0.00/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.09 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM 0.09/0.28 % Computer : n025.cluster.edu 0.09/0.28 % Model : x86_64 x86_64 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.28 % Memory : 8042.1875MB 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.28 % CPULimit : 1920 0.09/0.28 % WCLimit : 240 0.09/0.28 % DateTime : Wed Jul 30 03:48:19 EDT 2025 0.09/0.29 % CPUTime : 0.14/0.39 Running higher-order theorem proving 0.14/0.46 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.CBN2axI2wP/E---3.1_1400.p 17.14/2.68 # Version: 3.0.0-ho 17.14/2.68 # Preprocessing class: HSLMSLSSLLLCHFA. 17.14/2.68 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 17.14/2.68 # Starting ehoh_best5 with 240s (1) cores 17.14/2.68 # Starting almost_fo_3_lam with 240s (1) cores 17.14/2.68 # Starting new_bool_5 with 240s (1) cores 17.14/2.68 # Starting pre_casc_3 with 240s (1) cores 17.14/2.68 # Starting ho_unfolding_8 with 240s (1) cores 17.14/2.68 # Starting new_ho_10_cnf2 with 240s (1) cores 17.14/2.68 # Starting new_bool_3 with 240s (1) cores 17.14/2.68 # Starting new_ho_5 with 240s (1) cores 17.14/2.68 # new_bool_3 with pid 1485 completed with status 0 17.14/2.68 # Result found by new_bool_3 17.14/2.68 # Preprocessing class: HSLMSLSSLLLCHFA. 17.14/2.68 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 17.14/2.68 # Starting ehoh_best5 with 240s (1) cores 17.14/2.68 # Starting almost_fo_3_lam with 240s (1) cores 17.14/2.68 # Starting new_bool_5 with 240s (1) cores 17.14/2.68 # Starting pre_casc_3 with 240s (1) cores 17.14/2.68 # Starting ho_unfolding_8 with 240s (1) cores 17.14/2.68 # Starting new_ho_10_cnf2 with 240s (1) cores 17.14/2.68 # Starting new_bool_3 with 240s (1) cores 17.14/2.68 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 17.14/2.68 # Search class: HGHSM-FSLM32-MHFMMSBN 17.14/2.68 # Scheduled 9 strats onto 1 cores with 240 seconds (240 total) 17.14/2.68 # Starting ho_unfolding_8 with 49s (1) cores 17.14/2.68 # ho_unfolding_8 with pid 1494 completed with status 0 17.14/2.68 # Result found by ho_unfolding_8 17.14/2.68 # Preprocessing class: HSLMSLSSLLLCHFA. 17.14/2.68 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 17.14/2.68 # Starting ehoh_best5 with 240s (1) cores 17.14/2.68 # Starting almost_fo_3_lam with 240s (1) cores 17.14/2.68 # Starting new_bool_5 with 240s (1) cores 17.14/2.68 # Starting pre_casc_3 with 240s (1) cores 17.14/2.68 # Starting ho_unfolding_8 with 240s (1) cores 17.14/2.68 # Starting new_ho_10_cnf2 with 240s (1) cores 17.14/2.68 # Starting new_bool_3 with 240s (1) cores 17.14/2.68 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 17.14/2.68 # Search class: HGHSM-FSLM32-MHFMMSBN 17.14/2.68 # Scheduled 9 strats onto 1 cores with 240 seconds (240 total) 17.14/2.68 # Starting ho_unfolding_8 with 49s (1) cores 17.14/2.68 # Preprocessing time : 0.127 s 17.14/2.68 # Presaturation interreduction done 17.14/2.68 17.14/2.68 # Proof found! 17.14/2.68 # SZS status Theorem 17.14/2.68 # SZS output start CNFRefutation 17.14/2.68 thf(decl_23, type, in: $i > $i > $o). 17.14/2.68 thf(decl_24, type, exu: ($i > $o) > $o). 17.14/2.68 thf(decl_25, type, setextAx: $o). 17.14/2.68 thf(decl_26, type, emptyset: $i). 17.14/2.68 thf(decl_27, type, emptysetAx: $o). 17.14/2.68 thf(decl_28, type, setadjoin: $i > $i > $i). 17.14/2.68 thf(decl_29, type, setadjoinAx: $o). 17.14/2.68 thf(decl_30, type, powerset: $i > $i). 17.14/2.68 thf(decl_31, type, powersetAx: $o). 17.14/2.68 thf(decl_32, type, setunion: $i > $i). 17.14/2.68 thf(decl_33, type, setunionAx: $o). 17.14/2.68 thf(decl_34, type, omega: $i). 17.14/2.68 thf(decl_35, type, omega0Ax: $o). 17.14/2.68 thf(decl_36, type, omegaSAx: $o). 17.14/2.68 thf(decl_37, type, omegaIndAx: $o). 17.14/2.68 thf(decl_38, type, replAx: $o). 17.14/2.68 thf(decl_39, type, foundationAx: $o). 17.14/2.68 thf(decl_40, type, wellorderingAx: $o). 17.14/2.68 thf(decl_41, type, descr: ($i > $o) > $i). 17.14/2.68 thf(decl_42, type, descrp: $o). 17.14/2.68 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 17.14/2.68 thf(decl_44, type, dsetconstrI: $o). 17.14/2.68 thf(decl_45, type, dsetconstrEL: $o). 17.14/2.68 thf(decl_46, type, dsetconstrER: $o). 17.14/2.68 thf(decl_47, type, exuE1: $o). 17.14/2.68 thf(decl_48, type, prop2set: $o > $i). 17.14/2.68 thf(decl_49, type, prop2setE: $o). 17.14/2.68 thf(decl_50, type, emptysetE: $o). 17.14/2.68 thf(decl_51, type, emptysetimpfalse: $o). 17.14/2.68 thf(decl_52, type, notinemptyset: $o). 17.14/2.68 thf(decl_53, type, exuE3e: $o). 17.14/2.68 thf(decl_54, type, setext: $o). 17.14/2.68 thf(decl_55, type, emptyI: $o). 17.14/2.68 thf(decl_56, type, noeltsimpempty: $o). 17.14/2.68 thf(decl_57, type, setbeta: $o). 17.14/2.68 thf(decl_58, type, nonempty: $i > $o). 17.14/2.68 thf(decl_59, type, nonemptyE1: $o). 17.14/2.68 thf(decl_60, type, nonemptyI: $o). 17.14/2.68 thf(decl_61, type, nonemptyI1: $o). 17.14/2.68 thf(decl_62, type, setadjoinIL: $o). 17.14/2.68 thf(decl_63, type, emptyinunitempty: $o). 17.14/2.68 thf(decl_64, type, setadjoinIR: $o). 17.14/2.68 thf(decl_65, type, setadjoinE: $o). 17.14/2.68 thf(decl_66, type, setadjoinOr: $o). 17.14/2.68 thf(decl_67, type, setoftrueEq: $o). 17.14/2.68 thf(decl_68, type, powersetI: $o). 17.14/2.68 thf(decl_69, type, emptyinPowerset: $o). 17.14/2.68 thf(decl_70, type, emptyInPowerset: $o). 17.14/2.68 thf(decl_71, type, powersetE: $o). 17.14/2.68 thf(decl_72, type, setunionI: $o). 17.14/2.68 thf(decl_73, type, setunionE: $o). 17.14/2.68 thf(decl_74, type, subPowSU: $o). 17.14/2.68 thf(decl_75, type, exuE2: $o). 17.14/2.68 thf(decl_76, type, nonemptyImpWitness: $o). 17.14/2.68 thf(decl_77, type, uniqinunit: $o). 17.14/2.68 thf(decl_78, type, notinsingleton: $o). 17.14/2.68 thf(decl_79, type, eqinunit: $o). 17.14/2.68 thf(decl_80, type, singletonsswitch: $o). 17.14/2.68 thf(decl_81, type, upairsetE: $o). 17.14/2.68 thf(decl_82, type, upairsetIL: $o). 17.14/2.68 thf(decl_83, type, upairsetIR: $o). 17.14/2.68 thf(decl_84, type, emptyE1: $o). 17.14/2.68 thf(decl_85, type, vacuousDall: $o). 17.14/2.68 thf(decl_86, type, quantDeMorgan1: $o). 17.14/2.68 thf(decl_87, type, quantDeMorgan2: $o). 17.14/2.68 thf(decl_88, type, quantDeMorgan3: $o). 17.14/2.68 thf(decl_89, type, quantDeMorgan4: $o). 17.14/2.68 thf(decl_90, type, prop2setI: $o). 17.14/2.68 thf(decl_92, type, prop2set2propI: $o). 17.14/2.68 thf(decl_93, type, notdexE: $o). 17.14/2.68 thf(decl_94, type, notdallE: $o). 17.14/2.68 thf(decl_95, type, exuI1: $o). 17.14/2.68 thf(decl_96, type, exuI3: $o). 17.14/2.68 thf(decl_97, type, exuI2: $o). 17.14/2.68 thf(decl_98, type, inCongP: $o). 17.14/2.68 thf(decl_99, type, in__Cong: $o). 17.14/2.68 thf(decl_100, type, exuE3u: $o). 17.14/2.68 thf(decl_101, type, exu__Cong: $o). 17.14/2.68 thf(decl_102, type, emptyset__Cong: $o). 17.14/2.68 thf(decl_103, type, setadjoin__Cong: $o). 17.14/2.68 thf(decl_104, type, powerset__Cong: $o). 17.14/2.68 thf(decl_105, type, setunion__Cong: $o). 17.14/2.68 thf(decl_106, type, omega__Cong: $o). 17.14/2.68 thf(decl_107, type, exuEu: $o). 17.14/2.68 thf(decl_108, type, descr__Cong: $o). 17.14/2.68 thf(decl_109, type, dsetconstr__Cong: $o). 17.14/2.68 thf(decl_110, type, subset: $i > $i > $o). 17.14/2.68 thf(decl_113, type, subsetI1: $o). 17.14/2.68 thf(decl_114, type, eqimpsubset2: $o). 17.14/2.68 thf(decl_115, type, eqimpsubset1: $o). 17.14/2.68 thf(decl_116, type, subsetI2: $o). 17.14/2.68 thf(decl_117, type, emptysetsubset: $o). 17.14/2.68 thf(decl_118, type, subsetE: $o). 17.14/2.68 thf(decl_119, type, subsetE2: $o). 17.14/2.68 thf(decl_120, type, notsubsetI: $o). 17.14/2.68 thf(decl_121, type, notequalI1: $o). 17.14/2.68 thf(decl_122, type, notequalI2: $o). 17.14/2.68 thf(decl_123, type, subsetRefl: $o). 17.14/2.68 thf(decl_124, type, subsetTrans: $o). 17.14/2.68 thf(decl_125, type, setadjoinSub: $o). 17.14/2.68 thf(decl_126, type, setadjoinSub2: $o). 17.14/2.68 thf(decl_127, type, subset2powerset: $o). 17.14/2.68 thf(decl_128, type, setextsub: $o). 17.14/2.68 thf(decl_129, type, subsetemptysetimpeq: $o). 17.14/2.68 thf(decl_130, type, powersetI1: $o). 17.14/2.68 thf(decl_131, type, powersetE1: $o). 17.14/2.68 thf(decl_132, type, inPowerset: $o). 17.14/2.68 thf(decl_133, type, powersetsubset: $o). 17.14/2.68 thf(decl_134, type, sepInPowerset: $o). 17.14/2.68 thf(decl_135, type, sepSubset: $o). 17.14/2.68 thf(decl_136, type, binunion: $i > $i > $i). 17.14/2.68 thf(decl_137, type, binunionIL: $o). 17.14/2.68 thf(decl_138, type, upairset2IR: $o). 17.14/2.68 thf(decl_139, type, binunionIR: $o). 17.14/2.68 thf(decl_140, type, binunionEcases: $o). 17.14/2.68 thf(decl_141, type, binunionE: $o). 17.14/2.68 thf(decl_142, type, binunionLsub: $o). 17.14/2.68 thf(decl_143, type, binunionRsub: $o). 17.14/2.68 thf(decl_144, type, binintersect: $i > $i > $i). 17.14/2.68 thf(decl_145, type, binintersectI: $o). 17.14/2.68 thf(decl_146, type, binintersectSubset5: $o). 17.14/2.68 thf(decl_147, type, binintersectEL: $o). 17.14/2.68 thf(decl_148, type, binintersectLsub: $o). 17.14/2.68 thf(decl_149, type, binintersectSubset2: $o). 17.14/2.68 thf(decl_150, type, binintersectSubset3: $o). 17.14/2.68 thf(decl_151, type, binintersectER: $o). 17.14/2.68 thf(decl_152, type, disjointsetsI1: $o). 17.14/2.68 thf(decl_153, type, binintersectRsub: $o). 17.14/2.68 thf(decl_154, type, binintersectSubset4: $o). 17.14/2.68 thf(decl_155, type, binintersectSubset1: $o). 17.14/2.68 thf(decl_156, type, bs114d: $o). 17.14/2.68 thf(decl_158, type, setminus: $i > $i > $i). 17.14/2.68 thf(decl_159, type, setminusI: $o). 17.14/2.68 thf(decl_160, type, setminusEL: $o). 17.14/2.68 thf(decl_161, type, setminusER: $o). 17.14/2.68 thf(decl_162, type, setminusSubset2: $o). 17.14/2.68 thf(decl_163, type, setminusERneg: $o). 17.14/2.68 thf(decl_164, type, setminusELneg: $o). 17.14/2.68 thf(decl_165, type, setminusILneg: $o). 17.14/2.68 thf(decl_166, type, setminusIRneg: $o). 17.14/2.68 thf(decl_167, type, setminusLsub: $o). 17.14/2.68 thf(decl_168, type, setminusSubset1: $o). 17.14/2.68 thf(decl_169, type, symdiff: $i > $i > $i). 17.14/2.68 thf(decl_170, type, symdiffE: $o). 17.14/2.68 thf(decl_171, type, symdiffI1: $o). 17.14/2.68 thf(decl_172, type, symdiffI2: $o). 17.14/2.68 thf(decl_173, type, symdiffIneg1: $o). 17.14/2.68 thf(decl_174, type, symdiffIneg2: $o). 17.14/2.68 thf(decl_175, type, iskpair: $i > $o). 17.14/2.68 thf(decl_176, type, secondinupair: $o). 17.14/2.68 thf(decl_177, type, setukpairIL: $o). 17.14/2.68 thf(decl_178, type, setukpairIR: $o). 17.14/2.68 thf(decl_179, type, kpairiskpair: $o). 17.14/2.68 thf(decl_180, type, kpair: $i > $i > $i). 17.14/2.68 thf(decl_181, type, kpairp: $o). 17.14/2.68 thf(decl_182, type, cartprod: $i > $i > $i). 17.14/2.68 thf(decl_183, type, singletonsubset: $o). 17.14/2.68 thf(decl_184, type, singletoninpowerset: $o). 17.14/2.68 thf(decl_185, type, singletoninpowunion: $o). 17.14/2.68 thf(decl_186, type, upairset2E: $o). 17.14/2.68 thf(decl_187, type, upairsubunion: $o). 17.14/2.68 thf(decl_188, type, upairinpowunion: $o). 17.14/2.68 thf(decl_189, type, ubforcartprodlem1: $o). 17.14/2.68 thf(decl_190, type, ubforcartprodlem2: $o). 17.14/2.68 thf(decl_191, type, ubforcartprodlem3: $o). 17.14/2.68 thf(decl_192, type, cartprodpairin: $o). 17.14/2.68 thf(decl_193, type, cartprodmempair1: $o). 17.14/2.68 thf(decl_194, type, cartprodmempair: $o). 17.14/2.68 thf(decl_195, type, setunionE2: $o). 17.14/2.68 thf(decl_196, type, setunionsingleton1: $o). 17.14/2.68 thf(decl_197, type, setunionsingleton2: $o). 17.14/2.68 thf(decl_198, type, setunionsingleton: $o). 17.14/2.68 thf(decl_199, type, singleton: $i > $o). 17.14/2.68 thf(decl_200, type, singletonprop: $o). 17.14/2.68 thf(decl_201, type, ex1: $i > ($i > $o) > $o). 17.14/2.68 thf(decl_202, type, ex1E1: $o). 17.14/2.68 thf(decl_203, type, ex1I: $o). 17.14/2.68 thf(decl_204, type, ex1I2: $o). 17.14/2.68 thf(decl_205, type, singletonsuniq: $o). 17.14/2.68 thf(decl_210, type, setukpairinjL1: $o). 17.14/2.68 thf(decl_211, type, kfstsingleton: $o). 17.14/2.68 thf(decl_212, type, theprop: $o). 17.14/2.68 thf(decl_213, type, kfst: $i > $i). 17.14/2.68 thf(decl_214, type, kfstpairEq: $o). 17.14/2.68 thf(decl_215, type, cartprodfstin: $o). 17.14/2.68 thf(decl_216, type, setukpairinjL2: $o). 17.14/2.68 thf(decl_217, type, setukpairinjL: $o). 17.14/2.68 thf(decl_218, type, setukpairinjR11: $o). 17.14/2.68 thf(decl_219, type, setukpairinjR12: $o). 17.14/2.68 thf(decl_220, type, setukpairinjR1: $o). 17.14/2.68 thf(decl_221, type, upairequniteq: $o). 17.14/2.68 thf(decl_222, type, setukpairinjR2: $o). 17.14/2.68 thf(decl_223, type, setukpairinjR: $o). 17.14/2.68 thf(decl_224, type, ksndsingleton: $o). 17.14/2.68 thf(decl_225, type, ksnd: $i > $i). 17.14/2.68 thf(decl_226, type, ksndpairEq: $o). 17.14/2.68 thf(decl_227, type, kpairsurjEq: $o). 17.14/2.68 thf(decl_228, type, cartprodsndin: $o). 17.14/2.68 thf(decl_229, type, cartprodpairmemEL: $o). 17.14/2.68 thf(decl_230, type, cartprodpairmemER: $o). 17.14/2.68 thf(decl_231, type, cartprodmempaircEq: $o). 17.14/2.68 thf(decl_232, type, cartprodfstpairEq: $o). 17.14/2.68 thf(decl_233, type, cartprodsndpairEq: $o). 17.14/2.68 thf(decl_234, type, cartprodpairsurjEq: $o). 17.14/2.68 thf(decl_235, type, breln: $i > $i > $i > $o). 17.14/2.68 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 17.14/2.68 thf(decl_237, type, dpsetconstrI: $o). 17.14/2.68 thf(decl_238, type, dpsetconstrSub: $o). 17.14/2.68 thf(decl_239, type, setOfPairsIsBReln: $o). 17.14/2.68 thf(decl_240, type, dpsetconstrERa: $o). 17.14/2.68 thf(decl_241, type, dpsetconstrEL1: $o). 17.14/2.68 thf(decl_242, type, dpsetconstrEL2: $o). 17.14/2.68 thf(decl_243, type, dpsetconstrER: $o). 17.14/2.68 thf(decl_244, type, func: $i > $i > $i > $o). 17.14/2.68 thf(decl_245, type, funcSet: $i > $i > $i). 17.14/2.68 thf(decl_246, type, funcImageSingleton: $o). 17.14/2.68 thf(decl_247, type, apProp: $o). 17.14/2.68 thf(decl_248, type, ap: $i > $i > $i > $i > $i). 17.14/2.68 thf(decl_249, type, app: $o). 17.14/2.68 thf(decl_250, type, infuncsetfunc: $o). 17.14/2.68 thf(decl_251, type, ap2p: $o). 17.14/2.68 thf(decl_252, type, funcinfuncset: $o). 17.14/2.68 thf(decl_253, type, lamProp: $o). 17.14/2.68 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i). 17.14/2.68 thf(decl_255, type, lamp: $o). 17.14/2.68 thf(decl_256, type, lam2p: $o). 17.14/2.68 thf(decl_257, type, brelnall1: $o). 17.14/2.68 thf(decl_258, type, brelnall2: $o). 17.14/2.68 thf(decl_259, type, ex1E2: $o). 17.14/2.68 thf(decl_260, type, funcGraphProp1: $o). 17.14/2.68 thf(decl_261, type, funcGraphProp3: $o). 17.14/2.68 thf(decl_262, type, funcGraphProp2: $o). 17.14/2.68 thf(decl_263, type, funcextLem: $o). 17.14/2.68 thf(decl_264, type, funcGraphProp4: $o). 17.14/2.68 thf(decl_265, type, subbreln: $o). 17.14/2.68 thf(decl_266, type, eqbreln: $o). 17.14/2.68 thf(decl_267, type, funcext: $o). 17.14/2.68 thf(decl_268, type, funcext2: $o). 17.14/2.68 thf(decl_269, type, ap2apEq1: $o). 17.14/2.68 thf(decl_270, type, ap2apEq2: $o). 17.14/2.68 thf(decl_271, type, beta1: $o). 17.14/2.68 thf(decl_272, type, eta1: $o). 17.14/2.68 thf(decl_273, type, lam2lamEq: $o). 17.14/2.68 thf(decl_274, type, beta2: $o). 17.14/2.68 thf(decl_275, type, eta2: $o). 17.14/2.68 thf(decl_276, type, iffalseProp1: $o). 17.14/2.68 thf(decl_277, type, iffalseProp2: $o). 17.14/2.68 thf(decl_278, type, iftrueProp1: $o). 17.14/2.68 thf(decl_279, type, iftrueProp2: $o). 17.14/2.68 thf(decl_280, type, ifSingleton: $o). 17.14/2.68 thf(decl_281, type, if: $i > $o > $i > $i > $i). 17.14/2.68 thf(decl_282, type, ifp: $o). 17.14/2.68 thf(decl_283, type, theeq: $o). 17.14/2.68 thf(decl_284, type, iftrue: $o). 17.14/2.68 thf(decl_285, type, iffalse: $o). 17.14/2.68 thf(decl_286, type, iftrueorfalse: $o). 17.14/2.68 thf(decl_287, type, binintersectT_lem: $o). 17.14/2.68 thf(decl_288, type, binunionT_lem: $o). 17.14/2.68 thf(decl_289, type, powersetT_lem: $o). 17.14/2.68 thf(decl_290, type, setminusT_lem: $o). 17.14/2.68 thf(decl_291, type, complementT_lem: $o). 17.14/2.68 thf(decl_292, type, setextT: $o). 17.14/2.68 thf(decl_293, type, subsetTI: $o). 17.14/2.68 thf(decl_294, type, powersetTI1: $o). 17.14/2.68 thf(decl_295, type, powersetTE1: $o). 17.14/2.68 thf(decl_296, type, complementTI1: $o). 17.14/2.68 thf(decl_297, type, complementTE1: $o). 17.14/2.68 thf(decl_298, type, binintersectTELcontra: $o). 17.14/2.68 thf(decl_299, type, binintersectTERcontra: $o). 17.14/2.68 thf(decl_300, type, contrasubsetT: $o). 17.14/2.68 thf(decl_301, type, contrasubsetT1: $o). 17.14/2.68 thf(decl_302, type, contrasubsetT2: $o). 17.14/2.68 thf(decl_303, type, contrasubsetT3: $o). 17.14/2.68 thf(decl_304, type, doubleComplementI1: $o). 17.14/2.68 thf(decl_305, type, doubleComplementE1: $o). 17.14/2.68 thf(decl_306, type, doubleComplementSub1: $o). 17.14/2.68 thf(decl_307, type, doubleComplementSub2: $o). 17.14/2.68 thf(decl_308, type, doubleComplementEq: $o). 17.14/2.68 thf(decl_309, type, complementTnotintersectT: $o). 17.14/2.68 thf(decl_310, type, complementImpComplementIntersect: $o). 17.14/2.68 thf(decl_311, type, complementSubsetComplementIntersect: $o). 17.14/2.68 thf(decl_312, type, complementInPowersetComplementIntersect: $o). 17.14/2.68 thf(decl_313, type, contraSubsetComplement: $o). 17.14/2.68 thf(decl_314, type, complementTcontraSubset: $o). 17.14/2.68 thf(decl_315, type, binunionTILcontra: $o). 17.14/2.68 thf(decl_316, type, binunionTIRcontra: $o). 17.14/2.68 thf(decl_317, type, inIntersectImpInUnion: $o). 17.14/2.68 thf(decl_318, type, inIntersectImpInUnion2: $o). 17.14/2.68 thf(decl_319, type, inIntersectImpInIntersectUnions: $o). 17.14/2.68 thf(decl_320, type, intersectInPowersetIntersectUnions: $o). 17.14/2.68 thf(decl_321, type, inComplementUnionImpNotIn1: $o). 17.14/2.68 thf(decl_322, type, inComplementUnionImpInComplement1: $o). 17.14/2.68 thf(decl_323, type, binunionTE: $o). 17.14/2.68 thf(decl_324, type, binunionTEcontra: $o). 17.14/2.68 thf(decl_325, type, demorgan2a1: $o). 17.14/2.68 thf(decl_326, type, complementUnionInPowersetComplement: $o). 17.14/2.68 thf(decl_327, type, demorgan2a2: $o). 17.14/2.68 thf(decl_328, type, demorgan1a: $o). 17.14/2.68 thf(decl_329, type, demorgan1b: $o). 17.14/2.68 thf(decl_330, type, demorgan1: $o). 17.14/2.68 thf(decl_331, type, demorgan2a: $o). 17.14/2.68 thf(decl_332, type, demorgan2b2: $o). 17.14/2.68 thf(decl_333, type, demorgan2b: $o). 17.14/2.68 thf(decl_334, type, demorgan2: $o). 17.14/2.68 thf(decl_335, type, woz13rule0: $o). 17.14/2.68 thf(decl_336, type, woz13rule1: $o). 17.14/2.68 thf(decl_337, type, woz13rule2: $o). 17.14/2.68 thf(decl_338, type, woz13rule3: $o). 17.14/2.68 thf(decl_339, type, woz13rule4: $o). 17.14/2.68 thf(decl_340, type, woz1_1: $o). 17.14/2.68 thf(decl_341, type, woz1_2: $o). 17.14/2.68 thf(decl_342, type, woz1_3: $o). 17.14/2.68 thf(decl_343, type, woz1_4: $o). 17.14/2.68 thf(decl_344, type, woz1_5: $o). 17.14/2.68 thf(decl_345, type, breln1: $i > $i > $o). 17.14/2.68 thf(decl_346, type, breln1all2: $o). 17.14/2.68 thf(decl_347, type, breln1Set: $i > $i). 17.14/2.68 thf(decl_348, type, breln1SetBreln1: $o). 17.14/2.68 thf(decl_355, type, choice2fnsingleton: $o). 17.14/2.68 thf(decl_356, type, setOfPairsIsBReln1: $o). 17.14/2.68 thf(decl_357, type, breln1all1: $o). 17.14/2.68 thf(decl_358, type, subbreln1: $o). 17.14/2.68 thf(decl_359, type, eqbreln1: $o). 17.14/2.68 thf(decl_360, type, breln1invset: $i > $i > $i). 17.14/2.68 thf(decl_361, type, breln1invprop: $o). 17.14/2.68 thf(decl_362, type, breln1invI: $o). 17.14/2.68 thf(decl_363, type, breln1invE: $o). 17.14/2.68 thf(decl_364, type, breln1compset: $i > $i > $i > $i). 17.14/2.68 thf(decl_365, type, breln1compprop: $o). 17.14/2.68 thf(decl_366, type, breln1compI: $o). 17.14/2.68 thf(decl_367, type, breln1compE: $o). 17.14/2.68 thf(decl_368, type, breln1compEex: $o). 17.14/2.68 thf(decl_369, type, breln1unionprop: $o). 17.14/2.68 thf(decl_370, type, breln1unionIL: $o). 17.14/2.68 thf(decl_371, type, breln1unionIR: $o). 17.14/2.68 thf(decl_372, type, breln1unionI: $o). 17.14/2.68 thf(decl_373, type, breln1unionE: $o). 17.14/2.68 thf(decl_374, type, breln1unionEcases: $o). 17.14/2.68 thf(decl_375, type, breln1unionCommutes: $o). 17.14/2.68 thf(decl_376, type, woz2Ex: $o). 17.14/2.68 thf(decl_377, type, woz2W: $o). 17.14/2.68 thf(decl_378, type, woz2A: $o). 17.14/2.68 thf(decl_379, type, woz2B: $o). 17.14/2.68 thf(decl_380, type, image1Ex: $o). 17.14/2.68 thf(decl_381, type, image1Ex1: $o). 17.14/2.68 thf(decl_382, type, image1: $i > ($i > $i) > $i). 17.14/2.68 thf(decl_383, type, image1Equiv: $o). 17.14/2.68 thf(decl_384, type, image1E: $o). 17.14/2.68 thf(decl_385, type, image1I: $o). 17.14/2.68 thf(decl_386, type, injective: $i > $i > $i > $o). 17.14/2.68 thf(decl_387, type, injFuncSet: $i > $i > $i). 17.14/2.68 thf(decl_388, type, injFuncInInjFuncSet: $o). 17.14/2.68 thf(decl_389, type, injFuncSetFuncIn: $o). 17.14/2.68 thf(decl_390, type, injFuncSetFuncInj: $o). 17.14/2.68 thf(decl_391, type, surjective: $i > $i > $i > $o). 17.14/2.68 thf(decl_392, type, surjFuncSet: $i > $i > $i). 17.14/2.68 thf(decl_393, type, surjFuncSetFuncIn: $o). 17.14/2.68 thf(decl_394, type, surjFuncSetFuncSurj: $o). 17.14/2.68 thf(decl_395, type, leftInvIsSurj: $o). 17.14/2.68 thf(decl_396, type, surjCantorThm: $o). 17.14/2.68 thf(decl_397, type, foundation2: $o). 17.14/2.68 thf(decl_398, type, notinself: $o). 17.14/2.68 thf(decl_399, type, notinself2: $o). 17.14/2.68 thf(decl_400, type, omegaS: $i > $i). 17.14/2.68 thf(decl_401, type, omegaSp: $o). 17.14/2.68 thf(decl_402, type, omegaSclos: $o). 17.14/2.68 thf(decl_403, type, peano0notS: $o). 17.14/2.68 thf(decl_407, type, epred1_0: $o). 17.14/2.68 thf(decl_408, type, esk1_2: $i > $i > $i). 17.14/2.68 thf(decl_409, type, esk2_2: $i > $i > $i). 17.14/2.68 thf(decl_410, type, esk3_2: $i > $i > $i). 17.14/2.68 thf(decl_411, type, esk4_1: $i > $i). 17.14/2.68 thf(decl_412, type, esk5_2: ($i > $i > $o) > $i > $i). 17.14/2.68 thf(decl_413, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 17.14/2.68 thf(decl_414, type, esk7_2: ($i > $i > $o) > $i > $i). 17.14/2.68 thf(decl_415, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 17.14/2.68 thf(decl_416, type, esk9_1: $i > $i). 17.14/2.68 thf(decl_417, type, esk10_2: ($i > $o) > $i > $i). 17.14/2.68 thf(decl_418, type, esk11_2: ($i > $o) > $i > $i). 17.14/2.68 thf(decl_419, type, esk12_1: ($i > $o) > $i). 17.14/2.68 thf(decl_420, type, esk13_2: ($i > $o) > $i > $i). 17.14/2.68 thf(decl_421, type, esk14_1: ($i > $o) > $i). 17.14/2.68 thf(decl_422, type, esk15_2: $i > $i > $i). 17.14/2.68 thf(decl_423, type, esk16_2: $i > $i > $i). 17.14/2.68 thf(decl_424, type, esk17_1: $i > $i). 17.14/2.68 thf(decl_425, type, esk18_1: $i > $i). 17.14/2.68 thf(decl_426, type, esk19_1: $i > $i). 17.14/2.68 thf(decl_427, type, esk20_2: $i > $i > $i). 17.14/2.68 thf(decl_428, type, esk21_3: $i > $i > $o > $i). 17.14/2.68 thf(decl_429, type, esk22_2: ($i > $o) > $i > $i). 17.14/2.68 thf(decl_430, type, esk23_1: ($i > $o) > $i). 17.14/2.68 thf(decl_431, type, esk24_1: $i > $i). 17.14/2.68 thf(decl_432, type, esk25_2: $i > ($i > $o) > $i). 17.14/2.68 thf(decl_433, type, esk26_2: $i > ($i > $o) > $i). 17.14/2.68 thf(decl_434, type, esk27_2: $i > ($i > $o) > $i). 17.14/2.68 thf(decl_435, type, esk28_2: $i > ($i > $o) > $i). 17.14/2.68 thf(decl_436, type, esk29_2: $i > ($i > $o) > $i). 17.14/2.68 thf(decl_437, type, esk30_2: $i > ($i > $o) > $i). 17.14/2.68 thf(decl_438, type, esk31_2: ($i > $o) > $i > $i). 17.14/2.68 thf(decl_439, type, esk32_1: ($i > $o) > $i). 17.14/2.68 thf(decl_440, type, esk33_1: ($i > $o) > $i). 17.14/2.68 thf(decl_441, type, esk34_1: ($i > $o) > $i). 17.14/2.68 thf(decl_442, type, esk35_1: ($i > $o) > $i). 17.14/2.68 thf(decl_443, type, esk36_2: ($i > $o) > $i > $i). 17.14/2.68 thf(decl_444, type, esk37_1: ($i > $o) > $i). 17.14/2.68 thf(decl_445, type, esk38_2: ($i > $o) > $i > $i). 17.14/2.68 thf(decl_446, type, esk39_2: ($i > $o) > ($i > $o) > $i). 17.14/2.68 thf(decl_447, type, esk40_2: ($i > $o) > ($i > $o) > $i). 17.14/2.68 thf(decl_448, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 17.14/2.68 thf(decl_449, type, esk42_2: ($i > $o) > ($i > $o) > $i). 17.14/2.68 thf(decl_450, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 17.14/2.68 thf(decl_451, type, esk44_2: ($i > $o) > ($i > $o) > $i). 17.14/2.68 thf(decl_452, type, esk45_2: ($i > $o) > $i > $i). 17.14/2.68 thf(decl_453, type, esk46_2: ($i > $o) > ($i > $o) > $i). 17.14/2.68 thf(decl_454, type, esk47_2: ($i > $o) > ($i > $o) > $i). 17.14/2.68 thf(decl_455, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 17.14/2.68 thf(decl_456, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 17.14/2.68 thf(decl_457, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 17.14/2.68 thf(decl_458, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 17.14/2.68 thf(decl_459, type, esk52_2: $i > $i > $i). 17.14/2.68 thf(decl_460, type, esk53_2: $i > $i > $i). 17.14/2.68 thf(decl_461, type, esk54_2: $i > $i > $i). 17.14/2.68 thf(decl_462, type, esk55_3: $i > $i > $i > $i). 17.14/2.68 thf(decl_463, type, esk56_3: $i > $i > $i > $i). 17.14/2.68 thf(decl_464, type, esk57_2: $i > $i > $i). 17.14/2.68 thf(decl_465, type, esk58_2: $i > ($i > $o) > $i). 17.14/2.68 thf(decl_466, type, esk59_2: $i > ($i > $o) > $i). 17.14/2.68 thf(decl_467, type, esk60_2: $i > ($i > $o) > $i). 17.14/2.68 thf(decl_468, type, esk61_3: $i > ($i > $o) > $i > $i). 17.14/2.68 thf(decl_469, type, esk62_2: $i > ($i > $o) > $i). 17.14/2.68 thf(decl_470, type, esk63_2: $i > ($i > $o) > $i). 17.14/2.68 thf(decl_471, type, esk64_3: $i > $i > ($i > $i) > $i). 17.14/2.68 thf(decl_472, type, esk65_3: $i > $i > ($i > $i) > $i). 17.14/2.68 thf(decl_473, type, esk66_3: $i > $i > ($i > $i) > $i). 17.14/2.68 thf(decl_474, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 17.14/2.68 thf(decl_475, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 17.14/2.68 thf(decl_476, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 17.14/2.68 thf(decl_477, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 17.14/2.68 thf(decl_478, type, esk71_4: $i > $i > $i > $i > $i). 17.14/2.68 thf(decl_479, type, esk72_4: $i > $i > $i > $i > $i). 17.14/2.68 thf(decl_480, type, esk73_4: $i > $i > $i > $i > $i). 17.14/2.68 thf(decl_481, type, esk74_4: $i > $i > $i > $i > $i). 17.14/2.68 thf(decl_482, type, esk75_4: $i > $i > $i > $i > $i). 17.14/2.68 thf(decl_483, type, esk76_4: $i > $i > $i > $i > $i). 17.14/2.68 thf(decl_484, type, esk77_4: $i > $i > $i > $i > $i). 17.14/2.68 thf(decl_485, type, esk78_4: $i > $i > $i > $i > $i). 17.14/2.68 thf(decl_486, type, esk79_4: $i > $i > $i > $i > $i). 17.14/2.68 thf(decl_487, type, esk80_3: $i > $i > ($i > $i) > $i). 17.14/2.68 thf(decl_488, type, esk81_3: $i > $i > ($i > $i) > $i). 17.14/2.68 thf(decl_489, type, esk82_3: $i > $i > ($i > $i) > $i). 17.14/2.68 thf(decl_490, type, esk83_3: $i > $i > $i > $i). 17.14/2.68 thf(decl_491, type, esk84_3: $i > $i > $i > $i). 17.14/2.68 thf(decl_492, type, esk85_3: $i > $i > $i > $i). 17.14/2.68 thf(decl_493, type, esk86_3: $i > $i > $i > $i). 17.14/2.68 thf(decl_494, type, esk87_3: $i > $i > ($i > $o) > $i). 17.14/2.68 thf(decl_495, type, esk88_3: $i > $i > ($i > $o) > $i). 17.14/2.68 thf(decl_496, type, esk89_3: $i > $i > ($i > $o) > $i). 17.14/2.68 thf(decl_497, type, esk90_3: $i > $i > ($i > $o) > $i). 17.14/2.68 thf(decl_498, type, esk91_3: $i > $i > $i > $i). 17.14/2.68 thf(decl_499, type, esk92_3: $i > $i > $i > $i). 17.14/2.68 thf(decl_500, type, esk93_3: $i > $i > $i > $i). 17.14/2.68 thf(decl_501, type, esk94_3: $i > $i > $i > $i). 17.14/2.68 thf(decl_502, type, esk95_3: $i > $i > $i > $i). 17.14/2.68 thf(decl_503, type, esk96_3: $i > $i > $i > $i). 17.14/2.68 thf(decl_504, type, esk97_5: $i > $i > $i > $i > $i > $i). 17.14/2.68 thf(decl_505, type, esk98_6: $i > $i > $i > $i > $i > $o > $i). 17.14/2.68 thf(decl_506, type, esk99_2: $i > ($i > $i) > $i). 17.14/2.68 thf(decl_507, type, esk100_3: $i > ($i > $i) > $i > $i). 17.14/2.68 thf(decl_508, type, esk101_2: $i > ($i > $i) > $i). 17.14/2.68 thf(decl_509, type, esk102_3: $i > ($i > $i) > $i > $i). 17.14/2.68 thf(decl_510, type, esk103_3: $i > ($i > $i) > $i > $i). 17.14/2.68 thf(decl_511, type, esk104_3: $i > ($i > $i) > $i > $i). 17.14/2.68 thf(decl_512, type, esk105_3: $i > ($i > $i) > $i > $i). 17.14/2.68 thf(decl_513, type, esk106_3: $i > ($i > $i) > $i > $i). 17.14/2.68 thf(decl_514, type, esk107_3: $i > $i > ($i > $i) > $i). 17.14/2.68 thf(decl_515, type, esk108_4: $i > $i > ($i > $i) > $i > $i). 17.14/2.68 thf(decl_516, type, esk109_1: $i > $i). 17.14/2.68 thf(decl_517, type, esk110_0: $i). 17.14/2.68 thf(decl_518, type, esk111_0: $i). 17.14/2.68 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', exuE3u)). 17.14/2.68 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', exu)). 17.14/2.68 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', nonempty)). 17.14/2.68 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', nonemptyI)). 17.14/2.68 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', exuE3e)). 17.14/2.68 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', descrp)). 17.14/2.68 thf(omegaS, axiom, ((omegaS)=(^[X2:$i]:(setadjoin @ X2 @ X2))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', omegaS)). 17.14/2.68 thf(image1Ex1, axiom, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', image1Ex1)). 17.14/2.68 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', descr__Cong)). 17.14/2.68 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', exuEu)). 17.14/2.68 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', exu__Cong)). 17.14/2.68 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', exuI2)). 17.14/2.68 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', exuI3)). 17.14/2.68 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', exuI1)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', exuE2)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', exuE1)). 17.14/2.68 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', replAx)). 17.14/2.68 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', sepInPowerset)). 17.14/2.68 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', singletonprop)). 17.14/2.68 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', ex1E1)). 17.14/2.68 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', ex1I2)). 17.14/2.68 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', dpsetconstrEL1)). 17.14/2.68 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', dsetconstr__Cong)). 17.14/2.68 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', kfstsingleton)). 17.14/2.68 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', emptyE1)). 17.14/2.68 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', nonemptyImpWitness)). 17.14/2.68 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', nonemptyE1)). 17.14/2.68 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setbeta)). 17.14/2.68 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', ksndsingleton)). 17.14/2.68 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', dsetconstrI)). 17.14/2.68 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', dpsetconstrI)). 17.14/2.68 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', dpsetconstrERa)). 17.14/2.68 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', dpsetconstrER)). 17.14/2.68 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', funcImageSingleton)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', lamProp)). 17.14/2.68 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:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', lam2p)). 17.14/2.68 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', eta1)). 17.14/2.68 thf(beta2, axiom, ((beta2)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', beta2)). 17.14/2.68 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', iffalseProp1)). 17.14/2.68 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', ifSingleton)). 17.14/2.68 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setOfPairsIsBReln1)). 17.14/2.68 thf(image1Equiv, axiom, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X59 @ X3))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', image1Equiv)). 17.14/2.68 thf(foundation2, axiom, ((foundation2)<=>![X4:$i]:(((nonempty @ X4)=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', foundation2)). 17.14/2.68 thf(peano0notS, axiom, ((peano0notS)<=>![X2:$i]:(((in @ X2 @ omega)=>((omegaS @ X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', peano0notS)). 17.14/2.68 thf(omegaSp, axiom, ((omegaSp)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (omegaS @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', omegaSp)). 17.14/2.68 thf(image1I, axiom, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X61 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', image1I)). 17.14/2.68 thf(image1E, axiom, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X60 @ X3))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', image1E)). 17.14/2.68 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', iftrueProp2)). 17.14/2.68 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', iftrueProp1)). 17.14/2.68 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', iffalseProp2)). 17.14/2.68 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', eta2)). 17.14/2.68 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', lam2lamEq)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', beta1)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', ex1E2)). 17.14/2.68 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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', lamp)). 17.14/2.68 thf(apProp, axiom, ((apProp)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', apProp)). 17.14/2.68 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:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', dpsetconstrEL2)). 17.14/2.68 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setOfPairsIsBReln)). 17.14/2.68 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', dpsetconstrSub)). 17.14/2.68 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', ex1I)). 17.14/2.68 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', sepSubset)). 17.14/2.68 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setoftrueEq)). 17.14/2.68 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', nonemptyI1)). 17.14/2.68 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', dsetconstrER)). 17.14/2.68 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', dsetconstrEL)). 17.14/2.68 thf(peanoSinj, conjecture, ((setextAx)=>((((powersetAx)=>((((((replAx)=>((foundationAx)=>(((((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((((((((noeltsimpempty)=>(((((nonemptyI1)=>(((emptyinunitempty)=>((setadjoinIR)=>(((setadjoinOr)=>((setoftrueEq)=>(((emptyinPowerset)=>((emptyInPowerset)=>(((setunionI)=>((((exuE2)=>(((uniqinunit)=>((notinsingleton)=>((((((upairsetIR)=>((((quantDeMorgan1)=>((quantDeMorgan2)=>((((prop2setI)=>(((notdexE)=>(((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((((exu__Cong)=>(((setadjoin__Cong)=>(((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>(((((((emptysetsubset)=>((subsetE)=>(((notsubsetI)=>((notequalI1)=>(((subsetRefl)=>(((((subset2powerset)=>(((subsetemptysetimpeq)=>((powersetI1)=>(((inPowerset)=>((powersetsubset)=>(((sepSubset)=>((binunionIL)=>((upairset2IR)=>(((binunionEcases)=>(((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((((binintersectSubset2)=>((((disjointsetsI1)=>((binintersectRsub)=>(((binintersectSubset1)=>((((setminusEL)=>((((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>(((setminusSubset1)=>((((symdiffI2)=>((((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((((singletonsubset)=>((singletoninpowerset)=>(((upairset2E)=>(((upairinpowunion)=>(((((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((((setunionsingleton)=>((singletonprop)=>((ex1E1)=>(((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((((setukpairinjR11)=>(((setukpairinjR1)=>((upairequniteq)=>((((ksndsingleton)=>(((((((cartprodmempaircEq)=>(((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((((dpsetconstrERa)=>((dpsetconstrEL1)=>(((dpsetconstrER)=>((funcImageSingleton)=>((((((funcinfuncset)=>((lamProp)=>(((lam2p)=>((brelnall1)=>(((((funcGraphProp3)=>(((funcextLem)=>(((subbreln)=>((eqbreln)=>(((funcext2)=>((ap2apEq1)=>((((eta1)=>(((beta2)=>(((iffalseProp1)=>(((((ifSingleton)=>((((iftrue)=>(((iftrueorfalse)=>((binintersectT_lem)=>(((powersetT_lem)=>(((complementT_lem)=>(((subsetTI)=>((((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>(((contrasubsetT1)=>((((((doubleComplementSub1)=>((doubleComplementSub2)=>(((((complementSubsetComplementIntersect)=>(((contraSubsetComplement)=>(((binunionTILcontra)=>((binunionTIRcontra)=>((((((inComplementUnionImpNotIn1)=>(((binunionTE)=>((binunionTEcontra)=>((((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>(((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>(((((woz1_1)=>(((((((((setOfPairsIsBReln1)=>((breln1all1)=>((subbreln1)=>(((breln1invprop)=>((breln1invI)=>((breln1invE)=>(((breln1compI)=>(((breln1compEex)=>((breln1unionprop)=>(((breln1unionIR)=>((breln1unionI)=>((breln1unionE)=>((((((((image1Ex)=>(((image1Equiv)=>((((injFuncInInjFuncSet)=>((((((leftInvIsSurj)=>((surjCantorThm)=>((foundation2)=>((((((peano0notS)=>![X2:$i]:(((in @ X2 @ omega)=>![X3:$i]:(((((omegaS @ X2)=(omegaS @ X3))=>((X2)=(X3)))<=(in @ X3 @ omega))))))<=(omegaSclos))<=(omegaSp))<=(notinself2))<=(notinself)))))<=(surjFuncSetFuncSurj))<=(surjFuncSetFuncIn))<=(injFuncSetFuncInj))<=(injFuncSetFuncIn)))<=(image1I))<=(image1E)))<=(image1Ex1)))<=(woz2B))<=(woz2A))<=(woz2W))<=(woz2Ex))<=(breln1unionCommutes))<=(breln1unionEcases)))))<=(breln1unionIL))))<=(breln1compE)))<=(breln1compprop)))))<=(eqbreln1)))))<=(choice2fnsingleton))<=(breln1SetBreln1))<=(breln1all2))<=(woz1_5))<=(woz1_4))<=(woz1_3))<=(woz1_2)))<=(woz13rule4))<=(woz13rule3))<=(woz13rule2))))))<=(demorgan2b2)))))))<=(complementUnionInPowersetComplement))<=(demorgan2a1))))<=(inComplementUnionImpInComplement1)))<=(intersectInPowersetIntersectUnions))<=(inIntersectImpInIntersectUnions))<=(inIntersectImpInUnion2))<=(inIntersectImpInUnion))))<=(complementTcontraSubset)))<=(complementInPowersetComplementIntersect)))<=(complementImpComplementIntersect))<=(complementTnotintersectT))<=(doubleComplementEq))))<=(doubleComplementE1))<=(doubleComplementI1))<=(contrasubsetT3))<=(contrasubsetT2)))<=(contrasubsetT))))))<=(powersetTE1))<=(powersetTI1)))<=(setextT)))<=(setminusT_lem)))<=(binunionT_lem))))<=(iffalse)))<=(theeq))<=(ifp)))<=(iftrueProp2))<=(iftrueProp1))<=(iffalseProp2)))<=(eta2)))<=(lam2lamEq)))<=(beta1))<=(ap2apEq2))))<=(funcext))))<=(funcGraphProp4)))<=(funcGraphProp2)))<=(funcGraphProp1))<=(ex1E2))<=(brelnall2))))<=(lamp))))<=(ap2p))<=(infuncsetfunc))<=(app))<=(apProp))))<=(dpsetconstrEL2))))<=(setOfPairsIsBReln))<=(dpsetconstrSub)))))<=(cartprodfstpairEq)))<=(cartprodpairmemER))<=(cartprodpairmemEL))<=(cartprodsndin))<=(kpairsurjEq))<=(ksndpairEq)))<=(setukpairinjR))<=(setukpairinjR2))))<=(setukpairinjR12)))<=(setukpairinjL))<=(setukpairinjL2)))))))))<=(ex1I)))))<=(setunionsingleton2))<=(setunionsingleton1))))))<=(ubforcartprodlem3))<=(ubforcartprodlem2))<=(ubforcartprodlem1)))<=(upairsubunion)))<=(singletoninpowunion))))<=(kpairp))<=(kpairiskpair)))))<=(symdiffIneg2))<=(symdiffIneg1)))<=(symdiffI1))<=(symdiffE)))<=(setminusLsub))))))<=(setminusSubset2))<=(setminusER)))<=(setminusI))<=(bs114d)))<=(binintersectSubset4))))<=(binintersectER))<=(binintersectSubset3)))<=(binintersectLsub))<=(binintersectEL))))))<=(binunionE)))<=(binunionIR)))))<=(sepInPowerset))))<=(powersetE1))))<=(setextsub)))<=(setadjoinSub2))<=(setadjoinSub))<=(subsetTrans)))<=(notequalI2))))<=(subsetE2))))<=(subsetI2))<=(eqimpsubset1))<=(eqimpsubset2))<=(subsetI1))<=(dsetconstr__Cong))))))<=(powerset__Cong)))<=(emptyset__Cong)))<=(exuE3u))<=(in__Cong))))))<=(notdallE)))<=(prop2set2propI)))<=(quantDeMorgan4))<=(quantDeMorgan3))))<=(vacuousDall))<=(emptyE1)))<=(upairsetIL))<=(upairsetE))<=(singletonsswitch))<=(eqinunit))))<=(nonemptyImpWitness)))<=(subPowSU))<=(setunionE)))<=(powersetE))))<=(powersetI))))<=(setadjoinE))))<=(setadjoinIL)))<=(nonemptyI))<=(nonemptyE1))<=(setbeta)))<=(emptyI))<=(setext))<=(exuE3e))<=(notinemptyset))<=(emptysetimpfalse))<=(emptysetE))))))<=(dsetconstrI))<=(descrp))<=(wellorderingAx))))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax))<=(setunionAx)))<=(setadjoinAx))<=(emptysetAx))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', peanoSinj)). 17.14/2.68 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', singletonsuniq)). 17.14/2.68 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', emptysetAx)). 17.14/2.68 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', bs114d)). 17.14/2.68 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', singletoninpowerset)). 17.14/2.68 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binintersectSubset4)). 17.14/2.68 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binintersectER)). 17.14/2.68 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', cartprodmempair)). 17.14/2.68 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binintersectSubset3)). 17.14/2.68 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binintersectLsub)). 17.14/2.68 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binintersectEL)). 17.14/2.68 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setunionE2)). 17.14/2.68 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binunionE)). 17.14/2.68 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binunionIR)). 17.14/2.68 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setunionsingleton)). 17.14/2.68 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', powersetE1)). 17.14/2.68 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setextsub)). 17.14/2.68 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setadjoinSub2)). 17.14/2.68 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setadjoinSub)). 17.14/2.68 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', subsetTrans)). 17.14/2.68 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', notequalI2)). 17.14/2.68 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', subsetE2)). 17.14/2.68 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', subsetI2)). 17.14/2.68 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', eqimpsubset1)). 17.14/2.68 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', eqimpsubset2)). 17.14/2.68 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', subsetI1)). 17.14/2.68 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', upairset2E)). 17.14/2.68 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', powerset__Cong)). 17.14/2.68 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', emptyset__Cong)). 17.14/2.68 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.CBN2axI2wP/E---3.1_1400.p', setukpairinjL1)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', in__Cong)). 17.14/2.68 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', notdallE)). 17.14/2.68 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', quantDeMorgan4)). 17.14/2.68 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', quantDeMorgan3)). 17.14/2.68 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', vacuousDall)). 17.14/2.68 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', theprop)). 17.14/2.68 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', upairsetIL)). 17.14/2.68 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', kfstpairEq)). 17.14/2.68 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', upairsetE)). 17.14/2.68 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', singletonsswitch)). 17.14/2.68 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', eqinunit)). 17.14/2.68 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', cartprodfstin)). 17.14/2.68 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', subPowSU)). 17.14/2.68 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setukpairinjR11)). 17.14/2.68 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setunionE)). 17.14/2.68 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', powersetE)). 17.14/2.68 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', powersetI)). 17.14/2.68 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setukpairinjR1)). 17.14/2.68 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setadjoinE)). 17.14/2.68 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setadjoinIL)). 17.14/2.68 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', upairequniteq)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', upairinpowunion)). 17.14/2.68 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', emptyI)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', setext)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', cartprodmempaircEq)). 17.14/2.68 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', notinemptyset)). 17.14/2.68 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', emptysetimpfalse)). 17.14/2.68 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', emptysetE)). 17.14/2.68 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', cartprodsndpairEq)). 17.14/2.68 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', cartprodpairsurjEq)). 17.14/2.68 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', wellorderingAx)). 17.14/2.68 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', omegaIndAx)). 17.14/2.68 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', omegaSAx)). 17.14/2.68 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', omega0Ax)). 17.14/2.68 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setunionAx)). 17.14/2.68 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setadjoinAx)). 17.14/2.68 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binunionTILcontra)). 17.14/2.68 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binunionTIRcontra)). 17.14/2.68 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', funcinfuncset)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', brelnall1)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', funcGraphProp3)). 17.14/2.68 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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', funcextLem)). 17.14/2.68 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', cartprodpairin)). 17.14/2.68 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', subbreln)). 17.14/2.68 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', eqbreln)). 17.14/2.68 thf(funcext2, axiom, ((funcext2)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', funcext2)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', ap2apEq1)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', iftrue)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', iftrueorfalse)). 17.14/2.68 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binintersectT_lem)). 17.14/2.68 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', powersetT_lem)). 17.14/2.68 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', complementT_lem)). 17.14/2.68 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', subsetTI)). 17.14/2.68 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', complementTI1)). 17.14/2.68 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', complementTE1)). 17.14/2.68 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binintersectTELcontra)). 17.14/2.68 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binintersectTERcontra)). 17.14/2.68 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', contrasubsetT1)). 17.14/2.68 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', doubleComplementSub1)). 17.14/2.68 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', doubleComplementSub2)). 17.14/2.68 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', complementSubsetComplementIntersect)). 17.14/2.68 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', contraSubsetComplement)). 17.14/2.68 thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', woz13rule2)). 17.14/2.68 thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', demorgan2b2)). 17.14/2.68 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', complementUnionInPowersetComplement)). 17.14/2.68 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', inComplementUnionImpNotIn1)). 17.14/2.68 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binunionTE)). 17.14/2.68 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binunionTEcontra)). 17.14/2.68 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', demorgan2a2)). 17.14/2.68 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', demorgan1a)). 17.14/2.68 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', demorgan1b)). 17.14/2.68 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', demorgan1)). 17.14/2.68 thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', demorgan2a)). 17.14/2.68 thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', demorgan2b)). 17.14/2.68 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', demorgan2)). 17.14/2.68 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', woz13rule0)). 17.14/2.68 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', woz13rule1)). 17.14/2.68 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', woz1_1)). 17.14/2.68 thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1all1)). 17.14/2.68 thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', subbreln1)). 17.14/2.68 thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1invprop)). 17.14/2.68 thf(breln1invI, axiom, ((breln1invI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1invI)). 17.14/2.68 thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1invE)). 17.14/2.68 thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1compI)). 17.14/2.68 thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>![X54:$o]:((![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54))))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1compEex)). 17.14/2.68 thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1unionprop)). 17.14/2.68 thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1unionIR)). 17.14/2.68 thf(breln1unionI, axiom, ((breln1unionI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35))=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1unionI)). 17.14/2.68 thf(breln1unionE, axiom, ((breln1unionE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1unionE)). 17.14/2.68 thf(image1Ex, axiom, ((image1Ex)<=>![X4:$i, X57:$i > $i]:(?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X57 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', image1Ex)). 17.14/2.68 thf(injFuncInInjFuncSet, axiom, ((injFuncInInjFuncSet)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((injective @ X4 @ X5 @ X29)=>(in @ X29 @ (injFuncSet @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', injFuncInInjFuncSet)). 17.14/2.68 thf(leftInvIsSurj, axiom, ((leftInvIsSurj)<=>![X4:$i, X5:$i, X62:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X62 @ X2) @ X5)))=>![X34:$i]:(((in @ X34 @ (funcSet @ X5 @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X5 @ X4 @ X34 @ (X62 @ X2))=(X2))))=>(surjective @ X5 @ X4 @ X34))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', leftInvIsSurj)). 17.14/2.68 thf(surjCantorThm, axiom, ((surjCantorThm)<=>![X4:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ (powerset @ X4)))=>~((surjective @ X4 @ (powerset @ X4) @ X29))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', surjCantorThm)). 17.14/2.68 thf(omegaSclos, axiom, ((omegaSclos)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', omegaSclos)). 17.14/2.68 thf(notinself2, axiom, ((notinself2)<=>![X4:$i, X5:$i]:(((in @ X4 @ X5)=>~((in @ X5 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', notinself2)). 17.14/2.68 thf(notinself, axiom, ((notinself)<=>![X4:$i]:(~((in @ X4 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', notinself)). 17.14/2.68 thf(surjFuncSetFuncSurj, axiom, ((surjFuncSetFuncSurj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X2 @ X3))=>(surjective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', surjFuncSetFuncSurj)). 17.14/2.68 thf(surjFuncSetFuncIn, axiom, ((surjFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', surjFuncSetFuncIn)). 17.14/2.68 thf(injFuncSetFuncInj, axiom, ((injFuncSetFuncInj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X2 @ X3))=>(injective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', injFuncSetFuncInj)). 17.14/2.68 thf(injFuncSetFuncIn, axiom, ((injFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', injFuncSetFuncIn)). 17.14/2.68 thf(woz2B, axiom, ((woz2B)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X35))) @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X33)))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', woz2B)). 17.14/2.68 thf(woz2A, axiom, ((woz2A)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1compset @ X4 @ X33 @ X56) @ (breln1compset @ X4 @ X35 @ X56)))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', woz2A)). 17.14/2.68 thf(woz2W, axiom, ((woz2W)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((breln1invset @ X4 @ (breln1compset @ X4 @ X33 @ X35))=(breln1compset @ X4 @ (breln1invset @ X4 @ X35) @ (breln1invset @ X4 @ X33)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', woz2W)). 17.14/2.68 thf(woz2Ex, axiom, ((woz2Ex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>((X33)=(breln1invset @ X4 @ (breln1invset @ X4 @ X33)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', woz2Ex)). 17.14/2.68 thf(breln1unionCommutes, axiom, ((breln1unionCommutes)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((binunion @ X33 @ X35)=(binunion @ X35 @ X33))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1unionCommutes)). 17.14/2.68 thf(breln1unionEcases, axiom, ((breln1unionEcases)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>![X55:$o]:((((in @ (kpair @ X2 @ X3) @ X33)=>(X55))=>(((in @ (kpair @ X2 @ X3) @ X35)=>(X55))=>(X55)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1unionEcases)). 17.14/2.68 thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1unionIL)). 17.14/2.68 thf(breln1compE, axiom, ((breln1compE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1compE)). 17.14/2.68 thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1compprop)). 17.14/2.68 thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', eqbreln1)). 17.14/2.68 thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1SetBreln1)). 17.14/2.68 thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', breln1all2)). 17.14/2.68 thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', woz1_5)). 17.14/2.68 thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', woz1_4)). 17.14/2.68 thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', woz1_3)). 17.14/2.68 thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', woz1_2)). 17.14/2.68 thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', woz13rule4)). 17.14/2.68 thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', woz13rule3)). 17.14/2.68 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', demorgan2a1)). 17.14/2.68 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', inComplementUnionImpInComplement1)). 17.14/2.68 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', intersectInPowersetIntersectUnions)). 17.14/2.68 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', inIntersectImpInIntersectUnions)). 17.14/2.68 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', inIntersectImpInUnion2)). 17.14/2.68 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', inIntersectImpInUnion)). 17.14/2.68 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', complementTcontraSubset)). 17.14/2.68 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', complementInPowersetComplementIntersect)). 17.14/2.68 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', complementImpComplementIntersect)). 17.14/2.68 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', complementTnotintersectT)). 17.14/2.68 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', doubleComplementEq)). 17.14/2.68 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', doubleComplementE1)). 17.14/2.68 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', doubleComplementI1)). 17.14/2.68 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', contrasubsetT3)). 17.14/2.68 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', contrasubsetT2)). 17.14/2.68 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', contrasubsetT)). 17.14/2.68 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', powersetTE1)). 17.14/2.68 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', powersetTI1)). 17.14/2.68 thf(setextT, axiom, ((setextT)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', setextT)). 17.14/2.68 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setminusT_lem)). 17.14/2.68 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', binunionT_lem)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', iffalse)). 17.14/2.68 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', theeq)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', ifp)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', ap2apEq2)). 17.14/2.68 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', funcext)). 17.14/2.68 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', funcGraphProp4)). 17.14/2.68 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', funcGraphProp2)). 17.14/2.68 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', funcGraphProp1)). 17.14/2.68 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', brelnall2)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', ap2p)). 17.14/2.68 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', infuncsetfunc)). 17.14/2.68 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', app)). 17.14/2.68 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', cartprodfstpairEq)). 17.14/2.68 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', cartprodpairmemER)). 17.14/2.68 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', cartprodpairmemEL)). 17.14/2.68 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', cartprodsndin)). 17.14/2.68 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', kpairsurjEq)). 17.14/2.68 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', ksndpairEq)). 17.14/2.68 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setukpairinjR)). 17.14/2.68 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setukpairinjR2)). 17.14/2.68 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setukpairinjR12)). 17.14/2.68 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setukpairinjL)). 17.14/2.68 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setukpairinjL2)). 17.14/2.68 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setunionsingleton2)). 17.14/2.68 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setunionsingleton1)). 17.14/2.68 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', ubforcartprodlem3)). 17.14/2.68 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', ubforcartprodlem2)). 17.14/2.68 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', ubforcartprodlem1)). 17.14/2.68 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.CBN2axI2wP/E---3.1_1400.p', cartprodmempair1)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', upairsubunion)). 17.14/2.68 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', singletoninpowunion)). 17.14/2.68 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', kpairp)). 17.14/2.68 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', kpairiskpair)). 17.14/2.68 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', symdiffIneg2)). 17.14/2.68 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', symdiffIneg1)). 17.14/2.68 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', symdiffI1)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', symdiffE)). 17.14/2.68 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setminusLsub)). 17.14/2.68 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setminusSubset2)). 17.14/2.68 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setminusER)). 17.14/2.68 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setminusI)). 17.14/2.68 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', singletonsubset)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', setukpairIR)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', setukpairIL)). 17.14/2.68 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', secondinupair)). 17.14/2.68 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', symdiffI2)). 17.14/2.68 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setminusSubset1)). 17.14/2.68 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setminusIRneg)). 17.14/2.68 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setminusILneg)). 17.14/2.68 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setminusELneg)). 17.14/2.68 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setminusERneg)). 17.14/2.68 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setminusEL)). 17.14/2.68 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binintersectSubset1)). 17.14/2.68 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binintersectRsub)). 17.14/2.68 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', disjointsetsI1)). 17.14/2.68 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binintersectSubset2)). 17.14/2.68 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binintersectSubset5)). 17.14/2.68 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binintersectI)). 17.14/2.68 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binunionRsub)). 17.14/2.68 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binunionLsub)). 17.14/2.68 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binunionEcases)). 17.14/2.68 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', upairset2IR)). 17.14/2.68 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', binunionIL)). 17.14/2.68 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', powersetsubset)). 17.14/2.68 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', inPowerset)). 17.14/2.68 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', powersetI1)). 17.14/2.68 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', subsetemptysetimpeq)). 17.14/2.68 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', subset2powerset)). 17.14/2.68 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', subsetRefl)). 17.14/2.68 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', notequalI1)). 17.14/2.68 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', notsubsetI)). 17.14/2.68 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', subsetE)). 17.14/2.68 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', emptysetsubset)). 17.14/2.68 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', omega__Cong)). 17.14/2.68 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setunion__Cong)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', setadjoin__Cong)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', inCongP)). 17.14/2.68 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', notdexE)). 17.14/2.68 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', prop2setI)). 17.14/2.68 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', quantDeMorgan2)). 17.14/2.68 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', quantDeMorgan1)). 17.14/2.68 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', upairsetIR)). 17.14/2.68 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', notinsingleton)). 17.14/2.68 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', uniqinunit)). 17.14/2.68 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setunionI)). 17.14/2.68 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', emptyInPowerset)). 17.14/2.68 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', emptyinPowerset)). 17.14/2.68 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setadjoinOr)). 17.14/2.68 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setadjoinIR)). 17.14/2.68 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', emptyinunitempty)). 17.14/2.68 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', noeltsimpempty)). 17.14/2.68 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', prop2setE)). 17.14/2.68 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.CBN2axI2wP/E---3.1_1400.p', foundationAx)). 17.14/2.68 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', powersetAx)). 17.14/2.68 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.CBN2axI2wP/E---3.1_1400.p', setextAx)). 17.14/2.68 thf(c_0_329, 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])). 17.14/2.68 thf(c_0_330, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 17.14/2.68 thf(c_0_331, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 17.14/2.68 thf(c_0_332, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 17.14/2.68 thf(c_0_333, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 17.14/2.68 thf(c_0_334, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 17.14/2.68 thf(c_0_335, plain, ((omegaS)=(^[Z0/* 28 */:$i]:(setadjoin @ Z0 @ Z0))), inference(fof_simplification,[status(thm)],[omegaS])). 17.14/2.68 thf(c_0_336, plain, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[Z0/* 6 */:$i]:(![X2:$i]:(((in @ X2 @ Z0)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), inference(fof_simplification,[status(thm)],[image1Ex1])). 17.14/2.68 thf(c_0_337, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 17.14/2.68 thf(c_0_338, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 17.14/2.68 thf(c_0_339, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 17.14/2.68 thf(c_0_340, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 17.14/2.68 thf(c_0_341, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 17.14/2.68 thf(c_0_342, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 17.14/2.68 thf(c_0_343, 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])). 17.14/2.68 thf(c_0_344, 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])). 17.14/2.68 thf(c_0_345, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 17.14/2.68 thf(c_0_346, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 17.14/2.68 thf(c_0_347, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 17.14/2.68 thf(c_0_348, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 17.14/2.68 thf(c_0_349, plain, ((ex1I2)<=>![X4:$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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 17.14/2.68 thf(c_0_350, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 17.14/2.68 thf(c_0_351, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 17.14/2.68 thf(c_0_352, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X1142:$i]:((((X1 @ X1142))&![X1143:$i]:((((X1 @ X1143))=>((X1142)=(X1143)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_329, c_0_330])). 17.14/2.68 thf(c_0_353, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 17.14/2.68 thf(c_0_354, plain, ((emptyE1)<=>![X4:$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])). 17.14/2.68 thf(c_0_355, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_331])). 17.14/2.68 thf(c_0_356, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_332, c_0_331])). 17.14/2.68 thf(c_0_357, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_331])). 17.14/2.68 thf(c_0_358, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 17.14/2.68 thf(c_0_359, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 17.14/2.68 thf(c_0_360, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X1132:$i]:((((X1 @ X1132))&![X1133:$i]:((((X1 @ X1133))=>((X1132)=(X1133)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_333, c_0_330])). 17.14/2.68 thf(c_0_361, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 17.14/2.68 thf(c_0_362, plain, ((descrp)=(![X1:$i > $o]:(((?[X1128:$i]:((((X1 @ X1128))&![X1129:$i]:((((X1 @ X1129))=>((X1128)=(X1129)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_334, c_0_330])). 17.14/2.68 thf(c_0_363, 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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 17.14/2.68 thf(c_0_364, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 17.14/2.68 thf(c_0_365, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 17.14/2.68 thf(c_0_366, plain, ((funcImageSingleton)<=>![X4:$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])). 17.14/2.68 thf(c_0_367, 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])). 17.14/2.68 thf(c_0_368, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 17.14/2.68 thf(c_0_369, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 248 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])). 17.14/2.68 thf(c_0_370, plain, ((beta2)<=>![X4:$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])). 17.14/2.68 thf(c_0_371, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 17.14/2.68 thf(c_0_372, plain, ((ifSingleton)<=>![X4:$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])). 17.14/2.68 thf(c_0_373, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])). 17.14/2.68 thf(c_0_374, plain, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X59 @ Z0))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), inference(fof_simplification,[status(thm)],[image1Equiv])). 17.14/2.68 thf(c_0_375, axiom, ((foundation2)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset)))))))), inference(apply_def,[status(thm)],[foundation2, c_0_331])). 17.14/2.68 thf(c_0_376, axiom, ((peano0notS)=(![X2:$i]:(((in @ X2 @ omega)=>((setadjoin @ X2 @ X2)!=(emptyset)))))), inference(apply_def,[status(thm)],[peano0notS, c_0_335])). 17.14/2.68 thf(c_0_377, axiom, ((omegaSp)=(![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega))))), inference(apply_def,[status(thm)],[omegaSp, c_0_335])). 17.14/2.68 thf(c_0_378, plain, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X61 @ Z0))))))), inference(fof_simplification,[status(thm)],[image1I])). 17.14/2.68 thf(c_0_379, plain, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X60 @ Z0))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), inference(fof_simplification,[status(thm)],[image1E])). 17.14/2.68 thf(c_0_380, plain, ((image1Ex1)=(![X4:$i, X58:$i > $i]:((?[X1154:$i]:(((![X2:$i]:(((in @ X2 @ X1154)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3)))))))&![X1155:$i]:(((![X2:$i]:(((in @ X2 @ X1155)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3)))))))=>((X1154)=(X1155)))))))))), inference(apply_def,[status(thm)],[c_0_336, c_0_330])). 17.14/2.68 thf(c_0_381, plain, ((iftrueProp2)<=>![X4:$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])). 17.14/2.68 thf(c_0_382, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 17.14/2.68 thf(c_0_383, plain, ((iffalseProp2)<=>![X4:$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])). 17.14/2.68 thf(c_0_384, 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])). 17.14/2.68 thf(c_0_385, 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])). 17.14/2.68 thf(c_0_386, 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])). 17.14/2.68 thf(c_0_387, 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])). 17.14/2.68 thf(c_0_388, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 17.14/2.68 thf(c_0_389, plain, ((apProp)<=>![X4:$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])). 17.14/2.68 thf(c_0_390, 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:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 17.14/2.68 thf(c_0_391, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 17.14/2.68 thf(c_0_392, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 17.14/2.68 thf(c_0_393, plain, ((ex1I)<=>![X4:$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])). 17.14/2.68 thf(c_0_394, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 17.14/2.68 thf(c_0_395, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1150:$i]:((((X1 @ X1150))&![X1151:$i]:((((X1 @ X1151))=>((X1150)=(X1151)))))))=>((?[X1152:$i]:((((X17 @ X1152))&![X1153:$i]:((((X17 @ X1153))=>((X1152)=(X1153)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_337, c_0_330])). 17.14/2.68 thf(c_0_396, plain, ((exuEu)=(![X1:$i > $o]:(((?[X1148:$i]:((((X1 @ X1148))&![X1149:$i]:((((X1 @ X1149))=>((X1148)=(X1149)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_338, c_0_330])). 17.14/2.68 thf(c_0_397, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1144:$i]:((((X1 @ X1144))&![X1145:$i]:((((X1 @ X1145))=>((X1144)=(X1145)))))))<=>(?[X1146:$i]:((((X17 @ X1146))&![X1147:$i]:((((X17 @ X1147))=>((X1146)=(X1147)))))))))))), inference(apply_def,[status(thm)],[c_0_339, c_0_330])). 17.14/2.68 thf(c_0_398, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X1140:$i]:((((X1 @ X1140))&![X1141:$i]:((((X1 @ X1141))=>((X1140)=(X1141))))))))))), inference(apply_def,[status(thm)],[c_0_340, c_0_330])). 17.14/2.68 thf(c_0_399, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X1138:$i]:((((X1 @ X1138))&![X1139:$i]:((((X1 @ X1139))=>((X1138)=(X1139)))))))))))), inference(apply_def,[status(thm)],[c_0_341, c_0_330])). 17.14/2.68 thf(c_0_400, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X1136:$i]:((((X1 @ X1136))&![X1137:$i]:((((X1 @ X1137))=>((X1136)=(X1137))))))))))), inference(apply_def,[status(thm)],[c_0_342, c_0_330])). 17.14/2.68 thf(c_0_401, plain, ((exuE2)=(![X1:$i > $o]:(((?[X1134:$i]:((((X1 @ X1134))&![X1135:$i]:((((X1 @ X1135))=>((X1134)=(X1135)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_343, c_0_330])). 17.14/2.68 thf(c_0_402, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 17.14/2.68 thf(c_0_403, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_331])). 17.14/2.68 thf(c_0_404, plain, ((exuE1)=(![X1:$i > $o]:(((?[X1130:$i]:((((X1 @ X1130))&![X1131:$i]:((((X1 @ X1131))=>((X1130)=(X1131)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_344, c_0_330])). 17.14/2.68 thf(c_0_405, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 17.14/2.68 thf(c_0_406, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 17.14/2.68 thf(c_0_407, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X1126:$i]:((((X6 @ X2 @ X1126))&![X1127:$i]:((((X6 @ X2 @ X1127))=>((X1126)=(X1127)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_345, c_0_330])). 17.14/2.68 thf(c_0_408, plain, ((epred1_0)<=>![X2221:$i]:(?[X2222:$i]:((((![X2223:$i]:(((in @ X2223 @ X2222)=>![X2224:$i]:(((in @ X2224 @ X2223)=>(in @ X2224 @ X2221)))))&![X2225:$i, X2226:$i]:((((in @ X2225 @ X2221)&(in @ X2226 @ X2221))=>(![X2227:$i]:(((in @ X2227 @ X2222)=>((in @ X2225 @ X2227)<=>(in @ X2226 @ X2227))))=>((X2225)=(X2226))))))&![X2228:$i, X2229:$i]:((((in @ X2228 @ X2222)&(in @ X2229 @ X2222))=>(![X2230:$i]:(((in @ X2230 @ X2228)=>(in @ X2230 @ X2229)))|![X2231:$i]:(((in @ X2231 @ X2229)=>(in @ X2231 @ X2228)))))))&![X2232:$i]:(((![X2233:$i]:(((in @ X2233 @ X2232)=>(in @ X2233 @ X2221)))&?[X2234:$i]:((in @ X2234 @ X2232)))=>?[X2235:$i, X2236:$i]:(((((in @ X2235 @ X2222)&(in @ X2236 @ X2232))&~(?[X2237:$i]:(((in @ X2237 @ X2235)&(in @ X2237 @ X2232)))))&![X2238:$i]:(((in @ X2238 @ X2222)=>(![X2239:$i]:(((in @ X2239 @ X2238)=>(in @ X2239 @ X2235)))|(in @ X2236 @ X2238)))))))))))), introduced(definition)). 17.14/2.68 thf(c_0_409, negated_conjecture, ~((![X1156:$i, X1157:$i]:((![X1158:$i]:(((in @ X1158 @ X1156)<=>(in @ X1158 @ X1157)))=>((X1156)=(X1157))))=>(![X2250:$i]:(~(in @ X2250 @ emptyset))=>(![X2247:$i, X2248:$i, X2249:$i]:(((in @ X2249 @ (setadjoin @ X2247 @ X2248))<=>(((X2249)=(X2247))|(in @ X2249 @ X2248))))=>(![X1159:$i, X1160:$i]:(((in @ X1160 @ (powerset @ X1159))<=>![X1161:$i]:(((in @ X1161 @ X1160)=>(in @ X1161 @ X1159)))))=>(![X2244:$i, X2245:$i]:(((in @ X2245 @ (setunion @ X2244))<=>?[X2246:$i]:(((in @ X2245 @ X2246)&(in @ X2246 @ X2244)))))=>((in @ emptyset @ omega)=>(![X2243:$i]:(((in @ X2243 @ omega)=>(in @ (setadjoin @ X2243 @ X2243) @ omega)))=>(![X2240:$i]:((((in @ emptyset @ X2240)&![X2241:$i]:((((in @ X2241 @ omega)&(in @ X2241 @ X2240))=>(in @ (setadjoin @ X2241 @ X2241) @ X2240))))=>![X2242:$i]:(((in @ X2242 @ omega)=>(in @ X2242 @ X2240)))))=>(![X1162:$i > $i > $o, X1163:$i]:((![X1164:$i]:(((in @ X1164 @ X1163)=>?[X1165:$i]:(((X1162 @ X1164 @ X1165)&![X1166:$i]:(((X1162 @ X1164 @ X1166)=>((X1165)=(X1166))))))))=>?[X1167:$i]:(![X1168:$i]:(((in @ X1168 @ X1167)<=>?[X1169:$i]:(((in @ X1169 @ X1163)&(X1162 @ X1169 @ X1168))))))))=>(![X1170:$i]:((?[X1171:$i]:((in @ X1171 @ X1170))=>?[X1172:$i]:(((in @ X1172 @ X1170)&~(?[X1173:$i]:(((in @ X1173 @ X1172)&(in @ X1173 @ X1170))))))))=>((epred1_0)=>(![X2218:$i > $o]:((?[X2219:$i]:(((X2218 @ X2219)&![X2220:$i]:(((X2218 @ X2220)=>((X2219)=(X2220))))))=>(X2218 @ (descr @ (^[Z0/* 17 */:$i]:(X2218 @ Z0))))))=>(![X2215:$i, X2216:$i > $o, X2217:$i]:(((in @ X2217 @ X2215)=>((X2216 @ X2217)=>(in @ X2217 @ (dsetconstr @ X2215 @ X2216)))))=>(![X1174:$i, X1175:$i > $o, X1176:$i]:(((in @ X1176 @ (dsetconstr @ X1174 @ X1175))=>(in @ X1176 @ X1174)))=>(![X1177:$i, X1178:$i > $o, X1179:$i]:(((in @ X1179 @ (dsetconstr @ X1177 @ X1178))=>(X1178 @ X1179)))=>(![X1180:$i > $o]:((?[X1181:$i]:(((X1180 @ X1181)&![X1182:$i]:(((X1180 @ X1182)=>((X1181)=(X1182))))))=>?[X1183:$i]:(((X1180 @ X1183)&![X1184:$i]:(((X1180 @ X1184)=>((X1183)=(X1184))))))))=>(![X1185:$o, X1186:$i]:(((in @ X1186 @ (prop2set @ ((X1185))))=>(X1185)))=>(![X2213:$i]:(((in @ X2213 @ emptyset)=>![X2214:$o]:((X2214))))=>(![X2212:$i]:(((in @ X2212 @ emptyset)=>~($true)))=>(![X2211:$i]:(~(in @ X2211 @ emptyset))=>(![X2207:$i > $o]:((?[X2208:$i]:(((X2207 @ X2208)&![X2209:$i]:(((X2207 @ X2209)=>((X2208)=(X2209))))))=>?[X2210:$i]:((X2207 @ X2210))))=>(![X2203:$i, X2204:$i]:((![X2205:$i]:(((in @ X2205 @ X2203)=>(in @ X2205 @ X2204)))=>(![X2206:$i]:(((in @ X2206 @ X2204)=>(in @ X2206 @ X2203)))=>((X2203)=(X2204)))))=>(![X2201:$i]:((![X2202:$i]:(~(in @ X2202 @ X2201))=>((X2201)=(emptyset))))=>(![X1187:$i]:((![X1188:$i]:(~(in @ X1188 @ X1187))=>((X1187)=(emptyset))))=>(![X2198:$i, X2199:$i > $o, X2200:$i]:(((in @ X2200 @ X2198)=>((in @ X2200 @ (dsetconstr @ X2198 @ X2199))<=>(X2199 @ X2200))))=>(![X2196:$i]:((((X2196)!=(emptyset))=>?[X2197:$i]:((in @ X2197 @ X2196))))=>(![X2193:$i, X2194:$i > $o, X2195:$i]:(((in @ X2195 @ X2193)=>((X2194 @ X2195)=>((dsetconstr @ X2193 @ X2194)!=(emptyset)))))=>(![X1189:$i]:((?[X1190:$i]:((in @ X1190 @ X1189))=>((X1189)!=(emptyset))))=>(![X2191:$i, X2192:$i]:((in @ X2191 @ (setadjoin @ X2191 @ X2192)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1191:$i, X1192:$i, X1193:$i]:(((in @ X1193 @ X1192)=>(in @ X1193 @ (setadjoin @ X1191 @ X1192))))=>(![X2187:$i, X2188:$i, X2189:$i]:(((in @ X2189 @ (setadjoin @ X2187 @ X2188))=>![X2190:$o]:(((((X2189)=(X2187))=>(X2190))=>(((in @ X2189 @ X2188)=>(X2190))=>(X2190))))))=>(![X1194:$i, X1195:$i, X1196:$i]:(((in @ X1196 @ (setadjoin @ X1194 @ X1195))=>(((X1196)=(X1194))|(in @ X1196 @ X1195))))=>(![X1197:$i]:(((dsetconstr @ X1197 @ (^[Z0/* 1 */:$i]:($true)))=(X1197)))=>(![X2184:$i, X2185:$i]:((![X2186:$i]:(((in @ X2186 @ X2185)=>(in @ X2186 @ X2184)))=>(in @ X2185 @ (powerset @ X2184))))=>(![X1198:$i]:((in @ emptyset @ (powerset @ X1198)))=>(![X1199:$i]:((in @ emptyset @ (powerset @ X1199)))=>(![X2181:$i, X2182:$i, X2183:$i]:(((in @ X2182 @ (powerset @ X2181))=>((in @ X2183 @ X2182)=>(in @ X2183 @ X2181))))=>(![X1200:$i, X1201:$i, X1202:$i]:(((in @ X1201 @ X1202)=>((in @ X1202 @ X1200)=>(in @ X1201 @ (setunion @ X1200)))))=>(![X2177:$i, X2178:$i]:(((in @ X2178 @ (setunion @ X2177))=>![X2179:$o]:((![X2180:$i]:(((in @ X2178 @ X2180)=>((in @ X2180 @ X2177)=>(X2179))))=>(X2179)))))=>(![X2175:$i, X2176:$i]:(((in @ X2176 @ X2175)=>(in @ X2176 @ (powerset @ (setunion @ X2175)))))=>(![X1203:$i > $o]:((?[X1204:$i]:(((X1203 @ X1204)&![X1205:$i]:(((X1203 @ X1205)=>((X1204)=(X1205))))))=>?[X1206:$i]:(![X1207:$i]:(((X1203 @ X1207)<=>((X1207)=(X1206)))))))=>(![X2173:$i]:((((X2173)!=(emptyset))=>?[X2174:$i]:(((in @ X2174 @ X2173)&$true))))=>(![X1208:$i, X1209:$i]:(((in @ X1208 @ (setadjoin @ X1209 @ emptyset))=>((X1208)=(X1209))))=>(![X1210:$i, X1211:$i]:((((X1210)!=(X1211))=>~(in @ X1211 @ (setadjoin @ X1210 @ emptyset))))=>(![X2171:$i, X2172:$i]:((((X2171)=(X2172))=>(in @ X2171 @ (setadjoin @ X2172 @ emptyset))))=>(![X2169:$i, X2170:$i]:(((in @ X2169 @ (setadjoin @ X2170 @ emptyset))=>(in @ X2170 @ (setadjoin @ X2169 @ emptyset))))=>(![X2166:$i, X2167:$i, X2168:$i]:(((in @ X2168 @ (setadjoin @ X2166 @ (setadjoin @ X2167 @ emptyset)))=>(((X2168)=(X2166))|((X2168)=(X2167)))))=>(![X2164:$i, X2165:$i]:((in @ X2164 @ (setadjoin @ X2164 @ (setadjoin @ X2165 @ emptyset))))=>(![X1212:$i, X1213:$i]:((in @ X1213 @ (setadjoin @ X1212 @ (setadjoin @ X1213 @ emptyset))))=>(![X2161:$i, X2162:$i > $o]:((?[X2163:$i]:(((in @ X2163 @ X2161)&(X2162 @ X2163)))=>(((dsetconstr @ X2161 @ X2162)=(emptyset))=>~($true))))=>(![X2159:$i > $o, X2160:$i]:(((in @ X2160 @ emptyset)=>(X2159 @ X2160)))=>(![X1214:$i, X1215:$i > $o]:((~(![X1216:$i]:(((in @ X1216 @ X1214)=>(X1215 @ X1216))))=>?[X1217:$i]:(((in @ X1217 @ X1214)&~((X1215 @ X1217))))))=>(![X1218:$i, X1219:$i > $o]:((![X1220:$i]:(((in @ X1220 @ X1218)=>~((X1219 @ X1220))))=>~(?[X1221:$i]:(((in @ X1221 @ X1218)&(X1219 @ X1221))))))=>(![X2155:$i, X2156:$i > $o]:((~(?[X2157:$i]:(((in @ X2157 @ X2155)&(X2156 @ X2157))))=>![X2158:$i]:(((in @ X2158 @ X2155)=>~((X2156 @ X2158))))))=>(![X2151:$i, X2152:$i > $o]:((?[X2153:$i]:(((in @ X2153 @ X2151)&~((X2152 @ X2153))))=>~(![X2154:$i]:(((in @ X2154 @ X2151)=>(X2152 @ X2154))))))=>(![X1222:$o]:(((X1222)=>(in @ emptyset @ (prop2set @ ((X1222))))))=>((prop2set2propI)=>(![X1223:$i, X1224:$i > $o]:((~(?[X1225:$i]:(((in @ X1225 @ X1223)&(X1224 @ X1225))))=>![X1226:$i]:(((in @ X1226 @ X1223)=>~((X1224 @ X1226))))))=>(![X2147:$i, X2148:$i > $o]:((~(![X2149:$i]:(((in @ X2149 @ X2147)=>(X2148 @ X2149))))=>?[X2150:$i]:(((in @ X2150 @ X2147)&~((X2148 @ X2150))))))=>(![X1227:$i > $o]:((?[X1228:$i]:(((X1227 @ X1228)&![X1229:$i]:(((X1227 @ X1229)=>((X1228)=(X1229))))))=>?[X1230:$i]:(((X1227 @ X1230)&![X1231:$i]:(((X1227 @ X1231)=>((X1230)=(X1231))))))))=>(![X1232:$i > $o]:((?[X1233:$i]:((X1232 @ X1233))=>(![X1234:$i, X1235:$i]:(((X1232 @ X1234)=>((X1232 @ X1235)=>((X1234)=(X1235)))))=>?[X1236:$i]:(((X1232 @ X1236)&![X1237:$i]:(((X1232 @ X1237)=>((X1236)=(X1237)))))))))=>(![X1238:$i > $o]:((?[X1239:$i]:(![X1240:$i]:(((X1238 @ X1240)<=>((X1240)=(X1239)))))=>?[X1241:$i]:(((X1238 @ X1241)&![X1242:$i]:(((X1238 @ X1242)=>((X1241)=(X1242))))))))=>(![X1243:$i, X1244:$i]:((((X1243)=(X1244))=>![X1245:$i, X1246:$i]:((((X1245)=(X1246))=>((in @ X1245 @ X1243)=>(in @ X1246 @ X1244))))))=>(![X2143:$i, X2144:$i]:((((X2143)=(X2144))=>![X2145:$i, X2146:$i]:((((X2145)=(X2146))=>((in @ X2145 @ X2143)<=>(in @ X2146 @ X2144))))))=>(![X2138:$i > $o]:((?[X2139:$i]:(((X2138 @ X2139)&![X2140:$i]:(((X2138 @ X2140)=>((X2139)=(X2140))))))=>![X2141:$i, X2142:$i]:(((X2138 @ X2141)=>((X2138 @ X2142)=>((X2141)=(X2142)))))))=>(![X1247:$i > $o, X1248:$i > $o]:((![X1249:$i, X1250:$i]:((((X1249)=(X1250))=>((X1247 @ X1249)<=>(X1248 @ X1250))))=>(?[X1251:$i]:(((X1247 @ X1251)&![X1252:$i]:(((X1247 @ X1252)=>((X1251)=(X1252))))))<=>?[X1253:$i]:(((X1248 @ X1253)&![X1254:$i]:(((X1248 @ X1254)=>((X1253)=(X1254)))))))))=>(((emptyset)=(emptyset))=>(![X1255:$i, X1256:$i]:((((X1255)=(X1256))=>![X1257:$i, X1258:$i]:((((X1257)=(X1258))=>((setadjoin @ X1255 @ X1257)=(setadjoin @ X1256 @ X1258))))))=>(![X2136:$i, X2137:$i]:((((X2136)=(X2137))=>((powerset @ X2136)=(powerset @ X2137))))=>(![X1259:$i, X1260:$i]:((((X1259)=(X1260))=>((setunion @ X1259)=(setunion @ X1260))))=>(((omega)=(omega))=>(![X1261:$i > $o]:((?[X1262:$i]:(((X1261 @ X1262)&![X1263:$i]:(((X1261 @ X1263)=>((X1262)=(X1263))))))=>![X1264:$i, X1265:$i]:(((X1261 @ X1264)=>((X1261 @ X1265)=>((X1264)=(X1265)))))))=>(![X1266:$i > $o, X1267:$i > $o]:((![X1268:$i, X1269:$i]:((((X1268)=(X1269))=>((X1266 @ X1268)<=>(X1267 @ X1269))))=>(?[X1270:$i]:(((X1266 @ X1270)&![X1271:$i]:(((X1266 @ X1271)=>((X1270)=(X1271))))))=>(?[X1272:$i]:(((X1267 @ X1272)&![X1273:$i]:(((X1267 @ X1273)=>((X1272)=(X1273))))))=>((descr @ X1266)=(descr @ X1267))))))=>(![X2130:$i, X2131:$i]:((((X2130)=(X2131))=>![X2132:$i > $o, X2133:$i > $o]:((![X2134:$i]:(((in @ X2134 @ X2130)=>![X2135:$i]:(((in @ X2135 @ 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singletonsuniq]), emptysetAx]), bs114d]), singletoninpowerset]), binintersectSubset4]), binintersectER]), cartprodmempair]), binintersectSubset3]), binintersectLsub]), binintersectEL]), setunionE2]), binunionE]), binunionIR]), setunionsingleton]), c_0_346]), powersetE1]), setextsub]), c_0_347]), setadjoinSub2]), setadjoinSub]), c_0_348]), subsetTrans]), notequalI2]), subsetE2]), subsetI2]), c_0_349]), eqimpsubset1]), eqimpsubset2]), c_0_350]), subsetI1]), c_0_351]), upairset2E]), powerset__Cong]), emptyset__Cong]), setukpairinjL1]), c_0_352]), in__Cong]), notdallE]), c_0_353]), quantDeMorgan4]), quantDeMorgan3]), vacuousDall]), theprop]), c_0_354]), upairsetIL]), kfstpairEq]), upairsetE]), singletonsswitch]), eqinunit]), cartprodfstin]), c_0_355]), subPowSU]), setukpairinjR11]), setunionE]), powersetE]), powersetI]), setukpairinjR1]), setadjoinE]), setadjoinIL]), upairequniteq]), c_0_356]), upairinpowunion]), c_0_357]), c_0_358]), emptyI]), c_0_359]), setext]), c_0_360]), cartprodmempaircEq]), notinemptyset]), emptysetimpfalse]), emptysetE]), cartprodsndpairEq]), c_0_361]), c_0_362]), cartprodpairsurjEq]), wellorderingAx]), omegaIndAx]), omegaSAx]), c_0_363]), omega0Ax]), setunionAx]), c_0_364]), setadjoinAx]), binunionTILcontra]), binunionTIRcontra]), c_0_365]), c_0_366]), funcinfuncset]), c_0_367]), c_0_368]), brelnall1]), funcGraphProp3]), funcextLem]), cartprodpairin]), subbreln]), eqbreln]), funcext2]), ap2apEq1]), c_0_369]), c_0_370]), c_0_371]), c_0_372]), iftrue]), iftrueorfalse]), binintersectT_lem]), powersetT_lem]), complementT_lem]), subsetTI]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT1]), doubleComplementSub1]), doubleComplementSub2]), complementSubsetComplementIntersect]), contraSubsetComplement]), woz13rule2]), demorgan2b2]), complementUnionInPowersetComplement]), inComplementUnionImpNotIn1]), binunionTE]), binunionTEcontra]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), demorgan2b]), demorgan2]), woz13rule0]), woz13rule1]), woz1_1]), c_0_373]), breln1all1]), subbreln1]), breln1invprop]), breln1invI]), breln1invE]), breln1compI]), breln1compEex]), breln1unionprop]), breln1unionIR]), breln1unionI]), breln1unionE]), image1Ex]), c_0_374]), injFuncInInjFuncSet]), leftInvIsSurj]), surjCantorThm]), c_0_375]), c_0_376]), c_0_335]), omegaSclos]), c_0_377]), notinself2]), notinself]), surjFuncSetFuncSurj]), surjFuncSetFuncIn]), injFuncSetFuncInj]), injFuncSetFuncIn]), c_0_378]), c_0_379]), c_0_380]), woz2B]), woz2A]), woz2W]), woz2Ex]), breln1unionCommutes]), breln1unionEcases]), breln1unionIL]), breln1compE]), breln1compprop]), eqbreln1]), breln1SetBreln1]), breln1all2]), woz1_5]), woz1_4]), woz1_3]), woz1_2]), woz13rule4]), woz13rule3]), demorgan2a1]), inComplementUnionImpInComplement1]), intersectInPowersetIntersectUnions]), inIntersectImpInIntersectUnions]), inIntersectImpInUnion2]), inIntersectImpInUnion]), complementTcontraSubset]), complementInPowersetComplementIntersect]), complementImpComplementIntersect]), complementTnotintersectT]), doubleComplementEq]), doubleComplementE1]), doubleComplementI1]), contrasubsetT3]), contrasubsetT2]), contrasubsetT]), powersetTE1]), powersetTI1]), setextT]), setminusT_lem]), binunionT_lem]), iffalse]), theeq]), ifp]), c_0_381]), c_0_382]), c_0_383]), c_0_384]), c_0_385]), c_0_386]), ap2apEq2]), funcext]), funcGraphProp4]), funcGraphProp2]), funcGraphProp1]), c_0_387]), brelnall2]), c_0_388]), ap2p]), infuncsetfunc]), app]), c_0_389]), c_0_390]), c_0_391]), c_0_392]), cartprodfstpairEq]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), kpairsurjEq]), ksndpairEq]), setukpairinjR]), setukpairinjR2]), setukpairinjR12]), setukpairinjL]), setukpairinjL2]), c_0_393]), setunionsingleton2]), setunionsingleton1]), ubforcartprodlem3]), ubforcartprodlem2]), ubforcartprodlem1]), cartprodmempair1]), upairsubunion]), singletoninpowunion]), kpairp]), kpairiskpair]), symdiffIneg2]), symdiffIneg1]), symdiffI1]), symdiffE]), setminusLsub]), setminusSubset2]), setminusER]), setminusI]), singletonsubset]), setukpairIR]), setukpairIL]), secondinupair]), symdiffI2]), setminusSubset1]), setminusIRneg]), setminusILneg]), setminusELneg]), setminusERneg]), setminusEL]), binintersectSubset1]), binintersectRsub]), disjointsetsI1]), binintersectSubset2]), binintersectSubset5]), binintersectI]), binunionRsub]), binunionLsub]), binunionEcases]), upairset2IR]), binunionIL]), c_0_394]), powersetsubset]), inPowerset]), powersetI1]), subsetemptysetimpeq]), subset2powerset]), subsetRefl]), notequalI1]), notsubsetI]), subsetE]), emptysetsubset]), c_0_395]), c_0_396]), omega__Cong]), setunion__Cong]), setadjoin__Cong]), c_0_397]), inCongP]), c_0_398]), c_0_399]), c_0_400]), notdexE]), prop2setI]), quantDeMorgan2]), quantDeMorgan1]), upairsetIR]), notinsingleton]), uniqinunit]), c_0_401]), setunionI]), emptyInPowerset]), emptyinPowerset]), c_0_402]), setadjoinOr]), setadjoinIR]), emptyinunitempty]), c_0_403]), noeltsimpempty]), prop2setE]), c_0_404]), c_0_405]), c_0_406]), foundationAx]), c_0_407]), powersetAx]), setextAx])])]), c_0_408])). 17.14/2.68 thf(c_0_410, negated_conjecture, ![X2251:$i, X2252:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2264:$i, X2265:$i, X2267:$i, X2268:$i, X2269:$i, X2270:$i, X2271:$i, X2273:$i, X2274:$i > $i > $o, X2275:$i, X2277:$i, X2280:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2287:$i, X2288:$i > $o, X2289:$i, X2291:$i, X2292:$i > $o, X2293:$i, X2294:$i, X2295:$i > $o, X2296:$i, X2297:$i, X2298:$i > $o, X2299:$i, X2300:$i > $o, X2301:$i, X2304:$i, X2305:$o, X2306:$i, X2307:$i, X2308:$o, X2309:$i, X2310:$i, X2311:$i > $o, X2312:$i, X2315:$i, X2316:$i, X2319:$i, X2321:$i, X2323:$i, X2324:$i > $o, X2325:$i, X2326:$i, X2328:$i, X2329:$i > $o, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$o, X2342:$i, X2343:$i, X2344:$i, X2345:$i, X2346:$i, X2347:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$i, X2358:$i, X2359:$o, X2361:$i, X2362:$i, X2363:$i > $o, X2364:$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 > $o, X2388:$i, X2389:$i > $o, X2390:$i, X2391:$i, X2392:$i > $o, X2393:$i, X2395:$i, X2396:$i > $o, X2398:$i, X2399:$i, X2400:$i > $o, X2402:$i, X2403:$i, X2404:$i > $o, X2405:$i, X2407:$o, X2408:$i, X2409:$i > $o, X2411:$i, X2412:$i, X2413:$i > $o, X2414:$i, X2416:$i > $o, X2417:$i, X2420:$i, X2421:$i > $o, X2422:$i, X2426:$i, X2427:$i > $o, X2428:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i > $o, X2441:$i, X2443:$i, X2444:$i, X2445:$i > $o, X2446:$i > $o, X2449:$i, X2452:$i, X2453:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i > $o, X2466:$i, X2468:$i, X2469:$i, X2470:$i > $o, X2471:$i > $o, X2474:$i, X2476:$i, X2478:$i, X2479:$i, X2480:$i > $o, X2481:$i > $o, X2484:$i, X2485:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2494:$i, X2495:$i, X2496:$i, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i, X2502:$i, X2503:$i, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2510:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i > $o, X2532:$i, X2533:$i > $o, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$o, X2546:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2557:$i, X2558:$i, X2559:$i, X2560:$i, X2561:$i, X2562:$i, X2563:$i, X2564:$i, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i, X2582:$i, X2583:$i, X2584:$i, X2585:$i, X2586:$i, X2587:$i, X2588:$i, X2589:$i, X2590:$i, X2591:$i, X2592:$i, X2593:$i, X2594:$i, X2595:$i, X2596:$i, X2597:$i, X2598:$i, X2599:$i, X2600:$i, X2601:$i, X2602:$i, X2603:$i, X2604:$i, X2605:$i, X2606:$i, X2607:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2613:$o, X2614:$i, X2615:$i, X2616:$i, X2617:$i, X2618:$i, X2619:$i, X2620:$i, X2621:$i, X2622:$i, X2623:$i, X2624:$i, X2625:$i, X2626:$i, X2627:$i, X2628:$i, X2629:$i, X2630:$i, X2631:$i, X2632:$i, X2633:$i, X2634:$i, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i, X2640:$i, X2641:$i, X2642:$i, X2643:$i, X2644:$i, X2645:$i, X2646:$i, X2647:$i, X2648:$i, X2649:$i, X2650:$i, X2651:$i, X2652:$i, X2653:$i, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2658:$i, X2659:$i, X2660:$i, X2661:$i, X2662:$i, X2663:$i, X2664:$i, X2665:$i, X2666:$i, X2667:$i, X2668:$i, X2669:$i, X2670:$i, X2671:$i, X2672:$i, X2675:$i, X2676:$i, X2677:$i, X2678:$i, X2679:$i, X2681:$i, X2682:$i, X2683:$i, X2684:$i, X2685:$i > $o, X2688:$i, X2689:$i, X2690:$i > $o, X2692:$i, X2693:$i > $o, X2694:$i, X2696:$i, X2697:$i > $o, X2700:$i, X2701:$i, X2702:$i, X2703:$i, X2704:$i, X2705:$i, X2706:$i, X2707:$i, X2708:$i, X2709:$i, X2710:$i, X2711:$i, X2712:$i, X2713:$i, X2714:$i, X2715:$i, X2716:$i, X2717:$i, X2718:$i, X2719:$i, X2720:$i, X2721:$i, X2722:$i, X2723:$i, X2724:$i, X2725:$i, X2726:$i, X2727:$i, X2728:$i, X2729:$i, X2730:$i, X2731:$i, X2732:$i, X2733:$i, X2734:$i, X2735:$i, X2736:$i, X2737:$i, X2738:$i, X2739:$i, X2740:$i, X2741:$i, X2742:$i, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$i, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2760:$i, X2761:$i, X2762:$i, X2763:$i, X2764:$i, X2765:$i, X2766:$i, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i, X2772:$i > $i > $o, X2773:$i, X2774:$i, X2775:$i, X2776:$i, X2777:$i > $i > $o, X2778:$i, X2779:$i, X2780:$i > $i > $o, X2781:$i, X2782:$i, X2783:$i > $i > $o, X2784:$i, X2785:$i, X2786:$i, X2787:$i, X2788:$i > $i > $o, X2789:$i, X2790:$i, X2791:$i, X2792:$i, X2793:$i > $i > $o, X2794:$i, X2795:$i, X2796:$i, X2797:$i, X2798:$i > $i > $o, X2799:$i, X2800:$i, X2801:$i, X2802:$i, X2803:$i, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i, X2809:$i, X2810:$i, X2811:$i, X2812:$i, X2813:$i, X2814:$i, X2815:$i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i, X2825:$i > $i, X2827:$i, X2828:$i, X2829:$i > $i, X2831:$i, X2832:$i, X2833:$i > $i, X2835:$i, X2836:$i, X2837:$i, X2838:$i > $o, X2841:$i, X2842:$i, X2843:$i, X2844:$i, X2845:$i > $o, X2848:$i, X2849:$i, X2850:$i > $o, X2851:$i, X2852:$i, X2853:$i, X2854:$i, X2855:$i, X2856:$i, X2857:$i, X2858:$i, X2859:$i, X2860:$i, X2861:$i, X2862:$i, X2863:$i, X2864:$i, X2865:$i, X2866:$i, X2867:$i, X2868:$i, X2869:$i, X2871:$i, X2872:$i, X2873:$i, X2874:$i, X2875:$i, X2876:$i, X2877:$i, X2878:$i, X2879:$i, X2880:$i, X2881:$i, X2884:$i, X2885:$i, X2886:$i, X2887:$i, X2892:$i, X2893:$i, X2894:$i, X2895:$i, X2897:$i, X2898:$i, X2899:$i, X2900:$i, X2902:$i, X2903:$i, X2904:$i, X2905:$i, X2906:$i, X2907:$i, X2908:$i, X2909:$i, X2910:$i, X2911:$i, X2912:$i > $i, X2914:$i, X2915:$i, X2916:$i, X2917:$i, X2918:$i, X2919:$i, X2920:$i > $i, X2922:$i, X2923:$i, X2924:$i > $i, X2926:$i, X2927:$i, X2928:$i, X2929:$i, X2930:$i, X2931:$o, X2932:$i, X2933:$i, X2934:$i, X2935:$o, X2936:$i, X2937:$i, X2938:$i, X2939:$o, X2940:$i, X2941:$i, X2942:$i, X2943:$o, X2944:$i, X2945:$i, X2946:$i, X2947:$o, X2948:$i, X2949:$i, X2950:$i, X2951:$o, X2952:$i, X2953:$i, X2954:$i, X2955:$i, X2956:$i, X2957:$o, X2958:$i, X2959:$i, X2960:$i, X2961:$o, X2962:$i, X2963:$i, X2964:$i, X2965:$o, X2966:$i, X2967:$i, X2968:$i, X2969:$i, X2970:$i, X2971:$i, X2972:$i, X2973:$i, X2974:$i, X2975:$i, X2976:$i, X2977:$i, X2978:$i, X2979:$i, X2980:$i, X2981:$i, X2982:$i, X2983:$i, X2986:$i, X2987:$i, X2988:$i, X2990:$i, X2991:$i, X2992:$i, X2994:$i, X2995:$i, X2996:$i, X2997:$i, X2998:$i, X2999:$i, X3000:$i, X3001:$i, X3002:$i, X3003:$i, X3004:$i, X3005:$i, X3006:$i, X3007:$i, X3008:$i, X3009:$i, X3010:$i, X3011:$i, X3012:$i, X3013:$i, X3014:$i, X3015:$i, X3016:$i, X3017:$i, X3018:$i, X3019:$i, X3020:$i, X3021:$i, X3022:$i, X3023:$i, X3024:$i, X3025:$i, X3026:$i, X3027:$i, X3028:$i, X3029:$i, X3030:$i, X3031:$i, X3032:$i, X3033:$i, X3034:$i, X3035:$i, X3036:$i, X3037:$i, X3038:$i, X3039:$i, X3040:$i, X3041:$i, X3042:$i, X3043:$i, X3044:$i, X3045:$i, X3046:$i, X3047:$i, X3048:$i, X3049:$i, X3050:$i, X3051:$i, X3052:$i, X3053:$i, X3054:$i, X3055:$i, X3056:$i, X3057:$i, X3058:$i, X3059:$i, X3060:$i, X3061:$i, X3062:$i, X3063:$i, X3064:$i, X3065:$i, X3066:$i, X3067:$i, X3068:$i, X3069:$i, X3070:$i, X3071:$i, X3072:$i, X3073:$i, X3074:$i, X3075:$i, X3076:$i, X3077:$i, X3078:$i, X3079:$i, X3080:$i, X3081:$i, X3082:$i, X3083:$i, X3084:$i, X3085:$i, X3086:$i, X3087:$i, X3088:$i, X3089:$i, X3090:$i, X3091:$i, X3092:$i, X3093:$i, X3094:$i, X3095:$i, X3096:$i, X3097:$o, X3098:$i, X3099:$i, X3100:$i, X3101:$i, X3102:$i, X3103:$i, X3104:$i, X3105:$i, X3106:$i, X3107:$i, X3108:$i, X3109:$i, X3110:$i, X3111:$i, X3112:$i, X3113:$i, X3114:$i, X3115:$i, X3116:$i, X3117:$i, X3118:$i, X3119:$i, X3120:$i, X3121:$i, X3122:$i, X3123:$i, X3124:$i, X3125:$i, X3126:$i, X3127:$i, X3128:$i, X3129:$i, X3130:$i, X3131:$i, X3132:$i, X3133:$i, X3134:$i, X3135:$i, X3136:$i, X3137:$i, X3138:$i, X3139:$i, X3140:$i, X3141:$i, X3142:$i, X3143:$i, X3144:$i, X3145:$i, X3146:$i, X3147:$i, X3148:$i, X3149:$i, X3150:$i, X3151:$i, X3152:$i, X3153:$i, X3154:$i, X3155:$i, X3156:$i, X3157:$i, X3158:$i, X3159:$i, X3160:$i, X3161:$i, X3162:$i, X3163:$i, X3164:$i, X3165:$i, X3166:$i, X3167:$i, X3168:$i, X3169:$i, X3170:$i, X3171:$i, X3172:$i, X3173:$i, X3174:$i, X3175:$i, X3176:$i, X3177:$i, X3178:$i, X3179:$i, X3180:$i, X3181:$i > $o, X3184:$i, X3185:$i, X3186:$i, X3187:$i, X3188:$i > $i > $o, X3189:$i, X3190:$i, X3191:$i > $o, X3194:$i, X3195:$i, X3196:$i, X3197:$i, X3200:$i, X3201:$i, X3202:$i, X3207:$i, X3208:$i, X3209:$i, X3210:$i, X3211:$i, X3212:$i, X3213:$i, X3214:$i, X3215:$i, X3216:$i, X3217:$i, X3218:$i, X3219:$i, X3220:$i, X3221:$i, X3222:$i, X3223:$i, X3224:$i, X3225:$i, X3226:$i, X3227:$i, X3228:$i, X3229:$i, X3230:$i, X3232:$i, X3233:$i, X3234:$i, X3235:$i, X3236:$i, X3237:$o, X3239:$i, X3240:$i, X3241:$i, X3242:$i, X3243:$i, X3244:$i, X3245:$i, X3246:$i, X3247:$i, X3248:$i, X3249:$i, X3250:$i, X3251:$i, X3252:$i, X3253:$i, X3254:$i, X3255:$i, X3256:$i, X3257:$i, X3258:$i, X3259:$i, X3260:$i, X3261:$i, X3262:$i, X3263:$i, X3264:$i, X3265:$i, X3266:$i, X3267:$o, X3268:$i, X3269:$i, X3270:$i, X3271:$i, X3272:$i, X3273:$i, X3274:$i, X3275:$i, X3276:$i, X3277:$i, X3278:$i, X3279:$i, X3280:$i, X3281:$i, X3282:$i, X3283:$i, X3284:$i, X3285:$i > $i, X3287:$i, X3289:$i, X3290:$i, X3291:$i, X3292:$i > $i, X3294:$i, X3296:$i, X3297:$i, X3298:$i, X3300:$i, X3302:$i, X3303:$i > $i, X3304:$i, X3306:$i, X3307:$i > $i, X3308:$i, X3309:$i, X3310:$i, X3311:$i > $i, X3312:$i, X3314:$i, X3315:$i > $i, X3316:$i, X3317:$i, X3318:$i, X3319:$i, X3320:$i, X3321:$i, X3322:$i, X3323:$i, X3324:$i, X3325:$i, X3326:$i, X3327:$i, X3328:$i, X3329:$i, X3330:$i, X3331:$i, X3332:$i, X3333:$i, X3334:$i, X3335:$i > $i, X3337:$i, X3339:$i, X3340:$i, X3341:$i, X3343:$i, X3344:$i, X3345:$i, X3346:$i, X3347:$i, X3348:$i]:((((~(in @ (esk1_2 @ X2251 @ X2252) @ X2251)|~(in @ (esk1_2 @ X2251 @ X2252) @ X2252)|((X2251)=(X2252)))&((in @ (esk1_2 @ X2251 @ X2252) @ X2251)|(in @ (esk1_2 @ X2251 @ X2252) @ X2252)|((X2251)=(X2252))))&(~(in @ X2254 @ emptyset)&(((~(in @ X2257 @ (setadjoin @ X2255 @ X2256))|(((X2257)=(X2255))|(in @ X2257 @ X2256)))&((((X2257)!=(X2255))|(in @ X2257 @ (setadjoin @ X2255 @ X2256)))&(~(in @ X2257 @ X2256)|(in @ X2257 @ (setadjoin @ X2255 @ X2256)))))&(((~(in @ X2259 @ (powerset @ X2258))|(~(in @ X2260 @ X2259)|(in @ 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(kpair @ X3265 @ X3266) @ X3264)|(X3267)|(in @ (kpair @ X3265 @ X3266) @ X3263)|~(in @ (kpair @ X3265 @ X3266) @ (binunion @ X3263 @ X3264))|~(in @ X3266 @ X3262)|~(in @ X3265 @ X3262)|~(breln1 @ X3262 @ X3264)|~(breln1 @ X3262 @ X3263))&(~(X3267)|(X3267)|(in @ (kpair @ X3265 @ X3266) @ X3263)|~(in @ (kpair @ X3265 @ X3266) @ (binunion @ X3263 @ X3264))|~(in @ X3266 @ X3262)|~(in @ X3265 @ X3262)|~(breln1 @ X3262 @ X3264)|~(breln1 @ X3262 @ X3263)))&(((in @ (kpair @ X3265 @ X3266) @ X3264)|(X3267)|~(X3267)|~(in @ (kpair @ X3265 @ X3266) @ (binunion @ X3263 @ X3264))|~(in @ X3266 @ X3262)|~(in @ X3265 @ X3262)|~(breln1 @ X3262 @ X3264)|~(breln1 @ X3262 @ X3263))&(~(X3267)|(X3267)|~(X3267)|~(in @ (kpair @ X3265 @ X3266) @ (binunion @ X3263 @ X3264))|~(in @ X3266 @ X3262)|~(in @ X3265 @ X3262)|~(breln1 @ X3262 @ X3264)|~(breln1 @ X3262 @ X3263))))&((~(breln1 @ X3268 @ X3269)|(~(breln1 @ X3268 @ X3270)|((binunion @ X3269 @ X3270)=(binunion @ X3270 @ X3269))))&((~(breln1 @ X3271 @ X3272)|((X3272)=(breln1invset @ X3271 @ (breln1invset @ X3271 @ X3272))))&((~(breln1 @ X3273 @ X3274)|(~(breln1 @ X3273 @ X3275)|((breln1invset @ X3273 @ (breln1compset @ X3273 @ X3274 @ X3275))=(breln1compset @ X3273 @ (breln1invset @ X3273 @ X3275) @ (breln1invset @ X3273 @ X3274)))))&((~(breln1 @ X3276 @ X3277)|(~(breln1 @ X3276 @ X3278)|(~(breln1 @ X3276 @ X3279)|((breln1compset @ X3276 @ (binunion @ X3277 @ X3278) @ X3279)=(binunion @ (breln1compset @ X3276 @ X3277 @ X3279) @ (breln1compset @ X3276 @ X3278 @ X3279))))))&((~(breln1 @ X3280 @ X3281)|(~(breln1 @ X3280 @ X3282)|(~(breln1 @ X3280 @ X3283)|((breln1compset @ X3280 @ (binunion @ X3281 @ X3282) @ X3283)=(binunion @ (breln1invset @ X3280 @ (breln1compset @ X3280 @ (breln1invset @ X3280 @ X3283) @ (breln1invset @ X3280 @ X3282))) @ (breln1invset @ X3280 @ (breln1compset @ X3280 @ (breln1invset @ X3280 @ X3283) @ (breln1invset @ X3280 @ X3281))))))))&(((((in @ (esk100_3 @ X3284 @ X3285 @ X3287) @ X3284)|~(in @ X3287 @ (esk99_2 @ X3284 @ X3285)))&(((X3287)=(X3285 @ (esk100_3 @ X3284 @ X3285 @ X3287)))|~(in @ X3287 @ (esk99_2 @ X3284 @ X3285))))&(~(in @ X3290 @ X3284)|((X3289)!=(X3285 @ X3290))|(in @ X3289 @ (esk99_2 @ X3284 @ X3285))))&((((((in @ (esk102_3 @ X3291 @ X3292 @ X3294) @ X3291)|~(in @ X3294 @ (esk101_2 @ X3291 @ X3292)))&(((X3294)=(X3292 @ (esk102_3 @ X3291 @ X3292 @ X3294)))|~(in @ X3294 @ (esk101_2 @ X3291 @ X3292))))&(~(in @ X3297 @ X3291)|((X3296)!=(X3292 @ X3297))|(in @ X3296 @ (esk101_2 @ X3291 @ X3292))))&((~(in @ (esk103_3 @ X3291 @ X3292 @ X3298) @ X3298)|(~(in @ X3300 @ X3291)|((esk103_3 @ X3291 @ X3292 @ X3298)!=(X3292 @ X3300)))|((esk101_2 @ X3291 @ X3292)=(X3298)))&(((in @ (esk104_3 @ X3291 @ X3292 @ X3298) @ X3291)|(in @ (esk103_3 @ X3291 @ X3292 @ X3298) @ X3298)|((esk101_2 @ X3291 @ X3292)=(X3298)))&(((esk103_3 @ X3291 @ X3292 @ X3298)=(X3292 @ (esk104_3 @ X3291 @ X3292 @ X3298)))|(in @ (esk103_3 @ X3291 @ X3292 @ X3298) @ X3298)|((esk101_2 @ X3291 @ 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(surjFuncSet @ X3330 @ X3331))|(surjective @ X3330 @ X3331 @ X3332))&(((((in @ (esk108_4 @ X3333 @ X3334 @ X3335 @ X3337) @ X3333)|(surjective @ X3334 @ X3333 @ X3337)|~(in @ X3337 @ (funcSet @ X3334 @ X3333))|(in @ (esk107_3 @ X3333 @ X3334 @ X3335) @ X3333))&(((ap @ X3334 @ X3333 @ X3337 @ (X3335 @ (esk108_4 @ X3333 @ X3334 @ X3335 @ X3337)))!=(esk108_4 @ X3333 @ X3334 @ X3335 @ X3337))|(surjective @ X3334 @ X3333 @ X3337)|~(in @ X3337 @ (funcSet @ X3334 @ X3333))|(in @ (esk107_3 @ X3333 @ X3334 @ X3335) @ X3333)))&(((in @ (esk108_4 @ X3333 @ X3334 @ X3335 @ X3337) @ X3333)|(surjective @ X3334 @ X3333 @ X3337)|~(in @ X3337 @ (funcSet @ X3334 @ X3333))|~(in @ (X3335 @ (esk107_3 @ X3333 @ X3334 @ X3335)) @ X3334))&(((ap @ X3334 @ X3333 @ X3337 @ (X3335 @ (esk108_4 @ X3333 @ X3334 @ X3335 @ X3337)))!=(esk108_4 @ X3333 @ X3334 @ X3335 @ X3337))|(surjective @ X3334 @ X3333 @ X3337)|~(in @ X3337 @ (funcSet @ X3334 @ X3333))|~(in @ (X3335 @ (esk107_3 @ X3333 @ X3334 @ X3335)) @ X3334))))&((~(in @ X3340 @ (funcSet @ X3339 @ (powerset @ X3339)))|~(surjective @ X3339 @ (powerset @ X3339) @ X3340))&((((in @ (esk109_1 @ X3341) @ X3341)|((X3341)=(emptyset)))&(((binintersect @ (esk109_1 @ X3341) @ X3341)=(emptyset))|((X3341)=(emptyset))))&(~(in @ X3343 @ X3343)&((~(in @ X3344 @ X3345)|~(in @ X3345 @ X3344))&((~(in @ X3346 @ omega)|(in @ (setadjoin @ X3346 @ X3346) @ omega))&((~(in @ X3347 @ omega)|(in @ (setadjoin @ X3347 @ X3347) @ omega))&((~(in @ X3348 @ omega)|((setadjoin @ X3348 @ X3348)!=(emptyset)))&((in @ esk110_0 @ omega)&((in @ esk111_0 @ omega)&(((setadjoin @ esk110_0 @ esk110_0)=(setadjoin @ esk111_0 @ esk111_0))&((esk110_0)!=(esk111_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_409])])])])])])])). 17.14/2.68 thf(c_0_411, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_410])). 17.14/2.68 thf(c_0_412, negated_conjecture, ((setadjoin @ esk110_0 @ esk110_0)=(setadjoin @ esk111_0 @ esk111_0)), inference(split_conjunct,[status(thm)],[c_0_410])). 17.14/2.68 thf(c_0_413, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ X3)|((X2)=(X4))|~((in @ X2 @ (setadjoin @ X4 @ X3))))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_410])])])). 17.14/2.68 thf(c_0_414, negated_conjecture, (in @ esk111_0 @ (setadjoin @ esk110_0 @ esk110_0)), inference(spm,[status(thm)],[c_0_411, c_0_412])). 17.14/2.68 thf(c_0_415, negated_conjecture, ((esk110_0)!=(esk111_0)), inference(split_conjunct,[status(thm)],[c_0_410])). 17.14/2.68 thf(c_0_416, negated_conjecture, ![X3:$i, X2:$i]:((~((in @ X2 @ X3))|~((in @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_410])). 17.14/2.68 thf(c_0_417, negated_conjecture, (in @ esk111_0 @ esk110_0), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_413, c_0_414]), c_0_415])). 17.14/2.68 thf(c_0_418, negated_conjecture, ![X2:$i]:((((X2)=(esk111_0))|(in @ X2 @ esk111_0)|~((in @ X2 @ (setadjoin @ esk110_0 @ esk110_0))))), inference(spm,[status(thm)],[c_0_413, c_0_412])). 17.14/2.68 thf(c_0_419, negated_conjecture, ~((in @ esk110_0 @ esk111_0)), inference(spm,[status(thm)],[c_0_416, c_0_417])). 17.14/2.68 thf(c_0_420, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_418, c_0_411]), c_0_415]), c_0_419]), ['proof']). 17.14/2.68 # SZS output end CNFRefutation 17.14/2.68 # Parsed axioms : 715 17.14/2.68 # Removed by relevancy pruning/SinE : 386 17.14/2.68 # Initial clauses : 562 17.14/2.68 # Removed in clause preprocessing : 36 17.14/2.68 # Initial clauses in saturation : 526 17.14/2.68 # Processed clauses : 2382 17.14/2.68 # ...of these trivial : 29 17.14/2.68 # ...subsumed : 684 17.14/2.68 # ...remaining for further processing : 1669 17.14/2.68 # Other redundant clauses eliminated : 82 17.14/2.68 # Clauses deleted for lack of memory : 0 17.14/2.68 # Backward-subsumed : 5 17.14/2.68 # Backward-rewritten : 20 17.14/2.68 # Generated clauses : 48735 17.14/2.68 # ...of the previous two non-redundant : 47895 17.14/2.68 # ...aggressively subsumed : 0 17.14/2.68 # Contextual simplify-reflections : 29 17.14/2.68 # Paramodulations : 48625 17.14/2.68 # Factorizations : 2 17.14/2.68 # NegExts : 2 17.14/2.68 # Equation resolutions : 90 17.14/2.68 # Disequality decompositions : 0 17.14/2.68 # Total rewrite steps : 1552 17.14/2.68 # ...of those cached : 1301 17.14/2.68 # Propositional unsat checks : 0 17.14/2.68 # Propositional check models : 0 17.14/2.68 # Propositional check unsatisfiable : 0 17.14/2.68 # Propositional clauses : 0 17.14/2.68 # Propositional clauses after purity: 0 17.14/2.68 # Propositional unsat core size : 0 17.14/2.68 # Propositional preprocessing time : 0.000 17.14/2.68 # Propositional encoding time : 0.000 17.14/2.68 # Propositional solver time : 0.000 17.14/2.68 # Success case prop preproc time : 0.000 17.14/2.68 # Success case prop encoding time : 0.000 17.14/2.68 # Success case prop solver time : 0.000 17.14/2.68 # Current number of processed clauses : 1168 17.14/2.68 # Positive orientable unit clauses : 82 17.14/2.68 # Positive unorientable unit clauses: 0 17.14/2.68 # Negative unit clauses : 119 17.14/2.68 # Non-unit-clauses : 967 17.14/2.68 # Current number of unprocessed clauses: 46297 17.14/2.68 # ...number of literals in the above : 196199 17.14/2.68 # Current number of archived formulas : 0 17.14/2.68 # Current number of archived clauses : 482 17.14/2.68 # Clause-clause subsumption calls (NU) : 164361 17.14/2.68 # Rec. Clause-clause subsumption calls : 70888 17.14/2.68 # Non-unit clause-clause subsumptions : 473 17.14/2.68 # Unit Clause-clause subsumption calls : 13382 17.14/2.68 # Rewrite failures with RHS unbound : 0 17.14/2.68 # BW rewrite match attempts : 54 17.14/2.68 # BW rewrite match successes : 16 17.14/2.68 # Condensation attempts : 0 17.14/2.68 # Condensation successes : 0 17.14/2.68 # Termbank termtop insertions : 1045025 17.14/2.68 # Search garbage collected termcells : 36361 17.14/2.68 17.14/2.68 # ------------------------------------------------- 17.14/2.68 # User time : 1.948 s 17.14/2.68 # System time : 0.068 s 17.14/2.68 # Total time : 2.016 s 17.14/2.68 # Maximum resident set size: 10908 pages 17.14/2.68 17.14/2.68 # ------------------------------------------------- 17.14/2.68 # User time : 1.969 s 17.14/2.68 # System time : 0.072 s 17.14/2.68 # Total time : 2.041 s 17.14/2.68 # Maximum resident set size: 2904 pages 17.14/2.68 % E exiting 17.14/2.68 % E exiting 17.14/2.68 EOF