0.02/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.09 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM 0.08/0.28 % Computer : n021.cluster.edu 0.08/0.28 % Model : x86_64 x86_64 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.28 % Memory : 8042.1875MB 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64 0.08/0.28 % CPULimit : 1920 0.08/0.28 % WCLimit : 240 0.08/0.28 % DateTime : Wed Jul 30 02:01:19 EDT 2025 0.08/0.28 % CPUTime : 0.14/0.39 Running higher-order theorem proving 0.14/0.45 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p 52.88/240.08 # Version: 3.0.0-ho 52.88/240.08 # Preprocessing class: HSLMSLSSLLLCHFA. 52.88/240.08 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 52.88/240.08 # Starting ehoh_best5 with 240s (1) cores 52.88/240.08 # Starting almost_fo_3_lam with 240s (1) cores 52.88/240.08 # Starting new_bool_5 with 240s (1) cores 52.88/240.08 # Starting pre_casc_3 with 240s (1) cores 52.88/240.08 # Starting ho_unfolding_8 with 240s (1) cores 52.88/240.08 # Starting new_ho_10_cnf2 with 240s (1) cores 52.88/240.08 # Starting new_bool_3 with 240s (1) cores 52.88/240.08 # Starting new_ho_5 with 240s (1) cores 52.88/240.08 # almost_fo_3_lam with pid 5349 completed with status 0 52.88/240.08 # Result found by almost_fo_3_lam 52.88/240.08 # Preprocessing class: HSLMSLSSLLLCHFA. 52.88/240.08 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 52.88/240.08 # Starting ehoh_best5 with 240s (1) cores 52.88/240.08 # Starting almost_fo_3_lam with 240s (1) cores 52.88/240.08 # No SInE strategy applied 52.88/240.08 # Search class: HGHSM-FSLM32-MHFMMSBN 52.88/240.08 # Scheduled 10 strats onto 1 cores with 240 seconds (240 total) 52.88/240.08 # Starting ho_unfolding_8 with 44s (1) cores 52.88/240.08 # ho_unfolding_8 with pid 5360 completed with status 0 52.88/240.08 # Result found by ho_unfolding_8 52.88/240.08 # Preprocessing class: HSLMSLSSLLLCHFA. 52.88/240.08 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 52.88/240.08 # Starting ehoh_best5 with 240s (1) cores 52.88/240.08 # Starting almost_fo_3_lam with 240s (1) cores 52.88/240.08 # No SInE strategy applied 52.88/240.08 # Search class: HGHSM-FSLM32-MHFMMSBN 52.88/240.08 # Scheduled 10 strats onto 1 cores with 240 seconds (240 total) 52.88/240.08 # Starting ho_unfolding_8 with 44s (1) cores 52.88/240.08 # Preprocessing time : 0.103 s 52.88/240.08 # Presaturation interreduction done 52.88/240.08 52.88/240.08 # Proof found! 52.88/240.08 # SZS status Theorem 52.88/240.08 # SZS output start CNFRefutation 52.88/240.08 thf(decl_23, type, in: $i > $i > $o). 52.88/240.08 thf(decl_24, type, exu: ($i > $o) > $o). 52.88/240.08 thf(decl_25, type, setextAx: $o). 52.88/240.08 thf(decl_26, type, emptyset: $i). 52.88/240.08 thf(decl_27, type, emptysetAx: $o). 52.88/240.08 thf(decl_28, type, setadjoin: $i > $i > $i). 52.88/240.08 thf(decl_29, type, setadjoinAx: $o). 52.88/240.08 thf(decl_30, type, powerset: $i > $i). 52.88/240.08 thf(decl_31, type, powersetAx: $o). 52.88/240.08 thf(decl_32, type, setunion: $i > $i). 52.88/240.08 thf(decl_33, type, setunionAx: $o). 52.88/240.08 thf(decl_34, type, omega: $i). 52.88/240.08 thf(decl_35, type, omega0Ax: $o). 52.88/240.08 thf(decl_36, type, omegaSAx: $o). 52.88/240.08 thf(decl_37, type, omegaIndAx: $o). 52.88/240.08 thf(decl_38, type, replAx: $o). 52.88/240.08 thf(decl_39, type, foundationAx: $o). 52.88/240.08 thf(decl_40, type, wellorderingAx: $o). 52.88/240.08 thf(decl_41, type, descr: ($i > $o) > $i). 52.88/240.08 thf(decl_42, type, descrp: $o). 52.88/240.08 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 52.88/240.08 thf(decl_44, type, dsetconstrI: $o). 52.88/240.08 thf(decl_45, type, dsetconstrEL: $o). 52.88/240.08 thf(decl_46, type, dsetconstrER: $o). 52.88/240.08 thf(decl_47, type, exuE1: $o). 52.88/240.08 thf(decl_48, type, prop2set: $o > $i). 52.88/240.08 thf(decl_49, type, prop2setE: $o). 52.88/240.08 thf(decl_50, type, emptysetE: $o). 52.88/240.08 thf(decl_51, type, emptysetimpfalse: $o). 52.88/240.08 thf(decl_52, type, notinemptyset: $o). 52.88/240.08 thf(decl_53, type, exuE3e: $o). 52.88/240.08 thf(decl_54, type, setext: $o). 52.88/240.08 thf(decl_55, type, emptyI: $o). 52.88/240.08 thf(decl_56, type, noeltsimpempty: $o). 52.88/240.08 thf(decl_57, type, setbeta: $o). 52.88/240.08 thf(decl_58, type, nonempty: $i > $o). 52.88/240.08 thf(decl_59, type, nonemptyE1: $o). 52.88/240.08 thf(decl_60, type, nonemptyI: $o). 52.88/240.08 thf(decl_61, type, nonemptyI1: $o). 52.88/240.08 thf(decl_62, type, setadjoinIL: $o). 52.88/240.08 thf(decl_63, type, emptyinunitempty: $o). 52.88/240.08 thf(decl_64, type, setadjoinIR: $o). 52.88/240.08 thf(decl_65, type, setadjoinE: $o). 52.88/240.08 thf(decl_66, type, setadjoinOr: $o). 52.88/240.08 thf(decl_67, type, setoftrueEq: $o). 52.88/240.08 thf(decl_68, type, powersetI: $o). 52.88/240.08 thf(decl_69, type, emptyinPowerset: $o). 52.88/240.08 thf(decl_70, type, emptyInPowerset: $o). 52.88/240.08 thf(decl_71, type, powersetE: $o). 52.88/240.08 thf(decl_72, type, setunionI: $o). 52.88/240.08 thf(decl_73, type, setunionE: $o). 52.88/240.08 thf(decl_74, type, subPowSU: $o). 52.88/240.08 thf(decl_75, type, exuE2: $o). 52.88/240.08 thf(decl_76, type, nonemptyImpWitness: $o). 52.88/240.08 thf(decl_77, type, uniqinunit: $o). 52.88/240.08 thf(decl_78, type, notinsingleton: $o). 52.88/240.08 thf(decl_79, type, eqinunit: $o). 52.88/240.08 thf(decl_80, type, singletonsswitch: $o). 52.88/240.08 thf(decl_81, type, upairsetE: $o). 52.88/240.08 thf(decl_82, type, upairsetIL: $o). 52.88/240.08 thf(decl_83, type, upairsetIR: $o). 52.88/240.08 thf(decl_84, type, emptyE1: $o). 52.88/240.08 thf(decl_85, type, vacuousDall: $o). 52.88/240.08 thf(decl_86, type, quantDeMorgan1: $o). 52.88/240.08 thf(decl_87, type, quantDeMorgan2: $o). 52.88/240.08 thf(decl_88, type, quantDeMorgan3: $o). 52.88/240.08 thf(decl_89, type, quantDeMorgan4: $o). 52.88/240.08 thf(decl_90, type, prop2setI: $o). 52.88/240.08 thf(decl_91, type, set2prop: $i > $o). 52.88/240.08 thf(decl_92, type, prop2set2propI: $o). 52.88/240.09 thf(decl_93, type, notdexE: $o). 52.88/240.09 thf(decl_94, type, notdallE: $o). 52.88/240.09 thf(decl_95, type, exuI1: $o). 52.88/240.09 thf(decl_96, type, exuI3: $o). 52.88/240.09 thf(decl_97, type, exuI2: $o). 52.88/240.09 thf(decl_98, type, inCongP: $o). 52.88/240.09 thf(decl_99, type, in__Cong: $o). 52.88/240.09 thf(decl_100, type, exuE3u: $o). 52.88/240.09 thf(decl_101, type, exu__Cong: $o). 52.88/240.09 thf(decl_102, type, emptyset__Cong: $o). 52.88/240.09 thf(decl_103, type, setadjoin__Cong: $o). 52.88/240.09 thf(decl_104, type, powerset__Cong: $o). 52.88/240.09 thf(decl_105, type, setunion__Cong: $o). 52.88/240.09 thf(decl_106, type, omega__Cong: $o). 52.88/240.09 thf(decl_107, type, exuEu: $o). 52.88/240.09 thf(decl_108, type, descr__Cong: $o). 52.88/240.09 thf(decl_109, type, dsetconstr__Cong: $o). 52.88/240.09 thf(decl_110, type, subset: $i > $i > $o). 52.88/240.09 thf(decl_113, type, subsetI1: $o). 52.88/240.09 thf(decl_114, type, eqimpsubset2: $o). 52.88/240.09 thf(decl_115, type, eqimpsubset1: $o). 52.88/240.09 thf(decl_116, type, subsetI2: $o). 52.88/240.09 thf(decl_117, type, emptysetsubset: $o). 52.88/240.09 thf(decl_118, type, subsetE: $o). 52.88/240.09 thf(decl_119, type, subsetE2: $o). 52.88/240.09 thf(decl_120, type, notsubsetI: $o). 52.88/240.09 thf(decl_121, type, notequalI1: $o). 52.88/240.09 thf(decl_122, type, notequalI2: $o). 52.88/240.09 thf(decl_123, type, subsetRefl: $o). 52.88/240.09 thf(decl_124, type, subsetTrans: $o). 52.88/240.09 thf(decl_125, type, setadjoinSub: $o). 52.88/240.09 thf(decl_126, type, setadjoinSub2: $o). 52.88/240.09 thf(decl_127, type, subset2powerset: $o). 52.88/240.09 thf(decl_128, type, setextsub: $o). 52.88/240.09 thf(decl_129, type, subsetemptysetimpeq: $o). 52.88/240.09 thf(decl_130, type, powersetI1: $o). 52.88/240.09 thf(decl_131, type, powersetE1: $o). 52.88/240.09 thf(decl_132, type, inPowerset: $o). 52.88/240.09 thf(decl_133, type, powersetsubset: $o). 52.88/240.09 thf(decl_134, type, sepInPowerset: $o). 52.88/240.09 thf(decl_135, type, sepSubset: $o). 52.88/240.09 thf(decl_136, type, binunion: $i > $i > $i). 52.88/240.09 thf(decl_137, type, binunionIL: $o). 52.88/240.09 thf(decl_138, type, upairset2IR: $o). 52.88/240.09 thf(decl_139, type, binunionIR: $o). 52.88/240.09 thf(decl_140, type, binunionEcases: $o). 52.88/240.09 thf(decl_141, type, binunionE: $o). 52.88/240.09 thf(decl_142, type, binunionLsub: $o). 52.88/240.09 thf(decl_143, type, binunionRsub: $o). 52.88/240.09 thf(decl_144, type, binintersect: $i > $i > $i). 52.88/240.09 thf(decl_145, type, binintersectI: $o). 52.88/240.09 thf(decl_146, type, binintersectSubset5: $o). 52.88/240.09 thf(decl_147, type, binintersectEL: $o). 52.88/240.09 thf(decl_148, type, binintersectLsub: $o). 52.88/240.09 thf(decl_149, type, binintersectSubset2: $o). 52.88/240.09 thf(decl_150, type, binintersectSubset3: $o). 52.88/240.09 thf(decl_151, type, binintersectER: $o). 52.88/240.09 thf(decl_152, type, disjointsetsI1: $o). 52.88/240.09 thf(decl_153, type, binintersectRsub: $o). 52.88/240.09 thf(decl_154, type, binintersectSubset4: $o). 52.88/240.09 thf(decl_155, type, binintersectSubset1: $o). 52.88/240.09 thf(decl_156, type, bs114d: $o). 52.88/240.09 thf(decl_158, type, setminus: $i > $i > $i). 52.88/240.09 thf(decl_159, type, setminusI: $o). 52.88/240.09 thf(decl_160, type, setminusEL: $o). 52.88/240.09 thf(decl_161, type, setminusER: $o). 52.88/240.09 thf(decl_162, type, setminusSubset2: $o). 52.88/240.09 thf(decl_163, type, setminusERneg: $o). 52.88/240.09 thf(decl_164, type, setminusELneg: $o). 52.88/240.09 thf(decl_165, type, setminusILneg: $o). 52.88/240.09 thf(decl_166, type, setminusIRneg: $o). 52.88/240.09 thf(decl_167, type, setminusLsub: $o). 52.88/240.09 thf(decl_168, type, setminusSubset1: $o). 52.88/240.09 thf(decl_169, type, symdiff: $i > $i > $i). 52.88/240.09 thf(decl_170, type, symdiffE: $o). 52.88/240.09 thf(decl_171, type, symdiffI1: $o). 52.88/240.09 thf(decl_172, type, symdiffI2: $o). 52.88/240.09 thf(decl_173, type, symdiffIneg1: $o). 52.88/240.09 thf(decl_174, type, symdiffIneg2: $o). 52.88/240.09 thf(decl_175, type, iskpair: $i > $o). 52.88/240.09 thf(decl_176, type, secondinupair: $o). 52.88/240.09 thf(decl_177, type, setukpairIL: $o). 52.88/240.09 thf(decl_178, type, setukpairIR: $o). 52.88/240.09 thf(decl_179, type, kpairiskpair: $o). 52.88/240.09 thf(decl_180, type, kpair: $i > $i > $i). 52.88/240.09 thf(decl_181, type, kpairp: $o). 52.88/240.09 thf(decl_182, type, cartprod: $i > $i > $i). 52.88/240.09 thf(decl_183, type, singletonsubset: $o). 52.88/240.09 thf(decl_184, type, singletoninpowerset: $o). 52.88/240.09 thf(decl_185, type, singletoninpowunion: $o). 52.88/240.09 thf(decl_186, type, upairset2E: $o). 52.88/240.09 thf(decl_187, type, upairsubunion: $o). 52.88/240.09 thf(decl_188, type, upairinpowunion: $o). 52.88/240.09 thf(decl_189, type, ubforcartprodlem1: $o). 52.88/240.09 thf(decl_190, type, ubforcartprodlem2: $o). 52.88/240.09 thf(decl_191, type, ubforcartprodlem3: $o). 52.88/240.09 thf(decl_192, type, cartprodpairin: $o). 52.88/240.09 thf(decl_193, type, cartprodmempair1: $o). 52.88/240.09 thf(decl_194, type, cartprodmempair: $o). 52.88/240.09 thf(decl_195, type, setunionE2: $o). 52.88/240.09 thf(decl_196, type, setunionsingleton1: $o). 52.88/240.09 thf(decl_197, type, setunionsingleton2: $o). 52.88/240.09 thf(decl_198, type, setunionsingleton: $o). 52.88/240.09 thf(decl_199, type, singleton: $i > $o). 52.88/240.09 thf(decl_200, type, singletonprop: $o). 52.88/240.09 thf(decl_201, type, ex1: $i > ($i > $o) > $o). 52.88/240.09 thf(decl_202, type, ex1E1: $o). 52.88/240.09 thf(decl_203, type, ex1I: $o). 52.88/240.09 thf(decl_204, type, ex1I2: $o). 52.88/240.09 thf(decl_205, type, singletonsuniq: $o). 52.88/240.09 thf(decl_210, type, setukpairinjL1: $o). 52.88/240.09 thf(decl_211, type, kfstsingleton: $o). 52.88/240.09 thf(decl_212, type, theprop: $o). 52.88/240.09 thf(decl_213, type, kfst: $i > $i). 52.88/240.09 thf(decl_214, type, kfstpairEq: $o). 52.88/240.09 thf(decl_215, type, cartprodfstin: $o). 52.88/240.09 thf(decl_216, type, setukpairinjL2: $o). 52.88/240.09 thf(decl_217, type, setukpairinjL: $o). 52.88/240.09 thf(decl_218, type, setukpairinjR11: $o). 52.88/240.09 thf(decl_219, type, setukpairinjR12: $o). 52.88/240.09 thf(decl_220, type, setukpairinjR1: $o). 52.88/240.09 thf(decl_221, type, upairequniteq: $o). 52.88/240.09 thf(decl_222, type, setukpairinjR2: $o). 52.88/240.09 thf(decl_223, type, setukpairinjR: $o). 52.88/240.09 thf(decl_224, type, ksndsingleton: $o). 52.88/240.09 thf(decl_225, type, ksnd: $i > $i). 52.88/240.09 thf(decl_226, type, ksndpairEq: $o). 52.88/240.09 thf(decl_227, type, kpairsurjEq: $o). 52.88/240.09 thf(decl_228, type, cartprodsndin: $o). 52.88/240.09 thf(decl_229, type, cartprodpairmemEL: $o). 52.88/240.09 thf(decl_230, type, cartprodpairmemER: $o). 52.88/240.09 thf(decl_231, type, cartprodmempaircEq: $o). 52.88/240.09 thf(decl_232, type, cartprodfstpairEq: $o). 52.88/240.09 thf(decl_233, type, cartprodsndpairEq: $o). 52.88/240.09 thf(decl_234, type, cartprodpairsurjEq: $o). 52.88/240.09 thf(decl_235, type, breln: $i > $i > $i > $o). 52.88/240.09 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 52.88/240.09 thf(decl_237, type, dpsetconstrI: $o). 52.88/240.09 thf(decl_238, type, dpsetconstrSub: $o). 52.88/240.09 thf(decl_239, type, setOfPairsIsBReln: $o). 52.88/240.09 thf(decl_240, type, dpsetconstrERa: $o). 52.88/240.09 thf(decl_241, type, dpsetconstrEL1: $o). 52.88/240.09 thf(decl_242, type, dpsetconstrEL2: $o). 52.88/240.09 thf(decl_243, type, dpsetconstrER: $o). 52.88/240.09 thf(decl_244, type, func: $i > $i > $i > $o). 52.88/240.09 thf(decl_245, type, funcSet: $i > $i > $i). 52.88/240.09 thf(decl_246, type, funcImageSingleton: $o). 52.88/240.09 thf(decl_247, type, apProp: $o). 52.88/240.09 thf(decl_248, type, ap: $i > $i > $i > $i > $i). 52.88/240.09 thf(decl_249, type, app: $o). 52.88/240.09 thf(decl_250, type, infuncsetfunc: $o). 52.88/240.09 thf(decl_251, type, ap2p: $o). 52.88/240.09 thf(decl_252, type, funcinfuncset: $o). 52.88/240.09 thf(decl_253, type, lamProp: $o). 52.88/240.09 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i). 52.88/240.09 thf(decl_255, type, lamp: $o). 52.88/240.09 thf(decl_256, type, lam2p: $o). 52.88/240.09 thf(decl_257, type, brelnall1: $o). 52.88/240.09 thf(decl_258, type, brelnall2: $o). 52.88/240.09 thf(decl_259, type, ex1E2: $o). 52.88/240.09 thf(decl_260, type, funcGraphProp1: $o). 52.88/240.09 thf(decl_261, type, funcGraphProp3: $o). 52.88/240.09 thf(decl_262, type, funcGraphProp2: $o). 52.88/240.09 thf(decl_263, type, funcextLem: $o). 52.88/240.09 thf(decl_264, type, funcGraphProp4: $o). 52.88/240.09 thf(decl_265, type, subbreln: $o). 52.88/240.09 thf(decl_266, type, eqbreln: $o). 52.88/240.09 thf(decl_267, type, funcext: $o). 52.88/240.09 thf(decl_268, type, funcext2: $o). 52.88/240.09 thf(decl_269, type, ap2apEq1: $o). 52.88/240.09 thf(decl_270, type, ap2apEq2: $o). 52.88/240.09 thf(decl_271, type, beta1: $o). 52.88/240.09 thf(decl_272, type, eta1: $o). 52.88/240.09 thf(decl_273, type, lam2lamEq: $o). 52.88/240.09 thf(decl_274, type, beta2: $o). 52.88/240.09 thf(decl_275, type, eta2: $o). 52.88/240.09 thf(decl_276, type, iffalseProp1: $o). 52.88/240.09 thf(decl_277, type, iffalseProp2: $o). 52.88/240.09 thf(decl_278, type, iftrueProp1: $o). 52.88/240.09 thf(decl_279, type, iftrueProp2: $o). 52.88/240.09 thf(decl_280, type, ifSingleton: $o). 52.88/240.09 thf(decl_281, type, if: $i > $o > $i > $i > $i). 52.88/240.09 thf(decl_282, type, ifp: $o). 52.88/240.09 thf(decl_283, type, theeq: $o). 52.88/240.09 thf(decl_284, type, iftrue: $o). 52.88/240.09 thf(decl_285, type, iffalse: $o). 52.88/240.09 thf(decl_286, type, iftrueorfalse: $o). 52.88/240.09 thf(decl_287, type, binintersectT_lem: $o). 52.88/240.09 thf(decl_288, type, binunionT_lem: $o). 52.88/240.09 thf(decl_289, type, powersetT_lem: $o). 52.88/240.09 thf(decl_290, type, setminusT_lem: $o). 52.88/240.09 thf(decl_291, type, complementT_lem: $o). 52.88/240.09 thf(decl_292, type, setextT: $o). 52.88/240.09 thf(decl_293, type, subsetTI: $o). 52.88/240.09 thf(decl_294, type, powersetTI1: $o). 52.88/240.09 thf(decl_295, type, powersetTE1: $o). 52.88/240.09 thf(decl_296, type, complementTI1: $o). 52.88/240.09 thf(decl_297, type, complementTE1: $o). 52.88/240.09 thf(decl_298, type, binintersectTELcontra: $o). 52.88/240.09 thf(decl_299, type, binintersectTERcontra: $o). 52.88/240.09 thf(decl_300, type, contrasubsetT: $o). 52.88/240.09 thf(decl_301, type, contrasubsetT1: $o). 52.88/240.09 thf(decl_302, type, contrasubsetT2: $o). 52.88/240.09 thf(decl_303, type, contrasubsetT3: $o). 52.88/240.09 thf(decl_304, type, doubleComplementI1: $o). 52.88/240.09 thf(decl_305, type, doubleComplementE1: $o). 52.88/240.09 thf(decl_306, type, doubleComplementSub1: $o). 52.88/240.09 thf(decl_307, type, doubleComplementSub2: $o). 52.88/240.09 thf(decl_308, type, doubleComplementEq: $o). 52.88/240.09 thf(decl_309, type, complementTnotintersectT: $o). 52.88/240.09 thf(decl_310, type, complementImpComplementIntersect: $o). 52.88/240.09 thf(decl_311, type, complementSubsetComplementIntersect: $o). 52.88/240.09 thf(decl_312, type, complementInPowersetComplementIntersect: $o). 52.88/240.09 thf(decl_313, type, contraSubsetComplement: $o). 52.88/240.09 thf(decl_314, type, complementTcontraSubset: $o). 52.88/240.09 thf(decl_315, type, binunionTILcontra: $o). 52.88/240.09 thf(decl_316, type, binunionTIRcontra: $o). 52.88/240.09 thf(decl_317, type, inIntersectImpInUnion: $o). 52.88/240.09 thf(decl_318, type, inIntersectImpInUnion2: $o). 52.88/240.09 thf(decl_319, type, inIntersectImpInIntersectUnions: $o). 52.88/240.09 thf(decl_320, type, intersectInPowersetIntersectUnions: $o). 52.88/240.09 thf(decl_321, type, inComplementUnionImpNotIn1: $o). 52.88/240.09 thf(decl_322, type, inComplementUnionImpInComplement1: $o). 52.88/240.09 thf(decl_323, type, binunionTE: $o). 52.88/240.09 thf(decl_324, type, binunionTEcontra: $o). 52.88/240.09 thf(decl_325, type, demorgan2a1: $o). 52.88/240.09 thf(decl_326, type, complementUnionInPowersetComplement: $o). 52.88/240.09 thf(decl_327, type, demorgan2a2: $o). 52.88/240.09 thf(decl_328, type, demorgan1a: $o). 52.88/240.09 thf(decl_329, type, demorgan1b: $o). 52.88/240.09 thf(decl_330, type, demorgan1: $o). 52.88/240.09 thf(decl_331, type, demorgan2a: $o). 52.88/240.09 thf(decl_332, type, demorgan2b2: $o). 52.88/240.09 thf(decl_333, type, demorgan2b: $o). 52.88/240.09 thf(decl_334, type, demorgan2: $o). 52.88/240.09 thf(decl_335, type, woz13rule0: $o). 52.88/240.09 thf(decl_336, type, woz13rule1: $o). 52.88/240.09 thf(decl_337, type, woz13rule2: $o). 52.88/240.09 thf(decl_338, type, woz13rule3: $o). 52.88/240.09 thf(decl_339, type, woz13rule4: $o). 52.88/240.09 thf(decl_340, type, woz1_1: $o). 52.88/240.09 thf(decl_341, type, woz1_2: $o). 52.88/240.09 thf(decl_342, type, epred1_0: $o). 52.88/240.09 thf(decl_343, type, esk1_2: $i > $i > $i). 52.88/240.09 thf(decl_344, type, esk2_2: $i > $i > $i). 52.88/240.09 thf(decl_345, type, esk3_2: $i > $i > $i). 52.88/240.09 thf(decl_346, type, esk4_1: $i > $i). 52.88/240.09 thf(decl_347, type, esk5_2: ($i > $i > $o) > $i > $i). 52.88/240.09 thf(decl_348, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 52.88/240.09 thf(decl_349, type, esk7_2: ($i > $i > $o) > $i > $i). 52.88/240.09 thf(decl_350, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 52.88/240.09 thf(decl_351, type, esk9_1: $i > $i). 52.88/240.09 thf(decl_352, type, esk10_2: ($i > $o) > $i > $i). 52.88/240.09 thf(decl_353, type, esk11_2: ($i > $o) > $i > $i). 52.88/240.09 thf(decl_354, type, esk12_1: ($i > $o) > $i). 52.88/240.09 thf(decl_355, type, esk13_2: ($i > $o) > $i > $i). 52.88/240.09 thf(decl_356, type, esk14_1: ($i > $o) > $i). 52.88/240.09 thf(decl_357, type, esk15_2: $i > $i > $i). 52.88/240.09 thf(decl_358, type, esk16_2: $i > $i > $i). 52.88/240.09 thf(decl_359, type, esk17_1: $i > $i). 52.88/240.09 thf(decl_360, type, esk18_1: $i > $i). 52.88/240.09 thf(decl_361, type, esk19_1: $i > $i). 52.88/240.09 thf(decl_362, type, esk20_2: $i > $i > $i). 52.88/240.09 thf(decl_363, type, esk21_3: $i > $i > $o > $i). 52.88/240.09 thf(decl_364, type, esk22_2: ($i > $o) > $i > $i). 52.88/240.09 thf(decl_365, type, esk23_1: ($i > $o) > $i). 52.88/240.09 thf(decl_366, type, esk24_1: $i > $i). 52.88/240.09 thf(decl_367, type, esk25_2: $i > ($i > $o) > $i). 52.88/240.09 thf(decl_368, type, esk26_2: $i > ($i > $o) > $i). 52.88/240.09 thf(decl_369, type, esk27_2: $i > ($i > $o) > $i). 52.88/240.09 thf(decl_370, type, esk28_2: $i > ($i > $o) > $i). 52.88/240.09 thf(decl_371, type, esk29_2: $i > ($i > $o) > $i). 52.88/240.09 thf(decl_372, type, esk30_2: $i > ($i > $o) > $i). 52.88/240.09 thf(decl_373, type, esk31_2: ($i > $o) > $i > $i). 52.88/240.09 thf(decl_374, type, esk32_1: ($i > $o) > $i). 52.88/240.09 thf(decl_375, type, esk33_1: ($i > $o) > $i). 52.88/240.09 thf(decl_376, type, esk34_1: ($i > $o) > $i). 52.88/240.09 thf(decl_377, type, esk35_1: ($i > $o) > $i). 52.88/240.09 thf(decl_378, type, esk36_2: ($i > $o) > $i > $i). 52.88/240.09 thf(decl_379, type, esk37_1: ($i > $o) > $i). 52.88/240.09 thf(decl_380, type, esk38_2: ($i > $o) > $i > $i). 52.88/240.09 thf(decl_381, type, esk39_2: ($i > $o) > ($i > $o) > $i). 52.88/240.09 thf(decl_382, type, esk40_2: ($i > $o) > ($i > $o) > $i). 52.88/240.09 thf(decl_383, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 52.88/240.09 thf(decl_384, type, esk42_2: ($i > $o) > ($i > $o) > $i). 52.88/240.09 thf(decl_385, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 52.88/240.09 thf(decl_386, type, esk44_2: ($i > $o) > ($i > $o) > $i). 52.88/240.09 thf(decl_387, type, esk45_2: ($i > $o) > $i > $i). 52.88/240.09 thf(decl_388, type, esk46_2: ($i > $o) > ($i > $o) > $i). 52.88/240.09 thf(decl_389, type, esk47_2: ($i > $o) > ($i > $o) > $i). 52.88/240.09 thf(decl_390, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 52.88/240.09 thf(decl_391, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 52.88/240.09 thf(decl_392, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 52.88/240.09 thf(decl_393, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 52.88/240.09 thf(decl_394, type, esk52_2: $i > $i > $i). 52.88/240.09 thf(decl_395, type, esk53_2: $i > $i > $i). 52.88/240.09 thf(decl_396, type, esk54_2: $i > $i > $i). 52.88/240.09 thf(decl_397, type, esk55_3: $i > $i > $i > $i). 52.88/240.09 thf(decl_398, type, esk56_3: $i > $i > $i > $i). 52.88/240.09 thf(decl_399, type, esk57_2: $i > $i > $i). 52.88/240.09 thf(decl_400, type, esk58_2: $i > ($i > $o) > $i). 52.88/240.09 thf(decl_401, type, esk59_2: $i > ($i > $o) > $i). 52.88/240.09 thf(decl_402, type, esk60_2: $i > ($i > $o) > $i). 52.88/240.09 thf(decl_403, type, esk61_3: $i > ($i > $o) > $i > $i). 52.88/240.09 thf(decl_404, type, esk62_2: $i > ($i > $o) > $i). 52.88/240.09 thf(decl_405, type, esk63_2: $i > ($i > $o) > $i). 52.88/240.09 thf(decl_406, type, esk64_3: $i > $i > ($i > $i) > $i). 52.88/240.09 thf(decl_407, type, esk65_3: $i > $i > ($i > $i) > $i). 52.88/240.09 thf(decl_408, type, esk66_3: $i > $i > ($i > $i) > $i). 52.88/240.09 thf(decl_409, type, esk67_4: $i > $i > $i > ($i > $o) > $i). 52.88/240.09 thf(decl_410, type, esk68_4: $i > $i > $i > ($i > $o) > $i). 52.88/240.09 thf(decl_411, type, esk69_4: $i > $i > $i > ($i > $o) > $i). 52.88/240.09 thf(decl_412, type, esk70_4: $i > $i > $i > ($i > $o) > $i). 52.88/240.09 thf(decl_413, type, esk71_4: $i > $i > $i > $i > $i). 52.88/240.09 thf(decl_414, type, esk72_4: $i > $i > $i > $i > $i). 52.88/240.09 thf(decl_415, type, esk73_4: $i > $i > $i > $i > $i). 52.88/240.09 thf(decl_416, type, esk74_4: $i > $i > $i > $i > $i). 52.88/240.09 thf(decl_417, type, esk75_4: $i > $i > $i > $i > $i). 52.88/240.09 thf(decl_418, type, esk76_4: $i > $i > $i > $i > $i). 52.88/240.09 thf(decl_419, type, esk77_4: $i > $i > $i > $i > $i). 52.88/240.09 thf(decl_420, type, esk78_4: $i > $i > $i > $i > $i). 52.88/240.09 thf(decl_421, type, esk79_4: $i > $i > $i > $i > $i). 52.88/240.09 thf(decl_422, type, esk80_3: $i > $i > ($i > $i) > $i). 52.88/240.09 thf(decl_423, type, esk81_3: $i > $i > ($i > $i) > $i). 52.88/240.09 thf(decl_424, type, esk82_3: $i > $i > ($i > $i) > $i). 52.88/240.09 thf(decl_425, type, esk83_3: $i > $i > $i > $i). 52.88/240.09 thf(decl_426, type, esk84_3: $i > $i > $i > $i). 52.88/240.09 thf(decl_427, type, esk85_3: $i > $i > $i > $i). 52.88/240.09 thf(decl_428, type, esk86_3: $i > $i > $i > $i). 52.88/240.09 thf(decl_429, type, esk87_0: $i). 52.88/240.09 thf(decl_430, type, esk88_0: $i). 52.88/240.09 thf(decl_431, type, esk89_0: $i). 52.88/240.09 thf(decl_432, type, esk90_0: $i). 52.88/240.09 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', replAx)). 52.88/240.09 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', exu)). 52.88/240.09 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', descrp)). 52.88/240.09 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', exuE1)). 52.88/240.09 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', exuE3e)). 52.88/240.09 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', nonempty)). 52.88/240.09 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', nonemptyI)). 52.88/240.09 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', exuE2)). 52.88/240.09 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', exuI1)). 52.88/240.09 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', exuI3)). 52.88/240.09 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', exuI2)). 52.88/240.09 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', exuE3u)). 52.88/240.09 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', exu__Cong)). 52.88/240.09 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', exuEu)). 52.88/240.09 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', descr__Cong)). 52.88/240.09 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', ex1E1)). 52.88/240.09 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', ex1)). 52.88/240.09 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', ex1I)). 52.88/240.09 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', ex1I2)). 52.88/240.09 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setOfPairsIsBReln)). 52.88/240.09 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', breln)). 52.88/240.09 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', ex1E2)). 52.88/240.09 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', dsetconstrI)). 52.88/240.09 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', dsetconstrEL)). 52.88/240.09 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', dsetconstrER)). 52.88/240.09 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setbeta)). 52.88/240.09 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', nonemptyE1)). 52.88/240.09 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', nonemptyI1)). 52.88/240.09 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setoftrueEq)). 52.88/240.09 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', nonemptyImpWitness)). 52.88/240.09 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', emptyE1)). 52.88/240.09 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', dsetconstr__Cong)). 52.88/240.09 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', sepInPowerset)). 52.88/240.09 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', sepSubset)). 52.88/240.09 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', singletonprop)). 52.88/240.09 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', kfstsingleton)). 52.88/240.09 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', ksndsingleton)). 52.88/240.09 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', dpsetconstrI)). 52.88/240.09 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', dpsetconstrSub)). 52.88/240.09 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', dpsetconstrERa)). 52.88/240.09 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', dpsetconstrEL1)). 52.88/240.09 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', dpsetconstrEL2)). 52.88/240.09 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', dpsetconstrER)). 52.88/240.09 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', funcImageSingleton)). 52.88/240.09 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', apProp)). 52.88/240.09 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', lamProp)). 52.88/240.09 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', lamp)). 52.88/240.09 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', lam2p)). 52.88/240.09 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', brelnall1)). 52.88/240.09 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', brelnall2)). 52.88/240.09 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', subbreln)). 52.88/240.09 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', eqbreln)). 52.88/240.09 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', beta1)). 52.88/240.09 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', eta1)). 52.88/240.09 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', lam2lamEq)). 52.88/240.09 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', beta2)). 52.88/240.09 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', eta2)). 52.88/240.09 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', iffalseProp1)). 52.88/240.09 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', iffalseProp2)). 52.88/240.09 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', iftrueProp1)). 52.88/240.09 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', iftrueProp2)). 52.88/240.09 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', ifSingleton)). 52.88/240.09 thf(woz1_3, conjecture, ((setextAx)=>(((((((((replAx)=>((foundationAx)=>((((((dsetconstrER)=>((((emptysetE)=>(((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>(((nonemptyE1)=>((nonemptyI)=>(((((setadjoinIR)=>(((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>(((((nonemptyImpWitness)=>(((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((((((vacuousDall)=>(((quantDeMorgan2)=>(((quantDeMorgan4)=>(((((notdallE)=>((((((in__Cong)=>(((exu__Cong)=>((((powerset__Cong)=>(((omega__Cong)=>(((descr__Cong)=>((((((((subsetE)=>((((notequalI1)=>(((subsetRefl)=>((((setadjoinSub2)=>(((((((((sepInPowerset)=>((sepSubset)=>((binunionIL)=>(((((binunionE)=>((((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>(((binintersectSubset2)=>((binintersectSubset3)=>((((((binintersectSubset1)=>(((setminusI)=>((setminusEL)=>(((setminusSubset2)=>(((setminusELneg)=>((setminusILneg)=>((((((symdiffI1)=>(((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((((((singletoninpowerset)=>(((((upairinpowunion)=>(((((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>(((setunionsingleton)=>(((((ex1I2)=>((singletonsuniq)=>(((kfstsingleton)=>(((kfstpairEq)=>((cartprodfstin)=>(((setukpairinjL)=>((setukpairinjR11)=>(((setukpairinjR1)=>((upairequniteq)=>((((ksndsingleton)=>((((cartprodsndin)=>((((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>(((dpsetconstrSub)=>(((((dpsetconstrEL2)=>((dpsetconstrER)=>(((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>(((brelnall1)=>(((ex1E2)=>(((((funcextLem)=>((funcGraphProp4)=>((subbreln)=>(((funcext)=>((funcext2)=>(((ap2apEq2)=>(((eta1)=>((lam2lamEq)=>((beta2)=>(((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>(((ifSingleton)=>(((theeq)=>((((iftrueorfalse)=>((((powersetT_lem)=>((((((((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((((contrasubsetT2)=>((contrasubsetT3)=>(((doubleComplementE1)=>((doubleComplementSub1)=>(((((complementImpComplementIntersect)=>((((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>(((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>(((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((((demorgan2a1)=>(((demorgan2a2)=>((((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>(((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>![X4:$i, X21:$i]:((![X48:$i]:((![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))<=(in @ X48 @ (powerset @ X4))))<=(in @ X21 @ (powerset @ X4))))))))<=(woz13rule2)))))))))<=(demorgan1b))<=(demorgan1a)))<=(complementUnionInPowersetComplement)))<=(binunionTEcontra))<=(binunionTE))))<=(intersectInPowersetIntersectUnions))))<=(inIntersectImpInUnion))))))<=(complementInPowersetComplementIntersect))<=(complementSubsetComplementIntersect)))<=(complementTnotintersectT))<=(doubleComplementEq))<=(doubleComplementSub2))))<=(doubleComplementI1))))<=(contrasubsetT1))<=(contrasubsetT))))))<=(powersetTE1))<=(powersetTI1))<=(subsetTI))<=(setextT))<=(complementT_lem))<=(setminusT_lem)))<=(binunionT_lem))<=(binintersectT_lem)))<=(iffalse))<=(iftrue)))<=(ifp)))<=(iftrueProp2)))))<=(eta2)))))<=(beta1)))<=(ap2apEq1))))<=(eqbreln)))))<=(funcGraphProp2))<=(funcGraphProp3))<=(funcGraphProp1)))<=(brelnall2)))<=(lam2p)))))))))<=(funcImageSingleton))))<=(dpsetconstrEL1))<=(dpsetconstrERa))<=(setOfPairsIsBReln)))<=(dpsetconstrI))))))<=(cartprodpairmemER))<=(cartprodpairmemEL)))<=(kpairsurjEq))<=(ksndpairEq)))<=(setukpairinjR))<=(setukpairinjR2))))<=(setukpairinjR12))))<=(setukpairinjL2))))<=(theprop)))<=(setukpairinjL1))))<=(ex1I))<=(ex1E1))<=(singletonprop)))<=(setunionsingleton2)))))))<=(ubforcartprodlem3))<=(ubforcartprodlem2))<=(ubforcartprodlem1)))<=(upairsubunion))<=(upairset2E))<=(singletoninpowunion)))<=(singletonsubset))<=(kpairp))<=(kpairiskpair))<=(setukpairIR))))))<=(symdiffI2)))<=(symdiffE))<=(setminusSubset1))<=(setminusLsub))<=(setminusIRneg))))<=(setminusERneg)))<=(setminusER))))<=(bs114d)))<=(binintersectSubset4))<=(binintersectRsub))<=(disjointsetsI1))<=(binintersectER))))<=(binintersectLsub)))))<=(binunionRsub))<=(binunionLsub)))<=(binunionEcases))<=(binunionIR))<=(upairset2IR)))))<=(powersetsubset))<=(inPowerset))<=(powersetE1))<=(powersetI1))<=(subsetemptysetimpeq))<=(setextsub))<=(subset2powerset)))<=(setadjoinSub))<=(subsetTrans)))<=(notequalI2)))<=(notsubsetI))<=(subsetE2)))<=(emptysetsubset))<=(subsetI2))<=(eqimpsubset1))<=(eqimpsubset2))<=(subsetI1))<=(dsetconstr__Cong)))<=(exuEu)))<=(setunion__Cong)))<=(setadjoin__Cong))<=(emptyset__Cong)))<=(exuE3u)))<=(inCongP))<=(exuI2))<=(exuI3))<=(exuI1)))<=(notdexE))<=(prop2set2propI))<=(prop2setI)))<=(quantDeMorgan3)))<=(quantDeMorgan1)))<=(emptyE1))<=(upairsetIR))<=(upairsetIL))<=(upairsetE)))))<=(uniqinunit)))<=(exuE2))<=(subPowSU))<=(setunionE)))))))))<=(setadjoinE)))<=(emptyinunitempty))<=(setadjoinIL))<=(nonemptyI1))))<=(setbeta)))))))<=(emptysetimpfalse)))<=(prop2setE))<=(exuE1)))<=(dsetconstrEL))<=(dsetconstrI))<=(descrp))<=(wellorderingAx))))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax))<=(setunionAx))<=(powersetAx))<=(setadjoinAx))<=(emptysetAx))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', woz1_3)). 52.88/240.09 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setextAx)). 52.88/240.09 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', emptysetAx)). 52.88/240.09 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setadjoinAx)). 52.88/240.09 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', powersetAx)). 52.88/240.09 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setunionAx)). 52.88/240.09 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', omega0Ax)). 52.88/240.09 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', omegaSAx)). 52.88/240.09 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', omegaIndAx)). 52.88/240.09 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', foundationAx)). 52.88/240.09 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', wellorderingAx)). 52.88/240.09 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', prop2setE)). 52.88/240.09 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', emptysetE)). 52.88/240.09 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', emptysetimpfalse)). 52.88/240.09 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', notinemptyset)). 52.88/240.09 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setext)). 52.88/240.09 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', emptyI)). 52.88/240.09 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', noeltsimpempty)). 52.88/240.09 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setadjoinIL)). 52.88/240.09 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', emptyinunitempty)). 52.88/240.09 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setadjoinIR)). 52.88/240.09 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setadjoinE)). 52.88/240.09 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setadjoinOr)). 52.88/240.09 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', powersetI)). 52.88/240.09 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', emptyinPowerset)). 52.88/240.09 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', emptyInPowerset)). 52.88/240.09 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', powersetE)). 52.88/240.09 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setunionI)). 52.88/240.09 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setunionE)). 52.88/240.09 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', subPowSU)). 52.88/240.09 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', uniqinunit)). 52.88/240.09 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', notinsingleton)). 52.88/240.09 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', eqinunit)). 52.88/240.09 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', singletonsswitch)). 52.88/240.09 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', upairsetE)). 52.88/240.09 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', upairsetIL)). 52.88/240.09 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', upairsetIR)). 52.88/240.09 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', vacuousDall)). 52.88/240.09 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', quantDeMorgan1)). 52.88/240.09 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', quantDeMorgan2)). 52.88/240.09 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', quantDeMorgan3)). 52.88/240.09 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', quantDeMorgan4)). 52.88/240.09 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', prop2setI)). 52.88/240.09 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', prop2set2propI)). 52.88/240.09 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', notdexE)). 52.88/240.09 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', notdallE)). 52.88/240.09 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', inCongP)). 52.88/240.09 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', in__Cong)). 52.88/240.09 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', emptyset__Cong)). 52.88/240.09 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setadjoin__Cong)). 52.88/240.09 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', powerset__Cong)). 52.88/240.09 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setunion__Cong)). 52.88/240.09 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', omega__Cong)). 52.88/240.09 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', subsetI1)). 52.88/240.09 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', eqimpsubset2)). 52.88/240.09 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', eqimpsubset1)). 52.88/240.09 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', subsetI2)). 52.88/240.09 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', emptysetsubset)). 52.88/240.09 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', subsetE)). 52.88/240.09 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', subsetE2)). 52.88/240.09 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', notsubsetI)). 52.88/240.09 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', notequalI1)). 52.88/240.09 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', notequalI2)). 52.88/240.09 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', subsetRefl)). 52.88/240.09 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', subsetTrans)). 52.88/240.09 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setadjoinSub)). 52.88/240.09 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setadjoinSub2)). 52.88/240.09 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', subset2powerset)). 52.88/240.09 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setextsub)). 52.88/240.09 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', subsetemptysetimpeq)). 52.88/240.09 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', powersetI1)). 52.88/240.09 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', powersetE1)). 52.88/240.09 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', inPowerset)). 52.88/240.09 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', powersetsubset)). 52.88/240.09 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binunionIL)). 52.88/240.09 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', upairset2IR)). 52.88/240.09 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binunionIR)). 52.88/240.09 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binunionEcases)). 52.88/240.09 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binunionE)). 52.88/240.09 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binunionLsub)). 52.88/240.09 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binunionRsub)). 52.88/240.09 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binintersectI)). 52.88/240.09 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binintersectSubset5)). 52.88/240.09 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binintersectEL)). 52.88/240.09 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binintersectLsub)). 52.88/240.09 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binintersectSubset2)). 52.88/240.09 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binintersectSubset3)). 52.88/240.09 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binintersectER)). 52.88/240.09 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', disjointsetsI1)). 52.88/240.09 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binintersectRsub)). 52.88/240.09 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binintersectSubset4)). 52.88/240.09 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binintersectSubset1)). 52.88/240.09 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', bs114d)). 52.88/240.09 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setminusI)). 52.88/240.09 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setminusEL)). 52.88/240.09 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setminusER)). 52.88/240.09 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setminusSubset2)). 52.88/240.09 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setminusERneg)). 52.88/240.09 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setminusELneg)). 52.88/240.09 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setminusILneg)). 52.88/240.09 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setminusIRneg)). 52.88/240.09 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setminusLsub)). 52.88/240.09 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setminusSubset1)). 52.88/240.09 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', symdiffE)). 52.88/240.09 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', symdiffI1)). 52.88/240.09 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', symdiffI2)). 52.88/240.09 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', symdiffIneg1)). 52.88/240.09 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', symdiffIneg2)). 52.88/240.09 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', secondinupair)). 52.88/240.09 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setukpairIL)). 52.88/240.09 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setukpairIR)). 52.88/240.09 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', kpairiskpair)). 52.88/240.09 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', kpairp)). 52.88/240.09 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', singletonsubset)). 52.88/240.09 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', singletoninpowerset)). 52.88/240.09 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', singletoninpowunion)). 52.88/240.09 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', upairset2E)). 52.88/240.09 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', upairsubunion)). 52.88/240.09 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', upairinpowunion)). 52.88/240.09 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', ubforcartprodlem1)). 52.88/240.09 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', ubforcartprodlem2)). 52.88/240.09 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', ubforcartprodlem3)). 52.88/240.09 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', cartprodpairin)). 52.88/240.09 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', cartprodmempair1)). 52.88/240.09 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', cartprodmempair)). 52.88/240.09 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setunionE2)). 52.88/240.09 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setunionsingleton1)). 52.88/240.09 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setunionsingleton2)). 52.88/240.09 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setunionsingleton)). 52.88/240.09 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', singletonsuniq)). 52.88/240.09 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setukpairinjL1)). 52.88/240.09 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', theprop)). 52.88/240.09 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', kfstpairEq)). 52.88/240.09 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', cartprodfstin)). 52.88/240.09 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setukpairinjL2)). 52.88/240.09 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setukpairinjL)). 52.88/240.09 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setukpairinjR11)). 52.88/240.09 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setukpairinjR12)). 52.88/240.09 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setukpairinjR1)). 52.88/240.09 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', upairequniteq)). 52.88/240.09 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setukpairinjR2)). 52.88/240.09 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setukpairinjR)). 52.88/240.09 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', ksndpairEq)). 52.88/240.09 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', kpairsurjEq)). 52.88/240.09 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', cartprodsndin)). 52.88/240.09 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', cartprodpairmemEL)). 52.88/240.09 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', cartprodpairmemER)). 52.88/240.09 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', cartprodmempaircEq)). 52.88/240.09 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', cartprodfstpairEq)). 52.88/240.09 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', cartprodsndpairEq)). 52.88/240.09 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', cartprodpairsurjEq)). 52.88/240.09 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', app)). 52.88/240.09 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', infuncsetfunc)). 52.88/240.09 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', ap2p)). 52.88/240.09 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', funcinfuncset)). 52.88/240.09 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', funcGraphProp1)). 52.88/240.09 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', funcGraphProp3)). 52.88/240.09 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', funcGraphProp2)). 52.88/240.09 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', funcextLem)). 52.88/240.09 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', funcGraphProp4)). 52.88/240.09 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', funcext)). 52.88/240.09 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', funcext2)). 52.88/240.09 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', ap2apEq1)). 52.88/240.09 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', ap2apEq2)). 52.88/240.09 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', ifp)). 52.88/240.09 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', theeq)). 52.88/240.09 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', iftrue)). 52.88/240.09 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', iffalse)). 52.88/240.09 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', iftrueorfalse)). 52.88/240.09 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binintersectT_lem)). 52.88/240.09 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binunionT_lem)). 52.88/240.09 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', powersetT_lem)). 52.88/240.09 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setminusT_lem)). 52.88/240.09 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', complementT_lem)). 52.88/240.09 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', setextT)). 52.88/240.09 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', subsetTI)). 52.88/240.09 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', powersetTI1)). 52.88/240.09 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', powersetTE1)). 52.88/240.09 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', complementTI1)). 52.88/240.09 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', complementTE1)). 52.88/240.09 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binintersectTELcontra)). 52.88/240.09 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binintersectTERcontra)). 52.88/240.09 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', contrasubsetT)). 52.88/240.09 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', contrasubsetT1)). 52.88/240.09 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$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/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', contrasubsetT2)). 52.88/240.09 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', contrasubsetT3)). 52.88/240.09 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$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/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', doubleComplementI1)). 52.88/240.09 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', doubleComplementE1)). 52.88/240.09 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', doubleComplementSub1)). 52.88/240.09 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', doubleComplementSub2)). 52.88/240.09 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', doubleComplementEq)). 52.88/240.09 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', complementTnotintersectT)). 52.88/240.09 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', complementImpComplementIntersect)). 52.88/240.09 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$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/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', complementSubsetComplementIntersect)). 52.88/240.09 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', complementInPowersetComplementIntersect)). 52.88/240.09 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', contraSubsetComplement)). 52.88/240.09 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$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/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', complementTcontraSubset)). 52.88/240.09 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/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binunionTILcontra)). 52.88/240.09 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/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binunionTIRcontra)). 52.88/240.09 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', inIntersectImpInUnion)). 52.88/240.09 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$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/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', inIntersectImpInUnion2)). 52.88/240.09 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:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', inIntersectImpInIntersectUnions)). 52.88/240.09 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', intersectInPowersetIntersectUnions)). 52.88/240.09 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', inComplementUnionImpNotIn1)). 52.88/240.09 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', inComplementUnionImpInComplement1)). 52.88/240.09 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$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/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binunionTE)). 52.88/240.09 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/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', binunionTEcontra)). 52.88/240.09 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/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', demorgan2a1)). 52.88/240.09 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', complementUnionInPowersetComplement)). 52.88/240.09 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', demorgan2a2)). 52.88/240.09 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', demorgan1a)). 52.88/240.09 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', demorgan1b)). 52.88/240.09 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$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/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', demorgan1)). 52.88/240.09 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/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', demorgan2a)). 52.88/240.09 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/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', demorgan2b2)). 52.88/240.09 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/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', demorgan2b)). 52.88/240.09 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', demorgan2)). 52.88/240.09 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', woz13rule0)). 52.88/240.09 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', woz13rule1)). 52.88/240.09 thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', woz13rule2)). 52.88/240.09 thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', woz13rule3)). 52.88/240.09 thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$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/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', woz13rule4)). 52.88/240.09 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', woz1_1)). 52.88/240.09 thf(woz1_2, axiom, ((woz1_2)<=>![X4:$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/sandbox2/tmp/tmp.JgNRpNQKsx/E---3.1_5270.p', woz1_2)). 52.88/240.09 thf(c_0_286, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 52.88/240.09 thf(c_0_287, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 52.88/240.09 thf(c_0_288, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 52.88/240.09 thf(c_0_289, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 52.88/240.09 thf(c_0_290, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 52.88/240.09 thf(c_0_291, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 52.88/240.09 thf(c_0_292, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 52.88/240.09 thf(c_0_293, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 52.88/240.09 thf(c_0_294, 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])). 52.88/240.09 thf(c_0_295, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 52.88/240.09 thf(c_0_296, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 52.88/240.09 thf(c_0_297, 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])). 52.88/240.09 thf(c_0_298, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 52.88/240.09 thf(c_0_299, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 52.88/240.09 thf(c_0_300, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 52.88/240.09 thf(c_0_301, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 52.88/240.09 thf(c_0_302, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((singleton @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))))), inference(fof_simplification,[status(thm)],[ex1])). 52.88/240.09 thf(c_0_303, 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])). 52.88/240.09 thf(c_0_304, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 52.88/240.09 thf(c_0_305, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 52.88/240.09 thf(c_0_306, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])). 52.88/240.09 thf(c_0_307, 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])). 52.88/240.09 thf(c_0_308, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X953:$i]:((((X6 @ X2 @ X953))&![X954:$i]:((((X6 @ X2 @ X954))=>((X953)=(X954)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_286, c_0_287])). 52.88/240.09 thf(c_0_309, plain, ((descrp)=(![X1:$i > $o]:(((?[X955:$i]:((((X1 @ X955))&![X956:$i]:((((X1 @ X956))=>((X955)=(X956)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_288, c_0_287])). 52.88/240.09 thf(c_0_310, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 52.88/240.09 thf(c_0_311, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 52.88/240.09 thf(c_0_312, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 52.88/240.09 thf(c_0_313, plain, ((exuE1)=(![X1:$i > $o]:(((?[X957:$i]:((((X1 @ X957))&![X958:$i]:((((X1 @ X958))=>((X957)=(X958)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_289, c_0_287])). 52.88/240.09 thf(c_0_314, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X959:$i]:((((X1 @ X959))&![X960:$i]:((((X1 @ X960))=>((X959)=(X960)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_290, c_0_287])). 52.88/240.09 thf(c_0_315, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 52.88/240.09 thf(c_0_316, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_291])). 52.88/240.09 thf(c_0_317, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_292, c_0_291])). 52.88/240.09 thf(c_0_318, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_291])). 52.88/240.09 thf(c_0_319, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 52.88/240.09 thf(c_0_320, plain, ((exuE2)=(![X1:$i > $o]:(((?[X961:$i]:((((X1 @ X961))&![X962:$i]:((((X1 @ X962))=>((X961)=(X962)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_293, c_0_287])). 52.88/240.09 thf(c_0_321, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_291])). 52.88/240.09 thf(c_0_322, 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])). 52.88/240.09 thf(c_0_323, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X963:$i]:((((X1 @ X963))&![X964:$i]:((((X1 @ X964))=>((X963)=(X964))))))))))), inference(apply_def,[status(thm)],[c_0_294, c_0_287])). 52.88/240.09 thf(c_0_324, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X965:$i]:((((X1 @ X965))&![X966:$i]:((((X1 @ X966))=>((X965)=(X966)))))))))))), inference(apply_def,[status(thm)],[c_0_295, c_0_287])). 52.88/240.09 thf(c_0_325, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X967:$i]:((((X1 @ X967))&![X968:$i]:((((X1 @ X968))=>((X967)=(X968))))))))))), inference(apply_def,[status(thm)],[c_0_296, c_0_287])). 52.88/240.09 thf(c_0_326, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X969:$i]:((((X1 @ X969))&![X970:$i]:((((X1 @ X970))=>((X969)=(X970)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_297, c_0_287])). 52.88/240.09 thf(c_0_327, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X971:$i]:((((X1 @ X971))&![X972:$i]:((((X1 @ X972))=>((X971)=(X972)))))))<=>(?[X973:$i]:((((X17 @ X973))&![X974:$i]:((((X17 @ X974))=>((X973)=(X974)))))))))))), inference(apply_def,[status(thm)],[c_0_298, c_0_287])). 52.88/240.09 thf(c_0_328, plain, ((exuEu)=(![X1:$i > $o]:(((?[X975:$i]:((((X1 @ X975))&![X976:$i]:((((X1 @ X976))=>((X975)=(X976)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_299, c_0_287])). 52.88/240.09 thf(c_0_329, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X977:$i]:((((X1 @ X977))&![X978:$i]:((((X1 @ X978))=>((X977)=(X978)))))))=>((?[X979:$i]:((((X17 @ X979))&![X980:$i]:((((X17 @ X980))=>((X979)=(X980)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_300, c_0_287])). 52.88/240.09 thf(c_0_330, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 52.88/240.09 thf(c_0_331, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 52.88/240.09 thf(c_0_332, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 52.88/240.09 thf(c_0_333, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 52.88/240.09 thf(c_0_334, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_301, c_0_302])). 52.88/240.09 thf(c_0_335, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))))))))), inference(apply_def,[status(thm)],[c_0_303, c_0_302])). 52.88/240.09 thf(c_0_336, plain, ((ex1I2)=(![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))))))), inference(apply_def,[status(thm)],[c_0_304, c_0_302])). 52.88/240.09 thf(c_0_337, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 52.88/240.09 thf(c_0_338, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 52.88/240.09 thf(c_0_339, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 52.88/240.09 thf(c_0_340, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 52.88/240.09 thf(c_0_341, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_305, c_0_306])). 52.88/240.09 thf(c_0_342, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 52.88/240.09 thf(c_0_343, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 52.88/240.09 thf(c_0_344, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 52.88/240.09 thf(c_0_345, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 52.88/240.09 thf(c_0_346, plain, ((funcImageSingleton)<=>![X4:$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])). 52.88/240.09 thf(c_0_347, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 52.88/240.09 thf(c_0_348, plain, ((lamProp)<=>![X4:$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])). 52.88/240.09 thf(c_0_349, 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 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 52.88/240.09 thf(c_0_350, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 52.88/240.09 thf(c_0_351, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_306])). 52.88/240.09 thf(c_0_352, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_306])). 52.88/240.09 thf(c_0_353, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:((((singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_307, c_0_302])). 52.88/240.09 thf(c_0_354, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_306])). 52.88/240.09 thf(c_0_355, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_306])). 52.88/240.09 thf(c_0_356, 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])). 52.88/240.09 thf(c_0_357, 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])). 52.88/240.09 thf(c_0_358, 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])). 52.88/240.09 thf(c_0_359, 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])). 52.88/240.09 thf(c_0_360, 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])). 52.88/240.09 thf(c_0_361, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 52.88/240.09 thf(c_0_362, plain, ((iffalseProp2)<=>![X4:$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])). 52.88/240.09 thf(c_0_363, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])). 52.88/240.09 thf(c_0_364, plain, ((iftrueProp2)<=>![X4:$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])). 52.88/240.09 thf(c_0_365, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])). 52.88/240.09 thf(c_0_366, plain, ((epred1_0)<=>![X1873:$i]:(?[X1874:$i]:((((![X1875:$i]:(((in @ X1875 @ X1874)=>![X1876:$i]:(((in @ X1876 @ X1875)=>(in @ X1876 @ X1873)))))&![X1877:$i, X1878:$i]:((((in @ X1877 @ X1873)&(in @ X1878 @ X1873))=>(![X1879:$i]:(((in @ X1879 @ X1874)=>((in @ X1877 @ X1879)<=>(in @ X1878 @ X1879))))=>((X1877)=(X1878))))))&![X1880:$i, X1881:$i]:((((in @ X1880 @ X1874)&(in @ X1881 @ X1874))=>(![X1882:$i]:(((in @ X1882 @ X1880)=>(in @ X1882 @ X1881)))|![X1883:$i]:(((in @ X1883 @ X1881)=>(in @ X1883 @ X1880)))))))&![X1884:$i]:(((![X1885:$i]:(((in @ X1885 @ X1884)=>(in @ X1885 @ X1873)))&?[X1886:$i]:((in @ X1886 @ X1884)))=>?[X1887:$i, X1888:$i]:(((((in @ X1887 @ X1874)&(in @ X1888 @ X1884))&~(?[X1889:$i]:(((in @ X1889 @ X1887)&(in @ X1889 @ X1884)))))&![X1890:$i]:(((in @ X1890 @ X1874)=>(![X1891:$i]:(((in @ X1891 @ X1890)=>(in @ X1891 @ X1887)))|(in @ X1888 @ X1890)))))))))))), introduced(definition)). 52.88/240.09 thf(c_0_367, negated_conjecture, ~((![X981:$i, X982:$i]:((![X983:$i]:(((in @ X983 @ X981)<=>(in @ X983 @ X982)))=>((X981)=(X982))))=>(![X1905:$i]:(~(in @ X1905 @ emptyset))=>(![X1902:$i, X1903:$i, X1904:$i]:(((in @ X1904 @ (setadjoin @ X1902 @ X1903))<=>(((X1904)=(X1902))|(in @ X1904 @ X1903))))=>(![X1899:$i, X1900:$i]:(((in @ X1900 @ (powerset @ X1899))<=>![X1901:$i]:(((in @ X1901 @ X1900)=>(in @ X1901 @ X1899)))))=>(![X1896:$i, X1897:$i]:(((in @ X1897 @ (setunion @ X1896))<=>?[X1898:$i]:(((in @ X1897 @ X1898)&(in @ X1898 @ X1896)))))=>((in @ emptyset @ omega)=>(![X1895:$i]:(((in @ X1895 @ omega)=>(in @ (setadjoin @ X1895 @ X1895) @ omega)))=>(![X1892:$i]:((((in @ emptyset @ X1892)&![X1893:$i]:((((in @ X1893 @ omega)&(in @ X1893 @ X1892))=>(in @ (setadjoin @ X1893 @ X1893) @ X1892))))=>![X1894:$i]:(((in @ X1894 @ omega)=>(in @ X1894 @ X1892)))))=>(![X984:$i > $i > $o, X985:$i]:((![X986:$i]:(((in @ X986 @ X985)=>?[X987:$i]:(((X984 @ X986 @ X987)&![X988:$i]:(((X984 @ X986 @ X988)=>((X987)=(X988))))))))=>?[X989:$i]:(![X990:$i]:(((in @ X990 @ X989)<=>?[X991:$i]:(((in @ X991 @ X985)&(X984 @ X991 @ X990))))))))=>(![X992:$i]:((?[X993:$i]:((in @ X993 @ X992))=>?[X994:$i]:(((in @ X994 @ X992)&~(?[X995:$i]:(((in @ X995 @ X994)&(in @ X995 @ X992))))))))=>((epred1_0)=>(![X1870:$i > $o]:((?[X1871:$i]:(((X1870 @ X1871)&![X1872:$i]:(((X1870 @ X1872)=>((X1871)=(X1872))))))=>(X1870 @ (descr @ (^[Z0/* 17 */:$i]:(X1870 @ Z0))))))=>(![X1867:$i, X1868:$i > $o, X1869:$i]:(((in @ X1869 @ X1867)=>((X1868 @ X1869)=>(in @ X1869 @ (dsetconstr @ X1867 @ X1868)))))=>(![X1864:$i, X1865:$i > $o, X1866:$i]:(((in @ X1866 @ (dsetconstr @ X1864 @ X1865))=>(in @ X1866 @ X1864)))=>(![X996:$i, X997:$i > $o, X998:$i]:(((in @ X998 @ (dsetconstr @ X996 @ X997))=>(X997 @ X998)))=>(![X1859:$i > $o]:((?[X1860:$i]:(((X1859 @ X1860)&![X1861:$i]:(((X1859 @ X1861)=>((X1860)=(X1861))))))=>?[X1862:$i]:(((X1859 @ X1862)&![X1863:$i]:(((X1859 @ X1863)=>((X1862)=(X1863))))))))=>(![X1857:$o, X1858:$i]:(((in @ X1858 @ (prop2set @ ((X1857))))=>(X1857)))=>(![X999:$i]:(((in @ X999 @ emptyset)=>![X1000:$o]:((X1000))))=>(![X1856:$i]:(((in @ X1856 @ emptyset)=>~($true)))=>(![X1001:$i]:(~(in @ X1001 @ emptyset))=>(![X1002:$i > $o]:((?[X1003:$i]:(((X1002 @ X1003)&![X1004:$i]:(((X1002 @ X1004)=>((X1003)=(X1004))))))=>?[X1005:$i]:((X1002 @ X1005))))=>(![X1006:$i, X1007:$i]:((![X1008:$i]:(((in @ X1008 @ X1006)=>(in @ X1008 @ X1007)))=>(![X1009:$i]:(((in @ X1009 @ X1007)=>(in @ X1009 @ X1006)))=>((X1006)=(X1007)))))=>(![X1010:$i]:((![X1011:$i]:(~(in @ X1011 @ X1010))=>((X1010)=(emptyset))))=>(![X1012:$i]:((![X1013:$i]:(~(in @ X1013 @ X1012))=>((X1012)=(emptyset))))=>(![X1853:$i, X1854:$i > $o, X1855:$i]:(((in @ X1855 @ X1853)=>((in @ X1855 @ (dsetconstr @ X1853 @ X1854))<=>(X1854 @ X1855))))=>(![X1014:$i]:((((X1014)!=(emptyset))=>?[X1015:$i]:((in @ X1015 @ X1014))))=>(![X1016:$i, X1017:$i > $o, X1018:$i]:(((in @ X1018 @ X1016)=>((X1017 @ X1018)=>((dsetconstr @ X1016 @ X1017)!=(emptyset)))))=>(![X1851:$i]:((?[X1852:$i]:((in @ X1852 @ X1851))=>((X1851)!=(emptyset))))=>(![X1849:$i, X1850:$i]:((in @ X1849 @ (setadjoin @ X1849 @ X1850)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1019:$i, X1020:$i, X1021:$i]:(((in @ X1021 @ X1020)=>(in @ X1021 @ (setadjoin @ X1019 @ X1020))))=>(![X1845:$i, X1846:$i, X1847:$i]:(((in @ X1847 @ (setadjoin @ X1845 @ X1846))=>![X1848:$o]:(((((X1847)=(X1845))=>(X1848))=>(((in @ X1847 @ X1846)=>(X1848))=>(X1848))))))=>(![X1022:$i, X1023:$i, X1024:$i]:(((in @ X1024 @ (setadjoin @ X1022 @ X1023))=>(((X1024)=(X1022))|(in @ X1024 @ X1023))))=>(![X1025:$i]:(((dsetconstr @ X1025 @ (^[Z0/* 1 */:$i]:($true)))=(X1025)))=>(![X1026:$i, X1027:$i]:((![X1028:$i]:(((in @ X1028 @ X1027)=>(in @ X1028 @ X1026)))=>(in @ X1027 @ (powerset @ X1026))))=>(![X1029:$i]:((in @ emptyset @ (powerset @ X1029)))=>(![X1030:$i]:((in @ emptyset @ (powerset @ X1030)))=>(![X1031:$i, X1032:$i, X1033:$i]:(((in @ X1032 @ (powerset @ X1031))=>((in @ X1033 @ X1032)=>(in @ X1033 @ X1031))))=>(![X1034:$i, X1035:$i, X1036:$i]:(((in @ X1035 @ X1036)=>((in @ X1036 @ X1034)=>(in @ X1035 @ (setunion @ X1034)))))=>(![X1841:$i, X1842:$i]:(((in @ X1842 @ (setunion @ X1841))=>![X1843:$o]:((![X1844:$i]:(((in @ X1842 @ X1844)=>((in @ X1844 @ X1841)=>(X1843))))=>(X1843)))))=>(![X1839:$i, X1840:$i]:(((in @ X1840 @ X1839)=>(in @ X1840 @ (powerset @ (setunion @ X1839)))))=>(![X1834:$i > $o]:((?[X1835:$i]:(((X1834 @ X1835)&![X1836:$i]:(((X1834 @ X1836)=>((X1835)=(X1836))))))=>?[X1837:$i]:(![X1838:$i]:(((X1834 @ X1838)<=>((X1838)=(X1837)))))))=>(![X1037:$i]:((((X1037)!=(emptyset))=>?[X1038:$i]:(((in @ X1038 @ X1037)&$true))))=>(![X1832:$i, X1833:$i]:(((in @ X1832 @ (setadjoin @ X1833 @ emptyset))=>((X1832)=(X1833))))=>(![X1039:$i, X1040:$i]:((((X1039)!=(X1040))=>~(in @ X1040 @ (setadjoin @ X1039 @ emptyset))))=>(![X1041:$i, X1042:$i]:((((X1041)=(X1042))=>(in @ X1041 @ (setadjoin @ X1042 @ emptyset))))=>(![X1043:$i, X1044:$i]:(((in @ X1043 @ (setadjoin @ X1044 @ emptyset))=>(in @ X1044 @ (setadjoin @ X1043 @ emptyset))))=>(![X1829:$i, X1830:$i, X1831:$i]:(((in @ X1831 @ (setadjoin @ X1829 @ (setadjoin @ X1830 @ emptyset)))=>(((X1831)=(X1829))|((X1831)=(X1830)))))=>(![X1827:$i, X1828:$i]:((in @ X1827 @ (setadjoin @ X1827 @ (setadjoin @ X1828 @ emptyset))))=>(![X1825:$i, X1826:$i]:((in @ X1826 @ (setadjoin @ X1825 @ (setadjoin @ X1826 @ emptyset))))=>(![X1822:$i, X1823:$i > $o]:((?[X1824:$i]:(((in @ X1824 @ X1822)&(X1823 @ X1824)))=>(((dsetconstr @ X1822 @ X1823)=(emptyset))=>~($true))))=>(![X1045:$i > $o, X1046:$i]:(((in @ X1046 @ emptyset)=>(X1045 @ X1046)))=>(![X1818:$i, X1819:$i > $o]:((~(![X1820:$i]:(((in @ X1820 @ X1818)=>(X1819 @ X1820))))=>?[X1821:$i]:(((in @ X1821 @ X1818)&~((X1819 @ X1821))))))=>(![X1047:$i, X1048:$i > $o]:((![X1049:$i]:(((in @ X1049 @ X1047)=>~((X1048 @ X1049))))=>~(?[X1050:$i]:(((in @ X1050 @ X1047)&(X1048 @ X1050))))))=>(![X1814:$i, X1815:$i > $o]:((~(?[X1816:$i]:(((in @ X1816 @ X1814)&(X1815 @ X1816))))=>![X1817:$i]:(((in @ X1817 @ X1814)=>~((X1815 @ X1817))))))=>(![X1051:$i, X1052:$i > $o]:((?[X1053:$i]:(((in @ X1053 @ X1051)&~((X1052 @ X1053))))=>~(![X1054:$i]:(((in @ X1054 @ X1051)=>(X1052 @ X1054))))))=>(![X1813:$o]:(((X1813)=>(in @ emptyset @ (prop2set @ ((X1813))))))=>(![X1812:$o]:(((X1812)=>(set2prop @ (prop2set @ ((X1812))))))=>(![X1808:$i, X1809:$i > $o]:((~(?[X1810:$i]:(((in @ X1810 @ X1808)&(X1809 @ X1810))))=>![X1811:$i]:(((in @ X1811 @ X1808)=>~((X1809 @ X1811))))))=>(![X1055:$i, X1056:$i > $o]:((~(![X1057:$i]:(((in @ X1057 @ X1055)=>(X1056 @ X1057))))=>?[X1058:$i]:(((in @ X1058 @ X1055)&~((X1056 @ X1058))))))=>(![X1803:$i > $o]:((?[X1804:$i]:(((X1803 @ X1804)&![X1805:$i]:(((X1803 @ X1805)=>((X1804)=(X1805))))))=>?[X1806:$i]:(((X1803 @ X1806)&![X1807:$i]:(((X1803 @ X1807)=>((X1806)=(X1807))))))))=>(![X1797:$i > $o]:((?[X1798:$i]:((X1797 @ X1798))=>(![X1799:$i, X1800:$i]:(((X1797 @ X1799)=>((X1797 @ X1800)=>((X1799)=(X1800)))))=>?[X1801:$i]:(((X1797 @ X1801)&![X1802:$i]:(((X1797 @ X1802)=>((X1801)=(X1802)))))))))=>(![X1792:$i > $o]:((?[X1793:$i]:(![X1794:$i]:(((X1792 @ X1794)<=>((X1794)=(X1793)))))=>?[X1795:$i]:(((X1792 @ X1795)&![X1796:$i]:(((X1792 @ X1796)=>((X1795)=(X1796))))))))=>(![X1788:$i, X1789:$i]:((((X1788)=(X1789))=>![X1790:$i, X1791:$i]:((((X1790)=(X1791))=>((in @ X1790 @ X1788)=>(in @ X1791 @ X1789))))))=>(![X1059:$i, X1060:$i]:((((X1059)=(X1060))=>![X1061:$i, X1062:$i]:((((X1061)=(X1062))=>((in @ X1061 @ X1059)<=>(in @ X1062 @ X1060))))))=>(![X1783:$i > $o]:((?[X1784:$i]:(((X1783 @ X1784)&![X1785:$i]:(((X1783 @ X1785)=>((X1784)=(X1785))))))=>![X1786:$i, X1787:$i]:(((X1783 @ X1786)=>((X1783 @ X1787)=>((X1786)=(X1787)))))))=>(![X1063:$i > $o, X1064:$i > $o]:((![X1065:$i, X1066:$i]:((((X1065)=(X1066))=>((X1063 @ X1065)<=>(X1064 @ X1066))))=>(?[X1067:$i]:(((X1063 @ X1067)&![X1068:$i]:(((X1063 @ X1068)=>((X1067)=(X1068))))))<=>?[X1069:$i]:(((X1064 @ X1069)&![X1070:$i]:(((X1064 @ X1070)=>((X1069)=(X1070)))))))))=>(((emptyset)=(emptyset))=>(![X1779:$i, X1780:$i]:((((X1779)=(X1780))=>![X1781:$i, X1782:$i]:((((X1781)=(X1782))=>((setadjoin @ X1779 @ X1781)=(setadjoin @ X1780 @ X1782))))))=>(![X1071:$i, X1072:$i]:((((X1071)=(X1072))=>((powerset @ X1071)=(powerset @ X1072))))=>(![X1777:$i, X1778:$i]:((((X1777)=(X1778))=>((setunion @ X1777)=(setunion @ X1778))))=>(((omega)=(omega))=>(![X1772:$i > $o]:((?[X1773:$i]:(((X1772 @ X1773)&![X1774:$i]:(((X1772 @ X1774)=>((X1773)=(X1774))))))=>![X1775:$i, X1776:$i]:(((X1772 @ X1775)=>((X1772 @ X1776)=>((X1775)=(X1776)))))))=>(![X1073:$i > $o, X1074:$i > $o]:((![X1075:$i, X1076:$i]:((((X1075)=(X1076))=>((X1073 @ X1075)<=>(X1074 @ X1076))))=>(?[X1077:$i]:(((X1073 @ X1077)&![X1078:$i]:(((X1073 @ X1078)=>((X1077)=(X1078))))))=>(?[X1079:$i]:(((X1074 @ X1079)&![X1080:$i]:(((X1074 @ X1080)=>((X1079)=(X1080))))))=>((descr @ X1073)=(descr @ X1074))))))=>(![X1766:$i, X1767:$i]:((((X1766)=(X1767))=>![X1768:$i > $o, X1769:$i > $o]:((![X1770:$i]:(((in @ X1770 @ X1766)=>![X1771:$i]:(((in @ X1771 @ X1767)=>(((X1770)=(X1771))=>((X1768 @ X1770)<=>(X1769 @ X1771)))))))=>((dsetconstr @ X1766 @ X1768)=(dsetconstr @ X1767 @ X1769))))))=>(![X1763:$i, X1764:$i]:((![X1765:$i]:(((in @ X1765 @ X1763)=>(in @ X1765 @ X1764)))=>(subset @ X1763 @ X1764)))=>(![X1761:$i, X1762:$i]:((((X1761)=(X1762))=>(subset @ X1762 @ X1761)))=>(![X1759:$i, X1760:$i]:((((X1759)=(X1760))=>(subset @ X1759 @ X1760)))=>(![X1756:$i, X1757:$i]:((![X1758:$i]:(((in @ X1758 @ X1756)=>(in @ X1758 @ X1757)))=>(subset @ X1756 @ X1757)))=>(![X1755:$i]:((subset @ emptyset @ X1755))=>(![X1081:$i, X1082:$i, X1083:$i]:(((subset @ X1081 @ X1082)=>((in @ X1083 @ X1081)=>(in @ X1083 @ X1082))))=>(![X1752:$i, X1753:$i, X1754:$i]:(((subset @ X1752 @ X1753)=>(~(in @ X1754 @ X1753)=>~(in @ X1754 @ X1752))))=>(![X1749:$i, X1750:$i, X1751:$i]:(((in @ X1751 @ X1749)=>(~(in @ X1751 @ X1750)=>~(subset @ X1749 @ X1750))))=>(![X1084:$i, X1085:$i]:((~(subset @ X1084 @ X1085)=>((X1084)!=(X1085))))=>(![X1746:$i, X1747:$i, X1748:$i]:(((in @ X1748 @ X1746)=>(~(in @ X1748 @ X1747)=>((X1746)!=(X1747)))))=>(![X1086:$i]:((subset @ X1086 @ X1086))=>(![X1743:$i, X1744:$i, X1745:$i]:(((subset @ X1743 @ X1744)=>((subset @ X1744 @ X1745)=>(subset @ X1743 @ X1745))))=>(![X1741:$i, 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X1417:$i]:(((in @ X1417 @ (powerset @ X1416))=>![X1418:$i]:(((in @ X1418 @ (powerset @ X1416))=>![X1419:$i]:(((in @ X1419 @ (binintersect @ X1417 @ X1418))=>(in @ X1419 @ X1416)))))))=>(![X1420:$i, X1421:$i]:(((in @ X1421 @ (powerset @ X1420))=>![X1422:$i]:(((in @ X1422 @ (powerset @ X1420))=>![X1423:$i]:(((in @ X1423 @ (powerset @ X1420))=>((subset @ X1421 @ X1423)=>(subset @ (binintersect @ X1421 @ X1422) @ X1423))))))))=>(![X1441:$i, X1442:$i]:(((in @ X1442 @ (powerset @ X1441))=>![X1443:$i]:(((in @ X1443 @ (powerset @ X1441))=>![X1444:$i]:(((in @ X1444 @ (powerset @ X1441))=>((subset @ X1443 @ X1444)=>(subset @ (binintersect @ X1442 @ X1443) @ X1444))))))))=>(![X1424:$i, X1425:$i]:(((in @ X1425 @ (powerset @ X1424))=>![X1426:$i]:(((in @ X1426 @ (powerset @ X1424))=>![X1427:$i]:(((in @ X1427 @ (powerset @ X1424))=>((subset @ X1425 @ X1426)=>((subset @ X1425 @ X1427)=>(subset @ X1425 @ (binintersect @ X1426 @ X1427))))))))))=>(![X1428:$i, X1429:$i]:(((in @ X1429 @ (powerset @ 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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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_308]), foundationAx]), wellorderingAx]), c_0_309]), c_0_310]), c_0_311]), c_0_312]), c_0_313]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_314]), setext]), emptyI]), noeltsimpempty]), c_0_315]), c_0_316]), c_0_317]), c_0_318]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_319]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_320]), c_0_321]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_322]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_323]), c_0_324]), c_0_325]), inCongP]), in__Cong]), c_0_326]), c_0_327]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_328]), c_0_329]), c_0_330]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_331]), c_0_332]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg]), setminusLsub]), setminusSubset1]), symdiffE]), symdiffI1]), symdiffI2]), symdiffIneg1]), symdiffIneg2]), secondinupair]), setukpairIL]), setukpairIR]), kpairiskpair]), kpairp]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1]), cartprodmempair]), setunionE2]), setunionsingleton1]), setunionsingleton2]), setunionsingleton]), c_0_333]), c_0_334]), c_0_335]), c_0_336]), singletonsuniq]), setukpairinjL1]), c_0_337]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_338]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_339]), c_0_340]), c_0_341]), c_0_342]), c_0_343]), c_0_344]), c_0_345]), c_0_346]), c_0_347]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_348]), c_0_349]), c_0_350]), c_0_351]), c_0_352]), c_0_353]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_354]), c_0_355]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_356]), c_0_357]), c_0_358]), c_0_359]), c_0_360]), c_0_361]), c_0_362]), c_0_363]), c_0_364]), c_0_365]), 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])])]), c_0_366])). 52.88/240.09 thf(c_0_368, negated_conjecture, ![X1906:$i, X1907:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1919:$i, X1920:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1928:$i, X1929:$i > $i > $o, X1930:$i, X1932:$i, X1935:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1942:$i, X1943:$i > $o, X1944:$i, X1946:$i, X1947:$i > $o, X1948:$i, X1949:$i, X1950:$i > $o, X1951:$i, X1952:$i, X1953:$i > $o, X1954:$i, X1955:$i > $o, X1956:$i, X1959:$i, X1960:$o, X1961:$i, X1962:$i, X1963:$o, X1964:$i, X1965:$i, X1966:$i > $o, X1967:$i, X1970:$i, X1971:$i, X1974:$i, X1976:$i, X1978:$i, X1979:$i > $o, X1980:$i, X1981:$i, X1983:$i, X1984:$i > $o, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i, X1995:$i, X1996:$o, X1997:$i, X1998:$i, X1999:$i, X2000:$i, X2001:$i, X2002:$i, X2004:$i, X2005:$i, X2006:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$o, X2016:$i, X2017:$i, X2018:$i > $o, X2019:$i, X2022:$i, X2023:$i, X2024:$i, X2026:$i, X2027:$i, X2028:$i, X2029:$i, X2030:$i, X2031:$i, X2032:$i, X2033:$i, X2034:$i, X2035:$i, X2036:$i, X2037:$i, X2038:$i, X2039:$i, X2040:$i, X2041:$i, X2042:$i > $o, X2043:$i, X2044:$i > $o, X2045:$i, X2046:$i, X2047:$i > $o, X2048:$i, X2050:$i, X2051:$i > $o, X2053:$i, X2054:$i, X2055:$i > $o, X2057:$i, X2058:$i, X2059:$i > $o, X2060:$i, X2062:$o, X2063:$o, X2064:$i, X2065:$i > $o, X2067:$i, X2068:$i, X2069:$i > $o, X2070:$i, X2072:$i > $o, X2073:$i, X2076:$i, X2077:$i > $o, X2078:$i, X2082:$i, X2083:$i > $o, X2084:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2091:$i, X2092:$i, X2093:$i, X2094:$i, X2095:$i, X2096:$i > $o, X2097:$i, X2099:$i, X2100:$i, X2101:$i > $o, X2102:$i > $o, X2105:$i, X2108:$i, X2109:$i, X2112:$i, X2113:$i, X2114:$i, X2115:$i, X2116:$i, X2117:$i, X2118:$i, X2119:$i, X2120:$i, X2121:$i > $o, X2122:$i, X2124:$i, X2125:$i, X2126:$i > $o, X2127:$i > $o, X2130:$i, X2132:$i, X2134:$i, X2135:$i, X2136:$i > $o, X2137:$i > $o, X2140:$i, X2141:$i, X2143:$i, X2144:$i, X2145:$i, X2146:$i, X2147:$i, X2148:$i, X2150:$i, X2151:$i, X2152:$i, X2153:$i, X2154:$i, X2155:$i, X2156:$i, X2157:$i, X2158:$i, X2159:$i, X2160:$i, X2161:$i, X2162:$i, X2163:$i, X2164:$i, X2165:$i, X2166:$i, X2167:$i, X2168:$i, X2169:$i, X2170:$i, X2171:$i, X2172:$i, X2173:$i, X2174:$i, X2175:$i, X2176:$i, X2177:$i, X2178:$i, X2179:$i, X2180:$i, X2181:$i, X2182:$i, X2183:$i, X2184:$i, X2185:$i, X2186:$i, X2187:$i > $o, X2188:$i, X2189:$i > $o, X2190:$i, X2191:$i, X2192:$i, X2193:$i, X2194:$i, X2195:$i, X2196:$i, X2197:$i, X2198:$i, X2199:$i, X2200:$i, X2201:$o, X2202:$i, X2203:$i, X2204:$i, X2205:$i, X2206:$i, X2207:$i, X2208:$i, X2209:$i, X2210:$i, X2211:$i, X2212:$i, X2213:$i, X2214:$i, X2215:$i, X2216:$i, X2217:$i, X2218:$i, X2219:$i, X2220:$i, X2221:$i, X2222:$i, X2223:$i, X2224:$i, X2225:$i, X2226:$i, X2227:$i, X2228:$i, X2230:$i, X2231:$i, X2232:$i, X2233:$i, X2234:$i, X2235:$i, X2236:$i, X2237:$i, X2238:$i, X2239:$i, X2240:$i, X2241:$i, X2242:$i, X2243:$i, X2244:$i, X2245:$i, X2246:$i, X2247:$i, X2248:$i, X2249:$i, X2250:$i, X2251:$i, X2252:$i, X2253:$i, X2254:$i, X2255:$i, X2256:$i, X2257:$i, X2258:$i, X2259:$i, X2260:$i, X2261:$i, X2262:$i, X2263:$i, X2264:$i, X2265:$i, X2266:$i, X2267:$i, X2268:$i, X2269:$o, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2279:$i, X2280:$i, X2281:$i, X2282:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2288:$i, X2289:$i, X2290:$i, X2291:$i, X2292:$i, X2293:$i, X2294:$i, X2295:$i, X2296:$i, X2297:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2302:$i, X2303:$i, X2304:$i, X2305:$i, X2306:$i, X2307:$i, X2308:$i, X2309:$i, X2310:$i, X2311:$i, X2312:$i, X2313:$i, X2314:$i, X2315:$i, X2316:$i, X2317:$i, X2318:$i, X2319:$i, X2320:$i, X2321:$i, X2322:$i, X2323:$i, X2324:$i, X2325:$i, X2326:$i, X2327:$i, X2328:$i, X2331:$i, X2332:$i, X2333:$i, X2334:$i, X2335:$i, X2337:$i, X2338:$i, X2339:$i, X2340:$i, X2341:$i > $o, X2344:$i, X2345:$i, X2346:$i > $o, X2348:$i, X2349:$i > $o, X2350:$i, X2352:$i, X2353:$i > $o, X2356:$i, X2357:$i, X2358:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i, X2364:$i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2372:$i, X2373:$i, X2374:$i, X2375:$i, X2376:$i, X2377:$i, X2378:$i, X2379:$i, X2380:$i, X2381:$i, X2382:$i, X2383:$i, X2384:$i, X2385:$i, X2386:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i, X2404:$i, X2405:$i, X2406:$i, X2407:$i, X2408:$i, X2409:$i, X2410:$i, X2411:$i, X2412:$i, X2413:$i, X2414:$i, X2415:$i, X2416:$i, X2417:$i, X2418:$i, X2419:$i, X2420:$i, X2421:$i, X2422:$i, X2423:$i, X2424:$i, X2425:$i, X2426:$i, X2427:$i, X2428:$i > $i > $o, X2429:$i, X2430:$i, X2431:$i, X2432:$i, X2433:$i > $i > $o, X2434:$i, X2435:$i, X2436:$i > $i > $o, X2437:$i, X2438:$i, X2439:$i > $i > $o, X2440:$i, X2441:$i, X2442:$i, X2443:$i, X2444:$i > $i > $o, X2445:$i, X2446:$i, X2447:$i, X2448:$i, X2449:$i > $i > $o, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i > $i > $o, X2455:$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 > $i, X2483:$i, X2484:$i, X2485:$i > $i, X2487:$i, X2488:$i, X2489:$i > $i, X2491:$i, X2492:$i, X2493:$i, X2494:$i > $o, X2497:$i, X2498:$i, X2499:$i, X2500:$i, X2501:$i > $o, X2504:$i, X2505:$i, X2506:$i > $o, X2507:$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, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2548:$i, X2549:$i, X2550:$i, X2551:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2558:$i, X2559:$i, X2560:$i, X2561:$i, X2562:$i, X2563:$i, X2564:$i, X2565:$i, X2566:$i, X2567:$i, X2568:$i > $i, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i > $i, X2578:$i, X2579:$i, X2580:$i > $i, X2582:$i, X2583:$i, X2584:$i, X2585:$i, X2586:$i, X2587:$o, X2588:$i, X2589:$i, X2590:$i, X2591:$o, X2592:$i, X2593:$i, X2594:$i, X2595:$o, X2596:$i, X2597:$i, X2598:$i, X2599:$o, X2600:$i, X2601:$i, X2602:$i, X2603:$o, X2604:$i, X2605:$i, X2606:$i, X2607:$o, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2613:$o, X2614:$i, X2615:$i, X2616:$i, X2617:$o, X2618:$i, X2619:$i, X2620:$i, X2621:$o, X2622:$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:$i, X2642:$i, X2643:$i, X2644:$i, X2646:$i, X2647:$i, X2648:$i, X2650:$i, X2651:$i, X2652:$i, X2653:$i, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2658:$i, X2659:$i, X2660:$i, X2661:$i, X2662:$i, X2663:$i, X2664:$i, X2665:$i, X2666:$i, X2667:$i, X2668:$i, X2669:$i, X2670:$i, X2671:$i, X2672:$i, 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:$i, X2698:$i, X2699:$i, X2700:$i, X2701:$i, X2702:$i, X2703:$i, X2704:$i, X2705:$i, X2706:$i, X2707:$i, X2708:$i, X2709:$i, X2710:$i, X2711:$i, X2712:$i, X2713:$i, X2714:$i, X2715:$i, X2716:$i, X2717:$i, X2718:$i, X2719:$i, X2720:$i, X2721:$i, X2722:$i, X2723:$i, X2724:$i, X2725:$i, X2726:$i, X2727:$i, X2728:$i, X2729:$i, X2730:$i, X2731:$i, X2732:$i, X2733:$i, X2734:$i, X2735:$i, X2736:$i, X2737:$i, X2738:$i, X2739:$i, X2740:$i, X2741:$i, X2742:$i, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$o, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2760:$i, X2761:$i, X2762:$i, X2763:$i, X2764:$i, X2765:$i, X2766:$i, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i, X2772:$i, X2773:$i, X2774:$i, X2775:$i, X2776:$i, X2777:$i, X2778:$i, X2779:$i, X2780:$i, X2781:$i, X2782:$i, X2783:$i, X2784:$i, X2785:$i, X2786:$i, X2787:$i, X2788:$i, X2789:$i, X2790:$i, X2791:$i, X2792:$i, X2793:$i, X2794:$i, X2795:$i, X2796:$i, X2797:$i, X2798:$i, X2799:$i, X2800:$i, X2801:$i, X2802:$i, X2803:$i, X2804:$i, X2805:$i, X2806:$i, X2807:$i, X2808:$i, X2809:$i, X2810:$i, X2811:$i, X2812:$i, X2813:$i, X2814:$i, X2815:$i, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i]:((((~(in @ (esk1_2 @ X1906 @ X1907) @ X1906)|~(in @ (esk1_2 @ X1906 @ X1907) @ X1907)|((X1906)=(X1907)))&((in @ (esk1_2 @ X1906 @ X1907) @ X1906)|(in @ (esk1_2 @ X1906 @ X1907) @ X1907)|((X1906)=(X1907))))&(~(in @ X1909 @ emptyset)&(((~(in @ X1912 @ (setadjoin @ X1910 @ X1911))|(((X1912)=(X1910))|(in @ X1912 @ X1911)))&((((X1912)!=(X1910))|(in @ X1912 @ (setadjoin @ X1910 @ X1911)))&(~(in @ X1912 @ X1911)|(in @ X1912 @ (setadjoin @ X1910 @ X1911)))))&(((~(in @ X1914 @ (powerset @ X1913))|(~(in @ X1915 @ X1914)|(in @ X1915 @ X1913)))&(((in @ (esk2_2 @ X1916 @ X1917) @ X1917)|(in @ X1917 @ (powerset @ X1916)))&(~(in @ (esk2_2 @ X1916 @ X1917) @ X1916)|(in @ X1917 @ (powerset @ X1916)))))&(((((in @ X1920 @ (esk3_2 @ X1919 @ X1920))|~(in @ X1920 @ (setunion @ X1919)))&((in @ (esk3_2 @ X1919 @ X1920) @ X1919)|~(in @ X1920 @ (setunion @ X1919))))&(~(in @ X1923 @ X1924)|~(in @ X1924 @ X1922)|(in @ X1923 @ (setunion @ X1922))))&((in @ emptyset @ omega)&((~(in @ X1925 @ omega)|(in @ (setadjoin @ X1925 @ X1925) @ omega))&(((((in @ (esk4_1 @ X1926) @ omega)|~(in @ emptyset @ X1926)|(~(in @ X1928 @ omega)|(in @ X1928 @ X1926)))&((in @ (esk4_1 @ X1926) @ X1926)|~(in @ emptyset @ X1926)|(~(in @ X1928 @ omega)|(in @ X1928 @ X1926))))&(~(in @ (setadjoin @ (esk4_1 @ X1926) @ (esk4_1 @ X1926)) @ X1926)|~(in @ emptyset @ X1926)|(~(in @ X1928 @ omega)|(in @ X1928 @ X1926))))&((((((in @ (esk8_3 @ X1929 @ X1930 @ X1935) @ X1930)|~(in @ X1935 @ (esk7_2 @ X1929 @ X1930))|(in @ (esk5_2 @ X1929 @ X1930) @ X1930))&((X1929 @ (esk8_3 @ X1929 @ X1930 @ X1935) @ X1935)|~(in @ X1935 @ (esk7_2 @ X1929 @ X1930))|(in @ (esk5_2 @ X1929 @ X1930) @ X1930)))&(~(in @ X1938 @ X1930)|~(X1929 @ X1938 @ X1937)|(in @ X1937 @ (esk7_2 @ X1929 @ X1930))|(in @ (esk5_2 @ X1929 @ X1930) @ X1930)))&(((((in @ (esk8_3 @ X1929 @ X1930 @ X1935) @ X1930)|~(in @ X1935 @ (esk7_2 @ X1929 @ X1930))|((X1929 @ (esk5_2 @ X1929 @ X1930) @ (esk6_3 @ X1929 @ X1930 @ X1932))|~(X1929 @ (esk5_2 @ X1929 @ X1930) @ X1932)))&((X1929 @ (esk8_3 @ X1929 @ X1930 @ X1935) @ X1935)|~(in @ X1935 @ (esk7_2 @ X1929 @ X1930))|((X1929 @ (esk5_2 @ X1929 @ X1930) @ (esk6_3 @ X1929 @ X1930 @ X1932))|~(X1929 @ (esk5_2 @ X1929 @ X1930) @ X1932))))&(~(in @ X1938 @ X1930)|~(X1929 @ X1938 @ X1937)|(in @ X1937 @ (esk7_2 @ X1929 @ X1930))|((X1929 @ (esk5_2 @ X1929 @ X1930) @ (esk6_3 @ X1929 @ X1930 @ X1932))|~(X1929 @ (esk5_2 @ X1929 @ X1930) @ X1932))))&((((in @ (esk8_3 @ X1929 @ X1930 @ X1935) @ X1930)|~(in @ X1935 @ (esk7_2 @ X1929 @ X1930))|(((X1932)!=(esk6_3 @ X1929 @ X1930 @ X1932))|~(X1929 @ (esk5_2 @ X1929 @ X1930) @ X1932)))&((X1929 @ (esk8_3 @ X1929 @ X1930 @ X1935) @ X1935)|~(in @ X1935 @ (esk7_2 @ X1929 @ X1930))|(((X1932)!=(esk6_3 @ X1929 @ X1930 @ X1932))|~(X1929 @ (esk5_2 @ X1929 @ X1930) @ X1932))))&(~(in @ X1938 @ X1930)|~(X1929 @ X1938 @ 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@ X2638 @ X2639) @ X2639)|~(in @ X2639 @ (powerset @ X2637))|~(in @ X2638 @ (powerset @ X2637)))&(~(in @ (esk84_3 @ X2637 @ X2638 @ X2639) @ X2638)|((X2638)=(X2639))|~(in @ (esk83_3 @ X2637 @ X2638 @ X2639) @ X2639)|~(in @ X2639 @ (powerset @ X2637))|~(in @ X2638 @ (powerset @ X2637)))))))&((((in @ (esk85_3 @ X2642 @ X2643 @ X2644) @ X2642)|(subset @ X2643 @ X2644)|~(in @ X2644 @ (powerset @ X2642))|~(in @ X2643 @ (powerset @ X2642)))&(((in @ (esk85_3 @ X2642 @ X2643 @ X2644) @ X2643)|(subset @ X2643 @ X2644)|~(in @ X2644 @ (powerset @ X2642))|~(in @ X2643 @ (powerset @ X2642)))&(~(in @ (esk85_3 @ X2642 @ X2643 @ X2644) @ X2644)|(subset @ X2643 @ X2644)|~(in @ X2644 @ (powerset @ X2642))|~(in @ X2643 @ (powerset @ X2642)))))&((((in @ (esk86_3 @ X2646 @ X2647 @ X2648) @ X2646)|(in @ X2647 @ (powerset @ X2648))|~(in @ X2648 @ (powerset @ X2646))|~(in @ X2647 @ (powerset @ X2646)))&(((in @ (esk86_3 @ X2646 @ X2647 @ X2648) @ X2647)|(in @ X2647 @ (powerset @ X2648))|~(in @ X2648 @ (powerset @ X2646))|~(in @ X2647 @ (powerset @ X2646)))&(~(in @ (esk86_3 @ X2646 @ X2647 @ X2648) @ X2648)|(in @ X2647 @ (powerset @ X2648))|~(in @ X2648 @ (powerset @ X2646))|~(in @ X2647 @ (powerset @ X2646)))))&((~(in @ X2651 @ (powerset @ X2650))|(~(in @ X2652 @ (powerset @ X2650))|(~(in @ X2653 @ X2650)|(~(in @ X2651 @ (powerset @ X2652))|(~(in @ X2653 @ X2651)|(in @ X2653 @ X2652))))))&((~(in @ X2655 @ (powerset @ X2654))|(~(in @ X2656 @ X2654)|(~(in @ X2656 @ X2655)|~(in @ X2656 @ (setminus @ X2654 @ X2655)))))&((~(in @ X2658 @ (powerset @ X2657))|(~(in @ X2659 @ X2657)|((in @ X2659 @ (setminus @ X2657 @ X2658))|(in @ X2659 @ X2658))))&((~(in @ X2661 @ (powerset @ X2660))|(~(in @ X2662 @ (powerset @ X2660))|(~(in @ X2663 @ X2660)|((in @ X2663 @ X2661)|~(in @ X2663 @ (binintersect @ X2661 @ X2662))))))&((~(in @ X2665 @ (powerset @ X2664))|(~(in @ X2666 @ (powerset @ X2664))|(~(in @ X2667 @ X2664)|((in @ X2667 @ X2666)|~(in @ X2667 @ (binintersect @ X2665 @ X2666))))))&((~(in @ X2669 @ (powerset @ X2668))|(~(in @ X2670 @ (powerset @ X2668))|(~(in @ X2671 @ X2668)|(~(subset @ X2669 @ (setminus @ X2668 @ X2670))|(~(in @ X2671 @ X2670)|~(in @ X2671 @ X2669))))))&((~(in @ X2673 @ (powerset @ X2672))|(~(in @ X2674 @ (powerset @ X2672))|(~(in @ X2675 @ X2672)|(~(subset @ X2673 @ X2674)|((in @ X2675 @ X2674)|~(in @ X2675 @ X2673))))))&((~(in @ X2677 @ (powerset @ X2676))|(~(in @ X2678 @ (powerset @ X2676))|(~(subset @ X2677 @ X2678)|(subset @ (setminus @ X2676 @ X2678) @ (setminus @ X2676 @ X2677)))))&((~(in @ X2680 @ (powerset @ X2679))|(~(in @ X2681 @ (powerset @ X2679))|(~(subset @ (setminus @ X2679 @ X2681) @ (setminus @ X2679 @ X2680))|(subset @ X2680 @ X2681))))&((~(in @ X2683 @ (powerset @ X2682))|(~(in @ X2684 @ X2682)|(~(in @ X2684 @ X2683)|(in @ X2684 @ (setminus @ X2682 @ (setminus @ X2682 @ X2683))))))&((~(in @ X2686 @ (powerset @ X2685))|(~(in @ X2687 @ X2685)|(~(in @ X2687 @ (setminus @ X2685 @ (setminus @ X2685 @ X2686)))|(in @ X2687 @ X2686))))&((~(in @ X2689 @ (powerset @ X2688))|(subset @ X2689 @ (setminus @ X2688 @ (setminus @ X2688 @ X2689))))&((~(in @ X2691 @ (powerset @ X2690))|(subset @ (setminus @ X2690 @ (setminus @ X2690 @ X2691)) @ X2691))&((~(in @ X2693 @ (powerset @ X2692))|((X2693)=(setminus @ X2692 @ (setminus @ X2692 @ X2693))))&((~(in @ X2695 @ (powerset @ X2694))|(~(in @ X2696 @ (powerset @ X2694))|(~(in @ X2697 @ X2694)|(~(in @ X2697 @ (setminus @ X2694 @ X2695))|~(in @ X2697 @ (binintersect @ X2695 @ X2696))))))&((~(in @ X2699 @ (powerset @ X2698))|(~(in @ X2700 @ (powerset @ X2698))|(~(in @ X2701 @ X2698)|(~(in @ X2701 @ (setminus @ X2698 @ X2699))|(in @ X2701 @ (setminus @ X2698 @ (binintersect @ X2699 @ X2700)))))))&((~(in @ X2703 @ (powerset @ X2702))|(~(in @ X2704 @ (powerset @ X2702))|(subset @ (setminus @ X2702 @ X2703) @ (setminus @ X2702 @ (binintersect @ X2703 @ X2704)))))&((~(in @ X2706 @ (powerset @ X2705))|(~(in @ X2707 @ (powerset @ X2705))|(in @ (setminus @ X2705 @ X2706) @ (powerset @ (setminus @ X2705 @ (binintersect @ X2706 @ X2707))))))&((~(in @ X2709 @ (powerset @ X2708))|(~(in @ X2710 @ (powerset @ X2708))|(~(subset @ X2709 @ (setminus @ X2708 @ X2710))|(~(in @ X2711 @ X2708)|(~(in @ X2711 @ X2710)|(in @ X2711 @ (setminus @ X2708 @ X2709)))))))&((~(in @ X2713 @ (powerset @ X2712))|(~(in @ X2714 @ (powerset @ X2712))|(~(subset @ X2713 @ (setminus @ X2712 @ X2714))|(subset @ X2714 @ (setminus @ X2712 @ X2713)))))&((~(in @ X2716 @ (powerset @ X2715))|(~(in @ X2717 @ (powerset @ X2715))|(~(in @ X2718 @ X2715)|((in @ X2718 @ (binunion @ X2716 @ X2717))|~(in @ X2718 @ X2716)))))&((~(in @ X2720 @ (powerset @ X2719))|(~(in @ X2721 @ (powerset @ X2719))|(~(in @ X2722 @ X2719)|((in @ X2722 @ (binunion @ X2720 @ X2721))|~(in @ X2722 @ X2721)))))&((~(in @ X2724 @ (powerset @ X2723))|(~(in @ X2725 @ (powerset @ X2723))|(~(in @ X2726 @ (powerset @ X2723))|(~(in @ X2727 @ X2723)|(~(in @ X2727 @ (binintersect @ X2724 @ X2725))|(in @ X2727 @ (binunion @ X2724 @ X2726)))))))&((~(in @ X2729 @ (powerset @ X2728))|(~(in @ X2730 @ (powerset @ X2728))|(~(in @ X2731 @ (powerset @ X2728))|(~(in @ X2732 @ X2728)|(~(in @ X2732 @ (binintersect @ X2729 @ X2730))|(in @ X2732 @ (binunion @ X2730 @ X2731)))))))&((~(in @ X2734 @ (powerset @ X2733))|(~(in @ X2735 @ (powerset @ X2733))|(~(in @ X2736 @ (powerset @ X2733))|(~(in @ X2737 @ X2733)|(~(in @ X2737 @ (binintersect @ X2734 @ X2735))|(in @ X2737 @ (binintersect @ (binunion @ X2734 @ X2736) @ (binunion @ X2735 @ X2736))))))))&((~(in @ X2739 @ (powerset @ X2738))|(~(in @ X2740 @ (powerset @ X2738))|(~(in @ X2741 @ (powerset @ X2738))|(in @ (binintersect @ X2739 @ X2740) @ (powerset @ (binintersect @ (binunion @ X2739 @ X2741) @ (binunion @ X2740 @ X2741)))))))&((~(in @ X2743 @ (powerset @ X2742))|(~(in @ X2744 @ (powerset @ X2742))|(~(in @ X2745 @ X2742)|(~(in @ X2745 @ (setminus @ X2742 @ (binunion @ X2743 @ X2744)))|~(in @ X2745 @ X2743)))))&((~(in @ X2747 @ (powerset @ X2746))|(~(in @ X2748 @ (powerset @ X2746))|(~(in @ X2749 @ X2746)|(~(in @ X2749 @ (setminus @ X2746 @ (binunion @ X2747 @ X2748)))|(in @ X2749 @ (setminus @ X2746 @ X2747))))))&(((((in @ X2754 @ X2752)|(X2753)|(in @ X2754 @ X2751)|~(in @ X2754 @ (binunion @ X2751 @ X2752))|~(in @ X2754 @ X2750)|~(in @ X2752 @ (powerset @ X2750))|~(in @ X2751 @ (powerset @ X2750)))&(~(X2753)|(X2753)|(in @ X2754 @ X2751)|~(in @ X2754 @ (binunion @ X2751 @ X2752))|~(in @ X2754 @ X2750)|~(in @ X2752 @ (powerset @ X2750))|~(in @ X2751 @ (powerset @ X2750))))&(((in @ X2754 @ X2752)|(X2753)|~(X2753)|~(in @ X2754 @ (binunion @ X2751 @ X2752))|~(in @ X2754 @ X2750)|~(in @ X2752 @ (powerset @ X2750))|~(in @ X2751 @ (powerset @ X2750)))&(~(X2753)|(X2753)|~(X2753)|~(in @ X2754 @ (binunion @ X2751 @ X2752))|~(in @ X2754 @ X2750)|~(in @ X2752 @ (powerset @ X2750))|~(in @ X2751 @ (powerset @ X2750)))))&((~(in @ X2756 @ (powerset @ X2755))|(~(in @ X2757 @ (powerset @ X2755))|(~(in @ X2758 @ X2755)|((in @ X2758 @ X2756)|((in @ X2758 @ X2757)|~(in @ X2758 @ (binunion @ X2756 @ X2757)))))))&((~(in @ X2760 @ (powerset @ X2759))|(~(in @ X2761 @ (powerset @ X2759))|(~(in @ X2762 @ X2759)|(~(in @ X2762 @ (setminus @ X2759 @ (binunion @ X2760 @ X2761)))|(in @ X2762 @ (setminus @ X2759 @ X2760))))))&((~(in @ X2764 @ (powerset @ X2763))|(~(in @ X2765 @ (powerset @ X2763))|(in @ (setminus @ X2763 @ (binunion @ X2764 @ X2765)) @ (powerset @ (setminus @ X2763 @ X2764)))))&((~(in @ X2767 @ (powerset @ X2766))|(~(in @ X2768 @ (powerset @ X2766))|(~(in @ X2769 @ X2766)|(~(in @ X2769 @ (setminus @ X2766 @ (binunion @ X2767 @ X2768)))|(in @ X2769 @ (setminus @ X2766 @ X2768))))))&((~(in @ X2771 @ (powerset @ X2770))|(~(in @ X2772 @ (powerset @ X2770))|(~(in @ X2773 @ X2770)|(~(in @ X2773 @ (setminus @ X2770 @ (binintersect @ X2771 @ X2772)))|(in @ X2773 @ (binunion @ (setminus @ X2770 @ X2771) @ (setminus @ X2770 @ X2772)))))))&((~(in @ X2775 @ (powerset @ X2774))|(~(in @ X2776 @ (powerset @ X2774))|(~(in @ X2777 @ X2774)|(~(in @ X2777 @ (binunion @ (setminus @ X2774 @ X2775) @ (setminus @ X2774 @ X2776)))|(in @ X2777 @ (setminus @ X2774 @ (binintersect @ X2775 @ X2776)))))))&((~(in @ X2779 @ (powerset @ X2778))|(~(in @ X2780 @ (powerset @ X2778))|((setminus @ X2778 @ (binintersect @ X2779 @ X2780))=(binunion @ (setminus @ X2778 @ X2779) @ (setminus @ X2778 @ X2780)))))&((~(in @ X2782 @ (powerset @ X2781))|(~(in @ X2783 @ (powerset @ X2781))|(~(in @ X2784 @ X2781)|(~(in @ X2784 @ (setminus @ X2781 @ (binunion @ X2782 @ X2783)))|(in @ X2784 @ (binintersect @ (setminus @ X2781 @ X2782) @ (setminus @ X2781 @ X2783)))))))&((~(in @ X2786 @ (powerset @ X2785))|(~(in @ X2787 @ (powerset @ X2785))|(~(in @ X2788 @ X2785)|(~(in @ X2788 @ (setminus @ X2785 @ X2786))|(~(in @ X2788 @ (setminus @ X2785 @ X2787))|(in @ X2788 @ (setminus @ X2785 @ (binunion @ X2786 @ X2787))))))))&((~(in @ X2790 @ (powerset @ X2789))|(~(in @ X2791 @ (powerset @ X2789))|(~(in @ X2792 @ X2789)|(~(in @ X2792 @ (binintersect @ (setminus @ X2789 @ X2790) @ (setminus @ X2789 @ X2791)))|(in @ X2792 @ (setminus @ X2789 @ (binunion @ X2790 @ X2791)))))))&((~(in @ X2794 @ (powerset @ X2793))|(~(in @ X2795 @ (powerset @ X2793))|((setminus @ X2793 @ (binunion @ X2794 @ X2795))=(binintersect @ (setminus @ X2793 @ X2794) @ (setminus @ X2793 @ X2795)))))&((~(in @ X2797 @ (powerset @ X2796))|(~(in @ X2798 @ (powerset @ X2796))|(~(in @ X2799 @ (binintersect @ X2797 @ X2798))|(in @ X2799 @ X2796))))&((~(in @ X2801 @ (powerset @ X2800))|(~(in @ X2802 @ (powerset @ X2800))|(~(in @ X2803 @ (powerset @ X2800))|(~(subset @ X2801 @ X2803)|(subset @ (binintersect @ X2801 @ X2802) @ X2803)))))&((~(in @ X2805 @ (powerset @ X2804))|(~(in @ X2806 @ (powerset @ X2804))|(~(in @ X2807 @ (powerset @ X2804))|(~(subset @ X2806 @ X2807)|(subset @ (binintersect @ X2805 @ X2806) @ X2807)))))&((~(in @ X2809 @ (powerset @ X2808))|(~(in @ X2810 @ (powerset @ X2808))|(~(in @ X2811 @ (powerset @ X2808))|(~(subset @ X2809 @ X2810)|(~(subset @ X2809 @ X2811)|(subset @ X2809 @ (binintersect @ X2810 @ X2811)))))))&((~(in @ X2813 @ (powerset @ X2812))|(~(in @ X2814 @ (powerset @ X2812))|(~(in @ X2815 @ (powerset @ X2812))|(~(in @ X2816 @ (powerset @ X2812))|(~(subset @ X2813 @ X2815)|(~(subset @ X2814 @ X2816)|(subset @ (binintersect @ X2813 @ X2814) @ (binintersect @ X2815 @ X2816))))))))&((~(in @ X2818 @ (powerset @ X2817))|(~(in @ X2819 @ (powerset @ X2817))|(in @ (setminus @ X2817 @ X2818) @ (powerset @ (setminus @ X2817 @ (binintersect @ X2818 @ X2819))))))&((~(in @ X2821 @ (powerset @ X2820))|(~(in @ X2822 @ (powerset @ X2820))|(~(in @ X2823 @ (powerset @ X2820))|(~(in @ X2824 @ (powerset @ X2820))|((setminus @ X2820 @ (binintersect @ (binunion @ X2821 @ X2822) @ (binunion @ X2823 @ X2824)))=(binunion @ (binintersect @ (setminus @ X2820 @ X2821) @ (setminus @ X2820 @ X2822)) @ (binintersect @ (setminus @ X2820 @ X2823) @ (setminus @ X2820 @ X2824))))))))&((in @ esk88_0 @ (powerset @ esk87_0))&((in @ esk89_0 @ (powerset @ esk87_0))&((in @ esk90_0 @ (powerset @ esk87_0))&~(in @ (binintersect @ esk88_0 @ esk89_0) @ (powerset @ (binintersect @ (binunion @ esk88_0 @ esk90_0) @ (binunion @ esk89_0 @ esk90_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_367])])])])])])])). 52.88/240.09 thf(c_0_369, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (powerset @ X3))|~((subset @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_368])). 52.88/240.09 thf(c_0_370, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ X2 @ (binintersect @ X3 @ X4))|~((subset @ X2 @ X3))|~((subset @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_368])). 52.88/240.09 thf(c_0_371, negated_conjecture, ~((in @ (binintersect @ esk88_0 @ esk89_0) @ (powerset @ (binintersect @ (binunion @ esk88_0 @ esk90_0) @ (binunion @ esk89_0 @ esk90_0))))), inference(split_conjunct,[status(thm)],[c_0_368])). 52.88/240.09 thf(c_0_372, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (powerset @ (binintersect @ X3 @ X4)))|~((subset @ X2 @ X4))|~((subset @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_369, c_0_370])). 52.88/240.09 thf(c_0_373, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ X2 @ X4)|~((subset @ X2 @ X3))|~((subset @ X3 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_368])). 52.88/240.09 thf(c_0_374, negated_conjecture, ![X2:$i, X3:$i]:((subset @ X2 @ (binunion @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_368])). 52.88/240.09 thf(c_0_375, negated_conjecture, (~((subset @ (binintersect @ esk88_0 @ esk89_0) @ (binunion @ esk89_0 @ esk90_0)))|~((subset @ (binintersect @ esk88_0 @ esk89_0) @ (binunion @ esk88_0 @ esk90_0)))), inference(spm,[status(thm)],[c_0_371, c_0_372])). 52.88/240.09 thf(c_0_376, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((subset @ X2 @ (binunion @ X3 @ X4))|~((subset @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_373, c_0_374])). 52.88/240.09 thf(c_0_377, negated_conjecture, ![X2:$i, X3:$i]:((subset @ (binintersect @ X2 @ X3) @ X3)), inference(split_conjunct,[status(thm)],[c_0_368])). 52.88/240.09 thf(c_0_378, negated_conjecture, ~((subset @ (binintersect @ esk88_0 @ esk89_0) @ (binunion @ esk88_0 @ esk90_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_375, c_0_376]), c_0_377])])). 52.88/240.09 thf(c_0_379, negated_conjecture, ![X3:$i, X2:$i]:((subset @ (binintersect @ X2 @ X3) @ X2)), inference(split_conjunct,[status(thm)],[c_0_368])). 52.88/240.09 thf(c_0_380, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_378, c_0_376]), c_0_379])]), ['proof']). 52.88/240.09 # SZS output end CNFRefutation 52.88/240.09 # Parsed axioms : 605 52.88/240.09 # Removed by relevancy pruning/SinE : 0 52.88/240.09 # Initial clauses : 788 52.88/240.09 # Removed in clause preprocessing : 351 52.88/240.09 # Initial clauses in saturation : 437 52.88/240.09 # Processed clauses : 5695 52.88/240.09 # ...of these trivial : 37 52.88/240.09 # ...subsumed : 2790 52.88/240.09 # ...remaining for further processing : 2868 52.88/240.09 # Other redundant clauses eliminated : 69 52.88/240.09 # Clauses deleted for lack of memory : 0 52.88/240.09 # Backward-subsumed : 251 52.88/240.09 # Backward-rewritten : 38 52.88/240.09 # Generated clauses : 193669 52.88/240.09 # ...of the previous two non-redundant : 191926 52.88/240.09 # ...aggressively subsumed : 0 52.88/240.09 # Contextual simplify-reflections : 54 52.88/240.09 # Paramodulations : 193478 52.88/240.09 # Factorizations : 62 52.88/240.09 # NegExts : 36 52.88/240.09 # Equation resolutions : 77 52.88/240.09 # Disequality decompositions : 0 52.88/240.09 # Total rewrite steps : 18947 52.88/240.09 # ...of those cached : 18526 52.88/240.09 # Propositional unsat checks : 0 52.88/240.09 # Propositional check models : 0 52.88/240.09 # Propositional check unsatisfiable : 0 52.88/240.09 # Propositional clauses : 0 52.88/240.09 # Propositional clauses after purity: 0 52.88/240.09 # Propositional unsat core size : 0 52.88/240.09 # Propositional preprocessing time : 0.000 52.88/240.09 # Propositional encoding time : 0.000 52.88/240.09 # Propositional solver time : 0.000 52.88/240.09 # Success case prop preproc time : 0.000 52.88/240.09 # Success case prop encoding time : 0.000 52.88/240.09 # Success case prop solver time : 0.000 52.88/240.09 # Current number of processed clauses : 2185 52.88/240.09 # Positive orientable unit clauses : 67 52.88/240.09 # Positive unorientable unit clauses: 0 52.88/240.09 # Negative unit clauses : 109 52.88/240.09 # Non-unit-clauses : 2009 52.88/240.09 # Current number of unprocessed clauses: 186850 52.88/240.09 # ...number of literals in the above : 741297 52.88/240.09 # Current number of archived formulas : 0 52.88/240.09 # Current number of archived clauses : 668 52.88/240.09 # Clause-clause subsumption calls (NU) : 456879 52.88/240.09 # Rec. Clause-clause subsumption calls : 219384 52.88/240.09 # Non-unit clause-clause subsumptions : 1797 52.88/240.09 # Unit Clause-clause subsumption calls : 9044 52.88/240.09 # Rewrite failures with RHS unbound : 0 52.88/240.09 # BW rewrite match attempts : 109 52.88/240.09 # BW rewrite match successes : 20 52.88/240.09 # Condensation attempts : 0 52.88/240.09 # Condensation successes : 0 52.88/240.09 # Termbank termtop insertions : 3957099 52.88/240.09 # Search garbage collected termcells : 30100 52.88/240.09 52.88/240.09 # ------------------------------------------------- 52.88/240.09 # User time : 6.151 s 52.88/240.09 # System time : 0.209 s 52.88/240.09 # Total time : 6.361 s 52.88/240.09 # Maximum resident set size: 9056 pages 52.88/240.09 52.88/240.09 # ------------------------------------------------- 52.88/240.09 # User time : 6.169 s 52.88/240.09 # System time : 0.213 s 52.88/240.09 # Total time : 6.381 s 52.88/240.09 # Maximum resident set size: 2764 pages 52.88/240.09 % E exiting 52.88/240.09 % E exiting 52.88/240.09 EOF