0.05/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.11 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM 0.09/0.31 % Computer : n029.cluster.edu 0.09/0.31 % Model : x86_64 x86_64 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.31 % Memory : 8042.1875MB 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.31 % CPULimit : 1920 0.09/0.31 % WCLimit : 240 0.09/0.31 % DateTime : Wed Jul 30 09:34:49 EDT 2025 0.15/0.31 % CPUTime : 0.15/0.40 Running higher-order theorem proving 0.15/0.43 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p 359.80/46.12 # Version: 3.0.0-ho 359.80/46.12 # Preprocessing class: HSLMSLSSLLLCHFA. 359.80/46.12 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 359.80/46.12 # Starting ehoh_best5 with 240s (1) cores 359.80/46.12 # Starting almost_fo_3_lam with 240s (1) cores 359.80/46.12 # Starting new_bool_5 with 240s (1) cores 359.80/46.12 # Starting pre_casc_3 with 240s (1) cores 359.80/46.12 # Starting ho_unfolding_8 with 240s (1) cores 359.80/46.12 # Starting new_ho_10_cnf2 with 240s (1) cores 359.80/46.12 # Starting new_bool_3 with 240s (1) cores 359.80/46.12 # Starting new_ho_5 with 240s (1) cores 359.80/46.12 # almost_fo_3_lam with pid 29681 completed with status 0 359.80/46.12 # Result found by almost_fo_3_lam 359.80/46.12 # Preprocessing class: HSLMSLSSLLLCHFA. 359.80/46.12 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 359.80/46.12 # Starting ehoh_best5 with 240s (1) cores 359.80/46.12 # Starting almost_fo_3_lam with 240s (1) cores 359.80/46.12 # No SInE strategy applied 359.80/46.12 # Search class: HGHSM-FSLM32-MHFMMSBN 359.80/46.12 # Scheduled 10 strats onto 1 cores with 240 seconds (240 total) 359.80/46.12 # Starting ho_unfolding_8 with 44s (1) cores 359.80/46.12 # ho_unfolding_8 with pid 29694 completed with status 8 359.80/46.12 # Starting almost_fo_3_lam with 25s (1) cores 359.80/46.12 # almost_fo_3_lam with pid 32685 completed with status 0 359.80/46.12 # Result found by almost_fo_3_lam 359.80/46.12 # Preprocessing class: HSLMSLSSLLLCHFA. 359.80/46.12 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 359.80/46.12 # Starting ehoh_best5 with 240s (1) cores 359.80/46.12 # Starting almost_fo_3_lam with 240s (1) cores 359.80/46.12 # No SInE strategy applied 359.80/46.12 # Search class: HGHSM-FSLM32-MHFMMSBN 359.80/46.12 # Scheduled 10 strats onto 1 cores with 240 seconds (240 total) 359.80/46.12 # Starting ho_unfolding_8 with 44s (1) cores 359.80/46.12 # ho_unfolding_8 with pid 29694 completed with status 8 359.80/46.12 # Starting almost_fo_3_lam with 25s (1) cores 359.80/46.12 # Preprocessing time : 0.009 s 359.80/46.12 # Presaturation interreduction done 359.80/46.12 359.80/46.12 # Proof found! 359.80/46.12 # SZS status Theorem 359.80/46.12 # SZS output start CNFRefutation 359.80/46.12 thf(decl_23, type, in: $i > $i > $o). 359.80/46.12 thf(decl_24, type, exu: ($i > $o) > $o). 359.80/46.12 thf(decl_25, type, setextAx: $o). 359.80/46.12 thf(decl_26, type, emptyset: $i). 359.80/46.12 thf(decl_27, type, emptysetAx: $o). 359.80/46.12 thf(decl_28, type, setadjoin: $i > $i > $i). 359.80/46.12 thf(decl_29, type, setadjoinAx: $o). 359.80/46.12 thf(decl_30, type, powerset: $i > $i). 359.80/46.12 thf(decl_31, type, powersetAx: $o). 359.80/46.12 thf(decl_32, type, setunion: $i > $i). 359.80/46.12 thf(decl_33, type, setunionAx: $o). 359.80/46.12 thf(decl_34, type, omega: $i). 359.80/46.12 thf(decl_35, type, omega0Ax: $o). 359.80/46.12 thf(decl_36, type, omegaSAx: $o). 359.80/46.12 thf(decl_37, type, omegaIndAx: $o). 359.80/46.12 thf(decl_38, type, replAx: $o). 359.80/46.12 thf(decl_39, type, foundationAx: $o). 359.80/46.12 thf(decl_40, type, wellorderingAx: $o). 359.80/46.12 thf(decl_41, type, descr: ($i > $o) > $i). 359.80/46.12 thf(decl_42, type, descrp: $o). 359.80/46.12 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 359.80/46.12 thf(decl_44, type, dsetconstrI: $o). 359.80/46.12 thf(decl_45, type, dsetconstrEL: $o). 359.80/46.12 thf(decl_46, type, dsetconstrER: $o). 359.80/46.12 thf(decl_47, type, exuE1: $o). 359.80/46.12 thf(decl_48, type, prop2set: $o > $i). 359.80/46.12 thf(decl_49, type, prop2setE: $o). 359.80/46.12 thf(decl_50, type, emptysetE: $o). 359.80/46.12 thf(decl_51, type, emptysetimpfalse: $o). 359.80/46.12 thf(decl_52, type, notinemptyset: $o). 359.80/46.12 thf(decl_53, type, exuE3e: $o). 359.80/46.12 thf(decl_54, type, setext: $o). 359.80/46.12 thf(decl_55, type, emptyI: $o). 359.80/46.12 thf(decl_56, type, noeltsimpempty: $o). 359.80/46.12 thf(decl_57, type, setbeta: $o). 359.80/46.12 thf(decl_58, type, nonempty: $i > $o). 359.80/46.12 thf(decl_59, type, nonemptyE1: $o). 359.80/46.12 thf(decl_60, type, nonemptyI: $o). 359.80/46.12 thf(decl_61, type, nonemptyI1: $o). 359.80/46.12 thf(decl_62, type, setadjoinIL: $o). 359.80/46.12 thf(decl_63, type, emptyinunitempty: $o). 359.80/46.12 thf(decl_64, type, setadjoinIR: $o). 359.80/46.12 thf(decl_65, type, setadjoinE: $o). 359.80/46.12 thf(decl_66, type, setadjoinOr: $o). 359.80/46.12 thf(decl_67, type, setoftrueEq: $o). 359.80/46.12 thf(decl_68, type, powersetI: $o). 359.80/46.12 thf(decl_69, type, emptyinPowerset: $o). 359.80/46.12 thf(decl_70, type, emptyInPowerset: $o). 359.80/46.12 thf(decl_71, type, powersetE: $o). 359.80/46.12 thf(decl_72, type, setunionI: $o). 359.80/46.12 thf(decl_73, type, setunionE: $o). 359.80/46.12 thf(decl_74, type, subPowSU: $o). 359.80/46.12 thf(decl_75, type, exuE2: $o). 359.80/46.12 thf(decl_76, type, nonemptyImpWitness: $o). 359.80/46.12 thf(decl_77, type, uniqinunit: $o). 359.80/46.12 thf(decl_78, type, notinsingleton: $o). 359.80/46.12 thf(decl_79, type, eqinunit: $o). 359.80/46.12 thf(decl_80, type, singletonsswitch: $o). 359.80/46.12 thf(decl_81, type, upairsetE: $o). 359.80/46.12 thf(decl_82, type, upairsetIL: $o). 359.80/46.12 thf(decl_83, type, upairsetIR: $o). 359.80/46.12 thf(decl_84, type, emptyE1: $o). 359.80/46.12 thf(decl_85, type, vacuousDall: $o). 359.80/46.12 thf(decl_86, type, quantDeMorgan1: $o). 359.80/46.12 thf(decl_87, type, quantDeMorgan2: $o). 359.80/46.12 thf(decl_88, type, quantDeMorgan3: $o). 359.80/46.12 thf(decl_89, type, quantDeMorgan4: $o). 359.80/46.12 thf(decl_90, type, prop2setI: $o). 359.80/46.12 thf(decl_91, type, set2prop: $i > $o). 359.80/46.12 thf(decl_92, type, prop2set2propI: $o). 359.80/46.12 thf(decl_93, type, notdexE: $o). 359.80/46.12 thf(decl_94, type, notdallE: $o). 359.80/46.12 thf(decl_95, type, exuI1: $o). 359.80/46.12 thf(decl_96, type, exuI3: $o). 359.80/46.12 thf(decl_97, type, exuI2: $o). 359.80/46.12 thf(decl_98, type, inCongP: $o). 359.80/46.12 thf(decl_99, type, in__Cong: $o). 359.80/46.12 thf(decl_100, type, exuE3u: $o). 359.80/46.12 thf(decl_101, type, exu__Cong: $o). 359.80/46.12 thf(decl_102, type, emptyset__Cong: $o). 359.80/46.12 thf(decl_103, type, setadjoin__Cong: $o). 359.80/46.12 thf(decl_104, type, powerset__Cong: $o). 359.80/46.12 thf(decl_105, type, setunion__Cong: $o). 359.80/46.12 thf(decl_106, type, omega__Cong: $o). 359.80/46.12 thf(decl_107, type, exuEu: $o). 359.80/46.12 thf(decl_108, type, descr__Cong: $o). 359.80/46.12 thf(decl_109, type, dsetconstr__Cong: $o). 359.80/46.12 thf(decl_110, type, subset: $i > $i > $o). 359.80/46.12 thf(decl_113, type, subsetI1: $o). 359.80/46.12 thf(decl_114, type, eqimpsubset2: $o). 359.80/46.12 thf(decl_115, type, eqimpsubset1: $o). 359.80/46.12 thf(decl_116, type, subsetI2: $o). 359.80/46.12 thf(decl_117, type, emptysetsubset: $o). 359.80/46.12 thf(decl_118, type, subsetE: $o). 359.80/46.12 thf(decl_119, type, subsetE2: $o). 359.80/46.12 thf(decl_120, type, notsubsetI: $o). 359.80/46.12 thf(decl_121, type, notequalI1: $o). 359.80/46.12 thf(decl_122, type, notequalI2: $o). 359.80/46.12 thf(decl_123, type, subsetRefl: $o). 359.80/46.12 thf(decl_124, type, subsetTrans: $o). 359.80/46.12 thf(decl_125, type, setadjoinSub: $o). 359.80/46.12 thf(decl_126, type, setadjoinSub2: $o). 359.80/46.12 thf(decl_127, type, subset2powerset: $o). 359.80/46.12 thf(decl_128, type, setextsub: $o). 359.80/46.12 thf(decl_129, type, subsetemptysetimpeq: $o). 359.80/46.12 thf(decl_130, type, powersetI1: $o). 359.80/46.12 thf(decl_131, type, powersetE1: $o). 359.80/46.12 thf(decl_132, type, inPowerset: $o). 359.80/46.12 thf(decl_133, type, powersetsubset: $o). 359.80/46.12 thf(decl_134, type, sepInPowerset: $o). 359.80/46.12 thf(decl_135, type, sepSubset: $o). 359.80/46.12 thf(decl_136, type, binunion: $i > $i > $i). 359.80/46.12 thf(decl_137, type, binunionIL: $o). 359.80/46.12 thf(decl_138, type, upairset2IR: $o). 359.80/46.12 thf(decl_139, type, binunionIR: $o). 359.80/46.12 thf(decl_140, type, binunionEcases: $o). 359.80/46.12 thf(decl_141, type, binunionE: $o). 359.80/46.12 thf(decl_142, type, binunionLsub: $o). 359.80/46.12 thf(decl_143, type, binunionRsub: $o). 359.80/46.12 thf(decl_144, type, binintersect: $i > $i > $i). 359.80/46.12 thf(decl_145, type, binintersectI: $o). 359.80/46.12 thf(decl_146, type, binintersectSubset5: $o). 359.80/46.12 thf(decl_147, type, binintersectEL: $o). 359.80/46.12 thf(decl_148, type, binintersectLsub: $o). 359.80/46.12 thf(decl_149, type, binintersectSubset2: $o). 359.80/46.12 thf(decl_150, type, binintersectSubset3: $o). 359.80/46.12 thf(decl_151, type, binintersectER: $o). 359.80/46.12 thf(decl_152, type, disjointsetsI1: $o). 359.80/46.12 thf(decl_153, type, binintersectRsub: $o). 359.80/46.12 thf(decl_154, type, binintersectSubset4: $o). 359.80/46.12 thf(decl_155, type, binintersectSubset1: $o). 359.80/46.12 thf(decl_156, type, bs114d: $o). 359.80/46.12 thf(decl_158, type, setminus: $i > $i > $i). 359.80/46.12 thf(decl_159, type, setminusI: $o). 359.80/46.12 thf(decl_160, type, setminusEL: $o). 359.80/46.12 thf(decl_161, type, setminusER: $o). 359.80/46.12 thf(decl_162, type, setminusSubset2: $o). 359.80/46.12 thf(decl_163, type, setminusERneg: $o). 359.80/46.12 thf(decl_164, type, setminusELneg: $o). 359.80/46.12 thf(decl_165, type, setminusILneg: $o). 359.80/46.12 thf(decl_166, type, setminusIRneg: $o). 359.80/46.12 thf(decl_167, type, setminusLsub: $o). 359.80/46.12 thf(decl_168, type, setminusSubset1: $o). 359.80/46.12 thf(decl_169, type, symdiff: $i > $i > $i). 359.80/46.12 thf(decl_170, type, symdiffE: $o). 359.80/46.12 thf(decl_171, type, symdiffI1: $o). 359.80/46.12 thf(decl_172, type, symdiffI2: $o). 359.80/46.12 thf(decl_173, type, symdiffIneg1: $o). 359.80/46.12 thf(decl_174, type, symdiffIneg2: $o). 359.80/46.12 thf(decl_175, type, iskpair: $i > $o). 359.80/46.12 thf(decl_176, type, secondinupair: $o). 359.80/46.12 thf(decl_177, type, setukpairIL: $o). 359.80/46.12 thf(decl_178, type, setukpairIR: $o). 359.80/46.12 thf(decl_179, type, kpairiskpair: $o). 359.80/46.12 thf(decl_180, type, kpair: $i > $i > $i). 359.80/46.12 thf(decl_181, type, kpairp: $o). 359.80/46.12 thf(decl_182, type, cartprod: $i > $i > $i). 359.80/46.12 thf(decl_183, type, singletonsubset: $o). 359.80/46.12 thf(decl_184, type, singletoninpowerset: $o). 359.80/46.12 thf(decl_185, type, singletoninpowunion: $o). 359.80/46.12 thf(decl_186, type, upairset2E: $o). 359.80/46.12 thf(decl_187, type, upairsubunion: $o). 359.80/46.12 thf(decl_188, type, upairinpowunion: $o). 359.80/46.12 thf(decl_189, type, ubforcartprodlem1: $o). 359.80/46.12 thf(decl_190, type, ubforcartprodlem2: $o). 359.80/46.12 thf(decl_191, type, ubforcartprodlem3: $o). 359.80/46.12 thf(decl_192, type, cartprodpairin: $o). 359.80/46.12 thf(decl_193, type, cartprodmempair1: $o). 359.80/46.12 thf(decl_194, type, cartprodmempair: $o). 359.80/46.12 thf(decl_195, type, setunionE2: $o). 359.80/46.12 thf(decl_196, type, setunionsingleton1: $o). 359.80/46.12 thf(decl_197, type, setunionsingleton2: $o). 359.80/46.12 thf(decl_198, type, setunionsingleton: $o). 359.80/46.12 thf(decl_199, type, singleton: $i > $o). 359.80/46.12 thf(decl_200, type, singletonprop: $o). 359.80/46.12 thf(decl_201, type, ex1: $i > ($i > $o) > $o). 359.80/46.12 thf(decl_202, type, ex1E1: $o). 359.80/46.12 thf(decl_203, type, ex1I: $o). 359.80/46.12 thf(decl_204, type, ex1I2: $o). 359.80/46.12 thf(decl_205, type, singletonsuniq: $o). 359.80/46.12 thf(decl_210, type, setukpairinjL1: $o). 359.80/46.12 thf(decl_211, type, kfstsingleton: $o). 359.80/46.12 thf(decl_212, type, theprop: $o). 359.80/46.12 thf(decl_213, type, kfst: $i > $i). 359.80/46.12 thf(decl_214, type, kfstpairEq: $o). 359.80/46.12 thf(decl_215, type, cartprodfstin: $o). 359.80/46.12 thf(decl_216, type, setukpairinjL2: $o). 359.80/46.12 thf(decl_217, type, setukpairinjL: $o). 359.80/46.12 thf(decl_218, type, setukpairinjR11: $o). 359.80/46.12 thf(decl_219, type, setukpairinjR12: $o). 359.80/46.12 thf(decl_220, type, setukpairinjR1: $o). 359.80/46.12 thf(decl_221, type, upairequniteq: $o). 359.80/46.12 thf(decl_222, type, setukpairinjR2: $o). 359.80/46.12 thf(decl_223, type, setukpairinjR: $o). 359.80/46.12 thf(decl_224, type, ksndsingleton: $o). 359.80/46.12 thf(decl_225, type, ksnd: $i > $i). 359.80/46.12 thf(decl_226, type, ksndpairEq: $o). 359.80/46.12 thf(decl_227, type, kpairsurjEq: $o). 359.80/46.12 thf(decl_228, type, cartprodsndin: $o). 359.80/46.12 thf(decl_229, type, cartprodpairmemEL: $o). 359.80/46.12 thf(decl_230, type, cartprodpairmemER: $o). 359.80/46.12 thf(decl_231, type, cartprodmempaircEq: $o). 359.80/46.12 thf(decl_232, type, cartprodfstpairEq: $o). 359.80/46.12 thf(decl_233, type, cartprodsndpairEq: $o). 359.80/46.12 thf(decl_234, type, cartprodpairsurjEq: $o). 359.80/46.12 thf(decl_235, type, breln: $i > $i > $i > $o). 359.80/46.12 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 359.80/46.12 thf(decl_237, type, dpsetconstrI: $o). 359.80/46.12 thf(decl_238, type, dpsetconstrSub: $o). 359.80/46.12 thf(decl_239, type, setOfPairsIsBReln: $o). 359.80/46.12 thf(decl_240, type, dpsetconstrERa: $o). 359.80/46.12 thf(decl_241, type, dpsetconstrEL1: $o). 359.80/46.12 thf(decl_242, type, dpsetconstrEL2: $o). 359.80/46.12 thf(decl_243, type, dpsetconstrER: $o). 359.80/46.12 thf(decl_244, type, func: $i > $i > $i > $o). 359.80/46.12 thf(decl_245, type, funcSet: $i > $i > $i). 359.80/46.12 thf(decl_246, type, funcImageSingleton: $o). 359.80/46.12 thf(decl_247, type, apProp: $o). 359.80/46.12 thf(decl_248, type, ap: $i > $i > $i > $i > $i). 359.80/46.12 thf(decl_249, type, app: $o). 359.80/46.12 thf(decl_250, type, infuncsetfunc: $o). 359.80/46.12 thf(decl_251, type, ap2p: $o). 359.80/46.12 thf(decl_252, type, funcinfuncset: $o). 359.80/46.12 thf(decl_253, type, lamProp: $o). 359.80/46.12 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i). 359.80/46.12 thf(decl_255, type, lamp: $o). 359.80/46.12 thf(decl_256, type, lam2p: $o). 359.80/46.12 thf(decl_257, type, brelnall1: $o). 359.80/46.12 thf(decl_258, type, brelnall2: $o). 359.80/46.12 thf(decl_259, type, ex1E2: $o). 359.80/46.12 thf(decl_260, type, funcGraphProp1: $o). 359.80/46.12 thf(decl_261, type, funcGraphProp3: $o). 359.80/46.12 thf(decl_262, type, funcGraphProp2: $o). 359.80/46.12 thf(decl_263, type, funcextLem: $o). 359.80/46.12 thf(decl_264, type, funcGraphProp4: $o). 359.80/46.12 thf(decl_265, type, subbreln: $o). 359.80/46.12 thf(decl_266, type, eqbreln: $o). 359.80/46.12 thf(decl_267, type, funcext: $o). 359.80/46.12 thf(decl_268, type, funcext2: $o). 359.80/46.12 thf(decl_269, type, ap2apEq1: $o). 359.80/46.12 thf(decl_270, type, ap2apEq2: $o). 359.80/46.12 thf(decl_271, type, beta1: $o). 359.80/46.12 thf(decl_272, type, eta1: $o). 359.80/46.12 thf(decl_273, type, lam2lamEq: $o). 359.80/46.12 thf(decl_274, type, beta2: $o). 359.80/46.12 thf(decl_275, type, eta2: $o). 359.80/46.12 thf(decl_276, type, iffalseProp1: $o). 359.80/46.12 thf(decl_277, type, iffalseProp2: $o). 359.80/46.12 thf(decl_278, type, iftrueProp1: $o). 359.80/46.12 thf(decl_279, type, iftrueProp2: $o). 359.80/46.12 thf(decl_280, type, ifSingleton: $o). 359.80/46.12 thf(decl_281, type, if: $i > $o > $i > $i > $i). 359.80/46.12 thf(decl_282, type, ifp: $o). 359.80/46.12 thf(decl_283, type, theeq: $o). 359.80/46.12 thf(decl_284, type, iftrue: $o). 359.80/46.12 thf(decl_285, type, iffalse: $o). 359.80/46.12 thf(decl_286, type, iftrueorfalse: $o). 359.80/46.12 thf(decl_287, type, binintersectT_lem: $o). 359.80/46.12 thf(decl_288, type, binunionT_lem: $o). 359.80/46.12 thf(decl_289, type, powersetT_lem: $o). 359.80/46.12 thf(decl_290, type, setminusT_lem: $o). 359.80/46.12 thf(decl_291, type, complementT_lem: $o). 359.80/46.12 thf(decl_292, type, setextT: $o). 359.80/46.12 thf(decl_293, type, subsetTI: $o). 359.80/46.12 thf(decl_294, type, powersetTI1: $o). 359.80/46.12 thf(decl_295, type, powersetTE1: $o). 359.80/46.12 thf(decl_296, type, complementTI1: $o). 359.80/46.12 thf(decl_297, type, complementTE1: $o). 359.80/46.12 thf(decl_298, type, binintersectTELcontra: $o). 359.80/46.12 thf(decl_299, type, binintersectTERcontra: $o). 359.80/46.12 thf(decl_300, type, contrasubsetT: $o). 359.80/46.12 thf(decl_301, type, contrasubsetT1: $o). 359.80/46.12 thf(decl_302, type, contrasubsetT2: $o). 359.80/46.12 thf(decl_303, type, contrasubsetT3: $o). 359.80/46.12 thf(decl_304, type, doubleComplementI1: $o). 359.80/46.12 thf(decl_305, type, doubleComplementE1: $o). 359.80/46.12 thf(decl_306, type, epred1_0: $o). 359.80/46.12 thf(decl_307, type, esk1_2: $i > $i > $i). 359.80/46.12 thf(decl_308, type, esk2_2: $i > $i > $i). 359.80/46.12 thf(decl_309, type, esk3_2: $i > $i > $i). 359.80/46.12 thf(decl_310, type, esk4_1: $i > $i). 359.80/46.12 thf(decl_311, type, esk5_2: ($i > $i > $o) > $i > $i). 359.80/46.12 thf(decl_312, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 359.80/46.12 thf(decl_313, type, esk7_2: ($i > $i > $o) > $i > $i). 359.80/46.12 thf(decl_314, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 359.80/46.12 thf(decl_315, type, esk9_1: $i > $i). 359.80/46.12 thf(decl_316, type, esk10_2: ($i > $o) > $i > $i). 359.80/46.12 thf(decl_317, type, esk11_2: ($i > $o) > $i > $i). 359.80/46.12 thf(decl_318, type, esk12_1: ($i > $o) > $i). 359.80/46.12 thf(decl_319, type, esk13_2: ($i > $o) > $i > $i). 359.80/46.12 thf(decl_320, type, esk14_1: ($i > $o) > $i). 359.80/46.12 thf(decl_321, type, esk15_2: $i > $i > $i). 359.80/46.12 thf(decl_322, type, esk16_2: $i > $i > $i). 359.80/46.12 thf(decl_323, type, esk17_1: $i > $i). 359.80/46.12 thf(decl_324, type, esk18_1: $i > $i). 359.80/46.12 thf(decl_325, type, esk19_1: $i > $i). 359.80/46.12 thf(decl_326, type, esk20_2: $i > $i > $i). 359.80/46.12 thf(decl_327, type, esk21_3: $i > $i > $o > $i). 359.80/46.12 thf(decl_328, type, esk22_2: ($i > $o) > $i > $i). 359.80/46.12 thf(decl_329, type, esk23_1: ($i > $o) > $i). 359.80/46.12 thf(decl_330, type, esk24_1: $i > $i). 359.80/46.12 thf(decl_331, type, esk25_2: $i > ($i > $o) > $i). 359.80/46.12 thf(decl_332, type, esk26_2: $i > ($i > $o) > $i). 359.80/46.12 thf(decl_333, type, esk27_2: $i > ($i > $o) > $i). 359.80/46.12 thf(decl_334, type, esk28_2: $i > ($i > $o) > $i). 359.80/46.12 thf(decl_335, type, esk29_2: $i > ($i > $o) > $i). 359.80/46.12 thf(decl_336, type, esk30_2: $i > ($i > $o) > $i). 359.80/46.12 thf(decl_337, type, esk31_2: ($i > $o) > $i > $i). 359.80/46.12 thf(decl_338, type, esk32_1: ($i > $o) > $i). 359.80/46.12 thf(decl_339, type, esk33_1: ($i > $o) > $i). 359.80/46.12 thf(decl_340, type, esk34_1: ($i > $o) > $i). 359.80/46.12 thf(decl_341, type, esk35_1: ($i > $o) > $i). 359.80/46.12 thf(decl_342, type, esk36_2: ($i > $o) > $i > $i). 359.80/46.12 thf(decl_343, type, esk37_1: ($i > $o) > $i). 359.80/46.12 thf(decl_344, type, esk38_2: ($i > $o) > $i > $i). 359.80/46.12 thf(decl_345, type, esk39_2: ($i > $o) > ($i > $o) > $i). 359.80/46.12 thf(decl_346, type, esk40_2: ($i > $o) > ($i > $o) > $i). 359.80/46.12 thf(decl_347, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 359.80/46.12 thf(decl_348, type, esk42_2: ($i > $o) > ($i > $o) > $i). 359.80/46.12 thf(decl_349, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 359.80/46.12 thf(decl_350, type, esk44_2: ($i > $o) > ($i > $o) > $i). 359.80/46.12 thf(decl_351, type, esk45_2: ($i > $o) > $i > $i). 359.80/46.12 thf(decl_352, type, esk46_2: ($i > $o) > ($i > $o) > $i). 359.80/46.12 thf(decl_353, type, esk47_2: ($i > $o) > ($i > $o) > $i). 359.80/46.12 thf(decl_354, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 359.80/46.12 thf(decl_355, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 359.80/46.12 thf(decl_356, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 359.80/46.12 thf(decl_357, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 359.80/46.12 thf(decl_358, type, esk52_2: $i > $i > $i). 359.80/46.12 thf(decl_359, type, esk53_2: $i > $i > $i). 359.80/46.12 thf(decl_360, type, esk54_2: $i > $i > $i). 359.80/46.12 thf(decl_361, type, esk55_3: $i > $i > $i > $i). 359.80/46.12 thf(decl_362, type, esk56_3: $i > $i > $i > $i). 359.80/46.12 thf(decl_363, type, esk57_2: $i > $i > $i). 359.80/46.12 thf(decl_364, type, esk58_2: $i > ($i > $o) > $i). 359.80/46.12 thf(decl_365, type, esk59_2: $i > ($i > $o) > $i). 359.80/46.12 thf(decl_366, type, esk60_2: $i > ($i > $o) > $i). 359.80/46.12 thf(decl_367, type, esk61_3: $i > ($i > $o) > $i > $i). 359.80/46.12 thf(decl_368, type, esk62_2: $i > ($i > $o) > $i). 359.80/46.12 thf(decl_369, type, esk63_2: $i > ($i > $o) > $i). 359.80/46.12 thf(decl_370, type, esk64_3: $i > $i > ($i > $i) > $i). 359.80/46.12 thf(decl_371, type, esk65_3: $i > $i > ($i > $i) > $i). 359.80/46.12 thf(decl_372, type, esk66_3: $i > $i > ($i > $i) > $i). 359.80/46.12 thf(decl_373, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 359.80/46.12 thf(decl_374, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 359.80/46.12 thf(decl_375, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 359.80/46.12 thf(decl_376, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 359.80/46.12 thf(decl_377, type, esk71_4: $i > $i > $i > $i > $i). 359.80/46.12 thf(decl_378, type, esk72_4: $i > $i > $i > $i > $i). 359.80/46.12 thf(decl_379, type, esk73_4: $i > $i > $i > $i > $i). 359.80/46.12 thf(decl_380, type, esk74_4: $i > $i > $i > $i > $i). 359.80/46.12 thf(decl_381, type, esk75_4: $i > $i > $i > $i > $i). 359.80/46.12 thf(decl_382, type, esk76_4: $i > $i > $i > $i > $i). 359.80/46.12 thf(decl_383, type, esk77_4: $i > $i > $i > $i > $i). 359.80/46.12 thf(decl_384, type, esk78_4: $i > $i > $i > $i > $i). 359.80/46.12 thf(decl_385, type, esk79_4: $i > $i > $i > $i > $i). 359.80/46.12 thf(decl_386, type, esk80_3: $i > $i > ($i > $i) > $i). 359.80/46.12 thf(decl_387, type, esk81_3: $i > $i > ($i > $i) > $i). 359.80/46.12 thf(decl_388, type, esk82_3: $i > $i > ($i > $i) > $i). 359.80/46.12 thf(decl_389, type, esk83_3: $i > $i > $i > $i). 359.80/46.12 thf(decl_390, type, esk84_3: $i > $i > $i > $i). 359.80/46.12 thf(decl_391, type, esk85_3: $i > $i > $i > $i). 359.80/46.12 thf(decl_392, type, esk86_3: $i > $i > $i > $i). 359.80/46.12 thf(decl_393, type, esk87_0: $i). 359.80/46.12 thf(decl_394, type, esk88_0: $i). 359.80/46.12 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', replAx)). 359.80/46.12 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', exu)). 359.80/46.12 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', descrp)). 359.80/46.12 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', exuE1)). 359.80/46.12 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', exuE3e)). 359.80/46.12 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', nonempty)). 359.80/46.12 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', nonemptyI)). 359.80/46.12 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', exuE2)). 359.80/46.12 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', exuI1)). 359.80/46.12 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', exuI3)). 359.80/46.12 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', exuI2)). 359.80/46.12 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', exuE3u)). 359.80/46.12 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', exu__Cong)). 359.80/46.12 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', exuEu)). 359.80/46.12 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', descr__Cong)). 359.80/46.12 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', ex1E1)). 359.80/46.12 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', ex1)). 359.80/46.12 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', ex1I)). 359.80/46.12 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', ex1I2)). 359.80/46.12 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setOfPairsIsBReln)). 359.80/46.12 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', breln)). 359.80/46.12 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', ex1E2)). 359.80/46.12 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', dsetconstrI)). 359.80/46.12 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', dsetconstrEL)). 359.80/46.12 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', dsetconstrER)). 359.80/46.12 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setbeta)). 359.80/46.12 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', nonemptyE1)). 359.80/46.12 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', nonemptyI1)). 359.80/46.12 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setoftrueEq)). 359.80/46.12 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', nonemptyImpWitness)). 359.80/46.12 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', emptyE1)). 359.80/46.12 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', dsetconstr__Cong)). 359.80/46.12 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', sepInPowerset)). 359.80/46.12 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', sepSubset)). 359.80/46.12 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', singletonprop)). 359.80/46.12 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', kfstsingleton)). 359.80/46.12 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', ksndsingleton)). 359.80/46.12 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', dpsetconstrI)). 359.80/46.12 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', dpsetconstrSub)). 359.80/46.12 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', dpsetconstrERa)). 359.80/46.12 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', dpsetconstrEL1)). 359.80/46.12 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', dpsetconstrEL2)). 359.80/46.12 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', dpsetconstrER)). 359.80/46.12 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', funcImageSingleton)). 359.80/46.12 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', apProp)). 359.80/46.12 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', lamProp)). 359.80/46.12 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', lamp)). 359.80/46.12 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', lam2p)). 359.80/46.12 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', brelnall1)). 359.80/46.12 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', brelnall2)). 359.80/46.12 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', subbreln)). 359.80/46.12 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', eqbreln)). 359.80/46.12 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', beta1)). 359.80/46.12 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', eta1)). 359.80/46.12 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', lam2lamEq)). 359.80/46.12 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', beta2)). 359.80/46.12 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', eta2)). 359.80/46.12 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', iffalseProp1)). 359.80/46.12 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', iffalseProp2)). 359.80/46.12 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', iftrueProp1)). 359.80/46.12 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', iftrueProp2)). 359.80/46.12 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', ifSingleton)). 359.80/46.12 thf(doubleComplementSub1, conjecture, ((setextAx)=>(((setadjoinAx)=>((powersetAx)=>(((omega0Ax)=>(((omegaIndAx)=>((replAx)=>((((descrp)=>((((dsetconstrER)=>(((prop2setE)=>(((emptysetimpfalse)=>((notinemptyset)=>((((emptyI)=>((noeltsimpempty)=>((((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>(((setadjoinIR)=>((setadjoinE)=>(((setoftrueEq)=>((powersetI)=>(((emptyInPowerset)=>((powersetE)=>(((setunionE)=>((subPowSU)=>((exuE2)=>(((((((upairsetE)=>((upairsetIL)=>(((((((quantDeMorgan3)=>((((((((exuI3)=>((exuI2)=>((inCongP)=>(((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>(((powerset__Cong)=>((setunion__Cong)=>((((descr__Cong)=>((dsetconstr__Cong)=>(((((subsetI2)=>(((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((((subsetTrans)=>((setadjoinSub)=>((((((((inPowerset)=>(((((binunionIL)=>((upairset2IR)=>(((binunionEcases)=>((binunionE)=>((binunionLsub)=>((((binintersectSubset5)=>((binintersectEL)=>(((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((((binintersectSubset4)=>(((bs114d)=>(((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>(((setukpairIR)=>((((singletonsubset)=>((((((upairinpowunion)=>((((((((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>(((((ex1I)=>((ex1I2)=>(((setukpairinjL1)=>((kfstsingleton)=>(((kfstpairEq)=>((cartprodfstin)=>(((setukpairinjL)=>(((setukpairinjR12)=>((setukpairinjR1)=>(((setukpairinjR2)=>((((ksndpairEq)=>(((cartprodsndin)=>(((cartprodpairmemER)=>((cartprodmempaircEq)=>(((((dpsetconstrI)=>(((((dpsetconstrEL1)=>(((dpsetconstrER)=>(((apProp)=>(((infuncsetfunc)=>((ap2p)=>((((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>(((funcGraphProp3)=>(((((subbreln)=>((eqbreln)=>(((((ap2apEq2)=>(((((beta2)=>((eta2)=>((iffalseProp1)=>((((((ifp)=>(((iftrue)=>(((((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>(((setextT)=>(((((complementTI1)=>((complementTE1)=>((((contrasubsetT)=>((((((doubleComplementE1)=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))<=(doubleComplementI1))<=(contrasubsetT3))<=(contrasubsetT2))<=(contrasubsetT1)))<=(binintersectTERcontra))<=(binintersectTELcontra))))<=(powersetTE1))<=(powersetTI1))<=(subsetTI)))<=(complementT_lem)))))<=(binintersectT_lem))<=(iftrueorfalse))<=(iffalse)))<=(theeq)))<=(ifSingleton))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2)))))<=(lam2lamEq))<=(eta1))<=(beta1)))<=(ap2apEq1))<=(funcext2))<=(funcext))))<=(funcGraphProp4))<=(funcextLem))<=(funcGraphProp2)))<=(funcGraphProp1)))))))<=(lamProp))<=(funcinfuncset))))<=(app)))<=(funcImageSingleton)))<=(dpsetconstrEL2)))<=(dpsetconstrERa))<=(setOfPairsIsBReln))<=(dpsetconstrSub)))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq))))<=(cartprodpairmemEL)))<=(kpairsurjEq)))<=(ksndsingleton))<=(setukpairinjR)))<=(upairequniteq))))<=(setukpairinjR11)))<=(setukpairinjL2))))<=(theprop))))<=(singletonsuniq))))<=(ex1E1))<=(singletonprop))<=(setunionsingleton)))))<=(cartprodmempair))<=(cartprodmempair1))<=(cartprodpairin))<=(ubforcartprodlem3))<=(ubforcartprodlem2))<=(ubforcartprodlem1)))<=(upairsubunion))<=(upairset2E))<=(singletoninpowunion))<=(singletoninpowerset)))<=(kpairp))<=(kpairiskpair)))<=(setukpairIL))))))))<=(setminusSubset1))<=(setminusLsub)))))))))<=(setminusI)))<=(binintersectSubset1)))<=(binintersectRsub))<=(disjointsetsI1)))))<=(binintersectLsub))))<=(binintersectI))<=(binunionRsub)))))<=(binunionIR))))<=(sepSubset))<=(sepInPowerset))<=(powersetsubset)))<=(powersetE1))<=(powersetI1))<=(subsetemptysetimpeq))<=(setextsub))<=(subset2powerset))<=(setadjoinSub2))))<=(subsetRefl))<=(notequalI2))))))<=(emptysetsubset)))<=(eqimpsubset1))<=(eqimpsubset2))<=(subsetI1))))<=(exuEu))<=(omega__Cong))))<=(setadjoin__Cong)))))<=(in__Cong)))))<=(exuI1))<=(notdallE))<=(notdexE))<=(prop2set2propI))<=(prop2setI))<=(quantDeMorgan4)))<=(quantDeMorgan2))<=(quantDeMorgan1))<=(vacuousDall))<=(emptyE1))<=(upairsetIR))))<=(singletonsswitch))<=(eqinunit))<=(notinsingleton))<=(uniqinunit))<=(nonemptyImpWitness)))))<=(setunionI))))<=(emptyinPowerset))))<=(setadjoinOr))))<=(emptyinunitempty)))))<=(nonemptyE1))<=(setbeta))))<=(setext))<=(exuE3e))))<=(emptysetE)))<=(exuE1)))<=(dsetconstrEL))<=(dsetconstrI)))<=(wellorderingAx))<=(foundationAx))))<=(omegaSAx)))<=(setunionAx))))<=(emptysetAx))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', doubleComplementSub1)). 359.80/46.12 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setextAx)). 359.80/46.12 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', emptysetAx)). 359.80/46.12 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setadjoinAx)). 359.80/46.12 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', powersetAx)). 359.80/46.12 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setunionAx)). 359.80/46.12 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', omega0Ax)). 359.80/46.12 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', omegaSAx)). 359.80/46.12 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', omegaIndAx)). 359.80/46.12 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', foundationAx)). 359.80/46.12 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', wellorderingAx)). 359.80/46.12 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', prop2setE)). 359.80/46.12 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', emptysetE)). 359.80/46.12 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', emptysetimpfalse)). 359.80/46.12 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', notinemptyset)). 359.80/46.12 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setext)). 359.80/46.12 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', emptyI)). 359.80/46.12 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', noeltsimpempty)). 359.80/46.12 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setadjoinIL)). 359.80/46.12 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', emptyinunitempty)). 359.80/46.12 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setadjoinIR)). 359.80/46.12 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setadjoinE)). 359.80/46.12 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setadjoinOr)). 359.80/46.12 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', powersetI)). 359.80/46.12 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', emptyinPowerset)). 359.80/46.12 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', emptyInPowerset)). 359.80/46.12 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', powersetE)). 359.80/46.12 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setunionI)). 359.80/46.12 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setunionE)). 359.80/46.12 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', subPowSU)). 359.80/46.12 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', uniqinunit)). 359.80/46.12 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', notinsingleton)). 359.80/46.12 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', eqinunit)). 359.80/46.12 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', singletonsswitch)). 359.80/46.12 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', upairsetE)). 359.80/46.12 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', upairsetIL)). 359.80/46.12 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', upairsetIR)). 359.80/46.12 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', vacuousDall)). 359.80/46.12 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', quantDeMorgan1)). 359.80/46.12 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', quantDeMorgan2)). 359.80/46.12 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', quantDeMorgan3)). 359.80/46.12 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', quantDeMorgan4)). 359.80/46.12 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', prop2setI)). 359.80/46.12 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', prop2set2propI)). 359.80/46.12 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', notdexE)). 359.80/46.12 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', notdallE)). 359.80/46.12 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', inCongP)). 359.80/46.12 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', in__Cong)). 359.80/46.12 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', emptyset__Cong)). 359.80/46.12 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setadjoin__Cong)). 359.80/46.12 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', powerset__Cong)). 359.80/46.12 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setunion__Cong)). 359.80/46.12 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', omega__Cong)). 359.80/46.12 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', subsetI1)). 359.80/46.12 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', eqimpsubset2)). 359.80/46.12 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', eqimpsubset1)). 359.80/46.12 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', subsetI2)). 359.80/46.12 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', emptysetsubset)). 359.80/46.12 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', subsetE)). 359.80/46.12 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', subsetE2)). 359.80/46.12 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', notsubsetI)). 359.80/46.12 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', notequalI1)). 359.80/46.12 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', notequalI2)). 359.80/46.12 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', subsetRefl)). 359.80/46.12 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', subsetTrans)). 359.80/46.12 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setadjoinSub)). 359.80/46.12 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setadjoinSub2)). 359.80/46.12 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', subset2powerset)). 359.80/46.12 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setextsub)). 359.80/46.12 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', subsetemptysetimpeq)). 359.80/46.12 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', powersetI1)). 359.80/46.12 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', powersetE1)). 359.80/46.12 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', inPowerset)). 359.80/46.12 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', powersetsubset)). 359.80/46.12 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binunionIL)). 359.80/46.12 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', upairset2IR)). 359.80/46.12 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binunionIR)). 359.80/46.12 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binunionEcases)). 359.80/46.12 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binunionE)). 359.80/46.12 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binunionLsub)). 359.80/46.12 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binunionRsub)). 359.80/46.12 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binintersectI)). 359.80/46.12 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binintersectSubset5)). 359.80/46.12 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binintersectEL)). 359.80/46.12 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binintersectLsub)). 359.80/46.12 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binintersectSubset2)). 359.80/46.12 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binintersectSubset3)). 359.80/46.12 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binintersectER)). 359.80/46.12 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', disjointsetsI1)). 359.80/46.12 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binintersectRsub)). 359.80/46.12 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binintersectSubset4)). 359.80/46.12 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binintersectSubset1)). 359.80/46.12 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', bs114d)). 359.80/46.12 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setminusI)). 359.80/46.12 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setminusEL)). 359.80/46.12 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setminusER)). 359.80/46.12 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setminusSubset2)). 359.80/46.12 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setminusERneg)). 359.80/46.12 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setminusELneg)). 359.80/46.12 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setminusILneg)). 359.80/46.12 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setminusIRneg)). 359.80/46.12 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setminusLsub)). 359.80/46.12 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setminusSubset1)). 359.80/46.12 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', symdiffE)). 359.80/46.12 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', symdiffI1)). 359.80/46.12 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', symdiffI2)). 359.80/46.12 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', symdiffIneg1)). 359.80/46.12 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', symdiffIneg2)). 359.80/46.12 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', secondinupair)). 359.80/46.12 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setukpairIL)). 359.80/46.12 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setukpairIR)). 359.80/46.12 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', kpairiskpair)). 359.80/46.12 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', kpairp)). 359.80/46.12 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', singletonsubset)). 359.80/46.12 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', singletoninpowerset)). 359.80/46.12 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', singletoninpowunion)). 359.80/46.12 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', upairset2E)). 359.80/46.12 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', upairsubunion)). 359.80/46.12 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', upairinpowunion)). 359.80/46.12 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', ubforcartprodlem1)). 359.80/46.12 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', ubforcartprodlem2)). 359.80/46.12 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', ubforcartprodlem3)). 359.80/46.12 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', cartprodpairin)). 359.80/46.12 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', cartprodmempair1)). 359.80/46.12 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', cartprodmempair)). 359.80/46.12 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setunionE2)). 359.80/46.12 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setunionsingleton1)). 359.80/46.12 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setunionsingleton2)). 359.80/46.12 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setunionsingleton)). 359.80/46.12 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', singletonsuniq)). 359.80/46.12 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setukpairinjL1)). 359.80/46.12 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', theprop)). 359.80/46.12 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', kfstpairEq)). 359.80/46.12 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', cartprodfstin)). 359.80/46.12 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setukpairinjL2)). 359.80/46.12 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setukpairinjL)). 359.80/46.12 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setukpairinjR11)). 359.80/46.12 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setukpairinjR12)). 359.80/46.12 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setukpairinjR1)). 359.80/46.12 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', upairequniteq)). 359.80/46.12 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setukpairinjR2)). 359.80/46.12 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setukpairinjR)). 359.80/46.12 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', ksndpairEq)). 359.80/46.12 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', kpairsurjEq)). 359.80/46.12 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', cartprodsndin)). 359.80/46.12 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', cartprodpairmemEL)). 359.80/46.12 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', cartprodpairmemER)). 359.80/46.12 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', cartprodmempaircEq)). 359.80/46.12 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', cartprodfstpairEq)). 359.80/46.12 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', cartprodsndpairEq)). 359.80/46.12 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', cartprodpairsurjEq)). 359.80/46.12 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', app)). 359.80/46.12 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', infuncsetfunc)). 359.80/46.12 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', ap2p)). 359.80/46.12 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', funcinfuncset)). 359.80/46.12 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', funcGraphProp1)). 359.80/46.12 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', funcGraphProp3)). 359.80/46.12 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', funcGraphProp2)). 359.80/46.12 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', funcextLem)). 359.80/46.12 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', funcGraphProp4)). 359.80/46.12 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', funcext)). 359.80/46.12 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', funcext2)). 359.80/46.12 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', ap2apEq1)). 359.80/46.12 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', ap2apEq2)). 359.80/46.12 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', ifp)). 359.80/46.12 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', theeq)). 359.80/46.12 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', iftrue)). 359.80/46.12 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', iffalse)). 359.80/46.12 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', iftrueorfalse)). 359.80/46.12 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binintersectT_lem)). 359.80/46.12 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binunionT_lem)). 359.80/46.12 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', powersetT_lem)). 359.80/46.12 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setminusT_lem)). 359.80/46.12 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', complementT_lem)). 359.80/46.12 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', setextT)). 359.80/46.12 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', subsetTI)). 359.80/46.12 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', powersetTI1)). 359.80/46.12 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', powersetTE1)). 359.80/46.12 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', complementTI1)). 359.80/46.12 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', complementTE1)). 359.80/46.12 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binintersectTELcontra)). 359.80/46.12 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', binintersectTERcontra)). 359.80/46.12 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', contrasubsetT)). 359.80/46.12 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', contrasubsetT1)). 359.80/46.12 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', contrasubsetT2)). 359.80/46.12 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', contrasubsetT3)). 359.80/46.12 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', doubleComplementI1)). 359.80/46.12 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.mslqCJ0dX5/E---3.1_29602.p', doubleComplementE1)). 359.80/46.12 thf(c_0_250, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 359.80/46.12 thf(c_0_251, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 359.80/46.12 thf(c_0_252, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 359.80/46.12 thf(c_0_253, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 359.80/46.12 thf(c_0_254, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 359.80/46.12 thf(c_0_255, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 359.80/46.12 thf(c_0_256, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 359.80/46.12 thf(c_0_257, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 359.80/46.12 thf(c_0_258, 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])). 359.80/46.12 thf(c_0_259, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 359.80/46.12 thf(c_0_260, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 359.80/46.12 thf(c_0_261, 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])). 359.80/46.12 thf(c_0_262, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 359.80/46.12 thf(c_0_263, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 359.80/46.12 thf(c_0_264, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 359.80/46.12 thf(c_0_265, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 359.80/46.12 thf(c_0_266, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])). 359.80/46.12 thf(c_0_267, 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])). 359.80/46.12 thf(c_0_268, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 359.80/46.12 thf(c_0_269, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 359.80/46.12 thf(c_0_270, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])). 359.80/46.12 thf(c_0_271, 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])). 359.80/46.12 thf(c_0_272, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X811:$i]:((((X6 @ X2 @ X811))&![X812:$i]:((((X6 @ X2 @ X812))=>((X811)=(X812)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_250, c_0_251])). 359.80/46.12 thf(c_0_273, plain, ((descrp)=(![X1:$i > $o]:(((?[X813:$i]:((((X1 @ X813))&![X814:$i]:((((X1 @ X814))=>((X813)=(X814)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_252, c_0_251])). 359.80/46.12 thf(c_0_274, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 359.80/46.12 thf(c_0_275, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 359.80/46.12 thf(c_0_276, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 359.80/46.12 thf(c_0_277, plain, ((exuE1)=(![X1:$i > $o]:(((?[X815:$i]:((((X1 @ X815))&![X816:$i]:((((X1 @ X816))=>((X815)=(X816)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_253, c_0_251])). 359.80/46.12 thf(c_0_278, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X817:$i]:((((X1 @ X817))&![X818:$i]:((((X1 @ X818))=>((X817)=(X818)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_254, c_0_251])). 359.80/46.12 thf(c_0_279, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 359.80/46.12 thf(c_0_280, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_255])). 359.80/46.12 thf(c_0_281, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_256, c_0_255])). 359.80/46.12 thf(c_0_282, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_255])). 359.80/46.12 thf(c_0_283, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 359.80/46.12 thf(c_0_284, plain, ((exuE2)=(![X1:$i > $o]:(((?[X819:$i]:((((X1 @ X819))&![X820:$i]:((((X1 @ X820))=>((X819)=(X820)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_257, c_0_251])). 359.80/46.12 thf(c_0_285, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_255])). 359.80/46.12 thf(c_0_286, 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])). 359.80/46.12 thf(c_0_287, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X821:$i]:((((X1 @ X821))&![X822:$i]:((((X1 @ X822))=>((X821)=(X822))))))))))), inference(apply_def,[status(thm)],[c_0_258, c_0_251])). 359.80/46.12 thf(c_0_288, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X823:$i]:((((X1 @ X823))&![X824:$i]:((((X1 @ X824))=>((X823)=(X824)))))))))))), inference(apply_def,[status(thm)],[c_0_259, c_0_251])). 359.80/46.12 thf(c_0_289, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X825:$i]:((((X1 @ X825))&![X826:$i]:((((X1 @ X826))=>((X825)=(X826))))))))))), inference(apply_def,[status(thm)],[c_0_260, c_0_251])). 359.80/46.12 thf(c_0_290, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X827:$i]:((((X1 @ X827))&![X828:$i]:((((X1 @ X828))=>((X827)=(X828)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_261, c_0_251])). 359.80/46.12 thf(c_0_291, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X829:$i]:((((X1 @ X829))&![X830:$i]:((((X1 @ X830))=>((X829)=(X830)))))))<=>(?[X831:$i]:((((X17 @ X831))&![X832:$i]:((((X17 @ X832))=>((X831)=(X832)))))))))))), inference(apply_def,[status(thm)],[c_0_262, c_0_251])). 359.80/46.12 thf(c_0_292, plain, ((exuEu)=(![X1:$i > $o]:(((?[X833:$i]:((((X1 @ X833))&![X834:$i]:((((X1 @ X834))=>((X833)=(X834)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_263, c_0_251])). 359.80/46.12 thf(c_0_293, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X835:$i]:((((X1 @ X835))&![X836:$i]:((((X1 @ X836))=>((X835)=(X836)))))))=>((?[X837:$i]:((((X17 @ X837))&![X838:$i]:((((X17 @ X838))=>((X837)=(X838)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_264, c_0_251])). 359.80/46.12 thf(c_0_294, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 359.80/46.12 thf(c_0_295, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 359.80/46.12 thf(c_0_296, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 359.80/46.12 thf(c_0_297, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 359.80/46.12 thf(c_0_298, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_265, c_0_266])). 359.80/46.12 thf(c_0_299, plain, ((ex1I)=(![X4:$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_267, c_0_266])). 359.80/46.12 thf(c_0_300, 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 */:$i]:(((X1 @ Z0)))))))))))), inference(apply_def,[status(thm)],[c_0_268, c_0_266])). 359.80/46.12 thf(c_0_301, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 359.80/46.12 thf(c_0_302, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 359.80/46.12 thf(c_0_303, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 359.80/46.12 thf(c_0_304, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 359.80/46.12 thf(c_0_305, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_269, c_0_270])). 359.80/46.12 thf(c_0_306, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 359.80/46.12 thf(c_0_307, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 359.80/46.12 thf(c_0_308, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 359.80/46.12 thf(c_0_309, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 359.80/46.12 thf(c_0_310, plain, ((funcImageSingleton)<=>![X4:$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])). 359.80/46.12 thf(c_0_311, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 359.80/46.12 thf(c_0_312, plain, ((lamProp)<=>![X4:$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])). 359.80/46.12 thf(c_0_313, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 359.80/46.12 thf(c_0_314, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 359.80/46.12 thf(c_0_315, axiom, ((brelnall1)=(![X4:$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_270])). 359.80/46.12 thf(c_0_316, 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_270])). 359.80/46.12 thf(c_0_317, 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_271, c_0_266])). 359.80/46.12 thf(c_0_318, 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_270])). 359.80/46.12 thf(c_0_319, 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_270])). 359.80/46.12 thf(c_0_320, 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])). 359.80/46.12 thf(c_0_321, 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])). 359.80/46.12 thf(c_0_322, 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])). 359.80/46.12 thf(c_0_323, 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])). 359.80/46.12 thf(c_0_324, 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])). 359.80/46.12 thf(c_0_325, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 359.80/46.12 thf(c_0_326, plain, ((iffalseProp2)<=>![X4:$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])). 359.80/46.12 thf(c_0_327, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 359.80/46.12 thf(c_0_328, plain, ((iftrueProp2)<=>![X4:$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])). 359.80/46.12 thf(c_0_329, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 359.80/46.12 thf(c_0_330, plain, ((epred1_0)<=>![X1599:$i]:(?[X1600:$i]:((((![X1601:$i]:(((in @ X1601 @ X1600)=>![X1602:$i]:(((in @ X1602 @ X1601)=>(in @ X1602 @ X1599)))))&![X1603:$i, X1604:$i]:((((in @ X1603 @ X1599)&(in @ X1604 @ X1599))=>(![X1605:$i]:(((in @ X1605 @ X1600)=>((in @ X1603 @ X1605)<=>(in @ X1604 @ X1605))))=>((X1603)=(X1604))))))&![X1606:$i, X1607:$i]:((((in @ X1606 @ X1600)&(in @ X1607 @ X1600))=>(![X1608:$i]:(((in @ X1608 @ X1606)=>(in @ X1608 @ X1607)))|![X1609:$i]:(((in @ X1609 @ X1607)=>(in @ X1609 @ X1606)))))))&![X1610:$i]:(((![X1611:$i]:(((in @ X1611 @ X1610)=>(in @ X1611 @ X1599)))&?[X1612:$i]:((in @ X1612 @ X1610)))=>?[X1613:$i, X1614:$i]:(((((in @ X1613 @ X1600)&(in @ X1614 @ X1610))&~(?[X1615:$i]:(((in @ X1615 @ X1613)&(in @ X1615 @ X1610)))))&![X1616:$i]:(((in @ X1616 @ X1600)=>(![X1617:$i]:(((in @ X1617 @ X1616)=>(in @ X1617 @ X1613)))|(in @ X1614 @ X1616)))))))))))), introduced(definition)). 359.80/46.12 thf(c_0_331, negated_conjecture, ~((![X839:$i, X840:$i]:((![X841:$i]:(((in @ X841 @ X839)<=>(in @ X841 @ X840)))=>((X839)=(X840))))=>(![X1626:$i]:(~(in @ X1626 @ emptyset))=>(![X842:$i, X843:$i, X844:$i]:(((in @ X844 @ (setadjoin @ X842 @ X843))<=>(((X844)=(X842))|(in @ X844 @ X843))))=>(![X845:$i, X846:$i]:(((in @ X846 @ (powerset @ X845))<=>![X847:$i]:(((in @ X847 @ X846)=>(in @ X847 @ X845)))))=>(![X1623:$i, X1624:$i]:(((in @ X1624 @ (setunion @ X1623))<=>?[X1625:$i]:(((in @ X1624 @ X1625)&(in @ X1625 @ X1623)))))=>((in @ emptyset @ omega)=>(![X1622:$i]:(((in @ X1622 @ omega)=>(in @ (setadjoin @ X1622 @ X1622) @ omega)))=>(![X848:$i]:((((in @ emptyset @ X848)&![X849:$i]:((((in @ X849 @ omega)&(in @ X849 @ X848))=>(in @ (setadjoin @ X849 @ X849) @ X848))))=>![X850:$i]:(((in @ X850 @ omega)=>(in @ X850 @ X848)))))=>(![X851:$i > $i > $o, X852:$i]:((![X853:$i]:(((in @ X853 @ X852)=>?[X854:$i]:(((X851 @ X853 @ X854)&![X855:$i]:(((X851 @ X853 @ X855)=>((X854)=(X855))))))))=>?[X856:$i]:(![X857:$i]:(((in @ X857 @ X856)<=>?[X858:$i]:(((in @ X858 @ X852)&(X851 @ X858 @ X857))))))))=>(![X1618:$i]:((?[X1619:$i]:((in @ X1619 @ X1618))=>?[X1620:$i]:(((in @ X1620 @ X1618)&~(?[X1621:$i]:(((in @ X1621 @ X1620)&(in @ X1621 @ X1618))))))))=>((epred1_0)=>(![X859:$i > $o]:((?[X860:$i]:(((X859 @ X860)&![X861:$i]:(((X859 @ X861)=>((X860)=(X861))))))=>(X859 @ (descr @ (^[Z0/* 17 */:$i]:(X859 @ Z0))))))=>(![X1596:$i, X1597:$i > $o, X1598:$i]:(((in @ X1598 @ X1596)=>((X1597 @ X1598)=>(in @ X1598 @ (dsetconstr @ X1596 @ X1597)))))=>(![X1593:$i, X1594:$i > $o, X1595:$i]:(((in @ X1595 @ (dsetconstr @ X1593 @ X1594))=>(in @ X1595 @ X1593)))=>(![X862:$i, X863:$i > $o, X864:$i]:(((in @ X864 @ (dsetconstr @ X862 @ X863))=>(X863 @ X864)))=>(![X1588:$i > $o]:((?[X1589:$i]:(((X1588 @ X1589)&![X1590:$i]:(((X1588 @ X1590)=>((X1589)=(X1590))))))=>?[X1591:$i]:(((X1588 @ X1591)&![X1592:$i]:(((X1588 @ X1592)=>((X1591)=(X1592))))))))=>(![X865:$o, X866:$i]:(((in @ X866 @ (prop2set @ ((X865))))=>(X865)))=>(![X1586:$i]:(((in @ X1586 @ emptyset)=>![X1587:$o]:((X1587))))=>(![X867:$i]:(((in @ X867 @ emptyset)=>~($true)))=>(![X868:$i]:(~(in @ X868 @ emptyset))=>(![X1582:$i > $o]:((?[X1583:$i]:(((X1582 @ X1583)&![X1584:$i]:(((X1582 @ X1584)=>((X1583)=(X1584))))))=>?[X1585:$i]:((X1582 @ X1585))))=>(![X1578:$i, X1579:$i]:((![X1580:$i]:(((in @ X1580 @ X1578)=>(in @ X1580 @ X1579)))=>(![X1581:$i]:(((in @ X1581 @ X1579)=>(in @ X1581 @ X1578)))=>((X1578)=(X1579)))))=>(![X869:$i]:((![X870:$i]:(~(in @ X870 @ X869))=>((X869)=(emptyset))))=>(![X871:$i]:((![X872:$i]:(~(in @ X872 @ X871))=>((X871)=(emptyset))))=>(![X1575:$i, X1576:$i > $o, X1577:$i]:(((in @ X1577 @ X1575)=>((in @ X1577 @ (dsetconstr @ X1575 @ X1576))<=>(X1576 @ X1577))))=>(![X1573:$i]:((((X1573)!=(emptyset))=>?[X1574:$i]:((in @ X1574 @ X1573))))=>(![X873:$i, X874:$i > $o, X875:$i]:(((in @ X875 @ X873)=>((X874 @ X875)=>((dsetconstr @ X873 @ X874)!=(emptyset)))))=>(![X876:$i]:((?[X877:$i]:((in @ X877 @ X876))=>((X876)!=(emptyset))))=>(![X878:$i, X879:$i]:((in @ X878 @ (setadjoin @ X878 @ X879)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X880:$i, X881:$i, X882:$i]:(((in @ X882 @ X881)=>(in @ X882 @ (setadjoin @ X880 @ X881))))=>(![X883:$i, X884:$i, X885:$i]:(((in @ X885 @ (setadjoin @ X883 @ X884))=>![X886:$o]:(((((X885)=(X883))=>(X886))=>(((in @ X885 @ X884)=>(X886))=>(X886))))))=>(![X1570:$i, X1571:$i, X1572:$i]:(((in @ X1572 @ (setadjoin @ X1570 @ X1571))=>(((X1572)=(X1570))|(in @ X1572 @ X1571))))=>(![X887:$i]:(((dsetconstr @ X887 @ (^[Z0/* 1 */:$i]:($true)))=(X887)))=>(![X888:$i, X889:$i]:((![X890:$i]:(((in @ X890 @ X889)=>(in @ X890 @ X888)))=>(in @ X889 @ (powerset @ X888))))=>(![X1569:$i]:((in @ emptyset @ (powerset @ X1569)))=>(![X891:$i]:((in @ emptyset @ (powerset @ X891)))=>(![X892:$i, X893:$i, X894:$i]:(((in @ X893 @ (powerset @ X892))=>((in @ X894 @ X893)=>(in @ X894 @ X892))))=>(![X1566:$i, X1567:$i, X1568:$i]:(((in @ X1567 @ X1568)=>((in @ X1568 @ X1566)=>(in @ X1567 @ (setunion @ X1566)))))=>(![X895:$i, X896:$i]:(((in @ X896 @ (setunion @ X895))=>![X897:$o]:((![X898:$i]:(((in @ X896 @ X898)=>((in @ X898 @ X895)=>(X897))))=>(X897)))))=>(![X899:$i, X900:$i]:(((in @ X900 @ X899)=>(in @ X900 @ (powerset @ (setunion @ X899)))))=>(![X901:$i > $o]:((?[X902:$i]:(((X901 @ X902)&![X903:$i]:(((X901 @ X903)=>((X902)=(X903))))))=>?[X904:$i]:(![X905:$i]:(((X901 @ X905)<=>((X905)=(X904)))))))=>(![X1564:$i]:((((X1564)!=(emptyset))=>?[X1565:$i]:(((in @ X1565 @ X1564)&$true))))=>(![X1562:$i, X1563:$i]:(((in @ X1562 @ (setadjoin @ X1563 @ emptyset))=>((X1562)=(X1563))))=>(![X1560:$i, X1561:$i]:((((X1560)!=(X1561))=>~(in @ X1561 @ (setadjoin @ X1560 @ emptyset))))=>(![X1558:$i, X1559:$i]:((((X1558)=(X1559))=>(in @ X1558 @ (setadjoin @ X1559 @ emptyset))))=>(![X1556:$i, X1557:$i]:(((in @ X1556 @ (setadjoin @ X1557 @ emptyset))=>(in @ X1557 @ (setadjoin @ X1556 @ emptyset))))=>(![X906:$i, X907:$i, X908:$i]:(((in @ X908 @ (setadjoin @ X906 @ (setadjoin @ X907 @ emptyset)))=>(((X908)=(X906))|((X908)=(X907)))))=>(![X909:$i, X910:$i]:((in @ X909 @ (setadjoin @ X909 @ (setadjoin @ X910 @ emptyset))))=>(![X1554:$i, X1555:$i]:((in @ X1555 @ (setadjoin @ X1554 @ (setadjoin @ X1555 @ emptyset))))=>(![X1551:$i, X1552:$i > $o]:((?[X1553:$i]:(((in @ X1553 @ X1551)&(X1552 @ X1553)))=>(((dsetconstr @ X1551 @ X1552)=(emptyset))=>~($true))))=>(![X1549:$i > $o, X1550:$i]:(((in @ X1550 @ emptyset)=>(X1549 @ X1550)))=>(![X1545:$i, X1546:$i > $o]:((~(![X1547:$i]:(((in @ X1547 @ X1545)=>(X1546 @ X1547))))=>?[X1548:$i]:(((in @ X1548 @ X1545)&~((X1546 @ X1548))))))=>(![X1541:$i, X1542:$i > $o]:((![X1543:$i]:(((in @ X1543 @ X1541)=>~((X1542 @ X1543))))=>~(?[X1544:$i]:(((in @ X1544 @ X1541)&(X1542 @ X1544))))))=>(![X911:$i, X912:$i > $o]:((~(?[X913:$i]:(((in @ X913 @ X911)&(X912 @ X913))))=>![X914:$i]:(((in @ X914 @ X911)=>~((X912 @ X914))))))=>(![X1537:$i, X1538:$i > $o]:((?[X1539:$i]:(((in @ X1539 @ X1537)&~((X1538 @ X1539))))=>~(![X1540:$i]:(((in @ X1540 @ X1537)=>(X1538 @ X1540))))))=>(![X1536:$o]:(((X1536)=>(in @ emptyset @ (prop2set @ ((X1536))))))=>(![X1535:$o]:(((X1535)=>(set2prop @ (prop2set @ ((X1535))))))=>(![X1531:$i, X1532:$i > $o]:((~(?[X1533:$i]:(((in @ X1533 @ X1531)&(X1532 @ X1533))))=>![X1534:$i]:(((in @ X1534 @ X1531)=>~((X1532 @ X1534))))))=>(![X1527:$i, X1528:$i > $o]:((~(![X1529:$i]:(((in @ X1529 @ X1527)=>(X1528 @ X1529))))=>?[X1530:$i]:(((in @ X1530 @ X1527)&~((X1528 @ X1530))))))=>(![X1522:$i > $o]:((?[X1523:$i]:(((X1522 @ X1523)&![X1524:$i]:(((X1522 @ X1524)=>((X1523)=(X1524))))))=>?[X1525:$i]:(((X1522 @ X1525)&![X1526:$i]:(((X1522 @ X1526)=>((X1525)=(X1526))))))))=>(![X915:$i > $o]:((?[X916:$i]:((X915 @ X916))=>(![X917:$i, X918:$i]:(((X915 @ X917)=>((X915 @ X918)=>((X917)=(X918)))))=>?[X919:$i]:(((X915 @ X919)&![X920:$i]:(((X915 @ X920)=>((X919)=(X920)))))))))=>(![X921:$i > $o]:((?[X922:$i]:(![X923:$i]:(((X921 @ X923)<=>((X923)=(X922)))))=>?[X924:$i]:(((X921 @ X924)&![X925:$i]:(((X921 @ X925)=>((X924)=(X925))))))))=>(![X926:$i, X927:$i]:((((X926)=(X927))=>![X928:$i, X929:$i]:((((X928)=(X929))=>((in @ X928 @ X926)=>(in @ X929 @ X927))))))=>(![X1518:$i, X1519:$i]:((((X1518)=(X1519))=>![X1520:$i, X1521:$i]:((((X1520)=(X1521))=>((in @ X1520 @ X1518)<=>(in @ X1521 @ X1519))))))=>(![X930:$i > $o]:((?[X931:$i]:(((X930 @ X931)&![X932:$i]:(((X930 @ X932)=>((X931)=(X932))))))=>![X933:$i, X934:$i]:(((X930 @ X933)=>((X930 @ X934)=>((X933)=(X934)))))))=>(![X935:$i > $o, X936:$i > $o]:((![X937:$i, X938:$i]:((((X937)=(X938))=>((X935 @ X937)<=>(X936 @ X938))))=>(?[X939:$i]:(((X935 @ X939)&![X940:$i]:(((X935 @ X940)=>((X939)=(X940))))))<=>?[X941:$i]:(((X936 @ X941)&![X942:$i]:(((X936 @ X942)=>((X941)=(X942)))))))))=>(((emptyset)=(emptyset))=>(![X1514:$i, X1515:$i]:((((X1514)=(X1515))=>![X1516:$i, X1517:$i]:((((X1516)=(X1517))=>((setadjoin @ X1514 @ X1516)=(setadjoin @ X1515 @ X1517))))))=>(![X943:$i, X944:$i]:((((X943)=(X944))=>((powerset @ X943)=(powerset @ X944))))=>(![X945:$i, X946:$i]:((((X945)=(X946))=>((setunion @ X945)=(setunion @ X946))))=>(((omega)=(omega))=>(![X1509:$i > $o]:((?[X1510:$i]:(((X1509 @ X1510)&![X1511:$i]:(((X1509 @ X1511)=>((X1510)=(X1511))))))=>![X1512:$i, X1513:$i]:(((X1509 @ X1512)=>((X1509 @ X1513)=>((X1512)=(X1513)))))))=>(![X947:$i > $o, X948:$i > $o]:((![X949:$i, X950:$i]:((((X949)=(X950))=>((X947 @ X949)<=>(X948 @ X950))))=>(?[X951:$i]:(((X947 @ X951)&![X952:$i]:(((X947 @ X952)=>((X951)=(X952))))))=>(?[X953:$i]:(((X948 @ X953)&![X954:$i]:(((X948 @ X954)=>((X953)=(X954))))))=>((descr @ X947)=(descr @ X948))))))=>(![X955:$i, X956:$i]:((((X955)=(X956))=>![X957:$i > $o, X958:$i > $o]:((![X959:$i]:(((in @ X959 @ X955)=>![X960:$i]:(((in @ X960 @ X956)=>(((X959)=(X960))=>((X957 @ X959)<=>(X958 @ X960)))))))=>((dsetconstr @ X955 @ X957)=(dsetconstr @ X956 @ X958))))))=>(![X1506:$i, X1507:$i]:((![X1508:$i]:(((in @ X1508 @ X1506)=>(in @ X1508 @ X1507)))=>(subset @ X1506 @ X1507)))=>(![X1504:$i, X1505:$i]:((((X1504)=(X1505))=>(subset @ X1505 @ X1504)))=>(![X1502:$i, X1503:$i]:((((X1502)=(X1503))=>(subset @ X1502 @ X1503)))=>(![X961:$i, X962:$i]:((![X963:$i]:(((in @ X963 @ X961)=>(in @ X963 @ X962)))=>(subset @ X961 @ X962)))=>(![X1501:$i]:((subset @ emptyset @ X1501))=>(![X964:$i, X965:$i, X966:$i]:(((subset @ X964 @ X965)=>((in @ X966 @ X964)=>(in @ X966 @ X965))))=>(![X967:$i, X968:$i, X969:$i]:(((subset @ X967 @ X968)=>(~(in @ X969 @ X968)=>~(in @ X969 @ X967))))=>(![X970:$i, X971:$i, X972:$i]:(((in @ X972 @ X970)=>(~(in @ X972 @ X971)=>~(subset @ X970 @ X971))))=>(![X973:$i, X974:$i]:((~(subset @ X973 @ X974)=>((X973)!=(X974))))=>(![X1498:$i, X1499:$i, X1500:$i]:(((in @ X1500 @ X1498)=>(~(in @ X1500 @ X1499)=>((X1498)!=(X1499)))))=>(![X1497:$i]:((subset @ X1497 @ X1497))=>(![X975:$i, X976:$i, X977:$i]:(((subset @ X975 @ X976)=>((subset @ X976 @ X977)=>(subset @ X975 @ X977))))=>(![X978:$i, X979:$i]:((subset @ X979 @ (setadjoin @ X978 @ X979)))=>(![X1494:$i, X1495:$i, X1496:$i]:(((subset @ X1494 @ X1496)=>(subset @ X1494 @ (setadjoin @ X1495 @ 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X1232))=>((subset @ (setminus @ X1232 @ X1234) @ (setminus @ X1232 @ X1233))=>(subset @ X1233 @ X1234))))))=>(![X1229:$i, X1230:$i]:(((in @ X1230 @ (powerset @ X1229))=>![X1231:$i]:(((in @ X1231 @ X1229)=>((in @ X1231 @ X1230)=>(in @ X1231 @ (setminus @ X1229 @ (setminus @ X1229 @ X1230))))))))=>(![X1226:$i, X1227:$i]:(((in @ X1227 @ (powerset @ X1226))=>![X1228:$i]:(((in @ X1228 @ X1226)=>((in @ X1228 @ (setminus @ X1226 @ (setminus @ X1226 @ X1227)))=>(in @ X1228 @ X1227))))))=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_272]), foundationAx]), wellorderingAx]), c_0_273]), c_0_274]), c_0_275]), c_0_276]), c_0_277]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_278]), setext]), emptyI]), noeltsimpempty]), c_0_279]), c_0_280]), c_0_281]), c_0_282]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_283]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_284]), c_0_285]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_286]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_287]), c_0_288]), c_0_289]), inCongP]), in__Cong]), c_0_290]), c_0_291]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_292]), c_0_293]), c_0_294]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_295]), c_0_296]), 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_297]), c_0_298]), c_0_299]), c_0_300]), singletonsuniq]), setukpairinjL1]), c_0_301]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_302]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_303]), c_0_304]), c_0_305]), c_0_306]), c_0_307]), c_0_308]), c_0_309]), c_0_310]), c_0_311]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_312]), c_0_313]), c_0_314]), c_0_315]), c_0_316]), c_0_317]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_318]), c_0_319]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_320]), c_0_321]), c_0_322]), c_0_323]), c_0_324]), c_0_325]), c_0_326]), c_0_327]), c_0_328]), c_0_329]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1])])]), c_0_330])). 359.80/46.12 thf(c_0_332, negated_conjecture, ![X1627:$i, X1628:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1640:$i, X1641:$i, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1647:$i, X1649:$i, X1650:$i > $i > $o, X1651:$i, X1653:$i, X1656:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1663:$i, X1664:$i > $o, X1665:$i, X1667:$i, X1668:$i > $o, X1669:$i, X1670:$i, X1671:$i > $o, X1672:$i, X1673:$i, X1674:$i > $o, X1675:$i, X1676:$i > $o, X1677:$i, X1680:$i, X1681:$o, X1682:$i, X1683:$i, X1684:$o, X1685:$i, X1686:$i, X1687:$i > $o, X1688:$i, X1691:$i, X1692:$i, X1695:$i, X1697:$i, X1699:$i, X1700:$i > $o, X1701:$i, X1702:$i, X1704:$i, X1705:$i > $o, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i, X1717:$o, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1725:$i, X1726:$i, X1727:$i, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$o, X1737:$i, X1738:$i, X1739:$i > $o, X1740:$i, X1743:$i, X1744:$i, X1745:$i, X1747:$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 > $o, X1764:$i, X1765:$i > $o, X1766:$i, X1767:$i, X1768:$i > $o, X1769:$i, X1771:$i, X1772:$i > $o, X1774:$i, X1775:$i, X1776:$i > $o, X1778:$i, X1779:$i, X1780:$i > $o, X1781:$i, X1783:$o, X1784:$o, X1785:$i, X1786:$i > $o, X1788:$i, X1789:$i, X1790:$i > $o, X1791:$i, X1793:$i > $o, X1794:$i, X1797:$i, X1798:$i > $o, X1799:$i, X1803:$i, X1804:$i > $o, X1805:$i, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i > $o, X1818:$i, X1820:$i, X1821:$i, X1822:$i > $o, X1823:$i > $o, X1826:$i, X1829:$i, X1830:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i > $o, X1843:$i, X1845:$i, X1846:$i, X1847:$i > $o, X1848:$i > $o, X1851:$i, X1853:$i, X1855:$i, X1856:$i, X1857:$i > $o, X1858:$i > $o, X1861:$i, X1862:$i, X1864:$i, X1865:$i, X1866:$i, X1867:$i, X1868:$i, X1869:$i, X1871:$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 > $o, X1909:$i, X1910:$i > $o, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$o, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1941:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$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:$i, X1990:$o, 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, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i, X2048:$i, X2049:$i, X2052:$i, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i > $o, X2065:$i, X2066:$i, X2067:$i > $o, X2069:$i, X2070:$i > $o, X2071:$i, X2073:$i, X2074:$i > $o, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2085:$i, X2086:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2099:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2104:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, X2111:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i, X2122:$i, X2123:$i, X2124:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2134:$i, X2135:$i, X2136:$i, X2137:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2149:$i > $i > $o, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i > $i > $o, X2155:$i, X2156:$i, X2157:$i > $i > $o, X2158:$i, X2159:$i, X2160:$i > $i > $o, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i > $i > $o, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i > $i > $o, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i > $i > $o, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i, X2188:$i, X2189:$i, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$i, X2202:$i > $i, X2204:$i, X2205:$i, X2206:$i > $i, X2208:$i, X2209:$i, X2210:$i > $i, X2212:$i, X2213:$i, X2214:$i, X2215:$i > $o, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i > $o, X2225:$i, X2226:$i, X2227:$i > $o, X2228:$i, X2229:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2269:$i, X2270:$i, X2271:$i, X2272:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i > $i, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i > $i, X2299:$i, X2300:$i, X2301:$i > $i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$o, X2309:$i, X2310:$i, X2311:$i, X2312:$o, X2313:$i, X2314:$i, X2315:$i, X2316:$o, X2317:$i, X2318:$i, X2319:$i, X2320:$o, X2321:$i, X2322:$i, X2323:$i, X2324:$o, X2325:$i, X2326:$i, X2327:$i, X2328:$o, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$o, X2335:$i, X2336:$i, X2337:$i, X2338:$o, X2339:$i, X2340:$i, X2341:$i, X2342:$o, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2363:$i, X2364:$i, X2365:$i, X2367:$i, X2368:$i, X2369:$i, X2371:$i, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$i, X2384:$i, X2385:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i, X2405:$i, X2406:$i, X2407:$i, 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(esk76_4 @ X2261 @ X2262 @ X2263 @ X2264) @ X2261)|((X2263)=(X2264))|~(in @ (kpair @ (esk74_4 @ X2261 @ X2262 @ X2263 @ X2264) @ (esk75_4 @ X2261 @ X2262 @ X2263 @ X2264)) @ X2264)|~(subset @ X2264 @ (cartprod @ X2261 @ X2262))|~(subset @ X2263 @ (cartprod @ X2261 @ X2262)))&(((in @ (esk77_4 @ X2261 @ X2262 @ X2263 @ X2264) @ X2262)|((X2263)=(X2264))|~(in @ (kpair @ (esk74_4 @ X2261 @ X2262 @ X2263 @ X2264) @ (esk75_4 @ X2261 @ X2262 @ X2263 @ X2264)) @ X2264)|~(subset @ X2264 @ (cartprod @ X2261 @ X2262))|~(subset @ X2263 @ (cartprod @ X2261 @ X2262)))&(((in @ (kpair @ (esk76_4 @ X2261 @ X2262 @ X2263 @ X2264) @ (esk77_4 @ X2261 @ X2262 @ X2263 @ X2264)) @ X2264)|((X2263)=(X2264))|~(in @ (kpair @ (esk74_4 @ X2261 @ X2262 @ X2263 @ X2264) @ (esk75_4 @ X2261 @ X2262 @ X2263 @ X2264)) @ X2264)|~(subset @ X2264 @ (cartprod @ X2261 @ X2262))|~(subset @ X2263 @ (cartprod @ X2261 @ X2262)))&(~(in @ (kpair @ (esk76_4 @ X2261 @ X2262 @ X2263 @ X2264) @ (esk77_4 @ X2261 @ X2262 @ X2263 @ X2264)) @ X2263)|((X2263)=(X2264))|~(in @ (kpair @ (esk74_4 @ X2261 @ X2262 @ X2263 @ X2264) @ (esk75_4 @ X2261 @ X2262 @ X2263 @ X2264)) @ X2264)|~(subset @ X2264 @ (cartprod @ X2261 @ X2262))|~(subset @ X2263 @ (cartprod @ X2261 @ X2262)))))))))&((((in @ (esk78_4 @ X2269 @ X2270 @ X2271 @ X2272) @ X2269)|((X2271)=(X2272))|~(func @ X2269 @ X2270 @ X2272)|~(func @ X2269 @ X2270 @ X2271))&(((ap @ X2269 @ X2270 @ X2271 @ (esk78_4 @ X2269 @ X2270 @ X2271 @ X2272))!=(ap @ X2269 @ X2270 @ X2272 @ (esk78_4 @ X2269 @ X2270 @ X2271 @ X2272)))|((X2271)=(X2272))|~(func @ X2269 @ X2270 @ X2272)|~(func @ X2269 @ X2270 @ X2271)))&((((in @ (esk79_4 @ X2274 @ X2275 @ X2276 @ X2277) @ X2274)|((X2276)=(X2277))|~(in @ X2277 @ (funcSet @ X2274 @ X2275))|~(in @ X2276 @ (funcSet @ X2274 @ X2275)))&(((ap @ X2274 @ X2275 @ X2276 @ (esk79_4 @ X2274 @ X2275 @ X2276 @ X2277))!=(ap @ X2274 @ X2275 @ X2277 @ (esk79_4 @ X2274 @ X2275 @ X2276 @ X2277)))|((X2276)=(X2277))|~(in @ X2277 @ (funcSet @ X2274 @ X2275))|~(in @ X2276 @ (funcSet @ X2274 @ X2275))))&((~(in @ X2281 @ (funcSet @ X2279 @ X2280))|(~(in @ X2282 @ X2279)|((ap @ X2279 @ X2280 @ X2281 @ X2282)=(ap @ X2279 @ X2280 @ X2281 @ X2282))))&((~(func @ X2283 @ X2284 @ X2285)|(~(in @ X2286 @ X2283)|((ap @ X2283 @ X2284 @ X2285 @ X2286)=(ap @ X2283 @ X2284 @ X2285 @ X2286))))&((((in @ (esk80_3 @ X2287 @ X2288 @ X2289) @ X2287)|(~(in @ X2291 @ X2287)|((ap @ X2287 @ X2288 @ (lam @ X2287 @ X2288 @ X2289) @ X2291)=(X2289 @ X2291))))&(~(in @ (X2289 @ (esk80_3 @ X2287 @ X2288 @ X2289)) @ X2288)|(~(in @ X2291 @ X2287)|((ap @ X2287 @ X2288 @ (lam @ X2287 @ X2288 @ X2289) @ X2291)=(X2289 @ X2291)))))&((~(func @ X2292 @ X2293 @ X2294)|((lam @ X2292 @ X2293 @ (ap @ X2292 @ X2293 @ X2294))=(X2294)))&((((in @ (esk81_3 @ X2295 @ X2296 @ X2297) @ X2295)|((lam @ X2295 @ X2296 @ X2297)=(lam @ X2295 @ X2296 @ X2297)))&(~(in @ (X2297 @ (esk81_3 @ X2295 @ X2296 @ X2297)) @ X2296)|((lam @ X2295 @ X2296 @ X2297)=(lam @ X2295 @ X2296 @ X2297))))&((((in @ (esk82_3 @ X2299 @ X2300 @ X2301) @ X2299)|(~(in @ X2303 @ X2299)|((ap @ X2299 @ X2300 @ (lam @ X2299 @ X2300 @ X2301) @ X2303)=(X2301 @ X2303))))&(~(in @ (X2301 @ (esk82_3 @ X2299 @ X2300 @ X2301)) @ X2300)|(~(in @ X2303 @ X2299)|((ap @ X2299 @ X2300 @ (lam @ X2299 @ X2300 @ X2301) @ X2303)=(X2301 @ X2303)))))&((~(in @ X2306 @ (funcSet @ X2304 @ X2305))|((lam @ X2304 @ X2305 @ (ap @ X2304 @ X2305 @ X2306))=(X2306)))&((~(in @ X2309 @ X2307)|(~(in @ X2310 @ X2307)|((X2308)|(in @ X2310 @ (dsetconstr @ X2307 @ (^[Z0/* 9 */:$i]:((((X2308)&((Z0)=(X2309)))|(~((X2308))&((Z0)=(X2310)))))))))))&((~(in @ X2313 @ X2311)|(~(in @ X2314 @ X2311)|((X2312)|((dsetconstr @ X2311 @ (^[Z0/* 9 */:$i]:((((X2312)&((Z0)=(X2313)))|(~((X2312))&((Z0)=(X2314)))))))=(setadjoin @ X2314 @ emptyset)))))&((~(in @ X2317 @ X2315)|(~(in @ X2318 @ X2315)|(~(X2316)|(in @ X2317 @ (dsetconstr @ X2315 @ (^[Z0/* 9 */:$i]:((((X2316)&((Z0)=(X2317)))|(~((X2316))&((Z0)=(X2318)))))))))))&((~(in @ X2321 @ X2319)|(~(in @ X2322 @ X2319)|(~(X2320)|((dsetconstr @ X2319 @ (^[Z0/* 9 */:$i]:((((X2320)&((Z0)=(X2321)))|(~((X2320))&((Z0)=(X2322)))))))=(setadjoin @ X2321 @ emptyset)))))&((~(in @ X2325 @ X2323)|(~(in @ X2326 @ X2323)|(singleton @ (dsetconstr @ X2323 @ (^[Z0/* 9 */:$i]:((((X2324)&((Z0)=(X2325)))|(~((X2324))&((Z0)=(X2326))))))))))&((~(in @ X2329 @ X2327)|(~(in @ X2330 @ X2327)|(in @ (if @ X2327 @ ((X2328)) @ X2329 @ X2330) @ X2327)))&((~(singleton @ X2331)|(~(in @ X2332 @ X2331)|((setunion @ X2331)=(X2332))))&((~(in @ X2335 @ X2333)|(~(in @ X2336 @ X2333)|(~(X2334)|((if @ X2333 @ ((X2334)) @ X2335 @ X2336)=(X2335)))))&((~(in @ X2339 @ X2337)|(~(in @ X2340 @ X2337)|((X2338)|((if @ X2337 @ ((X2338)) @ X2339 @ X2340)=(X2340)))))&((~(in @ X2343 @ X2341)|(~(in @ X2344 @ X2341)|(in @ (if @ X2341 @ ((X2342)) @ X2343 @ X2344) @ (setadjoin @ X2343 @ (setadjoin @ X2344 @ emptyset)))))&((~(in @ X2346 @ (powerset @ X2345))|(~(in @ X2347 @ (powerset @ X2345))|(in @ (binintersect @ X2346 @ X2347) @ (powerset @ X2345))))&((~(in @ X2349 @ (powerset @ X2348))|(~(in @ X2350 @ (powerset @ X2348))|(in @ (binunion @ X2349 @ X2350) @ (powerset @ X2348))))&((~(in @ X2352 @ (powerset @ X2351))|(in @ (powerset @ X2352) @ (powerset @ (powerset @ X2351))))&((~(in @ X2354 @ (powerset @ X2353))|(~(in @ X2355 @ (powerset @ X2353))|(in @ (setminus @ X2354 @ X2355) @ (powerset @ X2353))))&((~(in @ X2357 @ (powerset @ X2356))|(in @ (setminus @ X2356 @ X2357) @ (powerset @ X2356)))&(((((in @ (esk84_3 @ X2358 @ X2359 @ X2360) @ X2358)|((X2359)=(X2360))|(in @ (esk83_3 @ X2358 @ X2359 @ X2360) @ X2358)|~(in @ X2360 @ (powerset @ X2358))|~(in @ X2359 @ (powerset @ X2358)))&(((in @ (esk84_3 @ X2358 @ X2359 @ X2360) @ X2360)|((X2359)=(X2360))|(in @ (esk83_3 @ X2358 @ X2359 @ X2360) @ X2358)|~(in @ X2360 @ (powerset @ X2358))|~(in @ X2359 @ (powerset @ X2358)))&(~(in @ (esk84_3 @ X2358 @ X2359 @ X2360) @ X2359)|((X2359)=(X2360))|(in @ (esk83_3 @ X2358 @ X2359 @ X2360) @ X2358)|~(in @ X2360 @ (powerset @ X2358))|~(in @ X2359 @ (powerset @ X2358)))))&((((in @ (esk84_3 @ X2358 @ X2359 @ X2360) @ X2358)|((X2359)=(X2360))|(in @ (esk83_3 @ X2358 @ X2359 @ X2360) @ X2359)|~(in @ X2360 @ (powerset @ X2358))|~(in @ X2359 @ (powerset @ X2358)))&(((in @ (esk84_3 @ X2358 @ X2359 @ X2360) @ X2360)|((X2359)=(X2360))|(in @ (esk83_3 @ X2358 @ X2359 @ X2360) @ X2359)|~(in @ X2360 @ (powerset @ X2358))|~(in @ X2359 @ (powerset @ X2358)))&(~(in @ (esk84_3 @ X2358 @ X2359 @ X2360) @ X2359)|((X2359)=(X2360))|(in @ (esk83_3 @ X2358 @ X2359 @ X2360) @ X2359)|~(in @ X2360 @ (powerset @ X2358))|~(in @ X2359 @ (powerset @ X2358)))))&(((in @ (esk84_3 @ X2358 @ X2359 @ X2360) @ X2358)|((X2359)=(X2360))|~(in @ (esk83_3 @ X2358 @ X2359 @ X2360) @ X2360)|~(in @ X2360 @ (powerset @ X2358))|~(in @ X2359 @ (powerset @ X2358)))&(((in @ (esk84_3 @ X2358 @ X2359 @ X2360) @ X2360)|((X2359)=(X2360))|~(in @ (esk83_3 @ X2358 @ X2359 @ X2360) @ X2360)|~(in @ X2360 @ (powerset @ X2358))|~(in @ X2359 @ (powerset @ X2358)))&(~(in @ (esk84_3 @ X2358 @ X2359 @ X2360) @ X2359)|((X2359)=(X2360))|~(in @ (esk83_3 @ X2358 @ X2359 @ X2360) @ X2360)|~(in @ X2360 @ (powerset @ X2358))|~(in @ X2359 @ (powerset @ X2358)))))))&((((in @ (esk85_3 @ X2363 @ X2364 @ X2365) @ X2363)|(subset @ X2364 @ X2365)|~(in @ X2365 @ (powerset @ X2363))|~(in @ X2364 @ (powerset @ X2363)))&(((in @ (esk85_3 @ X2363 @ X2364 @ X2365) @ X2364)|(subset @ X2364 @ X2365)|~(in @ X2365 @ (powerset @ X2363))|~(in @ X2364 @ (powerset @ X2363)))&(~(in @ (esk85_3 @ X2363 @ X2364 @ X2365) @ X2365)|(subset @ X2364 @ X2365)|~(in @ X2365 @ (powerset @ X2363))|~(in @ X2364 @ (powerset @ X2363)))))&((((in @ (esk86_3 @ X2367 @ X2368 @ X2369) @ X2367)|(in @ X2368 @ (powerset @ X2369))|~(in @ X2369 @ (powerset @ X2367))|~(in @ X2368 @ (powerset @ X2367)))&(((in @ (esk86_3 @ X2367 @ X2368 @ X2369) @ X2368)|(in @ X2368 @ (powerset @ X2369))|~(in @ X2369 @ (powerset @ X2367))|~(in @ X2368 @ (powerset @ X2367)))&(~(in @ (esk86_3 @ X2367 @ X2368 @ X2369) @ X2369)|(in @ X2368 @ (powerset @ X2369))|~(in @ X2369 @ (powerset @ X2367))|~(in @ X2368 @ (powerset @ X2367)))))&((~(in @ X2372 @ (powerset @ X2371))|(~(in @ X2373 @ (powerset @ X2371))|(~(in @ X2374 @ X2371)|(~(in @ X2372 @ (powerset @ X2373))|(~(in @ X2374 @ X2372)|(in @ X2374 @ X2373))))))&((~(in @ X2376 @ (powerset @ X2375))|(~(in @ X2377 @ X2375)|(~(in @ X2377 @ X2376)|~(in @ X2377 @ (setminus @ X2375 @ X2376)))))&((~(in @ X2379 @ (powerset @ X2378))|(~(in @ X2380 @ X2378)|((in @ X2380 @ (setminus @ X2378 @ X2379))|(in @ X2380 @ X2379))))&((~(in @ X2382 @ (powerset @ X2381))|(~(in @ X2383 @ (powerset @ X2381))|(~(in @ X2384 @ X2381)|((in @ X2384 @ X2382)|~(in @ X2384 @ (binintersect @ X2382 @ X2383))))))&((~(in @ X2386 @ (powerset @ X2385))|(~(in @ X2387 @ (powerset @ X2385))|(~(in @ X2388 @ X2385)|((in @ X2388 @ X2387)|~(in @ X2388 @ (binintersect @ X2386 @ X2387))))))&((~(in @ X2390 @ (powerset @ X2389))|(~(in @ X2391 @ (powerset @ X2389))|(~(in @ X2392 @ X2389)|(~(subset @ X2390 @ (setminus @ X2389 @ X2391))|(~(in @ X2392 @ X2391)|~(in @ X2392 @ X2390))))))&((~(in @ X2394 @ (powerset @ X2393))|(~(in @ X2395 @ (powerset @ X2393))|(~(in @ X2396 @ X2393)|(~(subset @ X2394 @ X2395)|((in @ X2396 @ X2395)|~(in @ X2396 @ X2394))))))&((~(in @ X2398 @ (powerset @ X2397))|(~(in @ X2399 @ (powerset @ X2397))|(~(subset @ X2398 @ X2399)|(subset @ (setminus @ X2397 @ X2399) @ (setminus @ X2397 @ X2398)))))&((~(in @ X2401 @ (powerset @ X2400))|(~(in @ X2402 @ (powerset @ X2400))|(~(subset @ (setminus @ X2400 @ X2402) @ (setminus @ X2400 @ X2401))|(subset @ X2401 @ X2402))))&((~(in @ X2404 @ (powerset @ X2403))|(~(in @ X2405 @ X2403)|(~(in @ X2405 @ X2404)|(in @ X2405 @ (setminus @ X2403 @ (setminus @ X2403 @ X2404))))))&((~(in @ X2407 @ (powerset @ X2406))|(~(in @ X2408 @ X2406)|(~(in @ X2408 @ (setminus @ X2406 @ (setminus @ X2406 @ X2407)))|(in @ X2408 @ X2407))))&((in @ esk88_0 @ (powerset @ esk87_0))&~(subset @ esk88_0 @ (setminus @ esk87_0 @ (setminus @ esk87_0 @ esk88_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_331])])])])])])])). 359.80/46.12 thf(c_0_333, negated_conjecture, ~((subset @ esk88_0 @ (setminus @ esk87_0 @ (setminus @ esk87_0 @ esk88_0)))), inference(split_conjunct,[status(thm)],[c_0_332])). 359.80/46.12 thf(c_0_334, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk53_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_332])). 359.80/46.12 thf(c_0_335, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ (setminus @ X3 @ (setminus @ X3 @ X2)))|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_332])). 359.80/46.12 thf(c_0_336, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_332])). 359.80/46.12 thf(c_0_337, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk53_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_332])). 359.80/46.12 thf(c_0_338, negated_conjecture, ~((in @ (esk53_2 @ esk88_0 @ (setminus @ esk87_0 @ (setminus @ esk87_0 @ esk88_0))) @ (setminus @ esk87_0 @ (setminus @ esk87_0 @ esk88_0)))), inference(spm,[status(thm)],[c_0_333, c_0_334])). 359.80/46.12 thf(c_0_339, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ (setminus @ X3 @ (setminus @ X3 @ X4)))|~((in @ X4 @ (powerset @ X3)))|~((in @ X2 @ X4)))), inference(csr,[status(thm)],[c_0_335, c_0_336])). 359.80/46.12 thf(c_0_340, negated_conjecture, (in @ esk88_0 @ (powerset @ esk87_0)), inference(split_conjunct,[status(thm)],[c_0_332])). 359.80/46.12 thf(c_0_341, negated_conjecture, (in @ (esk53_2 @ esk88_0 @ (setminus @ esk87_0 @ (setminus @ esk87_0 @ esk88_0))) @ esk88_0), inference(spm,[status(thm)],[c_0_333, c_0_337])). 359.80/46.12 thf(c_0_342, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_338, c_0_339]), c_0_340]), c_0_341])]), ['proof']). 359.80/46.12 # SZS output end CNFRefutation 359.80/46.12 # Parsed axioms : 533 359.80/46.12 # Removed by relevancy pruning/SinE : 0 359.80/46.12 # Initial clauses : 711 359.80/46.12 # Removed in clause preprocessing : 312 359.80/46.12 # Initial clauses in saturation : 399 359.80/46.12 # Processed clauses : 1832 359.80/46.12 # ...of these trivial : 83 359.80/46.12 # ...subsumed : 698 359.80/46.12 # ...remaining for further processing : 1051 359.80/46.12 # Other redundant clauses eliminated : 45 359.80/46.12 # Clauses deleted for lack of memory : 0 359.80/46.12 # Backward-subsumed : 4 359.80/46.12 # Backward-rewritten : 11 359.80/46.12 # Generated clauses : 13719 359.80/46.12 # ...of the previous two non-redundant : 12360 359.80/46.12 # ...aggressively subsumed : 0 359.80/46.12 # Contextual simplify-reflections : 4 359.80/46.12 # Paramodulations : 13662 359.80/46.12 # Factorizations : 2 359.80/46.12 # NegExts : 0 359.80/46.12 # Equation resolutions : 50 359.80/46.12 # Disequality decompositions : 0 359.80/46.12 # Total rewrite steps : 1968 359.80/46.12 # ...of those cached : 1546 359.80/46.12 # Propositional unsat checks : 0 359.80/46.12 # Propositional check models : 0 359.80/46.12 # Propositional check unsatisfiable : 0 359.80/46.12 # Propositional clauses : 0 359.80/46.12 # Propositional clauses after purity: 0 359.80/46.12 # Propositional unsat core size : 0 359.80/46.12 # Propositional preprocessing time : 0.000 359.80/46.12 # Propositional encoding time : 0.000 359.80/46.12 # Propositional solver time : 0.000 359.80/46.12 # Success case prop preproc time : 0.000 359.80/46.12 # Success case prop encoding time : 0.000 359.80/46.12 # Success case prop solver time : 0.000 359.80/46.12 # Current number of processed clauses : 673 359.80/46.12 # Positive orientable unit clauses : 183 359.80/46.12 # Positive unorientable unit clauses: 0 359.80/46.12 # Negative unit clauses : 36 359.80/46.12 # Non-unit-clauses : 454 359.80/46.12 # Current number of unprocessed clauses: 11184 359.80/46.12 # ...number of literals in the above : 32966 359.80/46.12 # Current number of archived formulas : 0 359.80/46.12 # Current number of archived clauses : 363 359.80/46.12 # Clause-clause subsumption calls (NU) : 38505 359.80/46.12 # Rec. Clause-clause subsumption calls : 17148 359.80/46.12 # Non-unit clause-clause subsumptions : 181 359.80/46.12 # Unit Clause-clause subsumption calls : 2712 359.80/46.12 # Rewrite failures with RHS unbound : 0 359.80/46.12 # BW rewrite match attempts : 66 359.80/46.12 # BW rewrite match successes : 12 359.80/46.12 # Condensation attempts : 0 359.80/46.12 # Condensation successes : 0 359.80/46.12 # Termbank termtop insertions : 371340 359.80/46.12 # Search garbage collected termcells : 25520 359.80/46.12 359.80/46.12 # ------------------------------------------------- 359.80/46.12 # User time : 43.298 s 359.80/46.12 # System time : 1.308 s 359.80/46.12 # Total time : 44.606 s 359.80/46.12 # Maximum resident set size: 8080 pages 359.80/46.12 359.80/46.12 # ------------------------------------------------- 359.80/46.12 # User time : 43.307 s 359.80/46.12 # System time : 1.312 s 359.80/46.12 # Total time : 44.619 s 359.80/46.12 # Maximum resident set size: 2604 pages 359.80/46.12 % E exiting 359.80/46.12 % E exiting 359.80/46.12 EOF