0.12/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM 0.13/0.34 % Computer : n025.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1920 0.13/0.34 % WCLimit : 240 0.13/0.34 % DateTime : Wed Jul 30 09:50:04 EDT 2025 0.13/0.34 % CPUTime : 0.20/0.49 Running higher-order theorem proving 0.20/0.56 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.96pdcPKisp/E---3.1_25469.p 923.64/240.10 # Version: 3.0.0-ho 923.64/240.10 # Preprocessing class: HSLMSLSSLLLCHFA. 923.64/240.10 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 923.64/240.10 # Starting ehoh_best5 with 240s (1) cores 923.64/240.10 # Starting almost_fo_3_lam with 240s (1) cores 923.64/240.10 # Starting new_bool_5 with 240s (1) cores 923.64/240.10 # Starting pre_casc_3 with 240s (1) cores 923.64/240.10 # Starting ho_unfolding_8 with 240s (1) cores 923.64/240.10 # Starting new_ho_10_cnf2 with 240s (1) cores 923.64/240.10 # Starting new_bool_3 with 240s (1) cores 923.64/240.10 # Starting new_ho_5 with 240s (1) cores 923.64/240.10 # almost_fo_3_lam with pid 25549 completed with status 0 923.64/240.10 # Result found by almost_fo_3_lam 923.64/240.10 # Preprocessing class: HSLMSLSSLLLCHFA. 923.64/240.10 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 923.64/240.10 # Starting ehoh_best5 with 240s (1) cores 923.64/240.10 # Starting almost_fo_3_lam with 240s (1) cores 923.64/240.10 # No SInE strategy applied 923.64/240.10 # Search class: HGHSM-FSLM32-DHFMMSBN 923.64/240.10 # partial match(1): HGHSM-FSLM32-MHFMMSBN 923.64/240.10 # Scheduled 10 strats onto 1 cores with 240 seconds (240 total) 923.64/240.10 # Starting ho_unfolding_8 with 44s (1) cores 923.64/240.10 # ho_unfolding_8 with pid 25562 completed with status 8 923.64/240.10 # Starting almost_fo_3_lam with 25s (1) cores 923.64/240.10 # almost_fo_3_lam with pid 25565 completed with status 8 923.64/240.10 # Starting additional_ho_3 with 22s (1) cores 923.64/240.10 # additional_ho_3 with pid 26267 completed with status 8 923.64/240.10 # Starting pre_casc_3 with 22s (1) cores 923.64/240.10 # pre_casc_3 with pid 26297 completed with status 8 923.64/240.10 # Starting ehoh_best6_lambda with 22s (1) cores 923.64/240.10 # ehoh_best6_lambda with pid 26321 completed with status 0 923.64/240.10 # Result found by ehoh_best6_lambda 923.64/240.10 # Preprocessing class: HSLMSLSSLLLCHFA. 923.64/240.10 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 923.64/240.10 # Starting ehoh_best5 with 240s (1) cores 923.64/240.10 # Starting almost_fo_3_lam with 240s (1) cores 923.64/240.10 # No SInE strategy applied 923.64/240.10 # Search class: HGHSM-FSLM32-DHFMMSBN 923.64/240.10 # partial match(1): HGHSM-FSLM32-MHFMMSBN 923.64/240.10 # Scheduled 10 strats onto 1 cores with 240 seconds (240 total) 923.64/240.10 # Starting ho_unfolding_8 with 44s (1) cores 923.64/240.10 # ho_unfolding_8 with pid 25562 completed with status 8 923.64/240.10 # Starting almost_fo_3_lam with 25s (1) cores 923.64/240.10 # almost_fo_3_lam with pid 25565 completed with status 8 923.64/240.10 # Starting additional_ho_3 with 22s (1) cores 923.64/240.10 # additional_ho_3 with pid 26267 completed with status 8 923.64/240.10 # Starting pre_casc_3 with 22s (1) cores 923.64/240.10 # pre_casc_3 with pid 26297 completed with status 8 923.64/240.10 # Starting ehoh_best6_lambda with 22s (1) cores 923.64/240.10 # Preprocessing time : 0.014 s 923.64/240.10 # Presaturation interreduction done 923.64/240.10 923.64/240.10 # Proof found! 923.64/240.10 # SZS status Theorem 923.64/240.10 # SZS output start CNFRefutation 923.64/240.10 thf(decl_23, type, in: $i > $i > $o). 923.64/240.10 thf(decl_24, type, exu: ($i > $o) > $o). 923.64/240.10 thf(decl_25, type, setextAx: $o). 923.64/240.10 thf(decl_26, type, emptyset: $i). 923.64/240.10 thf(decl_27, type, emptysetAx: $o). 923.64/240.10 thf(decl_28, type, setadjoin: $i > $i > $i). 923.64/240.10 thf(decl_29, type, setadjoinAx: $o). 923.64/240.10 thf(decl_30, type, powerset: $i > $i). 923.64/240.10 thf(decl_31, type, powersetAx: $o). 923.64/240.10 thf(decl_32, type, setunion: $i > $i). 923.64/240.10 thf(decl_33, type, setunionAx: $o). 923.64/240.10 thf(decl_34, type, omega: $i). 923.64/240.10 thf(decl_35, type, omega0Ax: $o). 923.64/240.10 thf(decl_36, type, omegaSAx: $o). 923.64/240.10 thf(decl_37, type, omegaIndAx: $o). 923.64/240.10 thf(decl_38, type, replAx: $o). 923.64/240.10 thf(decl_39, type, foundationAx: $o). 923.64/240.10 thf(decl_40, type, wellorderingAx: $o). 923.64/240.10 thf(decl_41, type, descr: ($i > $o) > $i). 923.64/240.10 thf(decl_42, type, descrp: $o). 923.64/240.10 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 923.64/240.10 thf(decl_44, type, dsetconstrI: $o). 923.64/240.10 thf(decl_45, type, dsetconstrEL: $o). 923.64/240.10 thf(decl_46, type, dsetconstrER: $o). 923.64/240.10 thf(decl_47, type, exuE1: $o). 923.64/240.10 thf(decl_48, type, prop2set: $o > $i). 923.64/240.10 thf(decl_49, type, prop2setE: $o). 923.64/240.10 thf(decl_50, type, emptysetE: $o). 923.64/240.10 thf(decl_51, type, emptysetimpfalse: $o). 923.64/240.10 thf(decl_52, type, notinemptyset: $o). 923.64/240.10 thf(decl_53, type, exuE3e: $o). 923.64/240.10 thf(decl_54, type, setext: $o). 923.64/240.10 thf(decl_55, type, emptyI: $o). 923.64/240.10 thf(decl_56, type, noeltsimpempty: $o). 923.64/240.10 thf(decl_57, type, setbeta: $o). 923.64/240.10 thf(decl_58, type, nonempty: $i > $o). 923.64/240.10 thf(decl_59, type, nonemptyE1: $o). 923.64/240.10 thf(decl_60, type, nonemptyI: $o). 923.64/240.10 thf(decl_61, type, nonemptyI1: $o). 923.64/240.10 thf(decl_62, type, setadjoinIL: $o). 923.64/240.10 thf(decl_63, type, emptyinunitempty: $o). 923.64/240.10 thf(decl_64, type, setadjoinIR: $o). 923.64/240.10 thf(decl_65, type, setadjoinE: $o). 923.64/240.10 thf(decl_66, type, setadjoinOr: $o). 923.64/240.10 thf(decl_67, type, setoftrueEq: $o). 923.64/240.10 thf(decl_68, type, powersetI: $o). 923.64/240.10 thf(decl_69, type, emptyinPowerset: $o). 923.64/240.10 thf(decl_70, type, emptyInPowerset: $o). 923.64/240.10 thf(decl_71, type, powersetE: $o). 923.64/240.10 thf(decl_72, type, setunionI: $o). 923.64/240.10 thf(decl_73, type, setunionE: $o). 923.64/240.10 thf(decl_74, type, subPowSU: $o). 923.64/240.10 thf(decl_75, type, exuE2: $o). 923.64/240.10 thf(decl_76, type, nonemptyImpWitness: $o). 923.64/240.10 thf(decl_77, type, uniqinunit: $o). 923.64/240.10 thf(decl_78, type, notinsingleton: $o). 923.64/240.10 thf(decl_79, type, eqinunit: $o). 923.64/240.10 thf(decl_80, type, singletonsswitch: $o). 923.64/240.10 thf(decl_81, type, upairsetE: $o). 923.64/240.10 thf(decl_82, type, upairsetIL: $o). 923.64/240.10 thf(decl_83, type, upairsetIR: $o). 923.64/240.10 thf(decl_84, type, emptyE1: $o). 923.64/240.10 thf(decl_85, type, vacuousDall: $o). 923.64/240.10 thf(decl_86, type, quantDeMorgan1: $o). 923.64/240.10 thf(decl_87, type, quantDeMorgan2: $o). 923.64/240.10 thf(decl_88, type, quantDeMorgan3: $o). 923.64/240.10 thf(decl_89, type, quantDeMorgan4: $o). 923.64/240.10 thf(decl_90, type, prop2setI: $o). 923.64/240.10 thf(decl_91, type, set2prop: $i > $o). 923.64/240.10 thf(decl_92, type, prop2set2propI: $o). 923.64/240.10 thf(decl_93, type, notdexE: $o). 923.64/240.10 thf(decl_94, type, notdallE: $o). 923.64/240.10 thf(decl_95, type, exuI1: $o). 923.64/240.10 thf(decl_96, type, exuI3: $o). 923.64/240.10 thf(decl_97, type, exuI2: $o). 923.64/240.10 thf(decl_98, type, inCongP: $o). 923.64/240.10 thf(decl_99, type, in__Cong: $o). 923.64/240.10 thf(decl_100, type, exuE3u: $o). 923.64/240.10 thf(decl_101, type, exu__Cong: $o). 923.64/240.10 thf(decl_102, type, emptyset__Cong: $o). 923.64/240.10 thf(decl_103, type, setadjoin__Cong: $o). 923.64/240.10 thf(decl_104, type, powerset__Cong: $o). 923.64/240.10 thf(decl_105, type, setunion__Cong: $o). 923.64/240.10 thf(decl_106, type, omega__Cong: $o). 923.64/240.10 thf(decl_107, type, exuEu: $o). 923.64/240.10 thf(decl_108, type, descr__Cong: $o). 923.64/240.10 thf(decl_109, type, dsetconstr__Cong: $o). 923.64/240.10 thf(decl_110, type, subset: $i > $i > $o). 923.64/240.10 thf(decl_113, type, subsetI1: $o). 923.64/240.10 thf(decl_114, type, eqimpsubset2: $o). 923.64/240.10 thf(decl_115, type, eqimpsubset1: $o). 923.64/240.10 thf(decl_116, type, subsetI2: $o). 923.64/240.10 thf(decl_117, type, emptysetsubset: $o). 923.64/240.10 thf(decl_118, type, subsetE: $o). 923.64/240.10 thf(decl_119, type, subsetE2: $o). 923.64/240.10 thf(decl_120, type, notsubsetI: $o). 923.64/240.10 thf(decl_121, type, notequalI1: $o). 923.64/240.10 thf(decl_122, type, notequalI2: $o). 923.64/240.10 thf(decl_123, type, subsetRefl: $o). 923.64/240.10 thf(decl_124, type, subsetTrans: $o). 923.64/240.10 thf(decl_125, type, setadjoinSub: $o). 923.64/240.10 thf(decl_126, type, setadjoinSub2: $o). 923.64/240.10 thf(decl_127, type, subset2powerset: $o). 923.64/240.10 thf(decl_128, type, setextsub: $o). 923.64/240.10 thf(decl_129, type, subsetemptysetimpeq: $o). 923.64/240.10 thf(decl_130, type, powersetI1: $o). 923.64/240.10 thf(decl_131, type, powersetE1: $o). 923.64/240.10 thf(decl_132, type, inPowerset: $o). 923.64/240.10 thf(decl_133, type, powersetsubset: $o). 923.64/240.10 thf(decl_134, type, sepInPowerset: $o). 923.64/240.10 thf(decl_135, type, sepSubset: $o). 923.64/240.10 thf(decl_136, type, binunion: $i > $i > $i). 923.64/240.10 thf(decl_137, type, binunionIL: $o). 923.64/240.10 thf(decl_138, type, upairset2IR: $o). 923.64/240.10 thf(decl_139, type, binunionIR: $o). 923.64/240.10 thf(decl_140, type, binunionEcases: $o). 923.64/240.10 thf(decl_141, type, binunionE: $o). 923.64/240.10 thf(decl_142, type, binunionLsub: $o). 923.64/240.10 thf(decl_143, type, binunionRsub: $o). 923.64/240.10 thf(decl_144, type, binintersect: $i > $i > $i). 923.64/240.10 thf(decl_145, type, binintersectI: $o). 923.64/240.10 thf(decl_146, type, binintersectSubset5: $o). 923.64/240.10 thf(decl_147, type, binintersectEL: $o). 923.64/240.10 thf(decl_148, type, binintersectLsub: $o). 923.64/240.10 thf(decl_149, type, binintersectSubset2: $o). 923.64/240.10 thf(decl_150, type, binintersectSubset3: $o). 923.64/240.10 thf(decl_151, type, binintersectER: $o). 923.64/240.10 thf(decl_152, type, disjointsetsI1: $o). 923.64/240.10 thf(decl_153, type, binintersectRsub: $o). 923.64/240.10 thf(decl_154, type, binintersectSubset4: $o). 923.64/240.10 thf(decl_155, type, binintersectSubset1: $o). 923.64/240.10 thf(decl_156, type, bs114d: $o). 923.64/240.10 thf(decl_158, type, setminus: $i > $i > $i). 923.64/240.10 thf(decl_159, type, setminusI: $o). 923.64/240.10 thf(decl_160, type, setminusEL: $o). 923.64/240.10 thf(decl_161, type, setminusER: $o). 923.64/240.10 thf(decl_162, type, setminusSubset2: $o). 923.64/240.10 thf(decl_163, type, setminusERneg: $o). 923.64/240.10 thf(decl_164, type, setminusELneg: $o). 923.64/240.10 thf(decl_165, type, setminusILneg: $o). 923.64/240.10 thf(decl_166, type, setminusIRneg: $o). 923.64/240.10 thf(decl_167, type, setminusLsub: $o). 923.64/240.10 thf(decl_168, type, setminusSubset1: $o). 923.64/240.10 thf(decl_169, type, symdiff: $i > $i > $i). 923.64/240.10 thf(decl_170, type, symdiffE: $o). 923.64/240.10 thf(decl_171, type, symdiffI1: $o). 923.64/240.10 thf(decl_172, type, symdiffI2: $o). 923.64/240.10 thf(decl_173, type, symdiffIneg1: $o). 923.64/240.10 thf(decl_174, type, symdiffIneg2: $o). 923.64/240.10 thf(decl_175, type, iskpair: $i > $o). 923.64/240.10 thf(decl_176, type, secondinupair: $o). 923.64/240.10 thf(decl_177, type, setukpairIL: $o). 923.64/240.10 thf(decl_178, type, setukpairIR: $o). 923.64/240.10 thf(decl_179, type, kpairiskpair: $o). 923.64/240.10 thf(decl_180, type, kpair: $i > $i > $i). 923.64/240.10 thf(decl_181, type, kpairp: $o). 923.64/240.10 thf(decl_182, type, cartprod: $i > $i > $i). 923.64/240.10 thf(decl_183, type, singletonsubset: $o). 923.64/240.10 thf(decl_184, type, singletoninpowerset: $o). 923.64/240.10 thf(decl_185, type, singletoninpowunion: $o). 923.64/240.10 thf(decl_186, type, upairset2E: $o). 923.64/240.10 thf(decl_187, type, upairsubunion: $o). 923.64/240.10 thf(decl_188, type, upairinpowunion: $o). 923.64/240.10 thf(decl_189, type, ubforcartprodlem1: $o). 923.64/240.10 thf(decl_190, type, ubforcartprodlem2: $o). 923.64/240.10 thf(decl_191, type, ubforcartprodlem3: $o). 923.64/240.10 thf(decl_192, type, cartprodpairin: $o). 923.64/240.10 thf(decl_193, type, cartprodmempair1: $o). 923.64/240.10 thf(decl_194, type, cartprodmempair: $o). 923.64/240.10 thf(decl_195, type, setunionE2: $o). 923.64/240.10 thf(decl_196, type, setunionsingleton1: $o). 923.64/240.10 thf(decl_197, type, setunionsingleton2: $o). 923.64/240.10 thf(decl_198, type, setunionsingleton: $o). 923.64/240.10 thf(decl_199, type, singleton: $i > $o). 923.64/240.10 thf(decl_200, type, singletonprop: $o). 923.64/240.10 thf(decl_201, type, ex1: $i > ($i > $o) > $o). 923.64/240.10 thf(decl_202, type, ex1E1: $o). 923.64/240.10 thf(decl_203, type, ex1I: $o). 923.64/240.10 thf(decl_204, type, ex1I2: $o). 923.64/240.10 thf(decl_205, type, singletonsuniq: $o). 923.64/240.10 thf(decl_210, type, setukpairinjL1: $o). 923.64/240.10 thf(decl_211, type, kfstsingleton: $o). 923.64/240.10 thf(decl_212, type, theprop: $o). 923.64/240.10 thf(decl_213, type, kfst: $i > $i). 923.64/240.10 thf(decl_214, type, kfstpairEq: $o). 923.64/240.10 thf(decl_215, type, cartprodfstin: $o). 923.64/240.10 thf(decl_216, type, setukpairinjL2: $o). 923.64/240.10 thf(decl_217, type, setukpairinjL: $o). 923.64/240.10 thf(decl_218, type, setukpairinjR11: $o). 923.64/240.10 thf(decl_219, type, setukpairinjR12: $o). 923.64/240.10 thf(decl_220, type, setukpairinjR1: $o). 923.64/240.10 thf(decl_221, type, upairequniteq: $o). 923.64/240.10 thf(decl_222, type, setukpairinjR2: $o). 923.64/240.10 thf(decl_223, type, setukpairinjR: $o). 923.64/240.10 thf(decl_224, type, ksndsingleton: $o). 923.64/240.10 thf(decl_225, type, ksnd: $i > $i). 923.64/240.10 thf(decl_226, type, ksndpairEq: $o). 923.64/240.10 thf(decl_227, type, kpairsurjEq: $o). 923.64/240.10 thf(decl_228, type, cartprodsndin: $o). 923.64/240.10 thf(decl_229, type, cartprodpairmemEL: $o). 923.64/240.10 thf(decl_230, type, cartprodpairmemER: $o). 923.64/240.10 thf(decl_231, type, cartprodmempaircEq: $o). 923.64/240.10 thf(decl_232, type, cartprodfstpairEq: $o). 923.64/240.10 thf(decl_233, type, cartprodsndpairEq: $o). 923.64/240.10 thf(decl_234, type, cartprodpairsurjEq: $o). 923.64/240.10 thf(decl_235, type, breln: $i > $i > $i > $o). 923.64/240.10 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 923.64/240.10 thf(decl_237, type, dpsetconstrI: $o). 923.64/240.10 thf(decl_238, type, dpsetconstrSub: $o). 923.64/240.10 thf(decl_239, type, setOfPairsIsBReln: $o). 923.64/240.10 thf(decl_240, type, dpsetconstrERa: $o). 923.64/240.10 thf(decl_241, type, dpsetconstrEL1: $o). 923.64/240.10 thf(decl_242, type, dpsetconstrEL2: $o). 923.64/240.10 thf(decl_243, type, dpsetconstrER: $o). 923.64/240.10 thf(decl_244, type, func: $i > $i > $i > $o). 923.64/240.10 thf(decl_245, type, funcSet: $i > $i > $i). 923.64/240.10 thf(decl_246, type, funcImageSingleton: $o). 923.64/240.10 thf(decl_247, type, apProp: $o). 923.64/240.10 thf(decl_248, type, ap: $i > $i > $i > $i > $i). 923.64/240.10 thf(decl_249, type, app: $o). 923.64/240.10 thf(decl_250, type, infuncsetfunc: $o). 923.64/240.10 thf(decl_251, type, ap2p: $o). 923.64/240.10 thf(decl_252, type, funcinfuncset: $o). 923.64/240.10 thf(decl_253, type, lamProp: $o). 923.64/240.10 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i). 923.64/240.10 thf(decl_255, type, lamp: $o). 923.64/240.10 thf(decl_256, type, lam2p: $o). 923.64/240.10 thf(decl_257, type, brelnall1: $o). 923.64/240.10 thf(decl_258, type, brelnall2: $o). 923.64/240.10 thf(decl_259, type, ex1E2: $o). 923.64/240.10 thf(decl_260, type, funcGraphProp1: $o). 923.64/240.10 thf(decl_261, type, funcGraphProp3: $o). 923.64/240.10 thf(decl_262, type, funcGraphProp2: $o). 923.64/240.10 thf(decl_263, type, funcextLem: $o). 923.64/240.10 thf(decl_264, type, funcGraphProp4: $o). 923.64/240.10 thf(decl_265, type, subbreln: $o). 923.64/240.10 thf(decl_266, type, eqbreln: $o). 923.64/240.10 thf(decl_267, type, funcext: $o). 923.64/240.10 thf(decl_268, type, funcext2: $o). 923.64/240.10 thf(decl_269, type, ap2apEq1: $o). 923.64/240.10 thf(decl_270, type, ap2apEq2: $o). 923.64/240.10 thf(decl_271, type, beta1: $o). 923.64/240.10 thf(decl_272, type, eta1: $o). 923.64/240.10 thf(decl_273, type, lam2lamEq: $o). 923.64/240.10 thf(decl_274, type, beta2: $o). 923.64/240.10 thf(decl_275, type, eta2: $o). 923.64/240.10 thf(decl_276, type, iffalseProp1: $o). 923.64/240.10 thf(decl_277, type, iffalseProp2: $o). 923.64/240.10 thf(decl_278, type, iftrueProp1: $o). 923.64/240.10 thf(decl_279, type, iftrueProp2: $o). 923.64/240.10 thf(decl_280, type, ifSingleton: $o). 923.64/240.10 thf(decl_281, type, if: $i > $o > $i > $i > $i). 923.64/240.10 thf(decl_282, type, ifp: $o). 923.64/240.10 thf(decl_283, type, theeq: $o). 923.64/240.10 thf(decl_284, type, iftrue: $o). 923.64/240.10 thf(decl_285, type, iffalse: $o). 923.64/240.10 thf(decl_286, type, iftrueorfalse: $o). 923.64/240.10 thf(decl_287, type, binintersectT_lem: $o). 923.64/240.10 thf(decl_288, type, binunionT_lem: $o). 923.64/240.10 thf(decl_289, type, powersetT_lem: $o). 923.64/240.10 thf(decl_290, type, setminusT_lem: $o). 923.64/240.10 thf(decl_291, type, complementT_lem: $o). 923.64/240.10 thf(decl_292, type, setextT: $o). 923.64/240.10 thf(decl_293, type, subsetTI: $o). 923.64/240.10 thf(decl_294, type, powersetTI1: $o). 923.64/240.10 thf(decl_295, type, powersetTE1: $o). 923.64/240.10 thf(decl_296, type, complementTI1: $o). 923.64/240.10 thf(decl_297, type, complementTE1: $o). 923.64/240.10 thf(decl_298, type, binintersectTELcontra: $o). 923.64/240.10 thf(decl_299, type, binintersectTERcontra: $o). 923.64/240.10 thf(decl_300, type, contrasubsetT: $o). 923.64/240.10 thf(decl_301, type, contrasubsetT1: $o). 923.64/240.10 thf(decl_302, type, contrasubsetT2: $o). 923.64/240.10 thf(decl_303, type, contrasubsetT3: $o). 923.64/240.10 thf(decl_304, type, doubleComplementI1: $o). 923.64/240.10 thf(decl_305, type, doubleComplementE1: $o). 923.64/240.10 thf(decl_306, type, doubleComplementSub1: $o). 923.64/240.10 thf(decl_307, type, doubleComplementSub2: $o). 923.64/240.10 thf(decl_308, type, doubleComplementEq: $o). 923.64/240.10 thf(decl_309, type, complementTnotintersectT: $o). 923.64/240.10 thf(decl_310, type, complementImpComplementIntersect: $o). 923.64/240.10 thf(decl_311, type, complementSubsetComplementIntersect: $o). 923.64/240.10 thf(decl_312, type, complementInPowersetComplementIntersect: $o). 923.64/240.10 thf(decl_313, type, contraSubsetComplement: $o). 923.64/240.10 thf(decl_314, type, complementTcontraSubset: $o). 923.64/240.10 thf(decl_315, type, binunionTILcontra: $o). 923.64/240.10 thf(decl_316, type, binunionTIRcontra: $o). 923.64/240.10 thf(decl_317, type, inIntersectImpInUnion: $o). 923.64/240.10 thf(decl_318, type, inIntersectImpInUnion2: $o). 923.64/240.10 thf(decl_319, type, inIntersectImpInIntersectUnions: $o). 923.64/240.10 thf(decl_320, type, intersectInPowersetIntersectUnions: $o). 923.64/240.10 thf(decl_321, type, inComplementUnionImpNotIn1: $o). 923.64/240.10 thf(decl_322, type, inComplementUnionImpInComplement1: $o). 923.64/240.10 thf(decl_323, type, binunionTE: $o). 923.64/240.10 thf(decl_324, type, binunionTEcontra: $o). 923.64/240.10 thf(decl_325, type, demorgan2a1: $o). 923.64/240.10 thf(decl_326, type, complementUnionInPowersetComplement: $o). 923.64/240.10 thf(decl_327, type, demorgan2a2: $o). 923.64/240.10 thf(decl_328, type, demorgan1a: $o). 923.64/240.10 thf(decl_329, type, demorgan1b: $o). 923.64/240.10 thf(decl_330, type, demorgan1: $o). 923.64/240.10 thf(decl_331, type, demorgan2a: $o). 923.64/240.10 thf(decl_332, type, demorgan2b2: $o). 923.64/240.10 thf(decl_333, type, demorgan2b: $o). 923.64/240.10 thf(decl_334, type, demorgan2: $o). 923.64/240.10 thf(decl_335, type, woz13rule0: $o). 923.64/240.10 thf(decl_336, type, woz13rule1: $o). 923.64/240.10 thf(decl_337, type, woz13rule2: $o). 923.64/240.10 thf(decl_338, type, woz13rule3: $o). 923.64/240.10 thf(decl_339, type, woz13rule4: $o). 923.64/240.10 thf(decl_340, type, woz1_1: $o). 923.64/240.10 thf(decl_341, type, woz1_2: $o). 923.64/240.10 thf(decl_342, type, woz1_3: $o). 923.64/240.10 thf(decl_343, type, woz1_4: $o). 923.64/240.10 thf(decl_344, type, woz1_5: $o). 923.64/240.10 thf(decl_345, type, breln1: $i > $i > $o). 923.64/240.10 thf(decl_346, type, breln1all2: $o). 923.64/240.10 thf(decl_347, type, breln1Set: $i > $i). 923.64/240.10 thf(decl_348, type, breln1SetBreln1: $o). 923.64/240.10 thf(decl_354, type, reflwellordering: $i > $i > $o). 923.64/240.10 thf(decl_355, type, choice2fnsingleton: $o). 923.64/240.10 thf(decl_356, type, setOfPairsIsBReln1: $o). 923.64/240.10 thf(decl_357, type, breln1all1: $o). 923.64/240.10 thf(decl_358, type, subbreln1: $o). 923.64/240.10 thf(decl_359, type, eqbreln1: $o). 923.64/240.10 thf(decl_360, type, breln1invset: $i > $i > $i). 923.64/240.10 thf(decl_361, type, breln1invprop: $o). 923.64/240.10 thf(decl_362, type, breln1invI: $o). 923.64/240.10 thf(decl_363, type, breln1invE: $o). 923.64/240.10 thf(decl_364, type, breln1compset: $i > $i > $i > $i). 923.64/240.10 thf(decl_365, type, breln1compprop: $o). 923.64/240.10 thf(decl_366, type, breln1compI: $o). 923.64/240.10 thf(decl_367, type, breln1compE: $o). 923.64/240.10 thf(decl_368, type, breln1compEex: $o). 923.64/240.10 thf(decl_369, type, breln1unionprop: $o). 923.64/240.10 thf(decl_370, type, breln1unionIL: $o). 923.64/240.10 thf(decl_371, type, breln1unionIR: $o). 923.64/240.10 thf(decl_372, type, breln1unionI: $o). 923.64/240.10 thf(decl_373, type, breln1unionE: $o). 923.64/240.10 thf(decl_374, type, breln1unionEcases: $o). 923.64/240.10 thf(decl_375, type, epred1_0: $o). 923.64/240.10 thf(decl_376, type, esk1_2: $i > $i > $i). 923.64/240.10 thf(decl_377, type, esk2_2: $i > $i > $i). 923.64/240.10 thf(decl_378, type, esk3_2: $i > $i > $i). 923.64/240.10 thf(decl_379, type, esk4_1: $i > $i). 923.64/240.10 thf(decl_380, type, esk5_2: ($i > $i > $o) > $i > $i). 923.64/240.10 thf(decl_381, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 923.64/240.10 thf(decl_382, type, esk7_2: ($i > $i > $o) > $i > $i). 923.64/240.10 thf(decl_383, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 923.64/240.10 thf(decl_384, type, esk9_1: $i > $i). 923.64/240.10 thf(decl_385, type, esk10_2: ($i > $o) > $i > $i). 923.64/240.10 thf(decl_386, type, esk11_2: ($i > $o) > $i > $i). 923.64/240.10 thf(decl_387, type, esk12_1: ($i > $o) > $i). 923.64/240.10 thf(decl_388, type, esk13_2: ($i > $o) > $i > $i). 923.64/240.10 thf(decl_389, type, esk14_1: ($i > $o) > $i). 923.64/240.10 thf(decl_390, type, esk15_2: $i > $i > $i). 923.64/240.10 thf(decl_391, type, esk16_2: $i > $i > $i). 923.64/240.10 thf(decl_392, type, esk17_1: $i > $i). 923.64/240.10 thf(decl_393, type, esk18_1: $i > $i). 923.64/240.10 thf(decl_394, type, esk19_1: $i > $i). 923.64/240.10 thf(decl_395, type, esk20_2: $i > $i > $i). 923.64/240.10 thf(decl_396, type, esk21_3: $i > $i > $o > $i). 923.64/240.10 thf(decl_397, type, esk22_2: ($i > $o) > $i > $i). 923.64/240.10 thf(decl_398, type, esk23_1: ($i > $o) > $i). 923.64/240.10 thf(decl_399, type, esk24_1: $i > $i). 923.64/240.10 thf(decl_400, type, esk25_2: $i > ($i > $o) > $i). 923.64/240.10 thf(decl_401, type, esk26_2: $i > ($i > $o) > $i). 923.64/240.10 thf(decl_402, type, esk27_2: $i > ($i > $o) > $i). 923.64/240.10 thf(decl_403, type, esk28_2: $i > ($i > $o) > $i). 923.64/240.10 thf(decl_404, type, esk29_2: $i > ($i > $o) > $i). 923.64/240.10 thf(decl_405, type, esk30_2: $i > ($i > $o) > $i). 923.64/240.10 thf(decl_406, type, esk31_2: ($i > $o) > $i > $i). 923.64/240.10 thf(decl_407, type, esk32_1: ($i > $o) > $i). 923.64/240.10 thf(decl_408, type, esk33_1: ($i > $o) > $i). 923.64/240.10 thf(decl_409, type, esk34_1: ($i > $o) > $i). 923.64/240.10 thf(decl_410, type, esk35_1: ($i > $o) > $i). 923.64/240.10 thf(decl_411, type, esk36_2: ($i > $o) > $i > $i). 923.64/240.10 thf(decl_412, type, esk37_1: ($i > $o) > $i). 923.64/240.10 thf(decl_413, type, esk38_2: ($i > $o) > $i > $i). 923.64/240.10 thf(decl_414, type, esk39_2: ($i > $o) > ($i > $o) > $i). 923.64/240.10 thf(decl_415, type, esk40_2: ($i > $o) > ($i > $o) > $i). 923.64/240.10 thf(decl_416, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 923.64/240.10 thf(decl_417, type, esk42_2: ($i > $o) > ($i > $o) > $i). 923.64/240.10 thf(decl_418, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 923.64/240.10 thf(decl_419, type, esk44_2: ($i > $o) > ($i > $o) > $i). 923.64/240.10 thf(decl_420, type, esk45_2: ($i > $o) > $i > $i). 923.64/240.10 thf(decl_421, type, esk46_2: ($i > $o) > ($i > $o) > $i). 923.64/240.10 thf(decl_422, type, esk47_2: ($i > $o) > ($i > $o) > $i). 923.64/240.10 thf(decl_423, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 923.64/240.10 thf(decl_424, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 923.64/240.10 thf(decl_425, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 923.64/240.10 thf(decl_426, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 923.64/240.10 thf(decl_427, type, esk52_2: $i > $i > $i). 923.64/240.10 thf(decl_428, type, esk53_2: $i > $i > $i). 923.64/240.10 thf(decl_429, type, esk54_2: $i > $i > $i). 923.64/240.10 thf(decl_430, type, esk55_3: $i > $i > $i > $i). 923.64/240.10 thf(decl_431, type, esk56_3: $i > $i > $i > $i). 923.64/240.10 thf(decl_432, type, esk57_2: $i > $i > $i). 923.64/240.10 thf(decl_433, type, esk58_2: $i > ($i > $o) > $i). 923.64/240.10 thf(decl_434, type, esk59_2: $i > ($i > $o) > $i). 923.64/240.10 thf(decl_435, type, esk60_2: $i > ($i > $o) > $i). 923.64/240.10 thf(decl_436, type, esk61_3: $i > ($i > $o) > $i > $i). 923.64/240.10 thf(decl_437, type, esk62_2: $i > ($i > $o) > $i). 923.64/240.10 thf(decl_438, type, esk63_2: $i > ($i > $o) > $i). 923.64/240.10 thf(decl_439, type, esk64_3: $i > $i > ($i > $i) > $i). 923.64/240.10 thf(decl_440, type, esk65_3: $i > $i > ($i > $i) > $i). 923.64/240.10 thf(decl_441, type, esk66_3: $i > $i > ($i > $i) > $i). 923.64/240.10 thf(decl_442, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 923.64/240.10 thf(decl_443, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 923.64/240.10 thf(decl_444, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 923.64/240.10 thf(decl_445, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 923.64/240.10 thf(decl_446, type, esk71_4: $i > $i > $i > $i > $i). 923.64/240.10 thf(decl_447, type, esk72_4: $i > $i > $i > $i > $i). 923.64/240.10 thf(decl_448, type, esk73_4: $i > $i > $i > $i > $i). 923.64/240.10 thf(decl_449, type, esk74_4: $i > $i > $i > $i > $i). 923.64/240.10 thf(decl_450, type, esk75_4: $i > $i > $i > $i > $i). 923.64/240.10 thf(decl_451, type, esk76_4: $i > $i > $i > $i > $i). 923.64/240.10 thf(decl_452, type, esk77_4: $i > $i > $i > $i > $i). 923.64/240.10 thf(decl_453, type, esk78_4: $i > $i > $i > $i > $i). 923.64/240.10 thf(decl_454, type, esk79_4: $i > $i > $i > $i > $i). 923.64/240.10 thf(decl_455, type, esk80_3: $i > $i > ($i > $i) > $i). 923.64/240.10 thf(decl_456, type, esk81_3: $i > $i > ($i > $i) > $i). 923.64/240.10 thf(decl_457, type, esk82_3: $i > $i > ($i > $i) > $i). 923.64/240.10 thf(decl_458, type, esk83_3: $i > $i > $i > $i). 923.64/240.10 thf(decl_459, type, esk84_3: $i > $i > $i > $i). 923.64/240.10 thf(decl_460, type, esk85_3: $i > $i > $i > $i). 923.64/240.10 thf(decl_461, type, esk86_3: $i > $i > $i > $i). 923.64/240.10 thf(decl_462, type, esk87_3: $i > $i > ($i > $o) > $i). 923.64/240.10 thf(decl_463, type, esk88_3: $i > $i > ($i > $o) > $i). 923.64/240.10 thf(decl_464, type, esk89_3: $i > $i > ($i > $i > $o) > $i). 923.64/240.10 thf(decl_465, type, esk90_3: $i > $i > ($i > $o) > $i). 923.64/240.10 thf(decl_466, type, esk91_3: $i > $i > ($i > $o) > $i). 923.64/240.10 thf(decl_467, type, esk92_3: $i > $i > $i > $i). 923.64/240.10 thf(decl_468, type, esk93_3: $i > $i > $i > $i). 923.64/240.10 thf(decl_469, type, esk94_3: $i > $i > $i > $i). 923.64/240.10 thf(decl_470, type, esk95_3: $i > $i > $i > $i). 923.64/240.10 thf(decl_471, type, esk96_3: $i > $i > $i > $i). 923.64/240.10 thf(decl_472, type, esk97_3: $i > $i > $i > $i). 923.64/240.10 thf(decl_473, type, esk98_5: $i > $i > $i > $i > $i > $i). 923.64/240.10 thf(decl_474, type, esk99_6: $i > $i > $i > $i > $i > $o > $i). 923.64/240.10 thf(decl_475, type, esk100_0: $i). 923.64/240.10 thf(decl_476, type, esk101_0: $i). 923.64/240.10 thf(decl_477, type, esk102_0: $i). 923.64/240.10 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', replAx)). 923.64/240.10 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', exu)). 923.64/240.10 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', descrp)). 923.64/240.10 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', exuE1)). 923.64/240.10 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', exuE3e)). 923.64/240.10 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', nonempty)). 923.64/240.10 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', nonemptyI)). 923.64/240.10 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', exuE2)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', exuI1)). 923.64/240.10 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', exuI3)). 923.64/240.10 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', exuI2)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', exuE3u)). 923.64/240.10 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', exu__Cong)). 923.64/240.10 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', exuEu)). 923.64/240.10 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', descr__Cong)). 923.64/240.10 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', dsetconstrI)). 923.64/240.10 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', dsetconstrEL)). 923.64/240.10 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', dsetconstrER)). 923.64/240.10 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setbeta)). 923.64/240.10 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', nonemptyE1)). 923.64/240.10 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', nonemptyI1)). 923.64/240.10 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setoftrueEq)). 923.64/240.10 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', nonemptyImpWitness)). 923.64/240.10 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', emptyE1)). 923.64/240.10 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', dsetconstr__Cong)). 923.64/240.10 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', sepInPowerset)). 923.64/240.10 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', sepSubset)). 923.64/240.10 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', singletonprop)). 923.64/240.10 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', ex1E1)). 923.64/240.10 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', ex1I)). 923.64/240.10 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', ex1I2)). 923.64/240.10 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', kfstsingleton)). 923.64/240.10 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', ksndsingleton)). 923.64/240.10 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', dpsetconstrI)). 923.64/240.10 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', dpsetconstrSub)). 923.64/240.10 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setOfPairsIsBReln)). 923.64/240.10 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', dpsetconstrERa)). 923.64/240.10 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', dpsetconstrEL1)). 923.64/240.10 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', dpsetconstrEL2)). 923.64/240.10 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', dpsetconstrER)). 923.64/240.10 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', funcImageSingleton)). 923.64/240.10 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', apProp)). 923.64/240.10 thf(lamProp, axiom, ((lamProp)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', lamProp)). 923.64/240.10 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:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', lamp)). 923.64/240.10 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', lam2p)). 923.64/240.10 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', ex1E2)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', beta1)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', eta1)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', lam2lamEq)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', beta2)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', eta2)). 923.64/240.10 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', iffalseProp1)). 923.64/240.10 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', iffalseProp2)). 923.64/240.10 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', iftrueProp1)). 923.64/240.10 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', iftrueProp2)). 923.64/240.10 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', ifSingleton)). 923.64/240.10 thf(choice2fnsingleton, axiom, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:(((X52 @ X2 @ X3)&![X14:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ X3 @ X14) @ X33))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', choice2fnsingleton)). 923.64/240.10 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setOfPairsIsBReln1)). 923.64/240.10 thf(breln1unionCommutes, conjecture, ((setextAx)=>(((setadjoinAx)=>(((((((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((((((emptysetE)=>((emptysetimpfalse)=>((((setext)=>(((noeltsimpempty)=>(((nonemptyE1)=>(((nonemptyI1)=>(((emptyinunitempty)=>(((setadjoinE)=>((setadjoinOr)=>(((powersetI)=>((emptyinPowerset)=>((((setunionI)=>((setunionE)=>((subPowSU)=>(((nonemptyImpWitness)=>((((((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>(((quantDeMorgan1)=>(((quantDeMorgan3)=>((((((((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((((emptyset__Cong)=>((((setunion__Cong)=>(((exuEu)=>(((dsetconstr__Cong)=>(((((subsetI2)=>(((((((notequalI2)=>((((setadjoinSub)=>((setadjoinSub2)=>(((((powersetI1)=>((powersetE1)=>((((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>(((((binunionLsub)=>((binunionRsub)=>((((binintersectEL)=>((((binintersectSubset3)=>((binintersectER)=>(((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>(((setminusI)=>(((((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>(((symdiffE)=>(((((symdiffIneg2)=>(((setukpairIL)=>(((kpairiskpair)=>(((singletonsubset)=>((singletoninpowerset)=>(((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((((ubforcartprodlem3)=>(((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((((setunionsingleton)=>(((((((((theprop)=>(((((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>(((((kpairsurjEq)=>((cartprodsndin)=>((((cartprodmempaircEq)=>((((cartprodpairsurjEq)=>(((((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>(((apProp)=>((((ap2p)=>((((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((((((funcextLem)=>((funcGraphProp4)=>(((eqbreln)=>((funcext)=>((funcext2)=>(((ap2apEq2)=>((((((eta2)=>((((iftrueProp1)=>(((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((((binintersectT_lem)=>((binunionT_lem)=>((((complementT_lem)=>(((((powersetTE1)=>((complementTI1)=>(((binintersectTELcontra)=>((binintersectTERcontra)=>(((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>(((doubleComplementSub2)=>((((complementImpComplementIntersect)=>(((complementInPowersetComplementIntersect)=>((((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>(((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((((binunionTEcontra)=>((demorgan2a1)=>(((demorgan2a2)=>(((demorgan1b)=>((((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>(((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>(((woz1_2)=>(((woz1_4)=>(((((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((((((breln1invI)=>(((breln1compprop)=>(((((breln1unionprop)=>((breln1unionIL)=>((((![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((binunion @ X33 @ X35)=(binunion @ X35 @ X33))))))<=(breln1unionEcases))<=(breln1unionE))<=(breln1unionI))<=(breln1unionIR))))<=(breln1compEex))<=(breln1compE))<=(breln1compI)))<=(breln1invE)))<=(breln1invprop))<=(eqbreln1))<=(subbreln1))<=(breln1all1))))<=(breln1SetBreln1))<=(breln1all2))<=(woz1_5)))<=(woz1_3)))<=(woz1_1)))))<=(woz13rule1))))))<=(demorgan2a))<=(demorgan1)))<=(demorgan1a)))<=(complementUnionInPowersetComplement))))<=(binunionTE))<=(inComplementUnionImpInComplement1)))))<=(inIntersectImpInUnion2)))))<=(complementTcontraSubset))<=(contraSubsetComplement)))<=(complementSubsetComplementIntersect)))<=(complementTnotintersectT))<=(doubleComplementEq)))<=(doubleComplementSub1)))))))<=(contrasubsetT))))<=(complementTE1))))<=(powersetTI1))<=(subsetTI))<=(setextT)))<=(setminusT_lem))<=(powersetT_lem))))<=(iftrueorfalse))<=(iffalse))))))<=(iftrueProp2)))<=(iffalseProp2))<=(iffalseProp1)))<=(beta2))<=(lam2lamEq))<=(eta1))<=(beta1)))<=(ap2apEq1)))))<=(subbreln))))<=(funcGraphProp2))<=(funcGraphProp3))<=(funcGraphProp1))<=(ex1E2))))))<=(lamProp))<=(funcinfuncset)))<=(infuncsetfunc))<=(app)))<=(funcImageSingleton))))))<=(setOfPairsIsBReln))<=(dpsetconstrSub))<=(dpsetconstrI)))<=(cartprodsndpairEq))<=(cartprodfstpairEq)))<=(cartprodpairmemER))<=(cartprodpairmemEL))))<=(ksndpairEq))<=(ksndsingleton))<=(setukpairinjR))))))))<=(setukpairinjL2))<=(cartprodfstin))<=(kfstpairEq)))<=(kfstsingleton))<=(setukpairinjL1))<=(singletonsuniq))<=(ex1I2))<=(ex1I))<=(ex1E1))<=(singletonprop)))<=(setunionsingleton2))<=(setunionsingleton1)))))<=(cartprodpairin)))<=(ubforcartprodlem2))<=(ubforcartprodlem1)))))<=(singletoninpowunion))))<=(kpairp)))<=(setukpairIR)))<=(secondinupair)))<=(symdiffIneg1))<=(symdiffI2))<=(symdiffI1)))<=(setminusSubset1)))))))<=(setminusSubset2))<=(setminusER))<=(setminusEL)))<=(bs114d)))))<=(disjointsetsI1))))<=(binintersectSubset2))<=(binintersectLsub)))<=(binintersectSubset5))<=(binintersectI))))<=(binunionE))<=(binunionEcases))<=(binunionIR))))))<=(powersetsubset))<=(inPowerset))))<=(subsetemptysetimpeq))<=(setextsub))<=(subset2powerset))))<=(subsetTrans))<=(subsetRefl)))<=(notequalI1))<=(notsubsetI))<=(subsetE2))<=(subsetE))<=(emptysetsubset)))<=(eqimpsubset1))<=(eqimpsubset2))<=(subsetI1)))<=(descr__Cong)))<=(omega__Cong)))<=(powerset__Cong))<=(setadjoin__Cong)))<=(exu__Cong))<=(exuE3u))))))<=(exuI1))<=(notdallE))<=(notdexE))<=(prop2set2propI))<=(prop2setI))<=(quantDeMorgan4)))<=(quantDeMorgan2)))<=(vacuousDall))))))<=(singletonsswitch))<=(eqinunit))<=(notinsingleton))<=(uniqinunit)))<=(exuE2)))))<=(powersetE))<=(emptyInPowerset))))<=(setoftrueEq))))<=(setadjoinIR)))<=(setadjoinIL)))<=(nonemptyI)))<=(setbeta)))<=(emptyI)))<=(exuE3e))<=(notinemptyset))))<=(prop2setE))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL)))))))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax))<=(setunionAx))<=(powersetAx)))<=(emptysetAx))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', breln1unionCommutes)). 923.64/240.10 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setextAx)). 923.64/240.10 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', emptysetAx)). 923.64/240.10 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setadjoinAx)). 923.64/240.10 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', powersetAx)). 923.64/240.10 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setunionAx)). 923.64/240.10 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', omega0Ax)). 923.64/240.10 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', omegaSAx)). 923.64/240.10 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', omegaIndAx)). 923.64/240.10 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', foundationAx)). 923.64/240.10 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', wellorderingAx)). 923.64/240.10 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', prop2setE)). 923.64/240.10 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', emptysetE)). 923.64/240.10 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', emptysetimpfalse)). 923.64/240.10 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', notinemptyset)). 923.64/240.10 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setext)). 923.64/240.10 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', emptyI)). 923.64/240.10 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', noeltsimpempty)). 923.64/240.10 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setadjoinIL)). 923.64/240.10 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', emptyinunitempty)). 923.64/240.10 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setadjoinIR)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', setadjoinE)). 923.64/240.10 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setadjoinOr)). 923.64/240.10 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', powersetI)). 923.64/240.10 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', emptyinPowerset)). 923.64/240.10 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', emptyInPowerset)). 923.64/240.10 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', powersetE)). 923.64/240.10 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setunionI)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', setunionE)). 923.64/240.10 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', subPowSU)). 923.64/240.10 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', uniqinunit)). 923.64/240.10 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', notinsingleton)). 923.64/240.10 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', eqinunit)). 923.64/240.10 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', singletonsswitch)). 923.64/240.10 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', upairsetE)). 923.64/240.10 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', upairsetIL)). 923.64/240.10 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', upairsetIR)). 923.64/240.10 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', vacuousDall)). 923.64/240.10 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', quantDeMorgan1)). 923.64/240.10 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', quantDeMorgan2)). 923.64/240.10 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', quantDeMorgan3)). 923.64/240.10 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', quantDeMorgan4)). 923.64/240.10 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', prop2setI)). 923.64/240.10 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', prop2set2propI)). 923.64/240.10 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', notdexE)). 923.64/240.10 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', notdallE)). 923.64/240.10 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', inCongP)). 923.64/240.10 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', in__Cong)). 923.64/240.10 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', emptyset__Cong)). 923.64/240.10 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setadjoin__Cong)). 923.64/240.10 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', powerset__Cong)). 923.64/240.10 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setunion__Cong)). 923.64/240.10 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', omega__Cong)). 923.64/240.10 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', subsetI1)). 923.64/240.10 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', eqimpsubset2)). 923.64/240.10 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', eqimpsubset1)). 923.64/240.10 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', subsetI2)). 923.64/240.10 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', emptysetsubset)). 923.64/240.10 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', subsetE)). 923.64/240.10 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', subsetE2)). 923.64/240.10 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', notsubsetI)). 923.64/240.10 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', notequalI1)). 923.64/240.10 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', notequalI2)). 923.64/240.10 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', subsetRefl)). 923.64/240.10 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', subsetTrans)). 923.64/240.10 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setadjoinSub)). 923.64/240.10 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setadjoinSub2)). 923.64/240.10 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', subset2powerset)). 923.64/240.10 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setextsub)). 923.64/240.10 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', subsetemptysetimpeq)). 923.64/240.10 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', powersetI1)). 923.64/240.10 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', powersetE1)). 923.64/240.10 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', inPowerset)). 923.64/240.10 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', powersetsubset)). 923.64/240.10 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binunionIL)). 923.64/240.10 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', upairset2IR)). 923.64/240.10 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binunionIR)). 923.64/240.10 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binunionEcases)). 923.64/240.10 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binunionE)). 923.64/240.10 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binunionLsub)). 923.64/240.10 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binunionRsub)). 923.64/240.10 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binintersectI)). 923.64/240.10 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binintersectSubset5)). 923.64/240.10 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binintersectEL)). 923.64/240.10 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binintersectLsub)). 923.64/240.10 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binintersectSubset2)). 923.64/240.10 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binintersectSubset3)). 923.64/240.10 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binintersectER)). 923.64/240.10 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', disjointsetsI1)). 923.64/240.10 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binintersectRsub)). 923.64/240.10 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binintersectSubset4)). 923.64/240.10 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binintersectSubset1)). 923.64/240.10 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', bs114d)). 923.64/240.10 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setminusI)). 923.64/240.10 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setminusEL)). 923.64/240.10 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setminusER)). 923.64/240.10 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setminusSubset2)). 923.64/240.10 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setminusERneg)). 923.64/240.10 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setminusELneg)). 923.64/240.10 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setminusILneg)). 923.64/240.10 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setminusIRneg)). 923.64/240.10 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setminusLsub)). 923.64/240.10 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setminusSubset1)). 923.64/240.10 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', symdiffE)). 923.64/240.10 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', symdiffI1)). 923.64/240.10 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', symdiffI2)). 923.64/240.10 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', symdiffIneg1)). 923.64/240.10 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', symdiffIneg2)). 923.64/240.10 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', secondinupair)). 923.64/240.10 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setukpairIL)). 923.64/240.10 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setukpairIR)). 923.64/240.10 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', kpairiskpair)). 923.64/240.10 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', kpairp)). 923.64/240.10 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', singletonsubset)). 923.64/240.10 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', singletoninpowerset)). 923.64/240.10 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', singletoninpowunion)). 923.64/240.10 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', upairset2E)). 923.64/240.10 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', upairsubunion)). 923.64/240.10 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', upairinpowunion)). 923.64/240.10 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', ubforcartprodlem1)). 923.64/240.10 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', ubforcartprodlem2)). 923.64/240.10 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', ubforcartprodlem3)). 923.64/240.10 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', cartprodpairin)). 923.64/240.10 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', cartprodmempair1)). 923.64/240.10 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', cartprodmempair)). 923.64/240.10 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setunionE2)). 923.64/240.10 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setunionsingleton1)). 923.64/240.10 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setunionsingleton2)). 923.64/240.10 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setunionsingleton)). 923.64/240.10 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', singletonsuniq)). 923.64/240.10 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.96pdcPKisp/E---3.1_25469.p', setukpairinjL1)). 923.64/240.10 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', theprop)). 923.64/240.10 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', kfstpairEq)). 923.64/240.10 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', cartprodfstin)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', setukpairinjL2)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', setukpairinjL)). 923.64/240.10 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setukpairinjR11)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', setukpairinjR12)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', setukpairinjR1)). 923.64/240.10 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', upairequniteq)). 923.64/240.10 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setukpairinjR2)). 923.64/240.10 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setukpairinjR)). 923.64/240.10 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', ksndpairEq)). 923.64/240.10 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', kpairsurjEq)). 923.64/240.10 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', cartprodsndin)). 923.64/240.10 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', cartprodpairmemEL)). 923.64/240.10 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', cartprodpairmemER)). 923.64/240.10 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', cartprodmempaircEq)). 923.64/240.10 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', cartprodfstpairEq)). 923.64/240.10 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', cartprodsndpairEq)). 923.64/240.10 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', cartprodpairsurjEq)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', app)). 923.64/240.10 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', infuncsetfunc)). 923.64/240.10 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', ap2p)). 923.64/240.10 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', funcinfuncset)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', brelnall1)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', brelnall2)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', funcGraphProp1)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', funcGraphProp3)). 923.64/240.10 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', funcGraphProp2)). 923.64/240.10 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', funcextLem)). 923.64/240.10 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', funcGraphProp4)). 923.64/240.10 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', subbreln)). 923.64/240.10 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', eqbreln)). 923.64/240.10 thf(funcext, axiom, ((funcext)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', funcext)). 923.64/240.10 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', funcext2)). 923.64/240.10 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', ap2apEq1)). 923.64/240.10 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', ap2apEq2)). 923.64/240.10 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', ifp)). 923.64/240.10 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', theeq)). 923.64/240.10 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', iftrue)). 923.64/240.10 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', iffalse)). 923.64/240.10 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', iftrueorfalse)). 923.64/240.10 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', binintersectT_lem)). 923.64/240.10 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binunionT_lem)). 923.64/240.10 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', powersetT_lem)). 923.64/240.10 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', setminusT_lem)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', complementT_lem)). 923.64/240.10 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', setextT)). 923.64/240.10 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', subsetTI)). 923.64/240.10 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', powersetTI1)). 923.64/240.10 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', powersetTE1)). 923.64/240.10 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', complementTI1)). 923.64/240.10 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', complementTE1)). 923.64/240.10 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binintersectTELcontra)). 923.64/240.10 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', binintersectTERcontra)). 923.64/240.10 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', contrasubsetT)). 923.64/240.10 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', contrasubsetT1)). 923.64/240.10 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', contrasubsetT2)). 923.64/240.10 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', contrasubsetT3)). 923.64/240.10 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', doubleComplementI1)). 923.64/240.10 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', doubleComplementE1)). 923.64/240.10 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', doubleComplementSub1)). 923.64/240.10 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', doubleComplementSub2)). 923.64/240.10 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', doubleComplementEq)). 923.64/240.10 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', complementTnotintersectT)). 923.64/240.10 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', complementImpComplementIntersect)). 923.64/240.10 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', complementSubsetComplementIntersect)). 923.64/240.10 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', complementInPowersetComplementIntersect)). 923.64/240.10 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', contraSubsetComplement)). 923.64/240.10 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', complementTcontraSubset)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', binunionTILcontra)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', binunionTIRcontra)). 923.64/240.10 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', inIntersectImpInUnion)). 923.64/240.10 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', inIntersectImpInUnion2)). 923.64/240.10 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', inIntersectImpInIntersectUnions)). 923.64/240.10 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', intersectInPowersetIntersectUnions)). 923.64/240.10 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', inComplementUnionImpNotIn1)). 923.64/240.10 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', inComplementUnionImpInComplement1)). 923.64/240.10 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', binunionTE)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', binunionTEcontra)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', demorgan2a1)). 923.64/240.10 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', complementUnionInPowersetComplement)). 923.64/240.10 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', demorgan2a2)). 923.64/240.10 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', demorgan1a)). 923.64/240.10 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', demorgan1b)). 923.64/240.10 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', demorgan1)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', demorgan2a)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', demorgan2b2)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', demorgan2b)). 923.64/240.10 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', demorgan2)). 923.64/240.10 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', woz13rule0)). 923.64/240.10 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', woz13rule1)). 923.64/240.10 thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', woz13rule2)). 923.64/240.10 thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', woz13rule3)). 923.64/240.10 thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', woz13rule4)). 923.64/240.10 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', woz1_1)). 923.64/240.10 thf(woz1_2, axiom, ((woz1_2)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', woz1_2)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', woz1_3)). 923.64/240.10 thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', woz1_4)). 923.64/240.10 thf(woz1_5, axiom, ((woz1_5)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', woz1_5)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', breln1all2)). 923.64/240.10 thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', breln1SetBreln1)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', breln1all1)). 923.64/240.10 thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', subbreln1)). 923.64/240.10 thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', eqbreln1)). 923.64/240.10 thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', breln1invprop)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', breln1invI)). 923.64/240.10 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.96pdcPKisp/E---3.1_25469.p', breln1invE)). 923.64/240.10 thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', breln1compprop)). 923.64/240.10 thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', breln1compI)). 923.64/240.10 thf(breln1compE, axiom, ((breln1compE)<=>![X4:$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:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', breln1compE)). 923.64/240.10 thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', breln1compEex)). 923.64/240.10 thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', breln1unionprop)). 923.64/240.10 thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', breln1unionIL)). 923.64/240.10 thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', breln1unionIR)). 923.64/240.10 thf(breln1unionI, axiom, ((breln1unionI)<=>![X4:$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.96pdcPKisp/E---3.1_25469.p', breln1unionI)). 923.64/240.10 thf(breln1unionE, axiom, ((breln1unionE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35)))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', breln1unionE)). 923.64/240.10 thf(breln1unionEcases, axiom, ((breln1unionEcases)<=>![X4:$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:$o]:((((in @ (kpair @ X2 @ X3) @ X33)=>(X55))=>(((in @ (kpair @ X2 @ X3) @ X35)=>(X55))=>(X55)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.96pdcPKisp/E---3.1_25469.p', breln1unionEcases)). 923.64/240.10 thf(c_0_307, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 923.64/240.10 thf(c_0_308, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 923.64/240.10 thf(c_0_309, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 923.64/240.10 thf(c_0_310, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 923.64/240.10 thf(c_0_311, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 923.64/240.10 thf(c_0_312, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 923.64/240.10 thf(c_0_313, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 923.64/240.10 thf(c_0_314, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 923.64/240.10 thf(c_0_315, 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])). 923.64/240.10 thf(c_0_316, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 923.64/240.10 thf(c_0_317, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 923.64/240.10 thf(c_0_318, 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])). 923.64/240.10 thf(c_0_319, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 923.64/240.10 thf(c_0_320, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 923.64/240.10 thf(c_0_321, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 923.64/240.10 thf(c_0_322, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X1062:$i]:((((X6 @ X2 @ X1062))&![X1063:$i]:((((X6 @ X2 @ X1063))=>((X1062)=(X1063)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_307, c_0_308])). 923.64/240.10 thf(c_0_323, plain, ((descrp)=(![X1:$i > $o]:(((?[X1064:$i]:((((X1 @ X1064))&![X1065:$i]:((((X1 @ X1065))=>((X1064)=(X1065)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_309, c_0_308])). 923.64/240.10 thf(c_0_324, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 923.64/240.10 thf(c_0_325, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 923.64/240.10 thf(c_0_326, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 923.64/240.10 thf(c_0_327, plain, ((exuE1)=(![X1:$i > $o]:(((?[X1066:$i]:((((X1 @ X1066))&![X1067:$i]:((((X1 @ X1067))=>((X1066)=(X1067)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_310, c_0_308])). 923.64/240.10 thf(c_0_328, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X1068:$i]:((((X1 @ X1068))&![X1069:$i]:((((X1 @ X1069))=>((X1068)=(X1069)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_311, c_0_308])). 923.64/240.10 thf(c_0_329, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 923.64/240.10 thf(c_0_330, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_312])). 923.64/240.10 thf(c_0_331, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_313, c_0_312])). 923.64/240.10 thf(c_0_332, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_312])). 923.64/240.10 thf(c_0_333, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 923.64/240.10 thf(c_0_334, plain, ((exuE2)=(![X1:$i > $o]:(((?[X1070:$i]:((((X1 @ X1070))&![X1071:$i]:((((X1 @ X1071))=>((X1070)=(X1071)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_314, c_0_308])). 923.64/240.10 thf(c_0_335, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_312])). 923.64/240.10 thf(c_0_336, 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])). 923.64/240.10 thf(c_0_337, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X1072:$i]:((((X1 @ X1072))&![X1073:$i]:((((X1 @ X1073))=>((X1072)=(X1073))))))))))), inference(apply_def,[status(thm)],[c_0_315, c_0_308])). 923.64/240.10 thf(c_0_338, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X1074:$i]:((((X1 @ X1074))&![X1075:$i]:((((X1 @ X1075))=>((X1074)=(X1075)))))))))))), inference(apply_def,[status(thm)],[c_0_316, c_0_308])). 923.64/240.10 thf(c_0_339, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X1076:$i]:((((X1 @ X1076))&![X1077:$i]:((((X1 @ X1077))=>((X1076)=(X1077))))))))))), inference(apply_def,[status(thm)],[c_0_317, c_0_308])). 923.64/240.10 thf(c_0_340, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X1078:$i]:((((X1 @ X1078))&![X1079:$i]:((((X1 @ X1079))=>((X1078)=(X1079)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_318, c_0_308])). 923.64/240.10 thf(c_0_341, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1080:$i]:((((X1 @ X1080))&![X1081:$i]:((((X1 @ X1081))=>((X1080)=(X1081)))))))<=>(?[X1082:$i]:((((X17 @ X1082))&![X1083:$i]:((((X17 @ X1083))=>((X1082)=(X1083)))))))))))), inference(apply_def,[status(thm)],[c_0_319, c_0_308])). 923.64/240.10 thf(c_0_342, plain, ((exuEu)=(![X1:$i > $o]:(((?[X1084:$i]:((((X1 @ X1084))&![X1085:$i]:((((X1 @ X1085))=>((X1084)=(X1085)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_320, c_0_308])). 923.64/240.10 thf(c_0_343, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1086:$i]:((((X1 @ X1086))&![X1087:$i]:((((X1 @ X1087))=>((X1086)=(X1087)))))))=>((?[X1088:$i]:((((X17 @ X1088))&![X1089:$i]:((((X17 @ X1089))=>((X1088)=(X1089)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_321, c_0_308])). 923.64/240.10 thf(c_0_344, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 923.64/240.10 thf(c_0_345, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 923.64/240.10 thf(c_0_346, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 923.64/240.10 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 923.64/240.10 thf(c_0_348, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 923.64/240.10 thf(c_0_349, plain, ((ex1I)<=>![X4:$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])). 923.64/240.10 thf(c_0_350, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 923.64/240.10 thf(c_0_351, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 923.64/240.10 thf(c_0_352, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 923.64/240.10 thf(c_0_353, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 923.64/240.10 thf(c_0_354, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 923.64/240.10 thf(c_0_355, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 923.64/240.10 thf(c_0_356, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 923.64/240.10 thf(c_0_357, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 923.64/240.10 thf(c_0_358, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 923.64/240.10 thf(c_0_359, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 923.64/240.10 thf(c_0_360, plain, ((funcImageSingleton)<=>![X4:$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])). 923.64/240.10 thf(c_0_361, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 923.64/240.10 thf(c_0_362, plain, ((lamProp)<=>![X4:$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])). 923.64/240.10 thf(c_0_363, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 923.64/240.10 thf(c_0_364, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 923.64/240.10 thf(c_0_365, plain, ((ex1E2)<=>![X4:$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])). 923.64/240.10 thf(c_0_366, 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])). 923.64/240.10 thf(c_0_367, 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])). 923.64/240.10 thf(c_0_368, 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])). 923.64/240.10 thf(c_0_369, 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])). 923.64/240.10 thf(c_0_370, 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])). 923.64/240.10 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 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 923.64/240.10 thf(c_0_372, plain, ((iffalseProp2)<=>![X4:$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])). 923.64/240.10 thf(c_0_373, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 923.64/240.10 thf(c_0_374, plain, ((iftrueProp2)<=>![X4:$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])). 923.64/240.10 thf(c_0_375, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 923.64/240.10 thf(c_0_376, plain, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 8 */:$i]:(((X52 @ X2 @ Z0)&![X14:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ Z0 @ X14) @ X33))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])). 923.64/240.10 thf(c_0_377, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])). 923.64/240.10 thf(c_0_378, plain, ((epred1_0)<=>![X1108:$i]:(?[X1109:$i]:((((![X1110:$i]:(((in @ X1110 @ X1109)=>![X1111:$i]:(((in @ X1111 @ X1110)=>(in @ X1111 @ X1108)))))&![X1112:$i, X1113:$i]:((((in @ X1112 @ X1108)&(in @ X1113 @ X1108))=>(![X1114:$i]:(((in @ X1114 @ X1109)=>((in @ X1112 @ X1114)<=>(in @ X1113 @ X1114))))=>((X1112)=(X1113))))))&![X1115:$i, X1116:$i]:((((in @ X1115 @ X1109)&(in @ X1116 @ X1109))=>(![X1117:$i]:(((in @ X1117 @ X1115)=>(in @ X1117 @ X1116)))|![X1118:$i]:(((in @ X1118 @ X1116)=>(in @ X1118 @ X1115)))))))&![X1119:$i]:(((![X1120:$i]:(((in @ X1120 @ X1119)=>(in @ X1120 @ X1108)))&?[X1121:$i]:((in @ X1121 @ X1119)))=>?[X1122:$i, X1123:$i]:(((((in @ X1122 @ X1109)&(in @ X1123 @ X1119))&~(?[X1124:$i]:(((in @ X1124 @ X1122)&(in @ X1124 @ X1119)))))&![X1125:$i]:(((in @ X1125 @ X1109)=>(![X1126:$i]:(((in @ X1126 @ X1125)=>(in @ X1126 @ X1122)))|(in @ X1123 @ X1125)))))))))))), introduced(definition)). 923.64/240.10 thf(c_0_379, negated_conjecture, ~((![X1090:$i, X1091:$i]:((![X1092:$i]:(((in @ X1092 @ X1090)<=>(in @ X1092 @ X1091)))=>((X1090)=(X1091))))=>(![X2121:$i]:(~(in @ X2121 @ emptyset))=>(![X1093:$i, X1094:$i, X1095:$i]:(((in @ X1095 @ (setadjoin @ X1093 @ X1094))<=>(((X1095)=(X1093))|(in @ X1095 @ X1094))))=>(![X2118:$i, X2119:$i]:(((in @ X2119 @ (powerset @ X2118))<=>![X2120:$i]:(((in @ X2120 @ X2119)=>(in @ X2120 @ X2118)))))=>(![X2115:$i, X2116:$i]:(((in @ X2116 @ (setunion @ X2115))<=>?[X2117:$i]:(((in @ X2116 @ X2117)&(in @ X2117 @ X2115)))))=>((in @ emptyset @ omega)=>(![X2114:$i]:(((in @ X2114 @ omega)=>(in @ (setadjoin @ X2114 @ X2114) @ omega)))=>(![X2111:$i]:((((in @ emptyset @ X2111)&![X2112:$i]:((((in @ X2112 @ omega)&(in @ X2112 @ X2111))=>(in @ (setadjoin @ X2112 @ X2112) @ X2111))))=>![X2113:$i]:(((in @ X2113 @ omega)=>(in @ X2113 @ X2111)))))=>(![X1096:$i > $i > $o, X1097:$i]:((![X1098:$i]:(((in @ X1098 @ X1097)=>?[X1099:$i]:(((X1096 @ X1098 @ X1099)&![X1100:$i]:(((X1096 @ X1098 @ X1100)=>((X1099)=(X1100))))))))=>?[X1101:$i]:(![X1102:$i]:(((in @ X1102 @ X1101)<=>?[X1103:$i]:(((in @ X1103 @ X1097)&(X1096 @ X1103 @ X1102))))))))=>(![X1104:$i]:((?[X1105:$i]:((in @ X1105 @ X1104))=>?[X1106:$i]:(((in @ X1106 @ X1104)&~(?[X1107:$i]:(((in @ X1107 @ X1106)&(in @ X1107 @ X1104))))))))=>((epred1_0)=>(![X1127:$i > $o]:((?[X1128:$i]:(((X1127 @ X1128)&![X1129:$i]:(((X1127 @ X1129)=>((X1128)=(X1129))))))=>(X1127 @ (descr @ (^[Z0/* 17 */:$i]:(X1127 @ Z0))))))=>(![X1130:$i, X1131:$i > $o, X1132:$i]:(((in @ X1132 @ X1130)=>((X1131 @ X1132)=>(in @ X1132 @ (dsetconstr @ X1130 @ X1131)))))=>(![X2108:$i, X2109:$i > $o, X2110:$i]:(((in @ X2110 @ (dsetconstr @ X2108 @ X2109))=>(in @ X2110 @ X2108)))=>(![X2105:$i, X2106:$i > $o, X2107:$i]:(((in @ X2107 @ (dsetconstr @ X2105 @ X2106))=>(X2106 @ X2107)))=>(![X2100:$i > $o]:((?[X2101:$i]:(((X2100 @ X2101)&![X2102:$i]:(((X2100 @ X2102)=>((X2101)=(X2102))))))=>?[X2103:$i]:(((X2100 @ X2103)&![X2104:$i]:(((X2100 @ X2104)=>((X2103)=(X2104))))))))=>(![X2098:$o, X2099:$i]:(((in @ X2099 @ (prop2set @ ((X2098))))=>(X2098)))=>(![X1133:$i]:(((in @ X1133 @ emptyset)=>![X1134:$o]:((X1134))))=>(![X1135:$i]:(((in @ X1135 @ emptyset)=>~($true)))=>(![X2097:$i]:(~(in @ X2097 @ emptyset))=>(![X2093:$i > $o]:((?[X2094:$i]:(((X2093 @ X2094)&![X2095:$i]:(((X2093 @ X2095)=>((X2094)=(X2095))))))=>?[X2096:$i]:((X2093 @ X2096))))=>(![X1136:$i, X1137:$i]:((![X1138:$i]:(((in @ X1138 @ X1136)=>(in @ X1138 @ X1137)))=>(![X1139:$i]:(((in @ X1139 @ X1137)=>(in @ X1139 @ X1136)))=>((X1136)=(X1137)))))=>(![X2091:$i]:((![X2092:$i]:(~(in @ X2092 @ X2091))=>((X2091)=(emptyset))))=>(![X1140:$i]:((![X1141:$i]:(~(in @ X1141 @ X1140))=>((X1140)=(emptyset))))=>(![X2088:$i, X2089:$i > $o, X2090:$i]:(((in @ X2090 @ X2088)=>((in @ X2090 @ (dsetconstr @ X2088 @ X2089))<=>(X2089 @ X2090))))=>(![X1142:$i]:((((X1142)!=(emptyset))=>?[X1143:$i]:((in @ X1143 @ X1142))))=>(![X2085:$i, X2086:$i > $o, X2087:$i]:(((in @ X2087 @ X2085)=>((X2086 @ X2087)=>((dsetconstr @ X2085 @ X2086)!=(emptyset)))))=>(![X1144:$i]:((?[X1145:$i]:((in @ X1145 @ X1144))=>((X1144)!=(emptyset))))=>(![X2083:$i, X2084:$i]:((in @ X2083 @ (setadjoin @ X2083 @ X2084)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X2080:$i, X2081:$i, X2082:$i]:(((in @ X2082 @ X2081)=>(in @ X2082 @ (setadjoin @ X2080 @ X2081))))=>(![X1146:$i, X1147:$i, X1148:$i]:(((in @ X1148 @ (setadjoin @ X1146 @ X1147))=>![X1149:$o]:(((((X1148)=(X1146))=>(X1149))=>(((in @ X1148 @ X1147)=>(X1149))=>(X1149))))))=>(![X1150:$i, X1151:$i, X1152:$i]:(((in @ X1152 @ (setadjoin @ X1150 @ X1151))=>(((X1152)=(X1150))|(in @ X1152 @ X1151))))=>(![X2079:$i]:(((dsetconstr @ X2079 @ (^[Z0/* 1 */:$i]:($true)))=(X2079)))=>(![X1153:$i, X1154:$i]:((![X1155:$i]:(((in @ X1155 @ X1154)=>(in @ X1155 @ X1153)))=>(in @ X1154 @ (powerset @ X1153))))=>(![X1156:$i]:((in @ emptyset @ (powerset @ X1156)))=>(![X2078:$i]:((in @ emptyset @ (powerset @ X2078)))=>(![X2075:$i, X2076:$i, X2077:$i]:(((in @ X2076 @ (powerset @ X2075))=>((in @ X2077 @ X2076)=>(in @ X2077 @ X2075))))=>(![X1157:$i, X1158:$i, 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kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_347]), c_0_348]), c_0_349]), c_0_350]), singletonsuniq]), setukpairinjL1]), c_0_351]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_352]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_353]), c_0_354]), c_0_355]), c_0_356]), c_0_357]), c_0_358]), c_0_359]), c_0_360]), c_0_361]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_362]), c_0_363]), c_0_364]), brelnall1]), brelnall2]), c_0_365]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), subbreln]), eqbreln]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_366]), c_0_367]), c_0_368]), c_0_369]), c_0_370]), c_0_371]), c_0_372]), c_0_373]), c_0_374]), c_0_375]), ifp]), theeq]), iftrue]), iffalse]), iftrueorfalse]), binintersectT_lem]), binunionT_lem]), powersetT_lem]), setminusT_lem]), complementT_lem]), setextT]), subsetTI]), powersetTI1]), powersetTE1]), complementTI1]), complementTE1]), binintersectTELcontra]), binintersectTERcontra]), contrasubsetT]), contrasubsetT1]), contrasubsetT2]), contrasubsetT3]), doubleComplementI1]), doubleComplementE1]), doubleComplementSub1]), doubleComplementSub2]), doubleComplementEq]), complementTnotintersectT]), complementImpComplementIntersect]), complementSubsetComplementIntersect]), complementInPowersetComplementIntersect]), contraSubsetComplement]), complementTcontraSubset]), binunionTILcontra]), binunionTIRcontra]), inIntersectImpInUnion]), inIntersectImpInUnion2]), inIntersectImpInIntersectUnions]), intersectInPowersetIntersectUnions]), inComplementUnionImpNotIn1]), inComplementUnionImpInComplement1]), binunionTE]), binunionTEcontra]), demorgan2a1]), complementUnionInPowersetComplement]), demorgan2a2]), demorgan1a]), demorgan1b]), demorgan1]), demorgan2a]), demorgan2b2]), demorgan2b]), demorgan2]), woz13rule0]), woz13rule1]), woz13rule2]), woz13rule3]), woz13rule4]), woz1_1]), woz1_2]), woz1_3]), woz1_4]), woz1_5]), breln1all2]), breln1SetBreln1]), c_0_376]), c_0_377]), breln1all1]), subbreln1]), eqbreln1]), breln1invprop]), breln1invI]), breln1invE]), breln1compprop]), breln1compI]), breln1compE]), breln1compEex]), breln1unionprop]), breln1unionIL]), breln1unionIR]), breln1unionI]), breln1unionE]), breln1unionEcases])])]), c_0_378])). 923.64/240.10 thf(c_0_380, negated_conjecture, ![X2122:$i, X2123:$i, X2125:$i, X2126:$i, X2127:$i, X2128:$i, X2129:$i, X2130:$i, X2131:$i, X2132:$i, X2133:$i, X2135:$i, X2136:$i, X2138:$i, X2139:$i, X2140:$i, X2141:$i, X2142:$i, X2144:$i, X2145:$i > $i > $o, X2146:$i, X2148:$i, X2151:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2158:$i, X2159:$i > $o, X2160:$i, X2162:$i, X2163:$i > $o, X2164:$i, X2165:$i, X2166:$i > $o, X2167:$i, X2168:$i, X2169:$i > $o, X2170:$i, X2171:$i > $o, X2172:$i, X2175:$i, X2176:$o, X2177:$i, X2178:$i, X2179:$o, X2180:$i, X2181:$i, X2182:$i > $o, X2183:$i, X2186:$i, X2187:$i, X2190:$i, X2192:$i, X2194:$i, X2195:$i > $o, X2196:$i, X2197:$i, X2199:$i, X2200:$i > $o, X2201:$i, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$o, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2229:$i, X2230:$o, X2232:$i, X2233:$i, X2234:$i > $o, X2235:$i, X2238:$i, X2239:$i, X2240:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i > $o, X2259:$i, X2260:$i > $o, X2261:$i, X2262:$i, X2263:$i > $o, X2264:$i, X2266:$i, X2267:$i > $o, X2269:$i, X2270:$i, X2271:$i > $o, X2273:$i, X2274:$i, X2275:$i > $o, X2276:$i, X2278:$o, X2279:$o, X2280:$i, X2281:$i > $o, X2283:$i, X2284:$i, X2285:$i > $o, X2286:$i, X2288:$i > $o, X2289:$i, X2292:$i, X2293:$i > $o, X2294:$i, X2298:$i, X2299:$i > $o, X2300:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i > $o, X2313:$i, X2315:$i, X2316:$i, X2317:$i > $o, X2318:$i > $o, X2321:$i, X2324:$i, X2325:$i, X2328:$i, X2329:$i, X2330:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2336:$i, X2337:$i > $o, X2338:$i, X2340:$i, X2341:$i, X2342:$i > $o, X2343:$i > $o, X2346:$i, X2348:$i, X2350:$i, X2351:$i, X2352:$i > $o, X2353:$i > $o, X2356:$i, X2357:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i, X2364:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$i, X2384:$i, X2385:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i > $o, X2404:$i, X2405:$i > $o, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$i, X2412:$i, X2413:$i, X2414:$i, X2415:$i, X2416:$i, X2417:$o, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2425:$i, X2426:$i, X2427:$i, X2428:$i, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i, X2434:$i, X2435:$i, X2436:$i, X2437:$i, X2438:$i, X2439:$i, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i, X2458:$i, X2459:$i, X2460:$i, X2461:$i, X2462:$i, X2463:$i, X2464:$i, X2465:$i, X2466:$i, X2467:$i, X2468:$i, X2469:$i, X2470:$i, X2471:$i, X2472:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i, X2483:$i, X2484:$i, X2485:$o, X2486:$i, X2487:$i, X2488:$i, X2489:$i, X2490:$i, X2491:$i, X2492:$i, X2493:$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, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2547:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2557:$i > $o, X2560:$i, X2561:$i, X2562:$i > $o, X2564:$i, X2565:$i > $o, X2566:$i, X2568:$i, X2569:$i > $o, X2572:$i, X2573:$i, X2574:$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:$i, X2614:$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 > $i > $o, X2645:$i, X2646:$i, X2647:$i, X2648:$i, X2649:$i > $i > $o, X2650:$i, X2651:$i, X2652:$i > $i > $o, X2653:$i, X2654:$i, X2655:$i > $i > $o, X2656:$i, X2657:$i, X2658:$i, X2659:$i, X2660:$i > $i > $o, X2661:$i, X2662:$i, X2663:$i, X2664:$i, X2665:$i > $i > $o, X2666:$i, X2667:$i, X2668:$i, X2669:$i, X2670:$i > $i > $o, X2671:$i, X2672:$i, X2673:$i, X2674:$i, X2675:$i, X2676:$i, X2677:$i, X2678:$i, X2679:$i, X2680:$i, X2681:$i, X2682:$i, X2683:$i, X2684:$i, X2685:$i, X2686:$i, X2687:$i, X2688:$i, X2689:$i, X2690:$i, X2691:$i, X2692:$i, X2693:$i, X2694:$i, X2695:$i, X2696:$i, X2697:$i > $i, X2699:$i, X2700:$i, X2701:$i > $i, X2703:$i, X2704:$i, X2705:$i > $i, X2707:$i, X2708:$i, X2709:$i, X2710:$i > $o, X2713:$i, X2714:$i, X2715:$i, X2716:$i, X2717:$i > $o, X2720:$i, X2721:$i, X2722:$i > $o, X2723:$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, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2764:$i, X2765:$i, X2766:$i, X2767:$i, X2769:$i, X2770:$i, X2771:$i, X2772:$i, X2774:$i, X2775:$i, X2776:$i, X2777:$i, X2778:$i, X2779:$i, X2780:$i, X2781:$i, X2782:$i, X2783:$i, X2784:$i > $i, X2786:$i, X2787:$i, X2788:$i, X2789:$i, X2790:$i, X2791:$i, X2792:$i > $i, X2794:$i, X2795:$i, X2796:$i > $i, X2798:$i, X2799:$i, X2800:$i, X2801:$i, X2802:$i, X2803:$o, X2804:$i, X2805:$i, X2806:$i, X2807:$o, X2808:$i, X2809:$i, X2810:$i, X2811:$o, X2812:$i, X2813:$i, X2814:$i, X2815:$o, X2816:$i, X2817:$i, X2818:$i, X2819:$o, X2820:$i, X2821:$i, X2822:$i, X2823:$o, X2824:$i, X2825:$i, X2826:$i, X2827:$i, X2828:$i, X2829:$o, X2830:$i, X2831:$i, X2832:$i, X2833:$o, X2834:$i, X2835:$i, X2836:$i, X2837:$o, X2838:$i, X2839:$i, X2840:$i, X2841:$i, X2842:$i, X2843:$i, X2844:$i, X2845:$i, X2846:$i, X2847:$i, X2848:$i, X2849:$i, X2850:$i, X2851:$i, X2852:$i, X2853:$i, X2854:$i, X2855:$i, X2858:$i, X2859:$i, X2860:$i, X2862:$i, X2863:$i, X2864:$i, X2866:$i, X2867:$i, X2868:$i, X2869:$i, X2870:$i, X2871:$i, X2872:$i, X2873:$i, X2874:$i, X2875:$i, X2876:$i, X2877:$i, X2878:$i, X2879:$i, X2880:$i, X2881:$i, X2882:$i, X2883:$i, X2884:$i, X2885:$i, X2886:$i, X2887:$i, X2888:$i, X2889:$i, X2890:$i, X2891:$i, X2892:$i, X2893:$i, X2894:$i, X2895:$i, X2896:$i, X2897:$i, X2898:$i, X2899:$i, X2900:$i, X2901:$i, X2902:$i, X2903:$i, X2904:$i, X2905:$i, X2906:$i, X2907:$i, X2908:$i, X2909:$i, X2910:$i, X2911:$i, X2912:$i, X2913:$i, X2914:$i, X2915:$i, X2916:$i, X2917:$i, X2918:$i, X2919:$i, X2920:$i, X2921:$i, X2922:$i, X2923:$i, X2924:$i, X2925:$i, X2926:$i, X2927:$i, X2928:$i, X2929:$i, X2930:$i, X2931:$i, X2932:$i, X2933:$i, X2934:$i, X2935:$i, X2936:$i, X2937:$i, X2938:$i, X2939:$i, X2940:$i, X2941:$i, X2942:$i, X2943:$i, X2944:$i, X2945:$i, X2946:$i, X2947:$i, X2948:$i, X2949:$i, X2950:$i, X2951:$i, X2952:$i, X2953:$i, X2954:$i, X2955:$i, X2956:$i, X2957:$i, X2958:$i, X2959:$i, X2960:$i, X2961:$i, X2962:$i, X2963:$i, X2964:$i, X2965:$i, X2966:$i, X2967:$i, X2968:$i, X2969:$o, X2970:$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:$i, X2984:$i, X2985:$i, X2986:$i, X2987:$i, X2988:$i, X2989:$i, X2990:$i, X2991:$i, X2992:$i, X2993:$i, X2994:$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 > $o, X3056:$i, X3057:$i, X3058:$i, X3059:$i, X3060:$i, X3061:$i > $i > $o, X3063:$i, X3064:$i, X3065:$i, X3066:$i, X3067:$i > $i > $o, X3068:$i, X3069:$i, X3070:$i > $o, X3073:$i, X3074:$i, X3075:$i, X3076:$i, X3079:$i, X3080:$i, X3081:$i, X3086:$i, X3087:$i, X3088:$i, X3089:$i, X3090:$i, X3091:$i, X3092:$i, X3093:$i, X3094:$i, X3095:$i, X3096:$i, X3097:$i, X3098:$i, X3099:$i, X3100:$i, X3101:$i, X3102:$i, X3103:$i, X3104:$i, X3105:$i, X3106:$i, X3107:$i, X3108:$i, X3109:$i, X3111:$i, X3112:$i, X3113:$i, X3114:$i, X3115:$i, X3116:$o, 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:$o]:((((~(in @ (esk1_2 @ X2122 @ X2123) @ X2122)|~(in @ (esk1_2 @ X2122 @ X2123) @ X2123)|((X2122)=(X2123)))&((in @ (esk1_2 @ X2122 @ X2123) @ X2122)|(in @ (esk1_2 @ X2122 @ X2123) @ X2123)|((X2122)=(X2123))))&(~(in @ X2125 @ emptyset)&(((~(in @ X2128 @ (setadjoin @ X2126 @ X2127))|(((X2128)=(X2126))|(in @ X2128 @ X2127)))&((((X2128)!=(X2126))|(in @ X2128 @ (setadjoin @ X2126 @ X2127)))&(~(in @ X2128 @ X2127)|(in @ X2128 @ (setadjoin @ X2126 @ X2127)))))&(((~(in @ X2130 @ (powerset @ X2129))|(~(in @ X2131 @ 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(dsetconstr @ X3060 @ (^[Z0/* 8 */:$i]:((X3061 @ X3065 @ Z0&![X1588:$i]:(((in @ X1588 @ X3060)=>(X3061 @ X3065 @ X1588=>(in @ (kpair @ Z0 @ X1588) @ X3064))))))))))))))&((breln1 @ X3066 @ (dpsetconstr @ X3066 @ X3066 @ X3067))&((((in @ (esk90_3 @ X3068 @ X3069 @ X3070) @ X3068)|(~(in @ X3073 @ X3069)|(X3070 @ X3073))|~(breln1 @ X3068 @ X3069))&(((in @ (esk91_3 @ X3068 @ X3069 @ X3070) @ X3068)|(~(in @ X3073 @ X3069)|(X3070 @ X3073))|~(breln1 @ X3068 @ X3069))&(((in @ (kpair @ (esk90_3 @ X3068 @ X3069 @ X3070) @ (esk91_3 @ X3068 @ X3069 @ X3070)) @ X3069)|(~(in @ X3073 @ X3069)|(X3070 @ X3073))|~(breln1 @ X3068 @ X3069))&(~(X3070 @ (kpair @ (esk90_3 @ X3068 @ X3069 @ X3070) @ (esk91_3 @ X3068 @ X3069 @ X3070)))|(~(in @ X3073 @ X3069)|(X3070 @ X3073))|~(breln1 @ X3068 @ X3069)))))&((((in @ (esk92_3 @ X3074 @ X3075 @ X3076) @ X3074)|(subset @ X3075 @ X3076)|~(breln1 @ X3074 @ X3076)|~(breln1 @ X3074 @ X3075))&(((in @ (esk93_3 @ X3074 @ X3075 @ X3076) @ X3074)|(subset @ X3075 @ X3076)|~(breln1 @ X3074 @ X3076)|~(breln1 @ X3074 @ X3075))&(((in @ (kpair @ (esk92_3 @ X3074 @ X3075 @ X3076) @ (esk93_3 @ X3074 @ X3075 @ X3076)) @ X3075)|(subset @ X3075 @ X3076)|~(breln1 @ X3074 @ X3076)|~(breln1 @ X3074 @ X3075))&(~(in @ (kpair @ (esk92_3 @ X3074 @ X3075 @ X3076) @ (esk93_3 @ X3074 @ X3075 @ X3076)) @ X3076)|(subset @ X3075 @ X3076)|~(breln1 @ X3074 @ X3076)|~(breln1 @ X3074 @ X3075)))))&(((((in @ (esk96_3 @ X3079 @ X3080 @ X3081) @ X3079)|((X3080)=(X3081))|(in @ (esk94_3 @ X3079 @ X3080 @ X3081) @ X3079)|~(breln1 @ X3079 @ X3081)|~(breln1 @ X3079 @ X3080))&(((in @ (esk97_3 @ X3079 @ X3080 @ X3081) @ X3079)|((X3080)=(X3081))|(in @ (esk94_3 @ X3079 @ X3080 @ X3081) @ X3079)|~(breln1 @ X3079 @ X3081)|~(breln1 @ X3079 @ X3080))&(((in @ (kpair @ (esk96_3 @ X3079 @ X3080 @ X3081) @ (esk97_3 @ X3079 @ X3080 @ X3081)) @ X3081)|((X3080)=(X3081))|(in @ (esk94_3 @ X3079 @ X3080 @ X3081) @ X3079)|~(breln1 @ X3079 @ X3081)|~(breln1 @ X3079 @ X3080))&(~(in @ (kpair @ (esk96_3 @ X3079 @ X3080 @ X3081) @ (esk97_3 @ X3079 @ X3080 @ X3081)) @ X3080)|((X3080)=(X3081))|(in @ (esk94_3 @ X3079 @ X3080 @ X3081) @ X3079)|~(breln1 @ X3079 @ X3081)|~(breln1 @ X3079 @ X3080)))))&((((in @ (esk96_3 @ X3079 @ X3080 @ X3081) @ X3079)|((X3080)=(X3081))|(in @ (esk95_3 @ X3079 @ X3080 @ X3081) @ X3079)|~(breln1 @ X3079 @ X3081)|~(breln1 @ X3079 @ X3080))&(((in @ (esk97_3 @ X3079 @ X3080 @ X3081) @ X3079)|((X3080)=(X3081))|(in @ (esk95_3 @ X3079 @ X3080 @ X3081) @ X3079)|~(breln1 @ X3079 @ X3081)|~(breln1 @ X3079 @ X3080))&(((in @ (kpair @ (esk96_3 @ X3079 @ X3080 @ X3081) @ (esk97_3 @ X3079 @ X3080 @ X3081)) @ X3081)|((X3080)=(X3081))|(in @ (esk95_3 @ X3079 @ X3080 @ X3081) @ X3079)|~(breln1 @ X3079 @ X3081)|~(breln1 @ X3079 @ X3080))&(~(in @ (kpair @ (esk96_3 @ X3079 @ X3080 @ X3081) @ (esk97_3 @ X3079 @ X3080 @ X3081)) @ X3080)|((X3080)=(X3081))|(in @ (esk95_3 @ X3079 @ X3080 @ X3081) @ X3079)|~(breln1 @ X3079 @ X3081)|~(breln1 @ X3079 @ X3080)))))&((((in @ (esk96_3 @ X3079 @ X3080 @ X3081) @ X3079)|((X3080)=(X3081))|(in @ (kpair @ (esk94_3 @ X3079 @ X3080 @ X3081) @ (esk95_3 @ X3079 @ X3080 @ X3081)) @ X3080)|~(breln1 @ X3079 @ X3081)|~(breln1 @ X3079 @ X3080))&(((in @ (esk97_3 @ X3079 @ X3080 @ X3081) @ X3079)|((X3080)=(X3081))|(in @ (kpair @ (esk94_3 @ X3079 @ X3080 @ X3081) @ (esk95_3 @ X3079 @ X3080 @ X3081)) @ X3080)|~(breln1 @ X3079 @ X3081)|~(breln1 @ X3079 @ X3080))&(((in @ (kpair @ (esk96_3 @ X3079 @ X3080 @ X3081) @ (esk97_3 @ X3079 @ X3080 @ X3081)) @ X3081)|((X3080)=(X3081))|(in @ (kpair @ (esk94_3 @ X3079 @ X3080 @ X3081) @ (esk95_3 @ X3079 @ X3080 @ X3081)) @ X3080)|~(breln1 @ X3079 @ X3081)|~(breln1 @ X3079 @ X3080))&(~(in @ (kpair @ (esk96_3 @ X3079 @ X3080 @ X3081) @ (esk97_3 @ X3079 @ X3080 @ X3081)) @ X3080)|((X3080)=(X3081))|(in @ (kpair @ (esk94_3 @ X3079 @ X3080 @ X3081) @ (esk95_3 @ X3079 @ X3080 @ X3081)) @ X3080)|~(breln1 @ X3079 @ X3081)|~(breln1 @ X3079 @ X3080)))))&(((in @ (esk96_3 @ X3079 @ X3080 @ X3081) @ X3079)|((X3080)=(X3081))|~(in @ (kpair @ (esk94_3 @ X3079 @ X3080 @ X3081) @ (esk95_3 @ X3079 @ X3080 @ X3081)) @ X3081)|~(breln1 @ X3079 @ X3081)|~(breln1 @ X3079 @ X3080))&(((in @ (esk97_3 @ X3079 @ X3080 @ X3081) @ X3079)|((X3080)=(X3081))|~(in @ (kpair @ (esk94_3 @ X3079 @ X3080 @ X3081) @ (esk95_3 @ X3079 @ X3080 @ X3081)) @ X3081)|~(breln1 @ X3079 @ X3081)|~(breln1 @ X3079 @ X3080))&(((in @ (kpair @ (esk96_3 @ X3079 @ X3080 @ X3081) @ (esk97_3 @ X3079 @ X3080 @ X3081)) @ X3081)|((X3080)=(X3081))|~(in @ (kpair @ (esk94_3 @ X3079 @ X3080 @ X3081) @ (esk95_3 @ X3079 @ X3080 @ X3081)) @ X3081)|~(breln1 @ X3079 @ X3081)|~(breln1 @ X3079 @ X3080))&(~(in @ (kpair @ (esk96_3 @ X3079 @ X3080 @ X3081) @ (esk97_3 @ X3079 @ X3080 @ X3081)) @ X3080)|((X3080)=(X3081))|~(in @ (kpair @ (esk94_3 @ X3079 @ X3080 @ X3081) @ (esk95_3 @ X3079 @ X3080 @ X3081)) @ X3081)|~(breln1 @ X3079 @ X3081)|~(breln1 @ X3079 @ X3080))))))))&((~(breln1 @ X3086 @ X3087)|(breln1 @ X3086 @ (breln1invset @ X3086 @ X3087)))&((~(breln1 @ X3088 @ X3089)|(~(in @ X3090 @ X3088)|(~(in @ X3091 @ X3088)|(~(in @ (kpair @ X3090 @ X3091) @ X3089)|(in @ (kpair @ X3091 @ X3090) @ (breln1invset @ X3088 @ X3089))))))&((~(breln1 @ X3092 @ X3093)|(~(in @ X3094 @ X3092)|(~(in @ X3095 @ X3092)|(~(in @ (kpair @ X3095 @ X3094) @ (breln1invset @ X3092 @ X3093))|(in @ (kpair @ X3094 @ X3095) @ X3093)))))&((~(breln1 @ X3096 @ X3097)|(~(breln1 @ X3096 @ X3098)|(breln1 @ X3096 @ (breln1compset @ X3096 @ X3097 @ X3098))))&((~(breln1 @ X3099 @ X3100)|(~(breln1 @ X3099 @ X3101)|(~(in @ X3102 @ X3099)|(~(in @ X3103 @ X3099)|(~(in @ X3104 @ X3099)|(~(in @ (kpair @ X3102 @ X3104) @ X3100)|(~(in @ (kpair @ X3104 @ X3103) @ X3101)|(in @ (kpair @ X3102 @ X3103) @ (breln1compset @ X3099 @ X3100 @ X3101)))))))))&(((((in @ (esk98_5 @ X3105 @ X3106 @ X3107 @ X3108 @ X3109) @ X3105)|~(in @ (kpair @ X3108 @ X3109) @ (breln1compset @ X3105 @ X3106 @ X3107))|~(in @ X3109 @ X3105)|~(in @ X3108 @ X3105)|~(breln1 @ X3105 @ X3107)|~(breln1 @ X3105 @ X3106))&((in @ (kpair @ X3108 @ (esk98_5 @ X3105 @ X3106 @ X3107 @ X3108 @ X3109)) @ X3106)|~(in @ (kpair @ X3108 @ X3109) @ (breln1compset @ X3105 @ X3106 @ X3107))|~(in @ X3109 @ X3105)|~(in @ X3108 @ X3105)|~(breln1 @ X3105 @ X3107)|~(breln1 @ X3105 @ X3106)))&((in @ (kpair @ (esk98_5 @ X3105 @ X3106 @ X3107 @ X3108 @ X3109) @ X3109) @ X3107)|~(in @ (kpair @ X3108 @ X3109) @ (breln1compset @ X3105 @ X3106 @ X3107))|~(in @ X3109 @ X3105)|~(in @ X3108 @ X3105)|~(breln1 @ X3105 @ X3107)|~(breln1 @ X3105 @ X3106)))&((((in @ (esk99_6 @ X3111 @ X3112 @ X3113 @ X3114 @ X3115 @ X3116) @ X3111)|(X3116)|~(in @ (kpair @ X3114 @ X3115) @ (breln1compset @ X3111 @ X3112 @ X3113))|~(in @ X3115 @ X3111)|~(in @ X3114 @ X3111)|~(breln1 @ X3111 @ X3113)|~(breln1 @ X3111 @ X3112))&(((in @ (kpair @ X3114 @ (esk99_6 @ X3111 @ X3112 @ X3113 @ X3114 @ X3115 @ X3116)) @ X3112)|(X3116)|~(in @ (kpair @ X3114 @ X3115) @ (breln1compset @ X3111 @ X3112 @ X3113))|~(in @ X3115 @ X3111)|~(in @ X3114 @ X3111)|~(breln1 @ X3111 @ X3113)|~(breln1 @ X3111 @ X3112))&(((in @ (kpair @ (esk99_6 @ X3111 @ X3112 @ X3113 @ X3114 @ X3115 @ X3116) @ X3115) @ X3113)|(X3116)|~(in @ (kpair @ X3114 @ X3115) @ (breln1compset @ X3111 @ X3112 @ X3113))|~(in @ X3115 @ X3111)|~(in @ X3114 @ X3111)|~(breln1 @ X3111 @ X3113)|~(breln1 @ X3111 @ X3112))&(~(X3116)|(X3116)|~(in @ (kpair @ X3114 @ X3115) @ (breln1compset @ X3111 @ X3112 @ X3113))|~(in @ X3115 @ X3111)|~(in @ X3114 @ X3111)|~(breln1 @ X3111 @ X3113)|~(breln1 @ X3111 @ X3112)))))&((~(breln1 @ X3118 @ X3119)|(~(breln1 @ X3118 @ X3120)|(breln1 @ X3118 @ (binunion @ X3119 @ X3120))))&((~(breln1 @ X3121 @ X3122)|(~(breln1 @ X3121 @ X3123)|(~(in @ X3124 @ X3121)|(~(in @ X3125 @ X3121)|(~(in @ (kpair @ X3124 @ X3125) @ X3122)|(in @ (kpair @ X3124 @ X3125) @ (binunion @ X3122 @ X3123)))))))&((~(breln1 @ X3126 @ X3127)|(~(breln1 @ X3126 @ X3128)|(~(in @ X3129 @ X3126)|(~(in @ X3130 @ X3126)|(~(in @ (kpair @ X3129 @ X3130) @ X3128)|(in @ (kpair @ X3129 @ X3130) @ (binunion @ X3127 @ X3128)))))))&(((~(in @ (kpair @ X3134 @ X3135) @ X3132)|(in @ (kpair @ X3134 @ X3135) @ (binunion @ X3132 @ X3133))|~(in @ X3135 @ X3131)|~(in @ X3134 @ X3131)|~(breln1 @ X3131 @ X3133)|~(breln1 @ X3131 @ X3132))&(~(in @ (kpair @ X3134 @ X3135) @ X3133)|(in @ (kpair @ X3134 @ X3135) @ (binunion @ X3132 @ X3133))|~(in @ X3135 @ X3131)|~(in @ X3134 @ X3131)|~(breln1 @ X3131 @ X3133)|~(breln1 @ X3131 @ X3132)))&((~(breln1 @ X3136 @ X3137)|(~(breln1 @ X3136 @ X3138)|(~(in @ X3139 @ X3136)|(~(in @ X3140 @ X3136)|(~(in @ (kpair @ X3139 @ X3140) @ (binunion @ X3137 @ X3138))|((in @ (kpair @ X3139 @ X3140) @ X3137)|(in @ (kpair @ X3139 @ X3140) @ X3138)))))))&(((((in @ (kpair @ X3144 @ X3145) @ X3143)|(X3146)|(in @ (kpair @ X3144 @ X3145) @ X3142)|~(in @ (kpair @ X3144 @ X3145) @ (binunion @ X3142 @ X3143))|~(in @ X3145 @ X3141)|~(in @ X3144 @ X3141)|~(breln1 @ X3141 @ X3143)|~(breln1 @ X3141 @ X3142))&(~(X3146)|(X3146)|(in @ (kpair @ X3144 @ X3145) @ X3142)|~(in @ (kpair @ X3144 @ X3145) @ (binunion @ X3142 @ X3143))|~(in @ X3145 @ X3141)|~(in @ X3144 @ X3141)|~(breln1 @ X3141 @ X3143)|~(breln1 @ X3141 @ X3142)))&(((in @ (kpair @ X3144 @ X3145) @ X3143)|(X3146)|~(X3146)|~(in @ (kpair @ X3144 @ X3145) @ (binunion @ X3142 @ X3143))|~(in @ X3145 @ X3141)|~(in @ X3144 @ X3141)|~(breln1 @ X3141 @ X3143)|~(breln1 @ X3141 @ X3142))&(~(X3146)|(X3146)|~(X3146)|~(in @ (kpair @ X3144 @ X3145) @ (binunion @ X3142 @ X3143))|~(in @ X3145 @ X3141)|~(in @ X3144 @ X3141)|~(breln1 @ X3141 @ X3143)|~(breln1 @ X3141 @ X3142))))&((breln1 @ esk100_0 @ esk101_0)&((breln1 @ esk100_0 @ esk102_0)&((binunion @ esk101_0 @ esk102_0)!=(binunion @ esk102_0 @ esk101_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_379])])])])])])])). 923.64/240.10 thf(c_0_381, negated_conjecture, ![X2:$i, X3:$i]:((((binintersect @ X3 @ X2)=(X2))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_380])). 923.64/240.10 thf(c_0_382, negated_conjecture, ![X2:$i]:((subset @ X2 @ X2)), inference(split_conjunct,[status(thm)],[c_0_380])). 923.64/240.10 thf(c_0_383, negated_conjecture, ![X2:$i, X3:$i]:((((binintersect @ X2 @ X3)=(X2))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_380])). 923.64/240.10 thf(c_0_384, negated_conjecture, ![X3:$i, X2:$i]:((subset @ X2 @ (binunion @ X3 @ X2))), inference(split_conjunct,[status(thm)],[c_0_380])). 923.64/240.10 thf(c_0_385, negated_conjecture, ![X2:$i, X3:$i]:((subset @ (binintersect @ X2 @ X3) @ X3)), inference(split_conjunct,[status(thm)],[c_0_380])). 923.64/240.10 thf(c_0_386, negated_conjecture, ![X2:$i, X3:$i]:((subset @ X2 @ (binunion @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_380])). 923.64/240.10 thf(c_0_387, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((binintersect @ X2 @ (binunion @ X3 @ X4))=(binunion @ (binintersect @ X2 @ X3) @ (binintersect @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_380])). 923.64/240.10 thf(c_0_388, negated_conjecture, ![X2:$i]:(((binintersect @ X2 @ X2)=(X2))), inference(spm,[status(thm)],[c_0_381, c_0_382])). 923.64/240.10 thf(c_0_389, negated_conjecture, ![X3:$i, X2:$i]:(((binintersect @ X2 @ (binunion @ X3 @ X2))=(X2))), inference(spm,[status(thm)],[c_0_383, c_0_384])). 923.64/240.10 thf(c_0_390, negated_conjecture, ![X3:$i, X2:$i]:(((binintersect @ X2 @ (binintersect @ X3 @ X2))=(binintersect @ X3 @ X2))), inference(spm,[status(thm)],[c_0_381, c_0_385])). 923.64/240.10 thf(c_0_391, negated_conjecture, ![X3:$i, X2:$i]:(((binintersect @ X2 @ (binunion @ X2 @ X3))=(X2))), inference(spm,[status(thm)],[c_0_383, c_0_386])). 923.64/240.10 thf(c_0_392, negated_conjecture, ![X3:$i, X2:$i]:(((binunion @ (binintersect @ X2 @ X3) @ X2)=(X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_387, c_0_388]), c_0_389])). 923.64/240.10 thf(c_0_393, negated_conjecture, ![X2:$i, X3:$i]:(((binintersect @ (binunion @ X2 @ X3) @ X3)=(X3))), inference(spm,[status(thm)],[c_0_381, c_0_384])). 923.64/240.10 thf(c_0_394, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((binintersect @ X2 @ (binunion @ X3 @ (binintersect @ X4 @ X2)))=(binunion @ (binintersect @ X2 @ X3) @ (binintersect @ X4 @ X2)))), inference(spm,[status(thm)],[c_0_387, c_0_390])). 923.64/240.10 thf(c_0_395, negated_conjecture, ![X3:$i, X2:$i]:(((binunion @ X2 @ (binintersect @ X2 @ X3))=(X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_387, c_0_388]), c_0_391])). 923.64/240.10 thf(c_0_396, negated_conjecture, ![X3:$i, X2:$i]:(((binintersect @ (binunion @ X2 @ X3) @ X2)=(X2))), inference(spm,[status(thm)],[c_0_381, c_0_386])). 923.64/240.10 thf(c_0_397, negated_conjecture, ![X3:$i, X2:$i]:(((binunion @ X2 @ (binunion @ X3 @ X2))=(binunion @ X3 @ X2))), inference(spm,[status(thm)],[c_0_392, c_0_393])). 923.64/240.10 thf(c_0_398, negated_conjecture, ![X2:$i, X3:$i]:(((binunion @ (binintersect @ X2 @ X3) @ (binintersect @ X3 @ X2))=(binintersect @ X2 @ X3))), inference(spm,[status(thm)],[c_0_394, c_0_395])). 923.64/240.10 thf(c_0_399, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((binintersect @ (binunion @ X2 @ X3) @ (binunion @ X4 @ X2))=(binunion @ (binintersect @ (binunion @ X2 @ X3) @ X4) @ X2))), inference(spm,[status(thm)],[c_0_387, c_0_396])). 923.64/240.10 thf(c_0_400, negated_conjecture, ![X3:$i, X2:$i]:(((binintersect @ X2 @ X3)=(binintersect @ X3 @ X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_397, c_0_398]), c_0_398])). 923.64/240.10 thf(c_0_401, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((binintersect @ (binunion @ X2 @ X3) @ (binunion @ X3 @ X4))=(binunion @ X3 @ (binintersect @ (binunion @ X2 @ X3) @ X4)))), inference(spm,[status(thm)],[c_0_387, c_0_393])). 923.64/240.10 thf(c_0_402, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((binunion @ (binintersect @ (binunion @ X2 @ X3) @ X4) @ X2)=(binunion @ X2 @ (binintersect @ (binunion @ X4 @ X2) @ X3)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_399, c_0_400]), c_0_401])). 923.64/240.10 thf(c_0_403, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((binintersect @ (binunion @ X2 @ X3) @ (binunion @ X4 @ X2))=(binunion @ X2 @ (binintersect @ (binunion @ X4 @ X2) @ X3)))), inference(rw,[status(thm)],[c_0_399, c_0_402])). 923.64/240.10 thf(c_0_404, negated_conjecture, ((binunion @ esk101_0 @ esk102_0)!=(binunion @ esk102_0 @ esk101_0)), inference(split_conjunct,[status(thm)],[c_0_380])). 923.64/240.10 thf(c_0_405, negated_conjecture, ![X3:$i, X2:$i]:(((binunion @ X2 @ X3)=(binunion @ X3 @ X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_401, c_0_403]), c_0_396]), c_0_400]), c_0_391])). 923.64/240.10 thf(c_0_406, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_404, c_0_405])]), ['proof']). 923.64/240.10 # SZS output end CNFRefutation 923.64/240.10 # Parsed axioms : 659 923.64/240.10 # Removed by relevancy pruning/SinE : 0 923.64/240.10 # Initial clauses : 877 923.64/240.10 # Removed in clause preprocessing : 388 923.64/240.10 # Initial clauses in saturation : 489 923.64/240.10 # Processed clauses : 6611 923.64/240.10 # ...of these trivial : 685 923.64/240.10 # ...subsumed : 4630 923.64/240.10 # ...remaining for further processing : 1296 923.64/240.10 # Other redundant clauses eliminated : 39 923.64/240.10 # Clauses deleted for lack of memory : 0 923.64/240.10 # Backward-subsumed : 46 923.64/240.10 # Backward-rewritten : 64 923.64/240.10 # Generated clauses : 44817 923.64/240.10 # ...of the previous two non-redundant : 26204 923.64/240.10 # ...aggressively subsumed : 0 923.64/240.10 # Contextual simplify-reflections : 14 923.64/240.10 # Paramodulations : 44699 923.64/240.10 # Factorizations : 2 923.64/240.10 # NegExts : 12 923.64/240.10 # Equation resolutions : 44 923.64/240.10 # Disequality decompositions : 0 923.64/240.10 # Total rewrite steps : 29724 923.64/240.10 # ...of those cached : 24775 923.64/240.10 # Propositional unsat checks : 0 923.64/240.10 # Propositional check models : 0 923.64/240.10 # Propositional check unsatisfiable : 0 923.64/240.10 # Propositional clauses : 0 923.64/240.10 # Propositional clauses after purity: 0 923.64/240.10 # Propositional unsat core size : 0 923.64/240.10 # Propositional preprocessing time : 0.000 923.64/240.10 # Propositional encoding time : 0.000 923.64/240.10 # Propositional solver time : 0.000 923.64/240.10 # Success case prop preproc time : 0.000 923.64/240.10 # Success case prop encoding time : 0.000 923.64/240.10 # Success case prop solver time : 0.000 923.64/240.10 # Current number of processed clauses : 745 923.64/240.10 # Positive orientable unit clauses : 285 923.64/240.10 # Positive unorientable unit clauses: 2 923.64/240.10 # Negative unit clauses : 5 923.64/240.10 # Non-unit-clauses : 453 923.64/240.10 # Current number of unprocessed clauses: 20316 923.64/240.10 # ...number of literals in the above : 35018 923.64/240.10 # Current number of archived formulas : 0 923.64/240.10 # Current number of archived clauses : 536 923.64/240.10 # Clause-clause subsumption calls (NU) : 93557 923.64/240.10 # Rec. Clause-clause subsumption calls : 46812 923.64/240.10 # Non-unit clause-clause subsumptions : 1751 923.64/240.10 # Unit Clause-clause subsumption calls : 5669 923.64/240.10 # Rewrite failures with RHS unbound : 0 923.64/240.10 # BW rewrite match attempts : 646 923.64/240.10 # BW rewrite match successes : 429 923.64/240.10 # Condensation attempts : 0 923.64/240.10 # Condensation successes : 0 923.64/240.10 # Termbank termtop insertions : 719402 923.64/240.10 # Search garbage collected termcells : 34083 923.64/240.10 923.64/240.10 # ------------------------------------------------- 923.64/240.10 # User time : 110.480 s 923.64/240.10 # System time : 3.515 s 923.64/240.10 # Total time : 113.995 s 923.64/240.10 # Maximum resident set size: 10036 pages 923.64/240.10 923.64/240.10 # ------------------------------------------------- 923.64/240.10 # User time : 110.506 s 923.64/240.10 # System time : 3.519 s 923.64/240.10 # Total time : 114.024 s 923.64/240.10 # Maximum resident set size: 2900 pages 923.64/240.10 % E exiting 923.64/240.11 % E exiting 923.64/240.11 EOF