0.04/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.12 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM 0.12/0.34 % Computer : n019.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 1920 0.12/0.34 % WCLimit : 240 0.12/0.34 % DateTime : Wed Jul 30 05:41:49 EDT 2025 0.12/0.34 % CPUTime : 0.20/0.48 Running higher-order theorem proving 0.20/0.53 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p 0.37/1.02 # Version: 3.0.0-ho 0.37/1.02 # Preprocessing class: HSLMSLSSLLLCHFA. 0.37/1.02 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 0.37/1.02 # Starting ehoh_best5 with 240s (1) cores 0.37/1.02 # Starting almost_fo_3_lam with 240s (1) cores 0.37/1.02 # Starting new_bool_5 with 240s (1) cores 0.37/1.02 # Starting pre_casc_3 with 240s (1) cores 0.37/1.02 # Starting ho_unfolding_8 with 240s (1) cores 0.37/1.02 # Starting new_ho_10_cnf2 with 240s (1) cores 0.37/1.02 # Starting new_bool_3 with 240s (1) cores 0.37/1.02 # Starting new_ho_5 with 240s (1) cores 0.37/1.02 # ho_unfolding_8 with pid 21728 completed with status 0 0.37/1.02 # Result found by ho_unfolding_8 0.37/1.02 # Preprocessing class: HSLMSLSSLLLCHFA. 0.37/1.02 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 0.37/1.02 # Starting ehoh_best5 with 240s (1) cores 0.37/1.02 # Starting almost_fo_3_lam with 240s (1) cores 0.37/1.02 # Starting new_bool_5 with 240s (1) cores 0.37/1.02 # Starting pre_casc_3 with 240s (1) cores 0.37/1.02 # Starting ho_unfolding_8 with 240s (1) cores 0.37/1.02 # No SInE strategy applied 0.37/1.02 # Search class: HGHSM-FSLM32-DHFMMSBN 0.37/1.02 # partial match(1): HGHSM-FSLM32-MHFMMSBN 0.37/1.02 # Scheduled 9 strats onto 1 cores with 240 seconds (240 total) 0.37/1.02 # Starting ho_unfolding_8 with 49s (1) cores 0.37/1.02 # ho_unfolding_8 with pid 21738 completed with status 0 0.37/1.02 # Result found by ho_unfolding_8 0.37/1.02 # Preprocessing class: HSLMSLSSLLLCHFA. 0.37/1.02 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 0.37/1.02 # Starting ehoh_best5 with 240s (1) cores 0.37/1.02 # Starting almost_fo_3_lam with 240s (1) cores 0.37/1.02 # Starting new_bool_5 with 240s (1) cores 0.37/1.02 # Starting pre_casc_3 with 240s (1) cores 0.37/1.02 # Starting ho_unfolding_8 with 240s (1) cores 0.37/1.02 # No SInE strategy applied 0.37/1.02 # Search class: HGHSM-FSLM32-DHFMMSBN 0.37/1.02 # partial match(1): HGHSM-FSLM32-MHFMMSBN 0.37/1.02 # Scheduled 9 strats onto 1 cores with 240 seconds (240 total) 0.37/1.02 # Starting ho_unfolding_8 with 49s (1) cores 0.37/1.02 # Preprocessing time : 0.125 s 0.37/1.02 # Presaturation interreduction done 0.37/1.02 0.37/1.02 # Proof found! 0.37/1.02 # SZS status Theorem 0.37/1.02 # SZS output start CNFRefutation 0.37/1.02 thf(decl_23, type, in: $i > $i > $o). 0.37/1.02 thf(decl_24, type, exu: ($i > $o) > $o). 0.37/1.02 thf(decl_25, type, setextAx: $o). 0.37/1.02 thf(decl_26, type, emptyset: $i). 0.37/1.02 thf(decl_27, type, emptysetAx: $o). 0.37/1.02 thf(decl_28, type, setadjoin: $i > $i > $i). 0.37/1.02 thf(decl_29, type, setadjoinAx: $o). 0.37/1.02 thf(decl_30, type, powerset: $i > $i). 0.37/1.02 thf(decl_31, type, powersetAx: $o). 0.37/1.02 thf(decl_32, type, setunion: $i > $i). 0.37/1.02 thf(decl_33, type, setunionAx: $o). 0.37/1.02 thf(decl_34, type, omega: $i). 0.37/1.02 thf(decl_35, type, omega0Ax: $o). 0.37/1.02 thf(decl_36, type, omegaSAx: $o). 0.37/1.02 thf(decl_37, type, omegaIndAx: $o). 0.37/1.02 thf(decl_38, type, replAx: $o). 0.37/1.02 thf(decl_39, type, foundationAx: $o). 0.37/1.02 thf(decl_40, type, wellorderingAx: $o). 0.37/1.02 thf(decl_41, type, descr: ($i > $o) > $i). 0.37/1.02 thf(decl_42, type, descrp: $o). 0.37/1.02 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 0.37/1.02 thf(decl_44, type, dsetconstrI: $o). 0.37/1.02 thf(decl_45, type, dsetconstrEL: $o). 0.37/1.02 thf(decl_46, type, dsetconstrER: $o). 0.37/1.02 thf(decl_47, type, exuE1: $o). 0.37/1.02 thf(decl_48, type, prop2set: $o > $i). 0.37/1.02 thf(decl_49, type, prop2setE: $o). 0.37/1.02 thf(decl_50, type, emptysetE: $o). 0.37/1.02 thf(decl_51, type, emptysetimpfalse: $o). 0.37/1.02 thf(decl_52, type, notinemptyset: $o). 0.37/1.02 thf(decl_53, type, exuE3e: $o). 0.37/1.02 thf(decl_54, type, setext: $o). 0.37/1.02 thf(decl_55, type, emptyI: $o). 0.37/1.02 thf(decl_56, type, noeltsimpempty: $o). 0.37/1.02 thf(decl_57, type, setbeta: $o). 0.37/1.02 thf(decl_58, type, nonempty: $i > $o). 0.37/1.02 thf(decl_59, type, nonemptyE1: $o). 0.37/1.02 thf(decl_60, type, nonemptyI: $o). 0.37/1.02 thf(decl_61, type, nonemptyI1: $o). 0.37/1.02 thf(decl_62, type, setadjoinIL: $o). 0.37/1.02 thf(decl_63, type, emptyinunitempty: $o). 0.37/1.02 thf(decl_64, type, setadjoinIR: $o). 0.37/1.02 thf(decl_65, type, setadjoinE: $o). 0.37/1.02 thf(decl_66, type, setadjoinOr: $o). 0.37/1.02 thf(decl_67, type, setoftrueEq: $o). 0.37/1.02 thf(decl_68, type, powersetI: $o). 0.37/1.02 thf(decl_69, type, emptyinPowerset: $o). 0.37/1.02 thf(decl_70, type, emptyInPowerset: $o). 0.37/1.02 thf(decl_71, type, powersetE: $o). 0.37/1.02 thf(decl_72, type, setunionI: $o). 0.37/1.02 thf(decl_73, type, setunionE: $o). 0.37/1.02 thf(decl_74, type, subPowSU: $o). 0.37/1.02 thf(decl_75, type, exuE2: $o). 0.37/1.02 thf(decl_76, type, nonemptyImpWitness: $o). 0.37/1.02 thf(decl_77, type, uniqinunit: $o). 0.37/1.02 thf(decl_78, type, notinsingleton: $o). 0.37/1.02 thf(decl_79, type, eqinunit: $o). 0.37/1.02 thf(decl_80, type, singletonsswitch: $o). 0.37/1.02 thf(decl_81, type, upairsetE: $o). 0.37/1.02 thf(decl_82, type, upairsetIL: $o). 0.37/1.02 thf(decl_83, type, upairsetIR: $o). 0.37/1.02 thf(decl_84, type, emptyE1: $o). 0.37/1.02 thf(decl_85, type, vacuousDall: $o). 0.37/1.02 thf(decl_86, type, quantDeMorgan1: $o). 0.37/1.02 thf(decl_87, type, quantDeMorgan2: $o). 0.37/1.02 thf(decl_88, type, quantDeMorgan3: $o). 0.37/1.02 thf(decl_89, type, quantDeMorgan4: $o). 0.37/1.02 thf(decl_90, type, prop2setI: $o). 0.37/1.02 thf(decl_91, type, set2prop: $i > $o). 0.37/1.02 thf(decl_92, type, prop2set2propI: $o). 0.37/1.02 thf(decl_93, type, notdexE: $o). 0.37/1.02 thf(decl_94, type, notdallE: $o). 0.37/1.02 thf(decl_95, type, exuI1: $o). 0.37/1.02 thf(decl_96, type, exuI3: $o). 0.37/1.02 thf(decl_97, type, exuI2: $o). 0.37/1.02 thf(decl_98, type, inCongP: $o). 0.37/1.02 thf(decl_99, type, in__Cong: $o). 0.37/1.02 thf(decl_100, type, exuE3u: $o). 0.37/1.02 thf(decl_101, type, exu__Cong: $o). 0.37/1.02 thf(decl_102, type, emptyset__Cong: $o). 0.37/1.02 thf(decl_103, type, setadjoin__Cong: $o). 0.37/1.02 thf(decl_104, type, powerset__Cong: $o). 0.37/1.02 thf(decl_105, type, setunion__Cong: $o). 0.37/1.02 thf(decl_106, type, omega__Cong: $o). 0.37/1.02 thf(decl_107, type, exuEu: $o). 0.37/1.02 thf(decl_108, type, descr__Cong: $o). 0.37/1.02 thf(decl_109, type, dsetconstr__Cong: $o). 0.37/1.02 thf(decl_110, type, subset: $i > $i > $o). 0.37/1.02 thf(decl_113, type, subsetI1: $o). 0.37/1.02 thf(decl_114, type, eqimpsubset2: $o). 0.37/1.02 thf(decl_115, type, eqimpsubset1: $o). 0.37/1.02 thf(decl_116, type, subsetI2: $o). 0.37/1.02 thf(decl_117, type, emptysetsubset: $o). 0.37/1.02 thf(decl_118, type, subsetE: $o). 0.37/1.02 thf(decl_119, type, subsetE2: $o). 0.37/1.02 thf(decl_120, type, notsubsetI: $o). 0.37/1.02 thf(decl_121, type, notequalI1: $o). 0.37/1.02 thf(decl_122, type, notequalI2: $o). 0.37/1.02 thf(decl_123, type, subsetRefl: $o). 0.37/1.02 thf(decl_124, type, subsetTrans: $o). 0.37/1.02 thf(decl_125, type, setadjoinSub: $o). 0.37/1.02 thf(decl_126, type, setadjoinSub2: $o). 0.37/1.02 thf(decl_127, type, subset2powerset: $o). 0.37/1.02 thf(decl_128, type, setextsub: $o). 0.37/1.02 thf(decl_129, type, subsetemptysetimpeq: $o). 0.37/1.02 thf(decl_130, type, powersetI1: $o). 0.37/1.02 thf(decl_131, type, powersetE1: $o). 0.37/1.02 thf(decl_132, type, inPowerset: $o). 0.37/1.02 thf(decl_133, type, powersetsubset: $o). 0.37/1.02 thf(decl_134, type, sepInPowerset: $o). 0.37/1.02 thf(decl_135, type, sepSubset: $o). 0.37/1.02 thf(decl_136, type, binunion: $i > $i > $i). 0.37/1.02 thf(decl_137, type, binunionIL: $o). 0.37/1.02 thf(decl_138, type, upairset2IR: $o). 0.37/1.02 thf(decl_139, type, binunionIR: $o). 0.37/1.02 thf(decl_140, type, binunionEcases: $o). 0.37/1.02 thf(decl_141, type, binunionE: $o). 0.37/1.02 thf(decl_142, type, binunionLsub: $o). 0.37/1.02 thf(decl_143, type, binunionRsub: $o). 0.37/1.02 thf(decl_144, type, binintersect: $i > $i > $i). 0.37/1.02 thf(decl_145, type, binintersectI: $o). 0.37/1.02 thf(decl_146, type, binintersectSubset5: $o). 0.37/1.02 thf(decl_147, type, binintersectEL: $o). 0.37/1.02 thf(decl_148, type, binintersectLsub: $o). 0.37/1.02 thf(decl_149, type, binintersectSubset2: $o). 0.37/1.02 thf(decl_150, type, binintersectSubset3: $o). 0.37/1.02 thf(decl_151, type, binintersectER: $o). 0.37/1.02 thf(decl_152, type, disjointsetsI1: $o). 0.37/1.02 thf(decl_153, type, binintersectRsub: $o). 0.37/1.02 thf(decl_154, type, binintersectSubset4: $o). 0.37/1.02 thf(decl_155, type, binintersectSubset1: $o). 0.37/1.02 thf(decl_156, type, bs114d: $o). 0.37/1.02 thf(decl_158, type, setminus: $i > $i > $i). 0.37/1.02 thf(decl_159, type, setminusI: $o). 0.37/1.02 thf(decl_160, type, setminusEL: $o). 0.37/1.02 thf(decl_161, type, setminusER: $o). 0.37/1.02 thf(decl_162, type, setminusSubset2: $o). 0.37/1.02 thf(decl_163, type, setminusERneg: $o). 0.37/1.02 thf(decl_164, type, setminusELneg: $o). 0.37/1.02 thf(decl_165, type, setminusILneg: $o). 0.37/1.02 thf(decl_166, type, setminusIRneg: $o). 0.37/1.02 thf(decl_167, type, setminusLsub: $o). 0.37/1.02 thf(decl_168, type, setminusSubset1: $o). 0.37/1.02 thf(decl_169, type, symdiff: $i > $i > $i). 0.37/1.02 thf(decl_170, type, symdiffE: $o). 0.37/1.02 thf(decl_171, type, symdiffI1: $o). 0.37/1.02 thf(decl_172, type, symdiffI2: $o). 0.37/1.02 thf(decl_173, type, symdiffIneg1: $o). 0.37/1.02 thf(decl_174, type, symdiffIneg2: $o). 0.37/1.02 thf(decl_175, type, iskpair: $i > $o). 0.37/1.02 thf(decl_176, type, secondinupair: $o). 0.37/1.02 thf(decl_177, type, setukpairIL: $o). 0.37/1.02 thf(decl_178, type, setukpairIR: $o). 0.37/1.02 thf(decl_179, type, kpairiskpair: $o). 0.37/1.02 thf(decl_180, type, kpair: $i > $i > $i). 0.37/1.02 thf(decl_181, type, kpairp: $o). 0.37/1.02 thf(decl_182, type, cartprod: $i > $i > $i). 0.37/1.02 thf(decl_183, type, singletonsubset: $o). 0.37/1.02 thf(decl_184, type, singletoninpowerset: $o). 0.37/1.02 thf(decl_185, type, singletoninpowunion: $o). 0.37/1.02 thf(decl_186, type, upairset2E: $o). 0.37/1.02 thf(decl_187, type, upairsubunion: $o). 0.37/1.02 thf(decl_188, type, upairinpowunion: $o). 0.37/1.02 thf(decl_189, type, ubforcartprodlem1: $o). 0.37/1.02 thf(decl_190, type, ubforcartprodlem2: $o). 0.37/1.02 thf(decl_191, type, ubforcartprodlem3: $o). 0.37/1.02 thf(decl_192, type, cartprodpairin: $o). 0.37/1.02 thf(decl_193, type, cartprodmempair1: $o). 0.37/1.02 thf(decl_194, type, cartprodmempair: $o). 0.37/1.02 thf(decl_195, type, setunionE2: $o). 0.37/1.02 thf(decl_196, type, setunionsingleton1: $o). 0.37/1.02 thf(decl_197, type, setunionsingleton2: $o). 0.37/1.02 thf(decl_198, type, setunionsingleton: $o). 0.37/1.02 thf(decl_199, type, singleton: $i > $o). 0.37/1.02 thf(decl_200, type, singletonprop: $o). 0.37/1.02 thf(decl_201, type, ex1: $i > ($i > $o) > $o). 0.37/1.02 thf(decl_202, type, ex1E1: $o). 0.37/1.02 thf(decl_203, type, ex1I: $o). 0.37/1.02 thf(decl_204, type, ex1I2: $o). 0.37/1.02 thf(decl_205, type, singletonsuniq: $o). 0.37/1.02 thf(decl_210, type, setukpairinjL1: $o). 0.37/1.02 thf(decl_211, type, kfstsingleton: $o). 0.37/1.02 thf(decl_212, type, theprop: $o). 0.37/1.02 thf(decl_213, type, kfst: $i > $i). 0.37/1.02 thf(decl_214, type, kfstpairEq: $o). 0.37/1.02 thf(decl_215, type, cartprodfstin: $o). 0.37/1.02 thf(decl_216, type, setukpairinjL2: $o). 0.37/1.02 thf(decl_217, type, setukpairinjL: $o). 0.37/1.02 thf(decl_218, type, setukpairinjR11: $o). 0.37/1.02 thf(decl_219, type, setukpairinjR12: $o). 0.37/1.02 thf(decl_220, type, setukpairinjR1: $o). 0.37/1.02 thf(decl_221, type, upairequniteq: $o). 0.37/1.02 thf(decl_222, type, setukpairinjR2: $o). 0.37/1.02 thf(decl_223, type, setukpairinjR: $o). 0.37/1.02 thf(decl_224, type, ksndsingleton: $o). 0.37/1.02 thf(decl_225, type, ksnd: $i > $i). 0.37/1.02 thf(decl_226, type, ksndpairEq: $o). 0.37/1.02 thf(decl_227, type, kpairsurjEq: $o). 0.37/1.02 thf(decl_228, type, cartprodsndin: $o). 0.37/1.02 thf(decl_229, type, cartprodpairmemEL: $o). 0.37/1.02 thf(decl_230, type, cartprodpairmemER: $o). 0.37/1.02 thf(decl_231, type, cartprodmempaircEq: $o). 0.37/1.02 thf(decl_232, type, cartprodfstpairEq: $o). 0.37/1.02 thf(decl_233, type, cartprodsndpairEq: $o). 0.37/1.02 thf(decl_234, type, cartprodpairsurjEq: $o). 0.37/1.02 thf(decl_235, type, breln: $i > $i > $i > $o). 0.37/1.02 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 0.37/1.02 thf(decl_237, type, dpsetconstrI: $o). 0.37/1.02 thf(decl_238, type, dpsetconstrSub: $o). 0.37/1.02 thf(decl_239, type, setOfPairsIsBReln: $o). 0.37/1.02 thf(decl_240, type, dpsetconstrERa: $o). 0.37/1.02 thf(decl_241, type, dpsetconstrEL1: $o). 0.37/1.02 thf(decl_242, type, dpsetconstrEL2: $o). 0.37/1.02 thf(decl_243, type, dpsetconstrER: $o). 0.37/1.02 thf(decl_244, type, func: $i > $i > $i > $o). 0.37/1.02 thf(decl_245, type, funcSet: $i > $i > $i). 0.37/1.02 thf(decl_246, type, funcImageSingleton: $o). 0.37/1.02 thf(decl_247, type, apProp: $o). 0.37/1.02 thf(decl_248, type, ap: $i > $i > $i > $i > $i). 0.37/1.02 thf(decl_249, type, app: $o). 0.37/1.02 thf(decl_250, type, infuncsetfunc: $o). 0.37/1.02 thf(decl_251, type, ap2p: $o). 0.37/1.02 thf(decl_252, type, funcinfuncset: $o). 0.37/1.02 thf(decl_253, type, lamProp: $o). 0.37/1.02 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i). 0.37/1.02 thf(decl_255, type, lamp: $o). 0.37/1.02 thf(decl_256, type, lam2p: $o). 0.37/1.02 thf(decl_257, type, brelnall1: $o). 0.37/1.02 thf(decl_258, type, brelnall2: $o). 0.37/1.02 thf(decl_259, type, ex1E2: $o). 0.37/1.02 thf(decl_260, type, funcGraphProp1: $o). 0.37/1.02 thf(decl_261, type, funcGraphProp3: $o). 0.37/1.02 thf(decl_262, type, funcGraphProp2: $o). 0.37/1.02 thf(decl_263, type, funcextLem: $o). 0.37/1.02 thf(decl_264, type, funcGraphProp4: $o). 0.37/1.02 thf(decl_265, type, subbreln: $o). 0.37/1.02 thf(decl_266, type, eqbreln: $o). 0.37/1.02 thf(decl_267, type, funcext: $o). 0.37/1.02 thf(decl_268, type, funcext2: $o). 0.37/1.02 thf(decl_269, type, ap2apEq1: $o). 0.37/1.02 thf(decl_270, type, ap2apEq2: $o). 0.37/1.02 thf(decl_271, type, beta1: $o). 0.37/1.02 thf(decl_272, type, eta1: $o). 0.37/1.02 thf(decl_273, type, lam2lamEq: $o). 0.37/1.02 thf(decl_274, type, beta2: $o). 0.37/1.02 thf(decl_275, type, eta2: $o). 0.37/1.02 thf(decl_276, type, iffalseProp1: $o). 0.37/1.02 thf(decl_277, type, iffalseProp2: $o). 0.37/1.02 thf(decl_278, type, iftrueProp1: $o). 0.37/1.02 thf(decl_279, type, iftrueProp2: $o). 0.37/1.02 thf(decl_280, type, ifSingleton: $o). 0.37/1.02 thf(decl_281, type, if: $i > $o > $i > $i > $i). 0.37/1.02 thf(decl_282, type, ifp: $o). 0.37/1.02 thf(decl_283, type, theeq: $o). 0.37/1.02 thf(decl_284, type, iftrue: $o). 0.37/1.02 thf(decl_285, type, epred1_0: $o). 0.37/1.02 thf(decl_286, type, esk1_2: $i > $i > $i). 0.37/1.02 thf(decl_287, type, esk2_2: $i > $i > $i). 0.37/1.02 thf(decl_288, type, esk3_2: $i > $i > $i). 0.37/1.02 thf(decl_289, type, esk4_1: $i > $i). 0.37/1.02 thf(decl_290, type, esk5_2: ($i > $i > $o) > $i > $i). 0.37/1.02 thf(decl_291, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 0.37/1.02 thf(decl_292, type, esk7_2: ($i > $i > $o) > $i > $i). 0.37/1.02 thf(decl_293, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 0.37/1.02 thf(decl_294, type, esk9_1: $i > $i). 0.37/1.02 thf(decl_295, type, esk10_2: ($i > $o) > $i > $i). 0.37/1.02 thf(decl_296, type, esk11_2: ($i > $o) > $i > $i). 0.37/1.02 thf(decl_297, type, esk12_1: ($i > $o) > $i). 0.37/1.02 thf(decl_298, type, esk13_2: ($i > $o) > $i > $i). 0.37/1.02 thf(decl_299, type, esk14_1: ($i > $o) > $i). 0.37/1.02 thf(decl_300, type, esk15_2: $i > $i > $i). 0.37/1.02 thf(decl_301, type, esk16_2: $i > $i > $i). 0.37/1.02 thf(decl_302, type, esk17_1: $i > $i). 0.37/1.02 thf(decl_303, type, esk18_1: $i > $i). 0.37/1.02 thf(decl_304, type, esk19_1: $i > $i). 0.37/1.02 thf(decl_305, type, esk20_2: $i > $i > $i). 0.37/1.02 thf(decl_306, type, esk21_3: $i > $i > $o > $i). 0.37/1.02 thf(decl_307, type, esk22_2: ($i > $o) > $i > $i). 0.37/1.02 thf(decl_308, type, esk23_1: ($i > $o) > $i). 0.37/1.02 thf(decl_309, type, esk24_1: $i > $i). 0.37/1.02 thf(decl_310, type, esk25_2: $i > ($i > $o) > $i). 0.37/1.02 thf(decl_311, type, esk26_2: $i > ($i > $o) > $i). 0.37/1.02 thf(decl_312, type, esk27_2: $i > ($i > $o) > $i). 0.37/1.02 thf(decl_313, type, esk28_2: $i > ($i > $o) > $i). 0.37/1.02 thf(decl_314, type, esk29_2: $i > ($i > $o) > $i). 0.37/1.02 thf(decl_315, type, esk30_2: $i > ($i > $o) > $i). 0.37/1.02 thf(decl_316, type, esk31_2: ($i > $o) > $i > $i). 0.37/1.02 thf(decl_317, type, esk32_1: ($i > $o) > $i). 0.37/1.02 thf(decl_318, type, esk33_1: ($i > $o) > $i). 0.37/1.02 thf(decl_319, type, esk34_1: ($i > $o) > $i). 0.37/1.02 thf(decl_320, type, esk35_1: ($i > $o) > $i). 0.37/1.02 thf(decl_321, type, esk36_2: ($i > $o) > $i > $i). 0.37/1.02 thf(decl_322, type, esk37_1: ($i > $o) > $i). 0.37/1.02 thf(decl_323, type, esk38_2: ($i > $o) > $i > $i). 0.37/1.02 thf(decl_324, type, esk39_2: ($i > $o) > ($i > $o) > $i). 0.37/1.02 thf(decl_325, type, esk40_2: ($i > $o) > ($i > $o) > $i). 0.37/1.02 thf(decl_326, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 0.37/1.02 thf(decl_327, type, esk42_2: ($i > $o) > ($i > $o) > $i). 0.37/1.02 thf(decl_328, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 0.37/1.02 thf(decl_329, type, esk44_2: ($i > $o) > ($i > $o) > $i). 0.37/1.02 thf(decl_330, type, esk45_2: ($i > $o) > $i > $i). 0.37/1.02 thf(decl_331, type, esk46_2: ($i > $o) > ($i > $o) > $i). 0.37/1.02 thf(decl_332, type, esk47_2: ($i > $o) > ($i > $o) > $i). 0.37/1.02 thf(decl_333, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 0.37/1.02 thf(decl_334, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 0.37/1.02 thf(decl_335, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.37/1.02 thf(decl_336, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.37/1.02 thf(decl_337, type, esk52_2: $i > $i > $i). 0.37/1.02 thf(decl_338, type, esk53_2: $i > $i > $i). 0.37/1.02 thf(decl_339, type, esk54_2: $i > $i > $i). 0.37/1.02 thf(decl_340, type, esk55_3: $i > $i > $i > $i). 0.37/1.02 thf(decl_341, type, esk56_3: $i > $i > $i > $i). 0.37/1.02 thf(decl_342, type, esk57_2: $i > $i > $i). 0.37/1.02 thf(decl_343, type, esk58_2: $i > ($i > $o) > $i). 0.37/1.02 thf(decl_344, type, esk59_2: $i > ($i > $o) > $i). 0.37/1.02 thf(decl_345, type, esk60_2: $i > ($i > $o) > $i). 0.37/1.02 thf(decl_346, type, esk61_3: $i > ($i > $o) > $i > $i). 0.37/1.02 thf(decl_347, type, esk62_2: $i > ($i > $o) > $i). 0.37/1.02 thf(decl_348, type, esk63_2: $i > ($i > $o) > $i). 0.37/1.02 thf(decl_349, type, esk64_3: $i > $i > ($i > $i) > $i). 0.37/1.02 thf(decl_350, type, esk65_3: $i > $i > ($i > $i) > $i). 0.37/1.02 thf(decl_351, type, esk66_3: $i > $i > ($i > $i) > $i). 0.37/1.02 thf(decl_352, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 0.37/1.02 thf(decl_353, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 0.37/1.02 thf(decl_354, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 0.37/1.02 thf(decl_355, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 0.37/1.02 thf(decl_356, type, esk71_4: $i > $i > $i > $i > $i). 0.37/1.02 thf(decl_357, type, esk72_4: $i > $i > $i > $i > $i). 0.37/1.02 thf(decl_358, type, esk73_4: $i > $i > $i > $i > $i). 0.37/1.02 thf(decl_359, type, esk74_4: $i > $i > $i > $i > $i). 0.37/1.02 thf(decl_360, type, esk75_4: $i > $i > $i > $i > $i). 0.37/1.02 thf(decl_361, type, esk76_4: $i > $i > $i > $i > $i). 0.37/1.02 thf(decl_362, type, esk77_4: $i > $i > $i > $i > $i). 0.37/1.02 thf(decl_363, type, esk78_4: $i > $i > $i > $i > $i). 0.37/1.02 thf(decl_364, type, esk79_4: $i > $i > $i > $i > $i). 0.37/1.02 thf(decl_365, type, esk80_3: $i > $i > ($i > $i) > $i). 0.37/1.02 thf(decl_366, type, esk81_3: $i > $i > ($i > $i) > $i). 0.37/1.02 thf(decl_367, type, esk82_3: $i > $i > ($i > $i) > $i). 0.37/1.02 thf(decl_368, type, esk83_0: $i). 0.37/1.02 thf(decl_369, type, epred2_0: $o). 0.37/1.02 thf(decl_370, type, esk84_0: $i). 0.37/1.02 thf(decl_371, type, esk85_0: $i). 0.37/1.02 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', replAx)). 0.37/1.02 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', exu)). 0.37/1.02 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', descrp)). 0.37/1.02 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', exuE1)). 0.37/1.02 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', exuE3e)). 0.37/1.02 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', nonempty)). 0.37/1.02 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', nonemptyI)). 0.37/1.02 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', exuE2)). 0.37/1.02 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', exuI1)). 0.37/1.02 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', exuI3)). 0.37/1.02 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', exuI2)). 0.37/1.02 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', exuE3u)). 0.37/1.02 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', exu__Cong)). 0.37/1.02 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', exuEu)). 0.37/1.02 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', descr__Cong)). 0.37/1.02 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', ex1E1)). 0.37/1.02 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', ex1)). 0.37/1.02 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', ex1I)). 0.37/1.02 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', ex1I2)). 0.37/1.02 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setOfPairsIsBReln)). 0.37/1.02 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', breln)). 0.37/1.02 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', ex1E2)). 0.37/1.02 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', dsetconstrI)). 0.37/1.02 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', dsetconstrEL)). 0.37/1.02 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', dsetconstrER)). 0.37/1.02 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setbeta)). 0.37/1.02 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', nonemptyE1)). 0.37/1.02 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', nonemptyI1)). 0.37/1.02 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setoftrueEq)). 0.37/1.02 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', nonemptyImpWitness)). 0.37/1.02 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', emptyE1)). 0.37/1.02 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', dsetconstr__Cong)). 0.37/1.02 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', sepInPowerset)). 0.37/1.02 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', sepSubset)). 0.37/1.02 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', singletonprop)). 0.37/1.02 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', kfstsingleton)). 0.37/1.02 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', ksndsingleton)). 0.37/1.02 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', dpsetconstrI)). 0.37/1.02 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', dpsetconstrSub)). 0.37/1.02 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', dpsetconstrERa)). 0.37/1.02 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', dpsetconstrEL1)). 0.37/1.02 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', dpsetconstrEL2)). 0.37/1.02 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', dpsetconstrER)). 0.37/1.02 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', funcImageSingleton)). 0.37/1.02 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', apProp)). 0.37/1.02 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', lamProp)). 0.37/1.02 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', lamp)). 0.37/1.02 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', lam2p)). 0.37/1.02 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', brelnall1)). 0.37/1.02 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', brelnall2)). 0.37/1.02 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', subbreln)). 0.37/1.02 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', eqbreln)). 0.37/1.02 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', beta1)). 0.37/1.02 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', eta1)). 0.37/1.02 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', lam2lamEq)). 0.37/1.02 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', beta2)). 0.37/1.02 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', eta2)). 0.37/1.02 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', iffalseProp1)). 0.37/1.02 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', iffalseProp2)). 0.37/1.02 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', iftrueProp1)). 0.37/1.02 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', iftrueProp2)). 0.37/1.02 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', ifSingleton)). 0.37/1.02 thf(iffalse, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>(((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>(((foundationAx)=>((wellorderingAx)=>((((dsetconstrEL)=>(((exuE1)=>((((emptysetimpfalse)=>((notinemptyset)=>(((((noeltsimpempty)=>((setbeta)=>((((nonemptyI1)=>((setadjoinIL)=>(((((((powersetI)=>((emptyinPowerset)=>((((setunionI)=>((((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>(((eqinunit)=>((singletonsswitch)=>(((upairsetIL)=>(((emptyE1)=>((((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>(((prop2set2propI)=>((((exuI1)=>((((inCongP)=>((in__Cong)=>(((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((((((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>(((subsetI2)=>(((subsetE)=>((subsetE2)=>((notsubsetI)=>((((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>(((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>(((powersetE1)=>((inPowerset)=>((powersetsubset)=>((((((binunionIR)=>((binunionEcases)=>((binunionE)=>(((binunionRsub)=>((((((binintersectSubset2)=>((binintersectSubset3)=>((((binintersectRsub)=>((binintersectSubset4)=>((((setminusI)=>((setminusEL)=>(((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((((((symdiffE)=>(((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>(((setukpairIR)=>(((kpairp)=>(((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>(((ubforcartprodlem3)=>((((cartprodmempair)=>((setunionE2)=>((((((ex1E1)=>(((ex1I2)=>((singletonsuniq)=>(((kfstsingleton)=>((theprop)=>(((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>(((setukpairinjR1)=>(((setukpairinjR2)=>(((ksndsingleton)=>(((kpairsurjEq)=>((((cartprodpairmemER)=>(((cartprodfstpairEq)=>((((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>(((dpsetconstrEL1)=>((((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>(((funcinfuncset)=>(((lamp)=>((((((funcGraphProp1)=>(((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((((funcext2)=>(((ap2apEq2)=>((((lam2lamEq)=>((beta2)=>(((iffalseProp1)=>((((iftrueProp2)=>(((ifp)=>((theeq)=>(![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(((if @ X4 @ ((X47)) @ X2 @ X3)=(X3))<=~((X47)))))))<=(iftrue))))<=(ifSingleton)))<=(iftrueProp1))<=(iffalseProp2)))<=(eta2))))<=(eta1))<=(beta1)))<=(ap2apEq1)))<=(funcext))<=(eqbreln))))))<=(funcGraphProp3)))<=(ex1E2))<=(brelnall2))<=(brelnall1))<=(lam2p)))<=(lamProp)))<=(ap2p))))))<=(dpsetconstrER))<=(dpsetconstrEL2)))<=(dpsetconstrERa)))))<=(cartprodpairsurjEq))<=(cartprodsndpairEq)))<=(cartprodmempaircEq)))<=(cartprodpairmemEL))<=(cartprodsndin)))<=(ksndpairEq)))<=(setukpairinjR)))<=(upairequniteq)))<=(setukpairinjR12))))))<=(kfstpairEq))))<=(setukpairinjL1))))<=(ex1I)))<=(singletonprop))<=(setunionsingleton))<=(setunionsingleton2))<=(setunionsingleton1))))<=(cartprodmempair1))<=(cartprodpairin)))<=(ubforcartprodlem2))))))))<=(singletonsubset)))<=(kpairiskpair)))<=(setukpairIL))))))<=(symdiffI1)))<=(setminusSubset1))<=(setminusLsub))<=(setminusIRneg))<=(setminusILneg)))))<=(setminusER))))<=(bs114d))<=(binintersectSubset1))))<=(disjointsetsI1))<=(binintersectER))))<=(binintersectLsub))<=(binintersectEL))<=(binintersectSubset5))<=(binintersectI)))<=(binunionLsub)))))<=(upairset2IR))<=(binunionIL))<=(sepSubset))<=(sepInPowerset)))))<=(powersetI1)))))<=(setadjoinSub2)))))<=(notequalI2))<=(notequalI1)))))<=(emptysetsubset)))<=(eqimpsubset1))))))<=(exuEu))<=(omega__Cong))<=(setunion__Cong))<=(powerset__Cong)))))<=(exuE3u))))<=(exuI2))<=(exuI3)))<=(notdallE))<=(notdexE)))<=(prop2setI)))))<=(quantDeMorgan1))<=(vacuousDall)))<=(upairsetIR)))<=(upairsetE))))<=(notinsingleton)))))<=(subPowSU))<=(setunionE)))<=(powersetE))<=(emptyInPowerset))))<=(setoftrueEq))<=(setadjoinOr))<=(setadjoinE))<=(setadjoinIR))<=(emptyinunitempty))))<=(nonemptyI))<=(nonemptyE1))))<=(emptyI))<=(setext))<=(exuE3e))))<=(emptysetE))<=(prop2setE)))<=(dsetconstrER)))<=(dsetconstrI))<=(descrp))))<=(replAx)))))<=(setunionAx)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', iffalse)). 0.37/1.02 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setextAx)). 0.37/1.02 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', emptysetAx)). 0.37/1.02 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setadjoinAx)). 0.37/1.02 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', powersetAx)). 0.37/1.02 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setunionAx)). 0.37/1.02 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', omega0Ax)). 0.37/1.02 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', omegaSAx)). 0.37/1.02 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', omegaIndAx)). 0.37/1.02 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', foundationAx)). 0.37/1.02 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', wellorderingAx)). 0.37/1.02 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', prop2setE)). 0.37/1.02 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', emptysetE)). 0.37/1.02 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', emptysetimpfalse)). 0.37/1.02 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', notinemptyset)). 0.37/1.02 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setext)). 0.37/1.02 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', emptyI)). 0.37/1.02 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', noeltsimpempty)). 0.37/1.02 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setadjoinIL)). 0.37/1.02 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', emptyinunitempty)). 0.37/1.02 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setadjoinIR)). 0.37/1.02 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setadjoinE)). 0.37/1.02 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setadjoinOr)). 0.37/1.02 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', powersetI)). 0.37/1.02 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', emptyinPowerset)). 0.37/1.02 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', emptyInPowerset)). 0.37/1.02 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', powersetE)). 0.37/1.02 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setunionI)). 0.37/1.02 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setunionE)). 0.37/1.02 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', subPowSU)). 0.37/1.02 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', uniqinunit)). 0.37/1.02 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', notinsingleton)). 0.37/1.02 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', eqinunit)). 0.37/1.02 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', singletonsswitch)). 0.37/1.02 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', upairsetE)). 0.37/1.02 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', upairsetIL)). 0.37/1.02 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', upairsetIR)). 0.37/1.02 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', vacuousDall)). 0.37/1.02 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', quantDeMorgan1)). 0.37/1.02 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', quantDeMorgan2)). 0.37/1.02 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', quantDeMorgan3)). 0.37/1.02 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', quantDeMorgan4)). 0.37/1.02 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', prop2setI)). 0.37/1.02 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', prop2set2propI)). 0.37/1.02 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', notdexE)). 0.37/1.02 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', notdallE)). 0.37/1.02 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', inCongP)). 0.37/1.02 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', in__Cong)). 0.37/1.02 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', emptyset__Cong)). 0.37/1.02 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setadjoin__Cong)). 0.37/1.02 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', powerset__Cong)). 0.37/1.02 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setunion__Cong)). 0.37/1.02 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', omega__Cong)). 0.37/1.02 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', subsetI1)). 0.37/1.02 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', eqimpsubset2)). 0.37/1.02 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', eqimpsubset1)). 0.37/1.02 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', subsetI2)). 0.37/1.02 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', emptysetsubset)). 0.37/1.02 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', subsetE)). 0.37/1.02 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', subsetE2)). 0.37/1.02 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', notsubsetI)). 0.37/1.02 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', notequalI1)). 0.37/1.02 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', notequalI2)). 0.37/1.02 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', subsetRefl)). 0.37/1.02 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', subsetTrans)). 0.37/1.02 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setadjoinSub)). 0.37/1.02 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setadjoinSub2)). 0.37/1.02 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', subset2powerset)). 0.37/1.02 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setextsub)). 0.37/1.02 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', subsetemptysetimpeq)). 0.37/1.02 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', powersetI1)). 0.37/1.02 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', powersetE1)). 0.37/1.02 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', inPowerset)). 0.37/1.02 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', powersetsubset)). 0.37/1.02 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', binunionIL)). 0.37/1.02 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', upairset2IR)). 0.37/1.02 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', binunionIR)). 0.37/1.02 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', binunionEcases)). 0.37/1.02 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', binunionE)). 0.37/1.02 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', binunionLsub)). 0.37/1.02 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', binunionRsub)). 0.37/1.02 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', binintersectI)). 0.37/1.02 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', binintersectSubset5)). 0.37/1.02 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', binintersectEL)). 0.37/1.02 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', binintersectLsub)). 0.37/1.02 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', binintersectSubset2)). 0.37/1.02 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', binintersectSubset3)). 0.37/1.02 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', binintersectER)). 0.37/1.02 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', disjointsetsI1)). 0.37/1.02 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', binintersectRsub)). 0.37/1.02 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', binintersectSubset4)). 0.37/1.02 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', binintersectSubset1)). 0.37/1.02 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', bs114d)). 0.37/1.02 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setminusI)). 0.37/1.02 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setminusEL)). 0.37/1.02 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setminusER)). 0.37/1.02 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setminusSubset2)). 0.37/1.02 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setminusERneg)). 0.37/1.02 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setminusELneg)). 0.37/1.02 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setminusILneg)). 0.37/1.02 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setminusIRneg)). 0.37/1.02 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setminusLsub)). 0.37/1.02 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setminusSubset1)). 0.37/1.02 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', symdiffE)). 0.37/1.02 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', symdiffI1)). 0.37/1.02 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', symdiffI2)). 0.37/1.02 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', symdiffIneg1)). 0.37/1.02 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', symdiffIneg2)). 0.37/1.02 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', secondinupair)). 0.37/1.02 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setukpairIL)). 0.37/1.02 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setukpairIR)). 0.37/1.02 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', kpairiskpair)). 0.37/1.02 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', kpairp)). 0.37/1.02 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', singletonsubset)). 0.37/1.02 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', singletoninpowerset)). 0.37/1.02 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', singletoninpowunion)). 0.37/1.02 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', upairset2E)). 0.37/1.02 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', upairsubunion)). 0.37/1.02 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', upairinpowunion)). 0.37/1.02 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', ubforcartprodlem1)). 0.37/1.02 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', ubforcartprodlem2)). 0.37/1.02 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', ubforcartprodlem3)). 0.37/1.02 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', cartprodpairin)). 0.37/1.02 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', cartprodmempair1)). 0.37/1.02 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', cartprodmempair)). 0.37/1.02 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setunionE2)). 0.37/1.02 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setunionsingleton1)). 0.37/1.02 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setunionsingleton2)). 0.37/1.02 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setunionsingleton)). 0.37/1.02 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', singletonsuniq)). 0.37/1.02 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setukpairinjL1)). 0.37/1.02 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', theprop)). 0.37/1.02 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', kfstpairEq)). 0.37/1.02 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', cartprodfstin)). 0.37/1.02 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setukpairinjL2)). 0.37/1.02 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setukpairinjL)). 0.37/1.02 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setukpairinjR11)). 0.37/1.02 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setukpairinjR12)). 0.37/1.02 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setukpairinjR1)). 0.37/1.02 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', upairequniteq)). 0.37/1.02 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setukpairinjR2)). 0.37/1.02 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', setukpairinjR)). 0.37/1.02 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', ksndpairEq)). 0.37/1.02 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', kpairsurjEq)). 0.37/1.02 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', cartprodsndin)). 0.37/1.02 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', cartprodpairmemEL)). 0.37/1.02 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', cartprodpairmemER)). 0.37/1.02 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', cartprodmempaircEq)). 0.37/1.02 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', cartprodfstpairEq)). 0.37/1.02 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', cartprodsndpairEq)). 0.37/1.02 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', cartprodpairsurjEq)). 0.37/1.02 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', app)). 0.37/1.02 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', infuncsetfunc)). 0.37/1.02 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', ap2p)). 0.37/1.02 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', funcinfuncset)). 0.37/1.02 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', funcGraphProp1)). 0.37/1.02 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', funcGraphProp3)). 0.37/1.02 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', funcGraphProp2)). 0.37/1.02 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', funcextLem)). 0.37/1.02 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', funcGraphProp4)). 0.37/1.02 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', funcext)). 0.37/1.02 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', funcext2)). 0.37/1.02 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', ap2apEq1)). 0.37/1.02 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', ap2apEq2)). 0.37/1.02 thf(ifp, axiom, ((ifp)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X45)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', ifp)). 0.37/1.02 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', theeq)). 0.37/1.02 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X46)=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', iftrue)). 0.37/1.02 thf(if, axiom, ((if)=(^[X4:$i, X44:$o, X2:$i, X3:$i]:(setunion @ (dsetconstr @ X4 @ (^[X14:$i]:((((X44)&((X14)=(X2)))|(~((X44))&((X14)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.yUbYieSLyo/E---3.1_21646.p', if)). 0.37/1.02 thf(c_0_230, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.37/1.02 thf(c_0_231, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 0.37/1.02 thf(c_0_232, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.37/1.02 thf(c_0_233, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 0.37/1.02 thf(c_0_234, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.37/1.02 thf(c_0_235, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 0.37/1.02 thf(c_0_236, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.37/1.02 thf(c_0_237, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 0.37/1.02 thf(c_0_238, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 0.37/1.02 thf(c_0_239, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.37/1.02 thf(c_0_240, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 0.37/1.02 thf(c_0_241, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 0.37/1.02 thf(c_0_242, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.37/1.02 thf(c_0_243, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 0.37/1.02 thf(c_0_244, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.37/1.02 thf(c_0_245, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 0.37/1.02 thf(c_0_246, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])). 0.37/1.02 thf(c_0_247, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])). 0.37/1.02 thf(c_0_248, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 0.37/1.02 thf(c_0_249, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 0.37/1.02 thf(c_0_250, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])). 0.37/1.02 thf(c_0_251, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])). 0.37/1.02 thf(c_0_252, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X740:$i]:((((X6 @ X2 @ X740))&![X741:$i]:((((X6 @ X2 @ X741))=>((X740)=(X741)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_230, c_0_231])). 0.37/1.02 thf(c_0_253, plain, ((descrp)=(![X1:$i > $o]:(((?[X742:$i]:((((X1 @ X742))&![X743:$i]:((((X1 @ X743))=>((X742)=(X743)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_232, c_0_231])). 0.37/1.02 thf(c_0_254, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.37/1.02 thf(c_0_255, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.37/1.02 thf(c_0_256, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.37/1.02 thf(c_0_257, plain, ((exuE1)=(![X1:$i > $o]:(((?[X744:$i]:((((X1 @ X744))&![X745:$i]:((((X1 @ X745))=>((X744)=(X745)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_233, c_0_231])). 0.37/1.02 thf(c_0_258, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X746:$i]:((((X1 @ X746))&![X747:$i]:((((X1 @ X747))=>((X746)=(X747)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_234, c_0_231])). 0.37/1.02 thf(c_0_259, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.37/1.02 thf(c_0_260, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_235])). 0.37/1.02 thf(c_0_261, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_236, c_0_235])). 0.37/1.02 thf(c_0_262, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_235])). 0.37/1.02 thf(c_0_263, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.37/1.02 thf(c_0_264, plain, ((exuE2)=(![X1:$i > $o]:(((?[X748:$i]:((((X1 @ X748))&![X749:$i]:((((X1 @ X749))=>((X748)=(X749)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_231])). 0.37/1.02 thf(c_0_265, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_235])). 0.37/1.02 thf(c_0_266, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 0.37/1.02 thf(c_0_267, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X750:$i]:((((X1 @ X750))&![X751:$i]:((((X1 @ X751))=>((X750)=(X751))))))))))), inference(apply_def,[status(thm)],[c_0_238, c_0_231])). 0.37/1.02 thf(c_0_268, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X752:$i]:((((X1 @ X752))&![X753:$i]:((((X1 @ X753))=>((X752)=(X753)))))))))))), inference(apply_def,[status(thm)],[c_0_239, c_0_231])). 0.37/1.02 thf(c_0_269, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X754:$i]:((((X1 @ X754))&![X755:$i]:((((X1 @ X755))=>((X754)=(X755))))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_231])). 0.37/1.02 thf(c_0_270, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X756:$i]:((((X1 @ X756))&![X757:$i]:((((X1 @ X757))=>((X756)=(X757)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_241, c_0_231])). 0.37/1.02 thf(c_0_271, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X758:$i]:((((X1 @ X758))&![X759:$i]:((((X1 @ X759))=>((X758)=(X759)))))))<=>(?[X760:$i]:((((X17 @ X760))&![X761:$i]:((((X17 @ X761))=>((X760)=(X761)))))))))))), inference(apply_def,[status(thm)],[c_0_242, c_0_231])). 0.37/1.02 thf(c_0_272, plain, ((exuEu)=(![X1:$i > $o]:(((?[X762:$i]:((((X1 @ X762))&![X763:$i]:((((X1 @ X763))=>((X762)=(X763)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_243, c_0_231])). 0.37/1.02 thf(c_0_273, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X764:$i]:((((X1 @ X764))&![X765:$i]:((((X1 @ X765))=>((X764)=(X765)))))))=>((?[X766:$i]:((((X17 @ X766))&![X767:$i]:((((X17 @ X767))=>((X766)=(X767)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_244, c_0_231])). 0.37/1.02 thf(c_0_274, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.37/1.02 thf(c_0_275, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 0.37/1.02 thf(c_0_276, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 0.37/1.02 thf(c_0_277, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 0.37/1.02 thf(c_0_278, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_245, c_0_246])). 0.37/1.02 thf(c_0_279, plain, ((ex1I)=(![X4:$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_247, c_0_246])). 0.37/1.02 thf(c_0_280, 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 */:$i]:(((X1 @ Z0)))))))))))), inference(apply_def,[status(thm)],[c_0_248, c_0_246])). 0.37/1.02 thf(c_0_281, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 0.37/1.02 thf(c_0_282, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 0.37/1.02 thf(c_0_283, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 0.37/1.02 thf(c_0_284, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 0.37/1.02 thf(c_0_285, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_249, c_0_250])). 0.37/1.02 thf(c_0_286, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 0.37/1.02 thf(c_0_287, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 0.37/1.02 thf(c_0_288, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 0.37/1.02 thf(c_0_289, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 0.37/1.02 thf(c_0_290, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 0.37/1.02 thf(c_0_291, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 0.37/1.02 thf(c_0_292, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])). 0.37/1.02 thf(c_0_293, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 0.37/1.02 thf(c_0_294, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 0.37/1.02 thf(c_0_295, axiom, ((brelnall1)=(![X4:$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_250])). 0.37/1.02 thf(c_0_296, 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_250])). 0.37/1.02 thf(c_0_297, 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_251, c_0_246])). 0.37/1.02 thf(c_0_298, 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_250])). 0.37/1.02 thf(c_0_299, 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_250])). 0.37/1.02 thf(c_0_300, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])). 0.37/1.02 thf(c_0_301, 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])). 0.37/1.02 thf(c_0_302, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])). 0.37/1.02 thf(c_0_303, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])). 0.37/1.02 thf(c_0_304, 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])). 0.37/1.02 thf(c_0_305, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 0.37/1.02 thf(c_0_306, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])). 0.37/1.02 thf(c_0_307, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 0.37/1.02 thf(c_0_308, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])). 0.37/1.02 thf(c_0_309, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 0.37/1.02 thf(c_0_310, plain, ((epred1_0)<=>![X786:$i]:(?[X787:$i]:((((![X788:$i]:(((in @ X788 @ X787)=>![X789:$i]:(((in @ X789 @ X788)=>(in @ X789 @ X786)))))&![X790:$i, X791:$i]:((((in @ X790 @ X786)&(in @ X791 @ X786))=>(![X792:$i]:(((in @ X792 @ X787)=>((in @ X790 @ X792)<=>(in @ X791 @ X792))))=>((X790)=(X791))))))&![X793:$i, X794:$i]:((((in @ X793 @ X787)&(in @ X794 @ X787))=>(![X795:$i]:(((in @ X795 @ X793)=>(in @ X795 @ X794)))|![X796:$i]:(((in @ X796 @ X794)=>(in @ X796 @ X793)))))))&![X797:$i]:(((![X798:$i]:(((in @ X798 @ X797)=>(in @ X798 @ X786)))&?[X799:$i]:((in @ X799 @ X797)))=>?[X800:$i, X801:$i]:(((((in @ X800 @ X787)&(in @ X801 @ X797))&~(?[X802:$i]:(((in @ X802 @ X800)&(in @ X802 @ X797)))))&![X803:$i]:(((in @ X803 @ X787)=>(![X804:$i]:(((in @ X804 @ X803)=>(in @ X804 @ X800)))|(in @ X801 @ X803)))))))))))), introduced(definition)). 0.37/1.02 thf(c_0_311, negated_conjecture, ~((![X768:$i, X769:$i]:((![X770:$i]:(((in @ X770 @ X768)<=>(in @ X770 @ X769)))=>((X768)=(X769))))=>(![X771:$i]:(~(in @ X771 @ emptyset))=>(![X772:$i, X773:$i, X774:$i]:(((in @ X774 @ (setadjoin @ X772 @ X773))<=>(((X774)=(X772))|(in @ X774 @ X773))))=>(![X775:$i, X776:$i]:(((in @ X776 @ (powerset @ X775))<=>![X777:$i]:(((in @ X777 @ X776)=>(in @ X777 @ X775)))))=>(![X1481:$i, X1482:$i]:(((in @ X1482 @ (setunion @ X1481))<=>?[X1483:$i]:(((in @ X1482 @ X1483)&(in @ X1483 @ X1481)))))=>((in @ emptyset @ omega)=>(![X778:$i]:(((in @ X778 @ omega)=>(in @ (setadjoin @ X778 @ X778) @ omega)))=>(![X779:$i]:((((in @ emptyset @ X779)&![X780:$i]:((((in @ X780 @ omega)&(in @ X780 @ X779))=>(in @ (setadjoin @ X780 @ X780) @ X779))))=>![X781:$i]:(((in @ X781 @ omega)=>(in @ X781 @ X779)))))=>(![X1473:$i > $i > $o, X1474:$i]:((![X1475:$i]:(((in @ X1475 @ X1474)=>?[X1476:$i]:(((X1473 @ X1475 @ X1476)&![X1477:$i]:(((X1473 @ X1475 @ X1477)=>((X1476)=(X1477))))))))=>?[X1478:$i]:(![X1479:$i]:(((in @ X1479 @ X1478)<=>?[X1480:$i]:(((in @ X1480 @ X1474)&(X1473 @ X1480 @ X1479))))))))=>(![X782:$i]:((?[X783:$i]:((in @ X783 @ X782))=>?[X784:$i]:(((in @ X784 @ X782)&~(?[X785:$i]:(((in @ X785 @ X784)&(in @ X785 @ X782))))))))=>((epred1_0)=>(![X1470:$i > $o]:((?[X1471:$i]:(((X1470 @ X1471)&![X1472:$i]:(((X1470 @ X1472)=>((X1471)=(X1472))))))=>(X1470 @ (descr @ (^[Z0/* 17 */:$i]:(X1470 @ Z0))))))=>(![X1467:$i, X1468:$i > $o, X1469:$i]:(((in @ X1469 @ X1467)=>((X1468 @ X1469)=>(in @ X1469 @ (dsetconstr @ X1467 @ X1468)))))=>(![X805:$i, X806:$i > $o, X807:$i]:(((in @ X807 @ (dsetconstr @ X805 @ X806))=>(in @ X807 @ X805)))=>(![X1464:$i, X1465:$i > $o, X1466:$i]:(((in @ X1466 @ (dsetconstr @ X1464 @ X1465))=>(X1465 @ X1466)))=>(![X808:$i > $o]:((?[X809:$i]:(((X808 @ X809)&![X810:$i]:(((X808 @ X810)=>((X809)=(X810))))))=>?[X811:$i]:(((X808 @ X811)&![X812:$i]:(((X808 @ X812)=>((X811)=(X812))))))))=>(![X1462:$o, X1463:$i]:(((in @ X1463 @ (prop2set @ ((X1462))))=>(X1462)))=>(![X1460:$i]:(((in @ X1460 @ emptyset)=>![X1461:$o]:((X1461))))=>(![X813:$i]:(((in @ X813 @ emptyset)=>~($true)))=>(![X814:$i]:(~(in @ X814 @ emptyset))=>(![X1456:$i > $o]:((?[X1457:$i]:(((X1456 @ X1457)&![X1458:$i]:(((X1456 @ X1458)=>((X1457)=(X1458))))))=>?[X1459:$i]:((X1456 @ X1459))))=>(![X1452:$i, X1453:$i]:((![X1454:$i]:(((in @ X1454 @ X1452)=>(in @ X1454 @ X1453)))=>(![X1455:$i]:(((in @ X1455 @ X1453)=>(in @ X1455 @ X1452)))=>((X1452)=(X1453)))))=>(![X1450:$i]:((![X1451:$i]:(~(in @ X1451 @ X1450))=>((X1450)=(emptyset))))=>(![X815:$i]:((![X816:$i]:(~(in @ X816 @ X815))=>((X815)=(emptyset))))=>(![X817:$i, X818:$i > $o, X819:$i]:(((in @ X819 @ X817)=>((in @ X819 @ (dsetconstr @ X817 @ X818))<=>(X818 @ X819))))=>(![X1448:$i]:((((X1448)!=(emptyset))=>?[X1449:$i]:((in @ X1449 @ X1448))))=>(![X1445:$i, X1446:$i > $o, X1447:$i]:(((in @ X1447 @ X1445)=>((X1446 @ X1447)=>((dsetconstr @ X1445 @ X1446)!=(emptyset)))))=>(![X820:$i]:((?[X821:$i]:((in @ X821 @ X820))=>((X820)!=(emptyset))))=>(![X822:$i, X823:$i]:((in @ X822 @ (setadjoin @ X822 @ X823)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1442:$i, X1443:$i, X1444:$i]:(((in @ X1444 @ X1443)=>(in @ X1444 @ (setadjoin @ X1442 @ X1443))))=>(![X1438:$i, X1439:$i, X1440:$i]:(((in @ X1440 @ (setadjoin @ X1438 @ X1439))=>![X1441:$o]:(((((X1440)=(X1438))=>(X1441))=>(((in @ X1440 @ X1439)=>(X1441))=>(X1441))))))=>(![X1435:$i, X1436:$i, X1437:$i]:(((in @ X1437 @ (setadjoin @ X1435 @ X1436))=>(((X1437)=(X1435))|(in @ X1437 @ X1436))))=>(![X1434:$i]:(((dsetconstr @ X1434 @ (^[Z0/* 1 */:$i]:($true)))=(X1434)))=>(![X824:$i, X825:$i]:((![X826:$i]:(((in @ X826 @ X825)=>(in @ X826 @ X824)))=>(in @ X825 @ (powerset @ X824))))=>(![X827:$i]:((in @ emptyset @ (powerset @ X827)))=>(![X1433:$i]:((in @ emptyset @ (powerset @ X1433)))=>(![X1430:$i, X1431:$i, X1432:$i]:(((in @ X1431 @ (powerset @ X1430))=>((in @ X1432 @ X1431)=>(in @ X1432 @ X1430))))=>(![X828:$i, X829:$i, X830:$i]:(((in @ X829 @ X830)=>((in @ X830 @ X828)=>(in @ X829 @ (setunion @ X828)))))=>(![X1426:$i, X1427:$i]:(((in @ X1427 @ (setunion @ X1426))=>![X1428:$o]:((![X1429:$i]:(((in @ X1427 @ X1429)=>((in @ X1429 @ X1426)=>(X1428))))=>(X1428)))))=>(![X1424:$i, X1425:$i]:(((in @ X1425 @ X1424)=>(in @ X1425 @ (powerset @ (setunion @ X1424)))))=>(![X831:$i > $o]:((?[X832:$i]:(((X831 @ X832)&![X833:$i]:(((X831 @ X833)=>((X832)=(X833))))))=>?[X834:$i]:(![X835:$i]:(((X831 @ X835)<=>((X835)=(X834)))))))=>(![X836:$i]:((((X836)!=(emptyset))=>?[X837:$i]:(((in @ X837 @ X836)&$true))))=>(![X838:$i, X839:$i]:(((in @ X838 @ (setadjoin @ X839 @ emptyset))=>((X838)=(X839))))=>(![X1422:$i, X1423:$i]:((((X1422)!=(X1423))=>~(in @ X1423 @ (setadjoin @ X1422 @ emptyset))))=>(![X840:$i, X841:$i]:((((X840)=(X841))=>(in @ X840 @ (setadjoin @ X841 @ emptyset))))=>(![X842:$i, X843:$i]:(((in @ X842 @ (setadjoin @ X843 @ emptyset))=>(in @ X843 @ (setadjoin @ X842 @ emptyset))))=>(![X1419:$i, X1420:$i, X1421:$i]:(((in @ X1421 @ (setadjoin @ X1419 @ (setadjoin @ X1420 @ emptyset)))=>(((X1421)=(X1419))|((X1421)=(X1420)))))=>(![X844:$i, X845:$i]:((in @ X844 @ (setadjoin @ X844 @ (setadjoin @ X845 @ emptyset))))=>(![X1417:$i, X1418:$i]:((in @ X1418 @ (setadjoin @ X1417 @ (setadjoin @ X1418 @ emptyset))))=>(![X846:$i, X847:$i > $o]:((?[X848:$i]:(((in @ X848 @ X846)&(X847 @ X848)))=>(((dsetconstr @ X846 @ X847)=(emptyset))=>~($true))))=>(![X1415:$i > $o, X1416:$i]:(((in @ X1416 @ emptyset)=>(X1415 @ X1416)))=>(![X1411:$i, X1412:$i > $o]:((~(![X1413:$i]:(((in @ X1413 @ X1411)=>(X1412 @ X1413))))=>?[X1414:$i]:(((in @ X1414 @ X1411)&~((X1412 @ X1414))))))=>(![X849:$i, X850:$i > $o]:((![X851:$i]:(((in @ X851 @ X849)=>~((X850 @ X851))))=>~(?[X852:$i]:(((in @ X852 @ X849)&(X850 @ X852))))))=>(![X853:$i, X854:$i > $o]:((~(?[X855:$i]:(((in @ X855 @ X853)&(X854 @ X855))))=>![X856:$i]:(((in @ X856 @ X853)=>~((X854 @ X856))))))=>(![X857:$i, X858:$i > 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_252]), foundationAx]), wellorderingAx]), c_0_253]), c_0_254]), c_0_255]), c_0_256]), c_0_257]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_258]), setext]), emptyI]), noeltsimpempty]), c_0_259]), c_0_260]), c_0_261]), c_0_262]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_263]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_264]), c_0_265]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_266]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_267]), c_0_268]), c_0_269]), inCongP]), in__Cong]), c_0_270]), c_0_271]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_272]), c_0_273]), c_0_274]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_275]), c_0_276]), 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_277]), c_0_278]), c_0_279]), c_0_280]), singletonsuniq]), setukpairinjL1]), c_0_281]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_282]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_283]), c_0_284]), c_0_285]), c_0_286]), c_0_287]), c_0_288]), c_0_289]), c_0_290]), c_0_291]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_292]), c_0_293]), c_0_294]), c_0_295]), c_0_296]), c_0_297]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_298]), c_0_299]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_300]), c_0_301]), c_0_302]), c_0_303]), c_0_304]), c_0_305]), c_0_306]), c_0_307]), c_0_308]), c_0_309]), ifp]), theeq]), iftrue])])]), c_0_310])). 0.37/1.02 thf(c_0_312, plain, ![X1484:$i, X1485:$o, X1486:$i, X1487:$i]:(((if @ X1484 @ ((X1485)) @ X1486 @ X1487)=(setunion @ (dsetconstr @ X1484 @ (^[Z0/* 9 */:$i]:((((X1485)&((Z0)=(X1486)))|(~((X1485))&((Z0)=(X1487)))))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[if])])). 0.37/1.02 thf(c_0_313, negated_conjecture, ![X1492:$i, X1493:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1505:$i, X1506:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1514:$i, X1515:$i > $i > $o, X1516:$i, X1518:$i, X1521:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1528:$i, X1529:$i > $o, X1530:$i, X1532:$i, X1533:$i > $o, X1534:$i, X1535:$i, X1536:$i > $o, X1537:$i, X1538:$i, X1539:$i > $o, X1540:$i, X1541:$i > $o, X1542:$i, X1545:$i, X1546:$o, X1547:$i, X1548:$i, X1549:$o, X1550:$i, X1551:$i, X1552:$i > $o, X1553:$i, X1556:$i, X1557:$i, X1560:$i, X1562:$i, X1564:$i, X1565:$i > $o, X1566:$i, X1567:$i, X1569:$i, X1570:$i > $o, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$o, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$i, X1600:$o, X1602:$i, X1603:$i, X1604:$i > $o, X1605:$i, X1608:$i, X1609:$i, X1610:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i, X1627:$i, X1628:$i > $o, X1629:$i, X1630:$i > $o, X1631:$i, X1632:$i, X1633:$i > $o, X1634:$i, X1636:$i, X1637:$i > $o, X1639:$i, X1640:$i, X1641:$i > $o, X1643:$i, X1644:$i, X1645:$i > $o, X1646:$i, X1648:$o, X1649:$o, X1650:$i, X1651:$i > $o, X1653:$i, X1654:$i, X1655:$i > $o, X1656:$i, X1658:$i > $o, X1659:$i, X1662:$i, X1663:$i > $o, X1664:$i, X1668:$i, X1669:$i > $o, X1670:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i > $o, X1683:$i, X1685:$i, X1686:$i, X1687:$i > $o, X1688:$i > $o, X1691:$i, X1694:$i, X1695:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i > $o, X1708:$i, X1710:$i, X1711:$i, X1712:$i > $o, X1713:$i > $o, X1716:$i, X1718:$i, X1720:$i, X1721:$i, X1722:$i > $o, X1723:$i > $o, X1726:$i, X1727:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1767:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1773:$i > $o, X1774:$i, X1775:$i > $o, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$o, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$o, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1874:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i, X1880:$i, X1881:$i, X1882:$i, X1883:$i, X1884:$i, X1885:$i, X1886:$i, X1887:$i, X1888:$i, X1889:$i, X1890:$i, X1891:$i, X1892:$i, X1893:$i, X1894:$i, X1895:$i, X1896:$i, X1897:$i, X1898:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1905:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i > $o, X1930:$i, X1931:$i, X1932:$i > $o, X1934:$i, X1935:$i > $o, X1936:$i, X1938:$i, X1939:$i > $o, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i, X1979:$i, X1980:$i, X1981:$i, X1982:$i, X1983:$i, X1984:$i, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i > $i > $o, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i > $i > $o, X2020:$i, X2021:$i, X2022:$i > $i > $o, X2023:$i, X2024:$i, X2025:$i > $i > $o, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i > $i > $o, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i > $i > $o, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i > $i > $o, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2050:$i, X2051:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i > $i, X2069:$i, X2070:$i, X2071:$i > $i, X2073:$i, X2074:$i, X2075:$i > $i, X2077:$i, X2078:$i, X2079:$i, X2080:$i > $o, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i > $o, X2090:$i, X2091:$i, X2092:$i > $o, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i > $i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i > $i, X2164:$i, X2165:$i, X2166:$i > $i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, 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(esk74_4 @ X2126 @ X2127 @ X2128 @ X2129) @ (esk75_4 @ X2126 @ X2127 @ X2128 @ X2129)) @ X2128)|~(subset @ X2129 @ (cartprod @ X2126 @ X2127))|~(subset @ X2128 @ (cartprod @ X2126 @ X2127))))))&(((in @ (esk76_4 @ X2126 @ X2127 @ X2128 @ X2129) @ X2126)|((X2128)=(X2129))|~(in @ (kpair @ (esk74_4 @ X2126 @ X2127 @ X2128 @ X2129) @ (esk75_4 @ X2126 @ X2127 @ X2128 @ X2129)) @ X2129)|~(subset @ X2129 @ (cartprod @ X2126 @ X2127))|~(subset @ X2128 @ (cartprod @ X2126 @ X2127)))&(((in @ (esk77_4 @ X2126 @ X2127 @ X2128 @ X2129) @ X2127)|((X2128)=(X2129))|~(in @ (kpair @ (esk74_4 @ X2126 @ X2127 @ X2128 @ X2129) @ (esk75_4 @ X2126 @ X2127 @ X2128 @ X2129)) @ X2129)|~(subset @ X2129 @ (cartprod @ X2126 @ X2127))|~(subset @ X2128 @ (cartprod @ X2126 @ X2127)))&(((in @ (kpair @ (esk76_4 @ X2126 @ X2127 @ X2128 @ X2129) @ (esk77_4 @ X2126 @ X2127 @ X2128 @ X2129)) @ X2129)|((X2128)=(X2129))|~(in @ (kpair @ (esk74_4 @ X2126 @ X2127 @ X2128 @ X2129) @ (esk75_4 @ X2126 @ X2127 @ X2128 @ X2129)) @ X2129)|~(subset @ X2129 @ (cartprod @ X2126 @ X2127))|~(subset @ X2128 @ (cartprod @ X2126 @ X2127)))&(~(in @ (kpair @ (esk76_4 @ X2126 @ X2127 @ X2128 @ X2129) @ (esk77_4 @ X2126 @ X2127 @ X2128 @ X2129)) @ X2128)|((X2128)=(X2129))|~(in @ (kpair @ (esk74_4 @ X2126 @ X2127 @ X2128 @ X2129) @ (esk75_4 @ X2126 @ X2127 @ X2128 @ X2129)) @ X2129)|~(subset @ X2129 @ (cartprod @ X2126 @ X2127))|~(subset @ X2128 @ (cartprod @ X2126 @ X2127)))))))))&((((in @ (esk78_4 @ X2134 @ X2135 @ X2136 @ X2137) @ X2134)|((X2136)=(X2137))|~(func @ X2134 @ X2135 @ X2137)|~(func @ X2134 @ X2135 @ X2136))&(((ap @ X2134 @ X2135 @ X2136 @ (esk78_4 @ X2134 @ X2135 @ X2136 @ X2137))!=(ap @ X2134 @ X2135 @ X2137 @ (esk78_4 @ X2134 @ X2135 @ X2136 @ X2137)))|((X2136)=(X2137))|~(func @ X2134 @ X2135 @ X2137)|~(func @ X2134 @ X2135 @ X2136)))&((((in @ (esk79_4 @ X2139 @ X2140 @ X2141 @ X2142) @ X2139)|((X2141)=(X2142))|~(in @ X2142 @ (funcSet @ X2139 @ X2140))|~(in @ X2141 @ (funcSet @ X2139 @ X2140)))&(((ap @ X2139 @ X2140 @ X2141 @ (esk79_4 @ X2139 @ X2140 @ X2141 @ X2142))!=(ap @ X2139 @ X2140 @ X2142 @ (esk79_4 @ X2139 @ X2140 @ X2141 @ X2142)))|((X2141)=(X2142))|~(in @ X2142 @ (funcSet @ X2139 @ X2140))|~(in @ X2141 @ (funcSet @ X2139 @ X2140))))&((~(in @ X2146 @ (funcSet @ X2144 @ X2145))|(~(in @ X2147 @ X2144)|((ap @ X2144 @ X2145 @ X2146 @ X2147)=(ap @ X2144 @ X2145 @ X2146 @ X2147))))&((~(func @ X2148 @ X2149 @ X2150)|(~(in @ X2151 @ X2148)|((ap @ X2148 @ X2149 @ X2150 @ X2151)=(ap @ X2148 @ X2149 @ X2150 @ X2151))))&((((in @ (esk80_3 @ X2152 @ X2153 @ X2154) @ X2152)|(~(in @ X2156 @ X2152)|((ap @ X2152 @ X2153 @ (lam @ X2152 @ X2153 @ X2154) @ X2156)=(X2154 @ X2156))))&(~(in @ (X2154 @ (esk80_3 @ X2152 @ X2153 @ X2154)) @ X2153)|(~(in @ X2156 @ X2152)|((ap @ X2152 @ X2153 @ (lam @ X2152 @ X2153 @ X2154) @ X2156)=(X2154 @ X2156)))))&((~(func @ X2157 @ X2158 @ X2159)|((lam @ X2157 @ X2158 @ (ap @ X2157 @ X2158 @ X2159))=(X2159)))&((((in @ (esk81_3 @ X2160 @ X2161 @ X2162) @ X2160)|((lam @ X2160 @ X2161 @ X2162)=(lam @ X2160 @ X2161 @ X2162)))&(~(in @ (X2162 @ (esk81_3 @ X2160 @ X2161 @ X2162)) @ X2161)|((lam @ X2160 @ X2161 @ X2162)=(lam @ X2160 @ X2161 @ X2162))))&((((in @ (esk82_3 @ X2164 @ X2165 @ X2166) @ X2164)|(~(in @ X2168 @ X2164)|((ap @ X2164 @ X2165 @ (lam @ X2164 @ X2165 @ X2166) @ X2168)=(X2166 @ X2168))))&(~(in @ (X2166 @ (esk82_3 @ X2164 @ X2165 @ X2166)) @ X2165)|(~(in @ X2168 @ X2164)|((ap @ X2164 @ X2165 @ (lam @ X2164 @ X2165 @ X2166) @ X2168)=(X2166 @ X2168)))))&((~(in @ X2171 @ (funcSet @ X2169 @ X2170))|((lam @ X2169 @ X2170 @ (ap @ X2169 @ X2170 @ X2171))=(X2171)))&((~(in @ X2174 @ X2172)|(~(in @ X2175 @ X2172)|((X2173)|(in @ X2175 @ (dsetconstr @ X2172 @ (^[Z0/* 9 */:$i]:((((X2173)&((Z0)=(X2174)))|(~((X2173))&((Z0)=(X2175)))))))))))&((~(in @ X2178 @ X2176)|(~(in @ X2179 @ X2176)|((X2177)|((dsetconstr @ X2176 @ (^[Z0/* 9 */:$i]:((((X2177)&((Z0)=(X2178)))|(~((X2177))&((Z0)=(X2179)))))))=(setadjoin @ X2179 @ emptyset)))))&((~(in @ X2182 @ X2180)|(~(in @ X2183 @ X2180)|(~(X2181)|(in @ X2182 @ (dsetconstr @ X2180 @ (^[Z0/* 9 */:$i]:((((X2181)&((Z0)=(X2182)))|(~((X2181))&((Z0)=(X2183)))))))))))&((~(in @ X2186 @ X2184)|(~(in @ X2187 @ X2184)|(~(X2185)|((dsetconstr @ X2184 @ (^[Z0/* 9 */:$i]:((((X2185)&((Z0)=(X2186)))|(~((X2185))&((Z0)=(X2187)))))))=(setadjoin @ X2186 @ emptyset)))))&((~(in @ X2190 @ X2188)|(~(in @ X2191 @ X2188)|(singleton @ (dsetconstr @ X2188 @ (^[Z0/* 9 */:$i]:((((X2189)&((Z0)=(X2190)))|(~((X2189))&((Z0)=(X2191))))))))))&((~(in @ X2194 @ X2192)|(~(in @ X2195 @ X2192)|(in @ (if @ X2192 @ ((X2193)) @ X2194 @ X2195) @ X2192)))&((~(singleton @ X2196)|(~(in @ X2197 @ X2196)|((setunion @ X2196)=(X2197))))&((~(in @ X2200 @ X2198)|(~(in @ X2201 @ X2198)|(~(X2199)|((if @ X2198 @ ((X2199)) @ X2200 @ X2201)=(X2200)))))&((in @ esk84_0 @ esk83_0)&((in @ esk85_0 @ esk83_0)&(~(epred2_0)&(((~(epred2_0)|(epred2_0))&(((if @ esk83_0 @ $false @ esk84_0 @ esk85_0)!=(esk85_0))|(epred2_0)))&((~(epred2_0)|((if @ esk83_0 @ $true @ esk84_0 @ esk85_0)!=(esk85_0)))&(((if @ esk83_0 @ $false @ esk84_0 @ esk85_0)!=(esk85_0))|((if @ esk83_0 @ $true @ esk84_0 @ esk85_0)!=(esk85_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_311])])])])])])])])). 0.37/1.02 thf(c_0_314, plain, ![X1488:$i, X1489:$o, X1490:$i, X1491:$i]:(((if @ X1488 @ ((X1489)) @ X1490 @ X1491)=(setunion @ (dsetconstr @ X1488 @ (^[Z0/* 9 */:$i]:((((X1489)&((Z0)=(X1490)))|(~((X1489))&((Z0)=(X1491)))))))))), inference(variable_rename,[status(thm)],[c_0_312])). 0.37/1.02 thf(c_0_315, negated_conjecture, ((epred2_0)|((if @ esk83_0 @ (~($true)) @ esk84_0 @ esk85_0)!=(esk85_0))), inference(split_conjunct,[status(thm)],[c_0_313])). 0.37/1.02 thf(c_0_316, plain, ![X2:$i, X3:$i, X10:$o, X4:$i]:(((if @ X2 @ ((X10)) @ X3 @ X4)=(setunion @ (dsetconstr @ X2 @ (^[Z0/* 9 */:$i]:((((X10)&((Z0)=(X3)))|(~((X10))&((Z0)=(X4)))))))))), inference(split_conjunct,[status(thm)],[c_0_314])). 0.37/1.02 thf(c_0_317, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:((((if @ X3 @ (($true)) @ X2 @ X4)=(X2))|~((in @ X2 @ X3))|~((in @ X4 @ X3)))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_313])])])). 0.37/1.02 thf(c_0_318, negated_conjecture, ((epred2_0)|((setunion @ (dsetconstr @ esk83_0 @ (^[Z0/* 9 */:$i]:(((~($true)&((Z0)=(esk84_0)))|(~(~($true))&((Z0)=(esk85_0))))))))!=(esk85_0))), inference(rw,[status(thm)],[c_0_315, c_0_316])). 0.37/1.02 thf(c_0_319, negated_conjecture, ~((epred2_0)), inference(split_conjunct,[status(thm)],[c_0_313])). 0.37/1.02 thf(c_0_320, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:((((setunion @ (dsetconstr @ X3 @ (^[Z0/* 9 */:$i]:(((($true)&((Z0)=(X2)))|(~(($true))&((Z0)=(X4))))))))=(X2))|~((in @ X4 @ X3))|~((in @ X2 @ X3)))), inference(rw,[status(thm)],[c_0_317, c_0_316])). 0.37/1.02 thf(c_0_321, negated_conjecture, ((setunion @ (dsetconstr @ esk83_0 @ (^[Z0/* 3 */:$i]:(((Z0)=(esk85_0))))))!=(esk85_0)), inference(cn,[status(thm)],[inference(sr,[status(thm)],[c_0_318, c_0_319])])). 0.37/1.02 thf(c_0_322, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:((((setunion @ (dsetconstr @ X2 @ (^[Z0/* 3 */:$i]:(((Z0)=(X3))))))=(X3))|~((in @ X4 @ X2))|~((in @ X3 @ X2)))), inference(cn,[status(thm)],[c_0_320])). 0.37/1.02 thf(c_0_323, negated_conjecture, (in @ esk85_0 @ esk83_0), inference(split_conjunct,[status(thm)],[c_0_313])). 0.37/1.02 thf(c_0_324, negated_conjecture, (in @ esk84_0 @ esk83_0), inference(split_conjunct,[status(thm)],[c_0_313])). 0.37/1.02 thf(c_0_325, plain, ![X2:$i]:(~((in @ X2 @ esk83_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_321, c_0_322])])]), c_0_323])])). 0.37/1.02 thf(c_0_326, negated_conjecture, ($false), inference(sr,[status(thm)],[c_0_324, c_0_325]), ['proof']). 0.37/1.02 # SZS output end CNFRefutation 0.37/1.02 # Parsed axioms : 492 0.37/1.02 # Removed by relevancy pruning/SinE : 0 0.37/1.02 # Initial clauses : 663 0.37/1.02 # Removed in clause preprocessing : 293 0.37/1.02 # Initial clauses in saturation : 370 0.37/1.02 # Processed clauses : 710 0.37/1.02 # ...of these trivial : 10 0.37/1.02 # ...subsumed : 31 0.37/1.02 # ...remaining for further processing : 669 0.37/1.02 # Other redundant clauses eliminated : 52 0.37/1.02 # Clauses deleted for lack of memory : 0 0.37/1.02 # Backward-subsumed : 2 0.37/1.02 # Backward-rewritten : 2 0.37/1.02 # Generated clauses : 8168 0.37/1.02 # ...of the previous two non-redundant : 7941 0.37/1.02 # ...aggressively subsumed : 0 0.37/1.02 # Contextual simplify-reflections : 0 0.37/1.02 # Paramodulations : 8079 0.37/1.02 # Factorizations : 2 0.37/1.02 # NegExts : 1 0.37/1.02 # Equation resolutions : 59 0.37/1.02 # Disequality decompositions : 0 0.37/1.02 # Total rewrite steps : 199 0.37/1.02 # ...of those cached : 136 0.37/1.02 # Propositional unsat checks : 0 0.37/1.02 # Propositional check models : 0 0.37/1.02 # Propositional check unsatisfiable : 0 0.37/1.02 # Propositional clauses : 0 0.37/1.02 # Propositional clauses after purity: 0 0.37/1.02 # Propositional unsat core size : 0 0.37/1.02 # Propositional preprocessing time : 0.000 0.37/1.02 # Propositional encoding time : 0.000 0.37/1.02 # Propositional solver time : 0.000 0.37/1.02 # Success case prop preproc time : 0.000 0.37/1.02 # Success case prop encoding time : 0.000 0.37/1.02 # Success case prop solver time : 0.000 0.37/1.02 # Current number of processed clauses : 325 0.37/1.02 # Positive orientable unit clauses : 30 0.37/1.02 # Positive unorientable unit clauses: 0 0.37/1.02 # Negative unit clauses : 4 0.37/1.02 # Non-unit-clauses : 291 0.37/1.02 # Current number of unprocessed clauses: 7921 0.37/1.02 # ...number of literals in the above : 35000 0.37/1.02 # Current number of archived formulas : 0 0.37/1.02 # Current number of archived clauses : 330 0.37/1.02 # Clause-clause subsumption calls (NU) : 46952 0.37/1.02 # Rec. Clause-clause subsumption calls : 17801 0.37/1.02 # Non-unit clause-clause subsumptions : 25 0.37/1.02 # Unit Clause-clause subsumption calls : 90 0.37/1.02 # Rewrite failures with RHS unbound : 0 0.37/1.02 # BW rewrite match attempts : 23 0.37/1.02 # BW rewrite match successes : 2 0.37/1.02 # Condensation attempts : 0 0.37/1.02 # Condensation successes : 0 0.37/1.02 # Termbank termtop insertions : 225814 0.37/1.02 # Search garbage collected termcells : 24735 0.37/1.02 0.37/1.02 # ------------------------------------------------- 0.37/1.02 # User time : 0.401 s 0.37/1.02 # System time : 0.026 s 0.37/1.02 # Total time : 0.427 s 0.37/1.02 # Maximum resident set size: 7544 pages 0.37/1.02 0.37/1.02 # ------------------------------------------------- 0.37/1.02 # User time : 0.413 s 0.37/1.02 # System time : 0.032 s 0.37/1.02 # Total time : 0.445 s 0.37/1.02 # Maximum resident set size: 2608 pages 0.37/1.02 % E exiting 0.37/1.02 % E exiting 0.37/1.02 EOF