)). 25.96/3.86 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', funcGraphProp2)). 25.96/3.86 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', funcextLem)). 25.96/3.86 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', funcGraphProp4)). 25.96/3.86 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', funcext)). 25.96/3.86 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', funcext2)). 25.96/3.86 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', ap2apEq1)). 25.96/3.86 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', ap2apEq2)). 25.96/3.86 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', ifp)). 25.96/3.86 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', theeq)). 25.96/3.86 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', iftrue)). 25.96/3.86 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', iffalse)). 25.96/3.86 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', iftrueorfalse)). 25.96/3.86 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binintersectT_lem)). 25.96/3.86 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binunionT_lem)). 25.96/3.86 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', powersetT_lem)). 25.96/3.86 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setminusT_lem)). 25.96/3.86 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', complementT_lem)). 25.96/3.86 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', setextT)). 25.96/3.86 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', subsetTI)). 25.96/3.86 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', powersetTI1)). 25.96/3.86 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', powersetTE1)). 25.96/3.86 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', complementTI1)). 25.96/3.86 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', complementTE1)). 25.96/3.86 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binintersectTELcontra)). 25.96/3.86 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binintersectTERcontra)). 25.96/3.86 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', contrasubsetT)). 25.96/3.86 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', contrasubsetT1)). 25.96/3.86 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', contrasubsetT2)). 25.96/3.86 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', contrasubsetT3)). 25.96/3.86 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', doubleComplementI1)). 25.96/3.86 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', doubleComplementE1)). 25.96/3.86 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', doubleComplementSub1)). 25.96/3.86 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', doubleComplementSub2)). 25.96/3.86 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', doubleComplementEq)). 25.96/3.86 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', complementTnotintersectT)). 25.96/3.86 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', complementImpComplementIntersect)). 25.96/3.86 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', complementSubsetComplementIntersect)). 25.96/3.86 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', complementInPowersetComplementIntersect)). 25.96/3.86 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', contraSubsetComplement)). 25.96/3.86 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', complementTcontraSubset)). 25.96/3.86 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binunionTILcontra)). 25.96/3.86 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binunionTIRcontra)). 25.96/3.86 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', inIntersectImpInUnion)). 25.96/3.86 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', inIntersectImpInUnion2)). 25.96/3.86 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', inIntersectImpInIntersectUnions)). 25.96/3.86 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', intersectInPowersetIntersectUnions)). 25.96/3.86 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', inComplementUnionImpNotIn1)). 25.96/3.86 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', inComplementUnionImpInComplement1)). 25.96/3.86 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binunionTE)). 25.96/3.86 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', binunionTEcontra)). 25.96/3.86 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', demorgan2a1)). 25.96/3.86 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', complementUnionInPowersetComplement)). 25.96/3.86 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', demorgan2a2)). 25.96/3.86 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.W6RAkALH4n/E---3.1_13747.p', demorgan1a)). 25.96/3.86 thf(c_0_273, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 25.96/3.86 thf(c_0_274, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 25.96/3.86 thf(c_0_275, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 25.96/3.86 thf(c_0_276, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 25.96/3.86 thf(c_0_277, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 25.96/3.86 thf(c_0_278, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 25.96/3.86 thf(c_0_279, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 25.96/3.86 thf(c_0_280, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 25.96/3.86 thf(c_0_281, 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])). 25.96/3.86 thf(c_0_282, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 25.96/3.86 thf(c_0_283, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 25.96/3.86 thf(c_0_284, 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])). 25.96/3.86 thf(c_0_285, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 25.96/3.86 thf(c_0_286, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 25.96/3.86 thf(c_0_287, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 25.96/3.86 thf(c_0_288, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 25.96/3.86 thf(c_0_289, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])). 25.96/3.86 thf(c_0_290, 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])). 25.96/3.86 thf(c_0_291, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 25.96/3.86 thf(c_0_292, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 25.96/3.86 thf(c_0_293, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])). 25.96/3.86 thf(c_0_294, 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])). 25.96/3.86 thf(c_0_295, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X901:$i]:((((X6 @ X2 @ X901))&![X902:$i]:((((X6 @ X2 @ X902))=>((X901)=(X902)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_273, c_0_274])). 25.96/3.86 thf(c_0_296, plain, ((descrp)=(![X1:$i > $o]:(((?[X903:$i]:((((X1 @ X903))&![X904:$i]:((((X1 @ X904))=>((X903)=(X904)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_275, c_0_274])). 25.96/3.86 thf(c_0_297, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 25.96/3.86 thf(c_0_298, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 25.96/3.86 thf(c_0_299, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 25.96/3.86 thf(c_0_300, plain, ((exuE1)=(![X1:$i > $o]:(((?[X905:$i]:((((X1 @ X905))&![X906:$i]:((((X1 @ X906))=>((X905)=(X906)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_276, c_0_274])). 25.96/3.86 thf(c_0_301, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X907:$i]:((((X1 @ X907))&![X908:$i]:((((X1 @ X908))=>((X907)=(X908)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_277, c_0_274])). 25.96/3.86 thf(c_0_302, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 25.96/3.86 thf(c_0_303, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_278])). 25.96/3.86 thf(c_0_304, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_279, c_0_278])). 25.96/3.86 thf(c_0_305, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_278])). 25.96/3.86 thf(c_0_306, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 25.96/3.86 thf(c_0_307, plain, ((exuE2)=(![X1:$i > $o]:(((?[X909:$i]:((((X1 @ X909))&![X910:$i]:((((X1 @ X910))=>((X909)=(X910)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_280, c_0_274])). 25.96/3.86 thf(c_0_308, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_278])). 25.96/3.86 thf(c_0_309, 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])). 25.96/3.86 thf(c_0_310, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X911:$i]:((((X1 @ X911))&![X912:$i]:((((X1 @ X912))=>((X911)=(X912))))))))))), inference(apply_def,[status(thm)],[c_0_281, c_0_274])). 25.96/3.86 thf(c_0_311, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X913:$i]:((((X1 @ X913))&![X914:$i]:((((X1 @ X914))=>((X913)=(X914)))))))))))), inference(apply_def,[status(thm)],[c_0_282, c_0_274])). 25.96/3.86 thf(c_0_312, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X915:$i]:((((X1 @ X915))&![X916:$i]:((((X1 @ X916))=>((X915)=(X916))))))))))), inference(apply_def,[status(thm)],[c_0_283, c_0_274])). 25.96/3.86 thf(c_0_313, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X917:$i]:((((X1 @ X917))&![X918:$i]:((((X1 @ X918))=>((X917)=(X918)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_284, c_0_274])). 25.96/3.86 thf(c_0_314, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X919:$i]:((((X1 @ X919))&![X920:$i]:((((X1 @ X920))=>((X919)=(X920)))))))<=>(?[X921:$i]:((((X17 @ X921))&![X922:$i]:((((X17 @ X922))=>((X921)=(X922)))))))))))), inference(apply_def,[status(thm)],[c_0_285, c_0_274])). 25.96/3.86 thf(c_0_315, plain, ((exuEu)=(![X1:$i > $o]:(((?[X923:$i]:((((X1 @ X923))&![X924:$i]:((((X1 @ X924))=>((X923)=(X924)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_286, c_0_274])). 25.96/3.86 thf(c_0_316, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X925:$i]:((((X1 @ X925))&![X926:$i]:((((X1 @ X926))=>((X925)=(X926)))))))=>((?[X927:$i]:((((X17 @ X927))&![X928:$i]:((((X17 @ X928))=>((X927)=(X928)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_287, c_0_274])). 25.96/3.86 thf(c_0_317, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 25.96/3.86 thf(c_0_318, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 25.96/3.86 thf(c_0_319, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 25.96/3.86 thf(c_0_320, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 25.96/3.86 thf(c_0_321, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_288, c_0_289])). 25.96/3.86 thf(c_0_322, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))))))))), inference(apply_def,[status(thm)],[c_0_290, c_0_289])). 25.96/3.86 thf(c_0_323, plain, ((ex1I2)=(![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))))))), inference(apply_def,[status(thm)],[c_0_291, c_0_289])). 25.96/3.86 thf(c_0_324, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 25.96/3.86 thf(c_0_325, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 25.96/3.86 thf(c_0_326, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 25.96/3.86 thf(c_0_327, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 25.96/3.86 thf(c_0_328, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_292, c_0_293])). 25.96/3.86 thf(c_0_329, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 25.96/3.86 thf(c_0_330, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 25.96/3.86 thf(c_0_331, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 25.96/3.86 thf(c_0_332, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 25.96/3.86 thf(c_0_333, plain, ((funcImageSingleton)<=>![X4:$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])). 25.96/3.86 thf(c_0_334, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 25.96/3.86 thf(c_0_335, plain, ((lamProp)<=>![X4:$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])). 25.96/3.86 thf(c_0_336, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 25.96/3.86 thf(c_0_337, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 25.96/3.86 thf(c_0_338, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_293])). 25.96/3.86 thf(c_0_339, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_293])). 25.96/3.86 thf(c_0_340, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_294, c_0_289])). 25.96/3.86 thf(c_0_341, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_293])). 25.96/3.86 thf(c_0_342, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_293])). 25.96/3.86 thf(c_0_343, 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])). 25.96/3.86 thf(c_0_344, 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])). 25.96/3.86 thf(c_0_345, 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])). 25.96/3.86 thf(c_0_346, 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])). 25.96/3.86 thf(c_0_347, 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])). 25.96/3.86 thf(c_0_348, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 25.96/3.86 thf(c_0_349, plain, ((iffalseProp2)<=>![X4:$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])). 25.96/3.86 thf(c_0_350, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 25.96/3.86 thf(c_0_351, plain, ((iftrueProp2)<=>![X4:$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])). 25.96/3.86 thf(c_0_352, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 25.96/3.86 thf(c_0_353, plain, ((epred1_0)<=>![X1761:$i]:(?[X1762:$i]:((((![X1763:$i]:(((in @ X1763 @ X1762)=>![X1764:$i]:(((in @ X1764 @ X1763)=>(in @ X1764 @ X1761)))))&![X1765:$i, X1766:$i]:((((in @ X1765 @ X1761)&(in @ X1766 @ X1761))=>(![X1767:$i]:(((in @ X1767 @ X1762)=>((in @ X1765 @ X1767)<=>(in @ X1766 @ X1767))))=>((X1765)=(X1766))))))&![X1768:$i, X1769:$i]:((((in @ X1768 @ X1762)&(in @ X1769 @ X1762))=>(![X1770:$i]:(((in @ X1770 @ X1768)=>(in @ X1770 @ X1769)))|![X1771:$i]:(((in @ X1771 @ X1769)=>(in @ X1771 @ X1768)))))))&![X1772:$i]:(((![X1773:$i]:(((in @ X1773 @ X1772)=>(in @ X1773 @ X1761)))&?[X1774:$i]:((in @ X1774 @ X1772)))=>?[X1775:$i, X1776:$i]:(((((in @ X1775 @ X1762)&(in @ X1776 @ X1772))&~(?[X1777:$i]:(((in @ X1777 @ X1775)&(in @ X1777 @ X1772)))))&![X1778:$i]:(((in @ X1778 @ X1762)=>(![X1779:$i]:(((in @ X1779 @ X1778)=>(in @ X1779 @ X1775)))|(in @ X1776 @ X1778)))))))))))), introduced(definition)). 25.96/3.86 thf(c_0_354, negated_conjecture, ~((![X929:$i, X930:$i]:((![X931:$i]:(((in @ X931 @ X929)<=>(in @ X931 @ X930)))=>((X929)=(X930))))=>(![X1802:$i]:(~(in @ X1802 @ emptyset))=>(![X1799:$i, X1800:$i, X1801:$i]:(((in @ X1801 @ (setadjoin @ X1799 @ X1800))<=>(((X1801)=(X1799))|(in @ X1801 @ X1800))))=>(![X1796:$i, X1797:$i]:(((in @ X1797 @ (powerset @ X1796))<=>![X1798:$i]:(((in @ X1798 @ X1797)=>(in @ X1798 @ X1796)))))=>(![X932:$i, X933:$i]:(((in @ X933 @ (setunion @ X932))<=>?[X934:$i]:(((in @ X933 @ X934)&(in @ X934 @ X932)))))=>((in @ emptyset @ omega)=>(![X1795:$i]:(((in @ X1795 @ omega)=>(in @ (setadjoin @ X1795 @ X1795) @ omega)))=>(![X1792:$i]:((((in @ emptyset @ X1792)&![X1793:$i]:((((in @ X1793 @ omega)&(in @ X1793 @ X1792))=>(in @ (setadjoin @ X1793 @ X1793) @ X1792))))=>![X1794:$i]:(((in @ X1794 @ omega)=>(in @ X1794 @ X1792)))))=>(![X1784:$i > $i > $o, X1785:$i]:((![X1786:$i]:(((in @ X1786 @ X1785)=>?[X1787:$i]:(((X1784 @ X1786 @ X1787)&![X1788:$i]:(((X1784 @ X1786 @ X1788)=>((X1787)=(X1788))))))))=>?[X1789:$i]:(![X1790:$i]:(((in @ X1790 @ X1789)<=>?[X1791:$i]:(((in @ X1791 @ X1785)&(X1784 @ X1791 @ X1790))))))))=>(![X1780:$i]:((?[X1781:$i]:((in @ X1781 @ X1780))=>?[X1782:$i]:(((in @ X1782 @ X1780)&~(?[X1783:$i]:(((in @ X1783 @ X1782)&(in @ X1783 @ X1780))))))))=>((epred1_0)=>(![X1758:$i > $o]:((?[X1759:$i]:(((X1758 @ X1759)&![X1760:$i]:(((X1758 @ X1760)=>((X1759)=(X1760))))))=>(X1758 @ (descr @ (^[Z0/* 17 */:$i]:(X1758 @ Z0))))))=>(![X935:$i, X936:$i > $o, X937:$i]:(((in @ X937 @ X935)=>((X936 @ X937)=>(in @ X937 @ (dsetconstr @ X935 @ X936)))))=>(![X1755:$i, X1756:$i > $o, X1757:$i]:(((in @ X1757 @ (dsetconstr @ X1755 @ X1756))=>(in @ X1757 @ X1755)))=>(![X938:$i, X939:$i > $o, X940:$i]:(((in @ X940 @ (dsetconstr @ X938 @ X939))=>(X939 @ X940)))=>(![X1750:$i > $o]:((?[X1751:$i]:(((X1750 @ X1751)&![X1752:$i]:(((X1750 @ X1752)=>((X1751)=(X1752))))))=>?[X1753:$i]:(((X1750 @ X1753)&![X1754:$i]:(((X1750 @ X1754)=>((X1753)=(X1754))))))))=>(![X1748:$o, X1749:$i]:(((in @ X1749 @ (prop2set @ ((X1748))))=>(X1748)))=>(![X941:$i]:(((in @ X941 @ emptyset)=>![X942:$o]:((X942))))=>(![X1747:$i]:(((in @ X1747 @ emptyset)=>~($true)))=>(![X1746:$i]:(~(in @ X1746 @ emptyset))=>(![X943:$i > $o]:((?[X944:$i]:(((X943 @ X944)&![X945:$i]:(((X943 @ X945)=>((X944)=(X945))))))=>?[X946:$i]:((X943 @ X946))))=>(![X947:$i, X948:$i]:((![X949:$i]:(((in @ X949 @ X947)=>(in @ X949 @ X948)))=>(![X950:$i]:(((in @ X950 @ X948)=>(in @ X950 @ X947)))=>((X947)=(X948)))))=>(![X1744:$i]:((![X1745:$i]:(~(in @ X1745 @ X1744))=>((X1744)=(emptyset))))=>(![X951:$i]:((![X952:$i]:(~(in @ X952 @ X951))=>((X951)=(emptyset))))=>(![X1741:$i, X1742:$i > $o, X1743:$i]:(((in @ X1743 @ X1741)=>((in @ X1743 @ (dsetconstr @ X1741 @ X1742))<=>(X1742 @ X1743))))=>(![X953:$i]:((((X953)!=(emptyset))=>?[X954:$i]:((in @ X954 @ 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_295]), foundationAx]), wellorderingAx]), c_0_296]), c_0_297]), c_0_298]), c_0_299]), c_0_300]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_301]), setext]), emptyI]), noeltsimpempty]), c_0_302]), c_0_303]), c_0_304]), c_0_305]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_306]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_307]), c_0_308]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_309]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_310]), c_0_311]), c_0_312]), inCongP]), in__Cong]), c_0_313]), c_0_314]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_315]), c_0_316]), c_0_317]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_318]), c_0_319]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_320]), c_0_321]), c_0_322]), c_0_323]), singletonsuniq]), setukpairinjL1]), c_0_324]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_325]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_326]), c_0_327]), c_0_328]), c_0_329]), c_0_330]), c_0_331]), c_0_332]), c_0_333]), c_0_334]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_335]), c_0_336]), c_0_337]), c_0_338]), c_0_339]), c_0_340]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_341]), c_0_342]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_343]), c_0_344]), c_0_345]), c_0_346]), c_0_347]), c_0_348]), c_0_349]), c_0_350]), c_0_351]), c_0_352]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a])])]), c_0_353])). 25.96/3.86 thf(c_0_355, negated_conjecture, ![X1803:$i, X1804:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1816:$i, X1817:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1825:$i, X1826:$i > $i > $o, X1827:$i, X1829:$i, X1832:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1839:$i, X1840:$i > $o, X1841:$i, X1843:$i, X1844:$i > $o, X1845:$i, X1846:$i, X1847:$i > $o, X1848:$i, X1849:$i, X1850:$i > $o, X1851:$i, X1852:$i > $o, X1853:$i, X1856:$i, X1857:$o, X1858:$i, X1859:$i, X1860:$o, X1861:$i, X1862:$i, X1863:$i > $o, X1864:$i, X1867:$i, X1868:$i, X1871:$i, X1873:$i, X1875:$i, X1876:$i > $o, X1877:$i, X1878:$i, X1880:$i, X1881:$i > $o, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$o, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$o, X1913:$i, X1914:$i, X1915:$i > $o, X1916:$i, X1919:$i, X1920:$i, X1921:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i > $o, X1940:$i, X1941:$i > $o, X1942:$i, X1943:$i, X1944:$i > $o, X1945:$i, X1947:$i, X1948:$i > $o, X1950:$i, X1951:$i, X1952:$i > $o, X1954:$i, X1955:$i, X1956:$i > $o, X1957:$i, X1959:$o, X1960:$o, X1961:$i, X1962:$i > $o, X1964:$i, X1965:$i, X1966:$i > $o, X1967:$i, X1969:$i > $o, X1970:$i, X1973:$i, X1974:$i > $o, X1975:$i, X1979:$i, X1980:$i > $o, X1981:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i > $o, X1994:$i, X1996:$i, X1997:$i, X1998:$i > $o, X1999:$i > $o, X2002:$i, X2005:$i, X2006:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i > $o, X2019:$i, X2021:$i, X2022:$i, X2023:$i > $o, X2024:$i > $o, X2027:$i, X2029:$i, X2031:$i, X2032:$i, X2033:$i > $o, X2034:$i > $o, X2037:$i, X2038:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2073:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i > $o, X2085:$i, X2086:$i > $o, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$o, X2099:$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, 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, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$o, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$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:$i, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i > $o, X2241:$i, X2242:$i, X2243:$i > $o, X2245:$i, X2246:$i > $o, X2247:$i, X2249:$i, X2250:$i > $o, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i > $i > $o, X2326:$i, X2327:$i, X2328:$i, X2329:$i, X2330:$i > $i > $o, X2331:$i, X2332:$i, X2333:$i > $i > $o, X2334:$i, X2335:$i, X2336:$i > $i > $o, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i > $i > $o, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i > $i > $o, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i > $i > $o, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i, X2364:$i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i > $i, X2380:$i, X2381:$i, X2382:$i > $i, X2384:$i, X2385:$i, X2386:$i > $i, X2388:$i, X2389:$i, X2390:$i, X2391:$i > $o, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i > $o, X2401:$i, X2402:$i, X2403:$i > $o, X2404:$i, X2405:$i, X2406:$i, 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@ X2639))|(~(in @ X2642 @ X2639)|(~(in @ X2642 @ (setminus @ X2639 @ (binunion @ X2640 @ X2641)))|~(in @ X2642 @ X2640)))))&((~(in @ X2644 @ (powerset @ X2643))|(~(in @ X2645 @ (powerset @ X2643))|(~(in @ X2646 @ X2643)|(~(in @ X2646 @ (setminus @ X2643 @ (binunion @ X2644 @ X2645)))|(in @ X2646 @ (setminus @ X2643 @ X2644))))))&(((((in @ X2651 @ X2649)|(X2650)|(in @ X2651 @ X2648)|~(in @ X2651 @ (binunion @ X2648 @ X2649))|~(in @ X2651 @ X2647)|~(in @ X2649 @ (powerset @ X2647))|~(in @ X2648 @ (powerset @ X2647)))&(~(X2650)|(X2650)|(in @ X2651 @ X2648)|~(in @ X2651 @ (binunion @ X2648 @ X2649))|~(in @ X2651 @ X2647)|~(in @ X2649 @ (powerset @ X2647))|~(in @ X2648 @ (powerset @ X2647))))&(((in @ X2651 @ X2649)|(X2650)|~(X2650)|~(in @ X2651 @ (binunion @ X2648 @ X2649))|~(in @ X2651 @ X2647)|~(in @ X2649 @ (powerset @ X2647))|~(in @ X2648 @ (powerset @ X2647)))&(~(X2650)|(X2650)|~(X2650)|~(in @ X2651 @ (binunion @ X2648 @ X2649))|~(in @ X2651 @ X2647)|~(in @ X2649 @ (powerset @ X2647))|~(in @ X2648 @ (powerset @ X2647)))))&((~(in @ X2653 @ (powerset @ X2652))|(~(in @ X2654 @ (powerset @ X2652))|(~(in @ X2655 @ X2652)|((in @ X2655 @ X2653)|((in @ X2655 @ X2654)|~(in @ X2655 @ (binunion @ X2653 @ X2654)))))))&((~(in @ X2657 @ (powerset @ X2656))|(~(in @ X2658 @ (powerset @ X2656))|(~(in @ X2659 @ X2656)|(~(in @ X2659 @ (setminus @ X2656 @ (binunion @ X2657 @ X2658)))|(in @ X2659 @ (setminus @ X2656 @ X2657))))))&((~(in @ X2661 @ (powerset @ X2660))|(~(in @ X2662 @ (powerset @ X2660))|(in @ (setminus @ X2660 @ (binunion @ X2661 @ X2662)) @ (powerset @ (setminus @ X2660 @ X2661)))))&((~(in @ X2664 @ (powerset @ X2663))|(~(in @ X2665 @ (powerset @ X2663))|(~(in @ X2666 @ X2663)|(~(in @ X2666 @ (setminus @ X2663 @ (binunion @ X2664 @ X2665)))|(in @ X2666 @ (setminus @ X2663 @ X2665))))))&((~(in @ X2668 @ (powerset @ X2667))|(~(in @ X2669 @ (powerset @ X2667))|(~(in @ X2670 @ X2667)|(~(in @ X2670 @ (setminus @ X2667 @ (binintersect @ X2668 @ X2669)))|(in @ X2670 @ (binunion @ (setminus @ X2667 @ X2668) @ (setminus @ X2667 @ X2669)))))))&((in @ esk88_0 @ (powerset @ esk87_0))&((in @ esk89_0 @ (powerset @ esk87_0))&((in @ esk90_0 @ esk87_0)&((in @ esk90_0 @ (binunion @ (setminus @ esk87_0 @ esk88_0) @ (setminus @ esk87_0 @ esk89_0)))&~(in @ esk90_0 @ (setminus @ esk87_0 @ (binintersect @ esk88_0 @ esk89_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_354])])])])])])])). 25.96/3.86 thf(c_0_356, negated_conjecture, ![X5:$i, X4:$i, X3:$i, X2:$i]:(((in @ X5 @ (setminus @ X3 @ (binintersect @ X2 @ X4)))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3)))|~((in @ X5 @ X3))|~((in @ X5 @ (setminus @ X3 @ X2))))), inference(split_conjunct,[status(thm)],[c_0_355])). 25.96/3.86 thf(c_0_357, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X3)|~((in @ X2 @ (setminus @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_355])). 25.96/3.86 thf(c_0_358, negated_conjecture, ~((in @ esk90_0 @ (setminus @ esk87_0 @ (binintersect @ esk88_0 @ esk89_0)))), inference(split_conjunct,[status(thm)],[c_0_355])). 25.96/3.86 thf(c_0_359, negated_conjecture, ![X2:$i, X5:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ (binintersect @ X4 @ X5)))|~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X5 @ (powerset @ X3)))|~((in @ X4 @ (powerset @ X3))))), inference(csr,[status(thm)],[c_0_356, c_0_357])). 25.96/3.86 thf(c_0_360, negated_conjecture, (in @ esk89_0 @ (powerset @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_355])). 25.96/3.86 thf(c_0_361, negated_conjecture, (in @ esk88_0 @ (powerset @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_355])). 25.96/3.86 thf(c_0_362, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setminus @ X3 @ X4))|(in @ X2 @ X4)|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_355])). 25.96/3.86 thf(c_0_363, negated_conjecture, (in @ esk90_0 @ esk87_0), inference(split_conjunct,[status(thm)],[c_0_355])). 25.96/3.86 thf(c_0_364, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ X3)|(in @ X2 @ X4)|~((in @ X2 @ (binunion @ X4 @ X3))))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_355])])])). 25.96/3.86 thf(c_0_365, negated_conjecture, (in @ esk90_0 @ (binunion @ (setminus @ esk87_0 @ esk88_0) @ (setminus @ esk87_0 @ esk89_0))), inference(split_conjunct,[status(thm)],[c_0_355])). 25.96/3.86 thf(c_0_366, negated_conjecture, ~((in @ esk90_0 @ (setminus @ esk87_0 @ esk88_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_358, c_0_359]), c_0_360]), c_0_361])])). 25.96/3.86 thf(c_0_367, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X4)|~((in @ X2 @ (binintersect @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_355])). 25.96/3.86 thf(c_0_368, negated_conjecture, (in @ esk90_0 @ (binintersect @ esk88_0 @ esk89_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_358, c_0_362]), c_0_363])])). 25.96/3.86 thf(c_0_369, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((~((in @ X2 @ (setminus @ X3 @ X4)))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_355])). 25.96/3.86 thf(c_0_370, negated_conjecture, (in @ esk90_0 @ (setminus @ esk87_0 @ esk89_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_364, c_0_365]), c_0_366])). 25.96/3.86 thf(c_0_371, negated_conjecture, (in @ esk90_0 @ esk89_0), inference(spm,[status(thm)],[c_0_367, c_0_368])). 25.96/3.86 thf(c_0_372, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_369, c_0_370]), c_0_371])]), ['proof']). 25.96/3.86 # SZS output end CNFRefutation 25.96/3.86 # Parsed axioms : 579 25.96/3.86 # Removed by relevancy pruning/SinE : 0 25.96/3.86 # Initial clauses : 763 25.96/3.86 # Removed in clause preprocessing : 338 25.96/3.86 # Initial clauses in saturation : 425 25.96/3.86 # Processed clauses : 3888 25.96/3.86 # ...of these trivial : 32 25.96/3.86 # ...subsumed : 1607 25.96/3.86 # ...remaining for further processing : 2249 25.96/3.86 # Other redundant clauses eliminated : 67 25.96/3.86 # Clauses deleted for lack of memory : 0 25.96/3.86 # Backward-subsumed : 121 25.96/3.86 # Backward-rewritten : 23 25.96/3.86 # Generated clauses : 91960 25.96/3.86 # ...of the previous two non-redundant : 90829 25.96/3.86 # ...aggressively subsumed : 0 25.96/3.86 # Contextual simplify-reflections : 22 25.96/3.86 # Paramodulations : 91820 25.96/3.86 # Factorizations : 22 25.96/3.86 # NegExts : 27 25.96/3.86 # Equation resolutions : 75 25.96/3.86 # Disequality decompositions : 0 25.96/3.86 # Total rewrite steps : 2982 25.96/3.86 # ...of those cached : 2700 25.96/3.86 # Propositional unsat checks : 0 25.96/3.86 # Propositional check models : 0 25.96/3.86 # Propositional check unsatisfiable : 0 25.96/3.86 # Propositional clauses : 0 25.96/3.86 # Propositional clauses after purity: 0 25.96/3.86 # Propositional unsat core size : 0 25.96/3.86 # Propositional preprocessing time : 0.000 25.96/3.86 # Propositional encoding time : 0.000 25.96/3.86 # Propositional solver time : 0.000 25.96/3.86 # Success case prop preproc time : 0.000 25.96/3.86 # Success case prop encoding time : 0.000 25.96/3.86 # Success case prop solver time : 0.000 25.96/3.86 # Current number of processed clauses : 1721 25.96/3.86 # Positive orientable unit clauses : 76 25.96/3.86 # Positive unorientable unit clauses: 0 25.96/3.86 # Negative unit clauses : 119 25.96/3.86 # Non-unit-clauses : 1526 25.96/3.86 # Current number of unprocessed clauses: 87550 25.96/3.86 # ...number of literals in the above : 334853 25.96/3.86 # Current number of archived formulas : 0 25.96/3.86 # Current number of archived clauses : 513 25.96/3.86 # Clause-clause subsumption calls (NU) : 262699 25.96/3.86 # Rec. Clause-clause subsumption calls : 123924 25.96/3.86 # Non-unit clause-clause subsumptions : 1147 25.96/3.86 # Unit Clause-clause subsumption calls : 5777 25.96/3.86 # Rewrite failures with RHS unbound : 0 25.96/3.86 # BW rewrite match attempts : 86 25.96/3.86 # BW rewrite match successes : 16 25.96/3.86 # Condensation attempts : 0 25.96/3.86 # Condensation successes : 0 25.96/3.86 # Termbank termtop insertions : 1873956 25.96/3.86 # Search garbage collected termcells : 28483 25.96/3.86 25.96/3.86 # ------------------------------------------------- 25.96/3.86 # User time : 3.033 s 25.96/3.86 # System time : 0.113 s 25.96/3.86 # Total time : 3.146 s 25.96/3.86 # Maximum resident set size: 8496 pages 25.96/3.86 25.96/3.86 # ------------------------------------------------- 25.96/3.86 # User time : 3.046 s 25.96/3.86 # System time : 0.121 s 25.96/3.86 # Total time : 3.167 s 25.96/3.86 # Maximum resident set size: 2760 pages 25.96/3.86 % E exiting 25.96/3.86 % E exiting 25.96/3.86 EOF