0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : run_E %s %d THM 0.12/0.33 % Computer : n028.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1440 0.12/0.33 % WCLimit : 180 0.12/0.33 % DateTime : Thu Jul 4 08:35:24 EDT 2024 0.12/0.34 % CPUTime : 0.20/0.50 Running higher-order theorem proving 0.20/0.56 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=180 /export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p 1.15/0.72 # Version: 3.2.0-ho 1.15/0.72 # Preprocessing class: HSLMSLSSLLLCHSA. 1.15/0.72 # Scheduled 5 strats onto 8 cores with 180 seconds (1440 total) 1.15/0.72 # Starting ho_unfolding_5 with 720s (4) cores 1.15/0.72 # Starting pre_casc_3 with 180s (1) cores 1.15/0.72 # Starting new_ho_10_cnf2 with 180s (1) cores 1.15/0.72 # Starting full_lambda_10 with 180s (1) cores 1.15/0.72 # Starting ehoh_best_nonlift_rwall with 180s (1) cores 1.15/0.72 # ho_unfolding_5 with pid 19652 completed with status 0 1.15/0.72 # Result found by ho_unfolding_5 1.15/0.72 # Preprocessing class: HSLMSLSSLLLCHSA. 1.15/0.72 # Scheduled 5 strats onto 8 cores with 180 seconds (1440 total) 1.15/0.72 # Starting ho_unfolding_5 with 720s (4) cores 1.15/0.72 # No SInE strategy applied 1.15/0.72 # Search class: HGHSM-FSLM31-MHSMMSBN 1.15/0.72 # Scheduled 6 strats onto 4 cores with 720 seconds (720 total) 1.15/0.72 # Starting new_ho_10_cnf2 with 376s (1) cores 1.15/0.72 # Starting ho_unfolding_5 with 73s (1) cores 1.15/0.72 # Starting new_bool_3 with 65s (1) cores 1.15/0.72 # Starting ho_unfolding_7 with 65s (1) cores 1.15/0.72 # new_bool_3 with pid 19663 completed with status 0 1.15/0.72 # Result found by new_bool_3 1.15/0.72 # Preprocessing class: HSLMSLSSLLLCHSA. 1.15/0.73 # Scheduled 5 strats onto 8 cores with 180 seconds (1440 total) 1.15/0.73 # Starting ho_unfolding_5 with 720s (4) cores 1.15/0.73 # No SInE strategy applied 1.15/0.73 # Search class: HGHSM-FSLM31-MHSMMSBN 1.15/0.73 # Scheduled 6 strats onto 4 cores with 720 seconds (720 total) 1.15/0.73 # Starting new_ho_10_cnf2 with 376s (1) cores 1.15/0.73 # Starting ho_unfolding_5 with 73s (1) cores 1.15/0.73 # Starting new_bool_3 with 65s (1) cores 1.15/0.73 # Preprocessing time : 0.008 s 1.15/0.73 # Presaturation interreduction done 1.15/0.73 1.15/0.73 # Proof found! 1.15/0.73 # SZS status Theorem 1.15/0.73 # SZS output start CNFRefutation 1.15/0.73 thf(decl_22, type, in: $i > $i > $o). 1.15/0.73 thf(decl_23, type, exu: ($i > $o) > $o). 1.15/0.73 thf(decl_24, type, setextAx: $o). 1.15/0.73 thf(decl_25, type, emptyset: $i). 1.15/0.73 thf(decl_26, type, emptysetAx: $o). 1.15/0.73 thf(decl_27, type, setadjoin: $i > $i > $i). 1.15/0.73 thf(decl_28, type, setadjoinAx: $o). 1.15/0.73 thf(decl_29, type, powerset: $i > $i). 1.15/0.73 thf(decl_30, type, powersetAx: $o). 1.15/0.73 thf(decl_31, type, setunion: $i > $i). 1.15/0.73 thf(decl_32, type, setunionAx: $o). 1.15/0.73 thf(decl_33, type, omega: $i). 1.15/0.73 thf(decl_34, type, omega0Ax: $o). 1.15/0.73 thf(decl_35, type, omegaSAx: $o). 1.15/0.73 thf(decl_36, type, omegaIndAx: $o). 1.15/0.73 thf(decl_37, type, replAx: $o). 1.15/0.73 thf(decl_38, type, foundationAx: $o). 1.15/0.73 thf(decl_39, type, wellorderingAx: $o). 1.15/0.73 thf(decl_40, type, descr: ($i > $o) > $i). 1.15/0.73 thf(decl_41, type, descrp: $o). 1.15/0.73 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 1.15/0.73 thf(decl_43, type, dsetconstrI: $o). 1.15/0.73 thf(decl_44, type, dsetconstrEL: $o). 1.15/0.73 thf(decl_45, type, dsetconstrER: $o). 1.15/0.73 thf(decl_46, type, exuE1: $o). 1.15/0.73 thf(decl_47, type, prop2set: $o > $i). 1.15/0.73 thf(decl_48, type, prop2setE: $o). 1.15/0.73 thf(decl_49, type, emptysetE: $o). 1.15/0.73 thf(decl_50, type, emptysetimpfalse: $o). 1.15/0.73 thf(decl_51, type, notinemptyset: $o). 1.15/0.73 thf(decl_52, type, exuE3e: $o). 1.15/0.73 thf(decl_53, type, setext: $o). 1.15/0.73 thf(decl_54, type, emptyI: $o). 1.15/0.73 thf(decl_55, type, noeltsimpempty: $o). 1.15/0.73 thf(decl_56, type, setbeta: $o). 1.15/0.73 thf(decl_57, type, nonempty: $i > $o). 1.15/0.73 thf(decl_58, type, nonemptyE1: $o). 1.15/0.73 thf(decl_59, type, nonemptyI: $o). 1.15/0.73 thf(decl_60, type, nonemptyI1: $o). 1.15/0.73 thf(decl_61, type, setadjoinIL: $o). 1.15/0.73 thf(decl_62, type, emptyinunitempty: $o). 1.15/0.73 thf(decl_63, type, setadjoinIR: $o). 1.15/0.73 thf(decl_64, type, setadjoinE: $o). 1.15/0.73 thf(decl_65, type, setadjoinOr: $o). 1.15/0.73 thf(decl_66, type, setoftrueEq: $o). 1.15/0.73 thf(decl_67, type, powersetI: $o). 1.15/0.73 thf(decl_68, type, emptyinPowerset: $o). 1.15/0.73 thf(decl_69, type, emptyInPowerset: $o). 1.15/0.73 thf(decl_70, type, powersetE: $o). 1.15/0.73 thf(decl_71, type, setunionI: $o). 1.15/0.73 thf(decl_72, type, setunionE: $o). 1.15/0.73 thf(decl_73, type, subPowSU: $o). 1.15/0.73 thf(decl_74, type, exuE2: $o). 1.15/0.73 thf(decl_75, type, nonemptyImpWitness: $o). 1.15/0.73 thf(decl_76, type, uniqinunit: $o). 1.15/0.73 thf(decl_77, type, notinsingleton: $o). 1.15/0.73 thf(decl_78, type, eqinunit: $o). 1.15/0.73 thf(decl_79, type, singletonsswitch: $o). 1.15/0.73 thf(decl_80, type, upairsetE: $o). 1.15/0.73 thf(decl_81, type, upairsetIL: $o). 1.15/0.73 thf(decl_82, type, upairsetIR: $o). 1.15/0.73 thf(decl_83, type, emptyE1: $o). 1.15/0.73 thf(decl_84, type, vacuousDall: $o). 1.15/0.73 thf(decl_85, type, quantDeMorgan1: $o). 1.15/0.73 thf(decl_86, type, quantDeMorgan2: $o). 1.15/0.73 thf(decl_87, type, quantDeMorgan3: $o). 1.15/0.73 thf(decl_88, type, quantDeMorgan4: $o). 1.15/0.73 thf(decl_89, type, prop2setI: $o). 1.15/0.73 thf(decl_90, type, set2prop: $i > $o). 1.15/0.73 thf(decl_91, type, prop2set2propI: $o). 1.15/0.73 thf(decl_92, type, notdexE: $o). 1.15/0.73 thf(decl_93, type, notdallE: $o). 1.15/0.73 thf(decl_94, type, exuI1: $o). 1.15/0.73 thf(decl_95, type, exuI3: $o). 1.15/0.73 thf(decl_96, type, exuI2: $o). 1.15/0.73 thf(decl_97, type, inCongP: $o). 1.15/0.73 thf(decl_98, type, in__Cong: $o). 1.15/0.73 thf(decl_99, type, exuE3u: $o). 1.15/0.73 thf(decl_100, type, exu__Cong: $o). 1.15/0.73 thf(decl_101, type, emptyset__Cong: $o). 1.15/0.73 thf(decl_102, type, setadjoin__Cong: $o). 1.15/0.73 thf(decl_103, type, powerset__Cong: $o). 1.15/0.73 thf(decl_104, type, setunion__Cong: $o). 1.15/0.73 thf(decl_105, type, omega__Cong: $o). 1.15/0.73 thf(decl_106, type, exuEu: $o). 1.15/0.73 thf(decl_107, type, descr__Cong: $o). 1.15/0.73 thf(decl_108, type, dsetconstr__Cong: $o). 1.15/0.73 thf(decl_109, type, subset: $i > $i > $o). 1.15/0.73 thf(decl_112, type, subsetI1: $o). 1.15/0.73 thf(decl_113, type, eqimpsubset2: $o). 1.15/0.73 thf(decl_114, type, eqimpsubset1: $o). 1.15/0.73 thf(decl_115, type, subsetI2: $o). 1.15/0.73 thf(decl_116, type, emptysetsubset: $o). 1.15/0.73 thf(decl_117, type, subsetE: $o). 1.15/0.73 thf(decl_118, type, subsetE2: $o). 1.15/0.73 thf(decl_119, type, notsubsetI: $o). 1.15/0.73 thf(decl_120, type, notequalI1: $o). 1.15/0.73 thf(decl_121, type, notequalI2: $o). 1.15/0.73 thf(decl_122, type, subsetRefl: $o). 1.15/0.73 thf(decl_123, type, subsetTrans: $o). 1.15/0.73 thf(decl_124, type, setadjoinSub: $o). 1.15/0.73 thf(decl_125, type, setadjoinSub2: $o). 1.15/0.73 thf(decl_126, type, subset2powerset: $o). 1.15/0.73 thf(decl_127, type, setextsub: $o). 1.15/0.73 thf(decl_128, type, subsetemptysetimpeq: $o). 1.15/0.73 thf(decl_129, type, powersetI1: $o). 1.15/0.73 thf(decl_130, type, powersetE1: $o). 1.15/0.73 thf(decl_131, type, inPowerset: $o). 1.15/0.73 thf(decl_132, type, powersetsubset: $o). 1.15/0.73 thf(decl_133, type, sepInPowerset: $o). 1.15/0.73 thf(decl_134, type, sepSubset: $o). 1.15/0.73 thf(decl_135, type, binunion: $i > $i > $i). 1.15/0.73 thf(decl_136, type, binunionIL: $o). 1.15/0.73 thf(decl_137, type, upairset2IR: $o). 1.15/0.73 thf(decl_138, type, binunionIR: $o). 1.15/0.73 thf(decl_139, type, binunionEcases: $o). 1.15/0.73 thf(decl_140, type, binunionE: $o). 1.15/0.73 thf(decl_141, type, binunionLsub: $o). 1.15/0.73 thf(decl_142, type, binunionRsub: $o). 1.15/0.73 thf(decl_143, type, binintersect: $i > $i > $i). 1.15/0.73 thf(decl_144, type, binintersectI: $o). 1.15/0.73 thf(decl_145, type, binintersectSubset5: $o). 1.15/0.73 thf(decl_146, type, binintersectEL: $o). 1.15/0.73 thf(decl_147, type, binintersectLsub: $o). 1.15/0.73 thf(decl_148, type, binintersectSubset2: $o). 1.15/0.73 thf(decl_149, type, binintersectSubset3: $o). 1.15/0.73 thf(decl_150, type, binintersectER: $o). 1.15/0.73 thf(decl_151, type, disjointsetsI1: $o). 1.15/0.73 thf(decl_152, type, binintersectRsub: $o). 1.15/0.73 thf(decl_153, type, binintersectSubset4: $o). 1.15/0.73 thf(decl_154, type, binintersectSubset1: $o). 1.15/0.73 thf(decl_155, type, bs114d: $o). 1.15/0.73 thf(decl_157, type, setminus: $i > $i > $i). 1.15/0.73 thf(decl_158, type, setminusI: $o). 1.15/0.73 thf(decl_159, type, setminusEL: $o). 1.15/0.73 thf(decl_160, type, setminusER: $o). 1.15/0.73 thf(decl_161, type, setminusSubset2: $o). 1.15/0.73 thf(decl_162, type, setminusERneg: $o). 1.15/0.73 thf(decl_163, type, setminusELneg: $o). 1.15/0.73 thf(decl_164, type, setminusILneg: $o). 1.15/0.73 thf(decl_165, type, setminusIRneg: $o). 1.15/0.73 thf(decl_166, type, setminusLsub: $o). 1.15/0.73 thf(decl_167, type, setminusSubset1: $o). 1.15/0.73 thf(decl_168, type, symdiff: $i > $i > $i). 1.15/0.73 thf(decl_169, type, symdiffE: $o). 1.15/0.73 thf(decl_170, type, symdiffI1: $o). 1.15/0.73 thf(decl_171, type, symdiffI2: $o). 1.15/0.73 thf(decl_172, type, symdiffIneg1: $o). 1.15/0.73 thf(decl_173, type, symdiffIneg2: $o). 1.15/0.73 thf(decl_174, type, iskpair: $i > $o). 1.15/0.73 thf(decl_175, type, secondinupair: $o). 1.15/0.73 thf(decl_176, type, setukpairIL: $o). 1.15/0.73 thf(decl_177, type, setukpairIR: $o). 1.15/0.73 thf(decl_178, type, kpairiskpair: $o). 1.15/0.73 thf(decl_179, type, kpair: $i > $i > $i). 1.15/0.73 thf(decl_180, type, kpairp: $o). 1.15/0.73 thf(decl_181, type, cartprod: $i > $i > $i). 1.15/0.73 thf(decl_182, type, singletonsubset: $o). 1.15/0.73 thf(decl_183, type, singletoninpowerset: $o). 1.15/0.73 thf(decl_184, type, singletoninpowunion: $o). 1.15/0.73 thf(decl_185, type, upairset2E: $o). 1.15/0.73 thf(decl_186, type, upairsubunion: $o). 1.15/0.73 thf(decl_187, type, upairinpowunion: $o). 1.15/0.73 thf(decl_188, type, ubforcartprodlem1: $o). 1.15/0.73 thf(decl_189, type, ubforcartprodlem2: $o). 1.15/0.73 thf(decl_190, type, ubforcartprodlem3: $o). 1.15/0.73 thf(decl_191, type, cartprodpairin: $o). 1.15/0.73 thf(decl_192, type, cartprodmempair1: $o). 1.15/0.73 thf(decl_193, type, cartprodmempair: $o). 1.15/0.73 thf(decl_194, type, setunionE2: $o). 1.15/0.73 thf(decl_195, type, setunionsingleton1: $o). 1.15/0.73 thf(decl_196, type, setunionsingleton2: $o). 1.15/0.73 thf(decl_197, type, setunionsingleton: $o). 1.15/0.73 thf(decl_198, type, singleton: $i > $o). 1.15/0.73 thf(decl_199, type, singletonprop: $o). 1.15/0.73 thf(decl_200, type, ex1: $i > ($i > $o) > $o). 1.15/0.73 thf(decl_201, type, ex1E1: $o). 1.15/0.73 thf(decl_202, type, ex1I: $o). 1.15/0.73 thf(decl_203, type, ex1I2: $o). 1.15/0.73 thf(decl_204, type, singletonsuniq: $o). 1.15/0.73 thf(decl_209, type, setukpairinjL1: $o). 1.15/0.73 thf(decl_210, type, kfstsingleton: $o). 1.15/0.73 thf(decl_211, type, theprop: $o). 1.15/0.73 thf(decl_212, type, kfst: $i > $i). 1.15/0.73 thf(decl_213, type, kfstpairEq: $o). 1.15/0.73 thf(decl_214, type, cartprodfstin: $o). 1.15/0.73 thf(decl_215, type, setukpairinjL2: $o). 1.15/0.73 thf(decl_216, type, setukpairinjL: $o). 1.15/0.73 thf(decl_217, type, setukpairinjR11: $o). 1.15/0.73 thf(decl_218, type, setukpairinjR12: $o). 1.15/0.73 thf(decl_219, type, setukpairinjR1: $o). 1.15/0.73 thf(decl_220, type, upairequniteq: $o). 1.15/0.73 thf(decl_221, type, setukpairinjR2: $o). 1.15/0.73 thf(decl_222, type, setukpairinjR: $o). 1.15/0.73 thf(decl_223, type, ksndsingleton: $o). 1.15/0.73 thf(decl_224, type, ksnd: $i > $i). 1.15/0.73 thf(decl_225, type, ksndpairEq: $o). 1.15/0.73 thf(decl_226, type, kpairsurjEq: $o). 1.15/0.73 thf(decl_227, type, cartprodsndin: $o). 1.15/0.73 thf(decl_228, type, cartprodpairmemEL: $o). 1.15/0.73 thf(decl_229, type, cartprodpairmemER: $o). 1.15/0.73 thf(decl_230, type, cartprodmempaircEq: $o). 1.15/0.73 thf(decl_231, type, cartprodfstpairEq: $o). 1.15/0.73 thf(decl_232, type, cartprodsndpairEq: $o). 1.15/0.73 thf(decl_233, type, cartprodpairsurjEq: $o). 1.15/0.73 thf(decl_234, type, breln: $i > $i > $i > $o). 1.15/0.73 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 1.15/0.73 thf(decl_236, type, dpsetconstrI: $o). 1.15/0.73 thf(decl_237, type, dpsetconstrSub: $o). 1.15/0.73 thf(decl_238, type, setOfPairsIsBReln: $o). 1.15/0.73 thf(decl_239, type, dpsetconstrERa: $o). 1.15/0.73 thf(decl_240, type, dpsetconstrEL1: $o). 1.15/0.73 thf(decl_241, type, dpsetconstrEL2: $o). 1.15/0.73 thf(decl_242, type, dpsetconstrER: $o). 1.15/0.73 thf(decl_243, type, func: $i > $i > $i > $o). 1.15/0.73 thf(decl_245, type, funcImageSingleton: $o). 1.15/0.73 thf(decl_246, type, epred1_0: $o). 1.15/0.73 thf(decl_247, type, esk1_2: $i > $i > $i). 1.15/0.73 thf(decl_248, type, esk2_2: $i > $i > $i). 1.15/0.73 thf(decl_249, type, esk3_2: $i > $i > $i). 1.15/0.73 thf(decl_250, type, esk4_1: $i > $i). 1.15/0.73 thf(decl_251, type, esk5_2: ($i > $i > $o) > $i > $i). 1.15/0.73 thf(decl_252, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 1.15/0.73 thf(decl_253, type, esk7_2: ($i > $i > $o) > $i > $i). 1.15/0.73 thf(decl_254, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 1.15/0.73 thf(decl_255, type, esk9_1: $i > $i). 1.15/0.73 thf(decl_256, type, esk10_2: ($i > $o) > $i > $i). 1.15/0.73 thf(decl_257, type, esk11_2: ($i > $o) > $i > $i). 1.15/0.73 thf(decl_258, type, esk12_1: ($i > $o) > $i). 1.15/0.73 thf(decl_259, type, esk13_2: ($i > $o) > $i > $i). 1.15/0.73 thf(decl_260, type, esk14_1: ($i > $o) > $i). 1.15/0.73 thf(decl_261, type, esk15_2: $i > $i > $i). 1.15/0.73 thf(decl_262, type, esk16_2: $i > $i > $i). 1.15/0.73 thf(decl_263, type, esk17_1: $i > $i). 1.15/0.73 thf(decl_264, type, esk18_1: $i > $i). 1.15/0.73 thf(decl_265, type, esk19_1: $i > $i). 1.15/0.73 thf(decl_266, type, esk20_2: $i > $i > $i). 1.15/0.73 thf(decl_267, type, esk21_3: $i > $i > $o > $i). 1.15/0.73 thf(decl_268, type, esk22_2: ($i > $o) > $i > $i). 1.15/0.73 thf(decl_269, type, esk23_1: ($i > $o) > $i). 1.15/0.73 thf(decl_270, type, esk24_1: $i > $i). 1.15/0.73 thf(decl_271, type, esk25_2: $i > ($i > $o) > $i). 1.15/0.73 thf(decl_272, type, esk26_2: $i > ($i > $o) > $i). 1.15/0.73 thf(decl_273, type, esk27_2: $i > ($i > $o) > $i). 1.15/0.73 thf(decl_274, type, esk28_2: $i > ($i > $o) > $i). 1.15/0.73 thf(decl_275, type, esk29_2: $i > ($i > $o) > $i). 1.15/0.73 thf(decl_276, type, esk30_2: $i > ($i > $o) > $i). 1.15/0.73 thf(decl_277, type, esk31_2: ($i > $o) > $i > $i). 1.15/0.73 thf(decl_278, type, esk32_1: ($i > $o) > $i). 1.15/0.73 thf(decl_279, type, esk33_1: ($i > $o) > $i). 1.15/0.73 thf(decl_280, type, esk34_1: ($i > $o) > $i). 1.15/0.73 thf(decl_281, type, esk35_1: ($i > $o) > $i). 1.15/0.73 thf(decl_282, type, esk36_2: ($i > $o) > $i > $i). 1.15/0.73 thf(decl_283, type, esk37_1: ($i > $o) > $i). 1.15/0.73 thf(decl_284, type, esk38_2: ($i > $o) > $i > $i). 1.15/0.73 thf(decl_285, type, esk39_2: ($i > $o) > ($i > $o) > $i). 1.15/0.73 thf(decl_286, type, esk40_2: ($i > $o) > ($i > $o) > $i). 1.15/0.73 thf(decl_287, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 1.15/0.73 thf(decl_288, type, esk42_2: ($i > $o) > ($i > $o) > $i). 1.15/0.73 thf(decl_289, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 1.15/0.73 thf(decl_290, type, esk44_2: ($i > $o) > ($i > $o) > $i). 1.15/0.73 thf(decl_291, type, esk45_2: ($i > $o) > $i > $i). 1.15/0.73 thf(decl_292, type, esk46_2: ($i > $o) > ($i > $o) > $i). 1.15/0.73 thf(decl_293, type, esk47_2: ($i > $o) > ($i > $o) > $i). 1.15/0.73 thf(decl_294, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 1.15/0.73 thf(decl_295, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 1.15/0.73 thf(decl_296, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 1.15/0.73 thf(decl_297, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 1.15/0.73 thf(decl_298, type, esk52_2: $i > $i > $i). 1.15/0.73 thf(decl_299, type, esk53_2: $i > $i > $i). 1.15/0.73 thf(decl_300, type, esk54_2: $i > $i > $i). 1.15/0.73 thf(decl_301, type, esk55_3: $i > $i > $i > $i). 1.15/0.73 thf(decl_302, type, esk56_3: $i > $i > $i > $i). 1.15/0.73 thf(decl_303, type, esk57_2: $i > $i > $i). 1.15/0.73 thf(decl_304, type, esk58_2: $i > ($i > $o) > $i). 1.15/0.73 thf(decl_305, type, esk59_2: $i > ($i > $o) > $i). 1.15/0.73 thf(decl_306, type, esk60_2: $i > ($i > $o) > $i). 1.15/0.73 thf(decl_307, type, esk61_2: $i > ($i > $o) > $i). 1.15/0.73 thf(decl_308, type, esk62_3: $i > ($i > $o) > $i > $i). 1.15/0.73 thf(decl_309, type, esk63_3: $i > ($i > $o) > $i > $i). 1.15/0.73 thf(decl_310, type, esk64_2: $i > ($i > $o) > $i). 1.15/0.73 thf(decl_311, type, esk65_2: $i > ($i > $o) > $i). 1.15/0.73 thf(decl_312, type, esk66_2: $i > ($i > $o) > $i). 1.15/0.73 thf(decl_313, type, esk67_1: $i > $i). 1.15/0.73 thf(decl_314, type, esk68_1: $i > $i). 1.15/0.73 thf(decl_315, type, esk69_3: $i > $i > $i > $i). 1.15/0.73 thf(decl_316, type, esk70_4: $i > $i > $i > $i > $i). 1.15/0.73 thf(decl_317, type, esk71_0: $i). 1.15/0.73 thf(decl_318, type, esk72_0: $i). 1.15/0.73 thf(decl_319, type, esk73_0: $i). 1.15/0.73 thf(decl_320, type, esk74_1: $i > $i). 1.15/0.73 thf(decl_321, type, esk75_0: $i). 1.15/0.73 thf(decl_327, type, epred2_1: $i > $i > $i > $o). 1.15/0.73 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', ex1)). 1.15/0.73 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', singleton)). 1.15/0.73 thf(func, axiom, ((func)=(^[X4:$i, X5:$i, X29:$i]:(((breln @ X4 @ X5 @ X29)&![X2:$i]:(((in @ X2 @ X4)=>(ex1 @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', func)). 1.15/0.73 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', breln)). 1.15/0.73 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', replAx)). 1.15/0.73 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', exu)). 1.15/0.73 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', descrp)). 1.15/0.73 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', exuE1)). 1.15/0.73 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', exuE3e)). 1.15/0.73 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', nonempty)). 1.15/0.73 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', nonemptyI)). 1.15/0.73 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', exuE2)). 1.15/0.73 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.g2101WDfHi/E---3.1_19524.p', exuI1)). 1.15/0.73 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', exuI3)). 1.15/0.73 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', exuI2)). 1.15/0.73 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.g2101WDfHi/E---3.1_19524.p', exuE3u)). 1.15/0.73 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', exu__Cong)). 1.15/0.73 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', exuEu)). 1.15/0.73 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', descr__Cong)). 1.15/0.73 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', singletonprop)). 1.15/0.73 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', ex1E1)). 1.15/0.73 thf(ex1I, axiom, ((ex1I)<=>![X4:$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.g2101WDfHi/E---3.1_19524.p', ex1I)). 1.15/0.73 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', ex1I2)). 1.15/0.73 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', kfstsingleton)). 1.15/0.73 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', ksndsingleton)). 1.15/0.73 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setOfPairsIsBReln)). 1.15/0.73 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30)))))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', funcImageSingleton)). 1.15/0.73 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', dsetconstrI)). 1.15/0.73 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', dsetconstrEL)). 1.15/0.73 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', dsetconstrER)). 1.15/0.73 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setbeta)). 1.15/0.73 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', nonemptyE1)). 1.15/0.73 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', nonemptyI1)). 1.15/0.73 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setoftrueEq)). 1.15/0.73 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', nonemptyImpWitness)). 1.15/0.73 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.g2101WDfHi/E---3.1_19524.p', emptyE1)). 1.15/0.73 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', dsetconstr__Cong)). 1.15/0.73 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', sepInPowerset)). 1.15/0.73 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', sepSubset)). 1.15/0.73 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', theprop)). 1.15/0.73 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', dpsetconstrI)). 1.15/0.73 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', dpsetconstrSub)). 1.15/0.73 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', dpsetconstrERa)). 1.15/0.73 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', dpsetconstrEL1)). 1.15/0.73 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', dpsetconstrEL2)). 1.15/0.73 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', dpsetconstrER)). 1.15/0.73 thf(apProp, conjecture, ((((((setunionAx)=>(((((replAx)=>(((((dsetconstrI)=>((((exuE1)=>(((((((setext)=>((emptyI)=>((((nonemptyE1)=>(((((emptyinunitempty)=>(((setadjoinE)=>(((setoftrueEq)=>((powersetI)=>((((powersetE)=>((setunionI)=>((setunionE)=>((((nonemptyImpWitness)=>(((notinsingleton)=>((eqinunit)=>(((upairsetE)=>((upairsetIL)=>((upairsetIR)=>(((vacuousDall)=>(((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>(((prop2set2propI)=>((notdexE)=>(((((((in__Cong)=>((exuE3u)=>(((((powerset__Cong)=>((setunion__Cong)=>((((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((((emptysetsubset)=>(((((((subsetRefl)=>((subsetTrans)=>(((((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>(((inPowerset)=>(((((binunionIL)=>((((binunionEcases)=>((((binunionRsub)=>((((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>(((disjointsetsI1)=>(((((((((setminusSubset2)=>(((setminusELneg)=>((((((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>(((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>(((((singletoninpowunion)=>((upairset2E)=>(((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((((((ex1E1)=>(((((setukpairinjL1)=>((kfstsingleton)=>(((((setukpairinjL2)=>((((setukpairinjR12)=>((setukpairinjR1)=>(((setukpairinjR2)=>((setukpairinjR)=>(((ksndpairEq)=>(((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((((((dpsetconstrI)=>(((setOfPairsIsBReln)=>((dpsetconstrERa)=>((((dpsetconstrER)=>(![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X30))))) @ X5)<=(in @ X2 @ X4)))))<=(funcImageSingleton)))<=(dpsetconstrEL2))<=(dpsetconstrEL1))))<=(dpsetconstrSub)))<=(cartprodpairsurjEq))<=(cartprodsndpairEq))<=(cartprodfstpairEq))<=(cartprodmempaircEq)))))<=(kpairsurjEq)))<=(ksndsingleton))))<=(upairequniteq))))<=(setukpairinjR11))<=(setukpairinjL)))<=(cartprodfstin))<=(kfstpairEq))<=(theprop))))<=(singletonsuniq))<=(ex1I2))<=(ex1I)))<=(singletonprop))<=(setunionsingleton))<=(setunionsingleton2))<=(setunionsingleton1))))))))))<=(upairsubunion))))<=(singletoninpowerset))<=(singletonsubset))<=(kpairp))))))<=(symdiffIneg2))))))<=(setminusSubset1))<=(setminusLsub))<=(setminusIRneg))<=(setminusILneg)))<=(setminusERneg)))<=(setminusER))<=(setminusEL))<=(setminusI))<=(bs114d))<=(binintersectSubset1))<=(binintersectSubset4))<=(binintersectRsub)))<=(binintersectER))))))<=(binintersectSubset5))<=(binintersectI)))<=(binunionLsub))<=(binunionE)))<=(binunionIR))<=(upairset2IR)))<=(sepSubset))<=(sepInPowerset))<=(powersetsubset)))<=(powersetE1)))))<=(subset2powerset))<=(setadjoinSub2))<=(setadjoinSub))))<=(notequalI2))<=(notequalI1))<=(notsubsetI))<=(subsetE2))<=(subsetE)))<=(subsetI2))<=(eqimpsubset1))))))<=(exuEu))<=(omega__Cong))))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong))))<=(inCongP))<=(exuI2))<=(exuI3))<=(exuI1))<=(notdallE))))<=(prop2setI)))))<=(quantDeMorgan1)))<=(emptyE1)))))<=(singletonsswitch))))<=(uniqinunit)))<=(exuE2))<=(subPowSU)))))<=(emptyInPowerset))<=(emptyinPowerset))))<=(setadjoinOr)))<=(setadjoinIR)))<=(setadjoinIL))<=(nonemptyI1))<=(nonemptyI)))<=(setbeta))<=(noeltsimpempty))))<=(exuE3e))<=(notinemptyset))<=(emptysetimpfalse))<=(emptysetE))<=(prop2setE)))<=(dsetconstrER))<=(dsetconstrEL)))<=(descrp))<=(wellorderingAx))<=(foundationAx)))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax)))<=(powersetAx))<=(setadjoinAx))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', apProp)). 1.15/0.73 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setextAx)). 1.15/0.73 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', emptysetAx)). 1.15/0.73 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setadjoinAx)). 1.15/0.73 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', powersetAx)). 1.15/0.73 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setunionAx)). 1.15/0.73 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', omega0Ax)). 1.15/0.73 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', omegaSAx)). 1.15/0.73 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', omegaIndAx)). 1.15/0.73 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', foundationAx)). 1.15/0.73 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.g2101WDfHi/E---3.1_19524.p', wellorderingAx)). 1.15/0.73 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', prop2setE)). 1.15/0.73 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', emptysetE)). 1.15/0.73 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', emptysetimpfalse)). 1.15/0.73 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', notinemptyset)). 1.15/0.73 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setext)). 1.15/0.73 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', emptyI)). 1.15/0.73 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', noeltsimpempty)). 1.15/0.73 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setadjoinIL)). 1.15/0.73 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', emptyinunitempty)). 1.15/0.73 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setadjoinIR)). 1.15/0.73 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.g2101WDfHi/E---3.1_19524.p', setadjoinE)). 1.15/0.73 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setadjoinOr)). 1.15/0.73 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', powersetI)). 1.15/0.73 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', emptyinPowerset)). 1.15/0.73 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', emptyInPowerset)). 1.15/0.73 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', powersetE)). 1.15/0.73 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setunionI)). 1.15/0.73 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.g2101WDfHi/E---3.1_19524.p', setunionE)). 1.15/0.73 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', subPowSU)). 1.15/0.73 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', uniqinunit)). 1.15/0.73 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', notinsingleton)). 1.15/0.73 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', eqinunit)). 1.15/0.73 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', singletonsswitch)). 1.15/0.73 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', upairsetE)). 1.15/0.73 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', upairsetIL)). 1.15/0.73 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', upairsetIR)). 1.15/0.73 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', vacuousDall)). 1.15/0.73 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', quantDeMorgan1)). 1.15/0.73 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', quantDeMorgan2)). 1.15/0.73 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', quantDeMorgan3)). 1.15/0.73 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', quantDeMorgan4)). 1.15/0.73 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', prop2setI)). 1.15/0.73 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', prop2set2propI)). 1.15/0.73 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', notdexE)). 1.15/0.73 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', notdallE)). 1.15/0.73 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', inCongP)). 1.15/0.73 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', in__Cong)). 1.15/0.73 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', emptyset__Cong)). 1.15/0.73 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setadjoin__Cong)). 1.15/0.73 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', powerset__Cong)). 1.15/0.73 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setunion__Cong)). 1.15/0.73 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', omega__Cong)). 1.15/0.73 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', subsetI1)). 1.15/0.73 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', eqimpsubset2)). 1.15/0.73 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', eqimpsubset1)). 1.15/0.73 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', subsetI2)). 1.15/0.73 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', emptysetsubset)). 1.15/0.73 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', subsetE)). 1.15/0.73 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', subsetE2)). 1.15/0.73 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', notsubsetI)). 1.15/0.73 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', notequalI1)). 1.15/0.73 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', notequalI2)). 1.15/0.73 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', subsetRefl)). 1.15/0.73 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', subsetTrans)). 1.15/0.73 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setadjoinSub)). 1.15/0.73 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setadjoinSub2)). 1.15/0.73 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', subset2powerset)). 1.15/0.73 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setextsub)). 1.15/0.73 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', subsetemptysetimpeq)). 1.15/0.73 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', powersetI1)). 1.15/0.73 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', powersetE1)). 1.15/0.73 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', inPowerset)). 1.15/0.73 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', powersetsubset)). 1.15/0.73 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', binunionIL)). 1.15/0.73 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', upairset2IR)). 1.15/0.73 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', binunionIR)). 1.15/0.73 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', binunionEcases)). 1.15/0.73 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', binunionE)). 1.15/0.73 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', binunionLsub)). 1.15/0.73 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', binunionRsub)). 1.15/0.73 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', binintersectI)). 1.15/0.73 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', binintersectSubset5)). 1.15/0.73 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', binintersectEL)). 1.15/0.73 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', binintersectLsub)). 1.15/0.73 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', binintersectSubset2)). 1.15/0.73 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', binintersectSubset3)). 1.15/0.73 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', binintersectER)). 1.15/0.73 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', disjointsetsI1)). 1.15/0.73 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', binintersectRsub)). 1.15/0.73 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', binintersectSubset4)). 1.15/0.73 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', binintersectSubset1)). 1.15/0.73 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', bs114d)). 1.15/0.73 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setminusI)). 1.15/0.73 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setminusEL)). 1.15/0.73 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setminusER)). 1.15/0.73 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setminusSubset2)). 1.15/0.73 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setminusERneg)). 1.15/0.73 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setminusELneg)). 1.15/0.73 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setminusILneg)). 1.15/0.73 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setminusIRneg)). 1.15/0.73 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setminusLsub)). 1.15/0.73 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setminusSubset1)). 1.15/0.73 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', symdiffE)). 1.15/0.73 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', symdiffI1)). 1.15/0.73 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', symdiffI2)). 1.15/0.73 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', symdiffIneg1)). 1.15/0.73 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', symdiffIneg2)). 1.15/0.73 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', secondinupair)). 1.15/0.73 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setukpairIL)). 1.15/0.73 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setukpairIR)). 1.15/0.73 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', kpairiskpair)). 1.15/0.73 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', kpairp)). 1.15/0.73 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', singletonsubset)). 1.15/0.73 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', singletoninpowerset)). 1.15/0.73 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', singletoninpowunion)). 1.15/0.73 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', upairset2E)). 1.15/0.73 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', upairsubunion)). 1.15/0.73 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', upairinpowunion)). 1.15/0.73 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', ubforcartprodlem1)). 1.15/0.73 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', ubforcartprodlem2)). 1.15/0.73 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', ubforcartprodlem3)). 1.15/0.73 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', cartprodpairin)). 1.15/0.73 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.g2101WDfHi/E---3.1_19524.p', cartprodmempair1)). 1.15/0.73 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', cartprodmempair)). 1.15/0.73 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setunionE2)). 1.15/0.73 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setunionsingleton1)). 1.15/0.73 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setunionsingleton2)). 1.15/0.73 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setunionsingleton)). 1.15/0.73 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', singletonsuniq)). 1.15/0.73 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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.g2101WDfHi/E---3.1_19524.p', setukpairinjL1)). 1.15/0.73 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', kfstpairEq)). 1.15/0.73 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', cartprodfstin)). 1.15/0.73 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setukpairinjL2)). 1.15/0.73 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setukpairinjL)). 1.15/0.73 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setukpairinjR11)). 1.15/0.73 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setukpairinjR12)). 1.15/0.73 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', setukpairinjR1)). 1.15/0.73 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', upairequniteq)). 1.15/0.73 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.g2101WDfHi/E---3.1_19524.p', setukpairinjR2)). 1.15/0.73 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.g2101WDfHi/E---3.1_19524.p', setukpairinjR)). 1.15/0.73 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', ksndpairEq)). 1.15/0.73 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', kpairsurjEq)). 1.15/0.73 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', cartprodsndin)). 1.15/0.73 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.g2101WDfHi/E---3.1_19524.p', cartprodpairmemEL)). 1.15/0.73 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.g2101WDfHi/E---3.1_19524.p', cartprodpairmemER)). 1.15/0.73 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.g2101WDfHi/E---3.1_19524.p', cartprodmempaircEq)). 1.15/0.73 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.g2101WDfHi/E---3.1_19524.p', cartprodfstpairEq)). 1.15/0.73 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.g2101WDfHi/E---3.1_19524.p', cartprodsndpairEq)). 1.15/0.73 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/tmp/tmp.g2101WDfHi/E---3.1_19524.p', cartprodpairsurjEq)). 1.15/0.73 thf(c_0_196, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X597:$i]:(((in @ X597 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X597 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])). 1.15/0.73 thf(c_0_197, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])). 1.15/0.73 thf(c_0_198, plain, ((func)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((((subset @ Z2 @ (cartprod @ Z0 @ Z1)))&![X2:$i]:(((in @ X2 @ Z0)=>(?[X604:$i]:(((in @ X604 @ (dsetconstr @ Z1 @ (^[Z3/* 3 */:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2))))))&((dsetconstr @ Z1 @ (^[Z3/* 3 */:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X604 @ emptyset))))))))))), inference(fof_simplification,[status(thm)],[func])). 1.15/0.73 thf(c_0_199, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X597:$i]:(((in @ X597 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X597 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_196, c_0_197])). 1.15/0.73 thf(c_0_200, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])). 1.15/0.73 thf(c_0_201, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 1.15/0.73 thf(c_0_202, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 1.15/0.73 thf(c_0_203, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 1.15/0.73 thf(c_0_204, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 1.15/0.73 thf(c_0_205, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 1.15/0.73 thf(c_0_206, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 1.15/0.73 thf(c_0_207, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 1.15/0.73 thf(c_0_208, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 1.15/0.73 thf(c_0_209, 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])). 1.15/0.73 thf(c_0_210, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 1.15/0.73 thf(c_0_211, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 1.15/0.73 thf(c_0_212, 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])). 1.15/0.73 thf(c_0_213, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 1.15/0.73 thf(c_0_214, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 1.15/0.73 thf(c_0_215, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 1.15/0.73 thf(c_0_216, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 1.15/0.73 thf(c_0_217, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 1.15/0.73 thf(c_0_218, plain, ((ex1I)<=>![X4:$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])). 1.15/0.73 thf(c_0_219, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 1.15/0.73 thf(c_0_220, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 1.15/0.73 thf(c_0_221, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 1.15/0.73 thf(c_0_222, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 1.15/0.73 thf(c_0_223, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X30:$i]:(((func @ X4 @ X5 @ X30)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 1.15/0.73 thf(c_0_224, plain, ((func)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((((subset @ Z2 @ (cartprod @ Z0 @ Z1)))&![X2:$i]:(((in @ X2 @ Z0)=>(?[X604:$i]:(((in @ X604 @ (dsetconstr @ Z1 @ (^[Z3/* 3 */:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2))))))&((dsetconstr @ Z1 @ (^[Z3/* 3 */:$i]:(((in @ (kpair @ X2 @ Z3) @ Z2)))))=(setadjoin @ X604 @ emptyset))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_198, c_0_199]), c_0_200])). 1.15/0.73 thf(c_0_225, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X568:$i]:((((X6 @ X2 @ X568))&![X569:$i]:((((X6 @ X2 @ X569))=>((X568)=(X569)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_201, c_0_202])). 1.15/0.73 thf(c_0_226, plain, ((descrp)=(![X1:$i > $o]:(((?[X570:$i]:((((X1 @ X570))&![X571:$i]:((((X1 @ X571))=>((X570)=(X571)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_203, c_0_202])). 1.15/0.73 thf(c_0_227, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 1.15/0.73 thf(c_0_228, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 1.15/0.73 thf(c_0_229, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 1.15/0.73 thf(c_0_230, plain, ((exuE1)=(![X1:$i > $o]:(((?[X572:$i]:((((X1 @ X572))&![X573:$i]:((((X1 @ X573))=>((X572)=(X573)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_204, c_0_202])). 1.15/0.73 thf(c_0_231, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X574:$i]:((((X1 @ X574))&![X575:$i]:((((X1 @ X575))=>((X574)=(X575)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_205, c_0_202])). 1.15/0.73 thf(c_0_232, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 1.15/0.73 thf(c_0_233, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_206])). 1.15/0.73 thf(c_0_234, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_207, c_0_206])). 1.15/0.73 thf(c_0_235, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_206])). 1.15/0.73 thf(c_0_236, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 1.15/0.73 thf(c_0_237, plain, ((exuE2)=(![X1:$i > $o]:(((?[X576:$i]:((((X1 @ X576))&![X577:$i]:((((X1 @ X577))=>((X576)=(X577)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_208, c_0_202])). 1.15/0.73 thf(c_0_238, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_206])). 1.15/0.73 thf(c_0_239, 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])). 1.15/0.73 thf(c_0_240, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X578:$i]:((((X1 @ X578))&![X579:$i]:((((X1 @ X579))=>((X578)=(X579))))))))))), inference(apply_def,[status(thm)],[c_0_209, c_0_202])). 1.15/0.73 thf(c_0_241, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X580:$i]:((((X1 @ X580))&![X581:$i]:((((X1 @ X581))=>((X580)=(X581)))))))))))), inference(apply_def,[status(thm)],[c_0_210, c_0_202])). 1.15/0.73 thf(c_0_242, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X582:$i]:((((X1 @ X582))&![X583:$i]:((((X1 @ X583))=>((X582)=(X583))))))))))), inference(apply_def,[status(thm)],[c_0_211, c_0_202])). 1.15/0.73 thf(c_0_243, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X584:$i]:((((X1 @ X584))&![X585:$i]:((((X1 @ X585))=>((X584)=(X585)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_212, c_0_202])). 1.15/0.73 thf(c_0_244, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X586:$i]:((((X1 @ X586))&![X587:$i]:((((X1 @ X587))=>((X586)=(X587)))))))<=>(?[X588:$i]:((((X17 @ X588))&![X589:$i]:((((X17 @ X589))=>((X588)=(X589)))))))))))), inference(apply_def,[status(thm)],[c_0_213, c_0_202])). 1.15/0.73 thf(c_0_245, plain, ((exuEu)=(![X1:$i > $o]:(((?[X590:$i]:((((X1 @ X590))&![X591:$i]:((((X1 @ X591))=>((X590)=(X591)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_214, c_0_202])). 1.15/0.73 thf(c_0_246, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X592:$i]:((((X1 @ X592))&![X593:$i]:((((X1 @ X593))=>((X592)=(X593)))))))=>((?[X594:$i]:((((X17 @ X594))&![X595:$i]:((((X17 @ X595))=>((X594)=(X595)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_215, c_0_202])). 1.15/0.73 thf(c_0_247, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 1.15/0.73 thf(c_0_248, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 1.15/0.73 thf(c_0_249, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 1.15/0.73 thf(c_0_250, 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)))=>(?[X596:$i]:(((in @ X596 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X596 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_216, c_0_197])). 1.15/0.73 thf(c_0_251, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X598:$i]:(((in @ X598 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X598 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_217, c_0_199])). 1.15/0.73 thf(c_0_252, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X599:$i]:(((in @ X599 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X599 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_218, c_0_199])). 1.15/0.73 thf(c_0_253, 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)))=>(?[X600:$i]:(((in @ X600 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X600 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_219, c_0_199])). 1.15/0.73 thf(c_0_254, plain, ((kfstsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X601:$i]:(((in @ X601 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X601 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_220, c_0_197])). 1.15/0.73 thf(c_0_255, axiom, ((theprop)=(![X21:$i]:(((?[X602:$i]:(((in @ X602 @ X21)&((X21)=(setadjoin @ X602 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_197])). 1.15/0.73 thf(c_0_256, plain, ((ksndsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X603:$i]:(((in @ X603 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X603 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_221, c_0_197])). 1.15/0.73 thf(c_0_257, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 1.15/0.73 thf(c_0_258, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 1.15/0.73 thf(c_0_259, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_222, c_0_200])). 1.15/0.73 thf(c_0_260, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 1.15/0.73 thf(c_0_261, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 1.15/0.73 thf(c_0_262, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 1.15/0.73 thf(c_0_263, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 1.15/0.73 thf(c_0_264, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X30:$i]:((((((subset @ X30 @ (cartprod @ X4 @ X5)))&![X605:$i]:(((in @ X605 @ X4)=>(?[X606:$i]:(((in @ X606 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X605 @ Z0) @ X30))))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:(((in @ (kpair @ X605 @ Z0) @ X30)))))=(setadjoin @ X606 @ emptyset)))))))))=>![X2:$i]:(((in @ X2 @ X4)=>(?[X607:$i]:(((in @ X607 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30)))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X30))))=(setadjoin @ X607 @ emptyset))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_223, c_0_197]), c_0_224])). 1.15/0.73 thf(c_0_265, plain, ((epred1_0)<=>![X1146:$i]:(?[X1147:$i]:((((![X1148:$i]:(((in @ X1148 @ X1147)=>![X1149:$i]:(((in @ X1149 @ X1148)=>(in @ X1149 @ X1146)))))&![X1150:$i, X1151:$i]:((((in @ X1150 @ X1146)&(in @ X1151 @ X1146))=>(![X1152:$i]:(((in @ X1152 @ X1147)=>((in @ X1150 @ X1152)<=>(in @ X1151 @ X1152))))=>((X1150)=(X1151))))))&![X1153:$i, X1154:$i]:((((in @ X1153 @ X1147)&(in @ X1154 @ X1147))=>(![X1155:$i]:(((in @ X1155 @ X1153)=>(in @ X1155 @ X1154)))|![X1156:$i]:(((in @ X1156 @ X1154)=>(in @ X1156 @ X1153)))))))&![X1157:$i]:(((![X1158:$i]:(((in @ X1158 @ X1157)=>(in @ X1158 @ X1146)))&?[X1159:$i]:((in @ X1159 @ X1157)))=>?[X1160:$i, X1161:$i]:(((((in @ X1160 @ X1147)&(in @ X1161 @ X1157))&~(?[X1162:$i]:(((in @ X1162 @ X1160)&(in @ X1162 @ X1157)))))&![X1163:$i]:(((in @ X1163 @ X1147)=>(![X1164:$i]:(((in @ X1164 @ X1163)=>(in @ X1164 @ X1160)))|(in @ X1161 @ X1163)))))))))))), introduced(definition)). 1.15/0.73 thf(c_0_266, negated_conjecture, ~((![X1180:$i, X1181:$i]:((![X1182:$i]:(((in @ X1182 @ X1180)<=>(in @ X1182 @ X1181)))=>((X1180)=(X1181))))=>(![X1179:$i]:(~(in @ X1179 @ emptyset))=>(![X1176:$i, X1177:$i, X1178:$i]:(((in @ X1178 @ (setadjoin @ X1176 @ X1177))<=>(((X1178)=(X1176))|(in @ X1178 @ X1177))))=>(![X1173:$i, X1174:$i]:(((in @ X1174 @ (powerset @ X1173))<=>![X1175:$i]:(((in @ X1175 @ X1174)=>(in @ X1175 @ X1173)))))=>(![X610:$i, X611:$i]:(((in @ X611 @ (setunion @ X610))<=>?[X612:$i]:(((in @ X611 @ X612)&(in @ X612 @ X610)))))=>((in @ emptyset @ omega)=>(![X1172:$i]:(((in @ X1172 @ omega)=>(in @ (setadjoin @ X1172 @ X1172) @ omega)))=>(![X1169:$i]:((((in @ emptyset @ X1169)&![X1170:$i]:((((in @ X1170 @ omega)&(in @ X1170 @ X1169))=>(in @ (setadjoin @ X1170 @ X1170) @ X1169))))=>![X1171:$i]:(((in @ X1171 @ omega)=>(in @ X1171 @ X1169)))))=>(![X613:$i > $i > $o, X614:$i]:((![X615:$i]:(((in @ X615 @ X614)=>?[X616:$i]:(((X613 @ X615 @ X616)&![X617:$i]:(((X613 @ X615 @ X617)=>((X616)=(X617))))))))=>?[X618:$i]:(![X619:$i]:(((in @ X619 @ X618)<=>?[X620:$i]:(((in @ X620 @ X614)&(X613 @ X620 @ X619))))))))=>(![X1165:$i]:((?[X1166:$i]:((in @ X1166 @ X1165))=>?[X1167:$i]:(((in @ X1167 @ X1165)&~(?[X1168:$i]:(((in @ X1168 @ X1167)&(in @ X1168 @ X1165))))))))=>((epred1_0)=>(![X1143:$i > $o]:((?[X1144:$i]:(((X1143 @ X1144)&![X1145:$i]:(((X1143 @ X1145)=>((X1144)=(X1145))))))=>(X1143 @ (descr @ (^[Z0/* 17 */:$i]:(X1143 @ Z0))))))=>(![X621:$i, X622:$i > $o, X623:$i]:(((in @ X623 @ X621)=>((X622 @ X623)=>(in @ X623 @ (dsetconstr @ X621 @ X622)))))=>(![X1140:$i, X1141:$i > $o, X1142:$i]:(((in @ X1142 @ (dsetconstr @ X1140 @ X1141))=>(in @ X1142 @ X1140)))=>(![X1137:$i, X1138:$i > $o, X1139:$i]:(((in @ X1139 @ (dsetconstr @ X1137 @ X1138))=>(X1138 @ X1139)))=>(![X624:$i > $o]:((?[X625:$i]:(((X624 @ X625)&![X626:$i]:(((X624 @ X626)=>((X625)=(X626))))))=>?[X627:$i]:(((X624 @ X627)&![X628:$i]:(((X624 @ X628)=>((X627)=(X628))))))))=>(![X1135:$o, X1136:$i]:(((in @ X1136 @ (prop2set @ ((X1135))))=>(X1135)))=>(![X1133:$i]:(((in @ X1133 @ emptyset)=>![X1134:$o]:((X1134))))=>(![X1132:$i]:(((in @ X1132 @ emptyset)=>~($true)))=>(![X1131:$i]:(~(in @ X1131 @ emptyset))=>(![X1127:$i > $o]:((?[X1128:$i]:(((X1127 @ X1128)&![X1129:$i]:(((X1127 @ X1129)=>((X1128)=(X1129))))))=>?[X1130:$i]:((X1127 @ X1130))))=>(![X629:$i, X630:$i]:((![X631:$i]:(((in @ X631 @ X629)=>(in @ X631 @ X630)))=>(![X632:$i]:(((in @ X632 @ X630)=>(in @ X632 @ X629)))=>((X629)=(X630)))))=>(![X633:$i]:((![X634:$i]:(~(in @ X634 @ X633))=>((X633)=(emptyset))))=>(![X1125:$i]:((![X1126:$i]:(~(in @ X1126 @ X1125))=>((X1125)=(emptyset))))=>(![X1122:$i, X1123:$i > $o, X1124:$i]:(((in @ X1124 @ X1122)=>((in @ X1124 @ (dsetconstr @ X1122 @ X1123))<=>(X1123 @ X1124))))=>(![X635:$i]:((((X635)!=(emptyset))=>?[X636:$i]:((in @ X636 @ X635))))=>(![X1119:$i, X1120:$i > $o, X1121:$i]:(((in @ X1121 @ X1119)=>((X1120 @ X1121)=>((dsetconstr @ X1119 @ X1120)!=(emptyset)))))=>(![X1117:$i]:((?[X1118:$i]:((in @ X1118 @ X1117))=>((X1117)!=(emptyset))))=>(![X1115:$i, X1116:$i]:((in @ X1115 @ (setadjoin @ X1115 @ X1116)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1112:$i, X1113:$i, X1114:$i]:(((in @ X1114 @ X1113)=>(in @ X1114 @ (setadjoin @ X1112 @ X1113))))=>(![X637:$i, X638:$i, X639:$i]:(((in @ X639 @ (setadjoin @ X637 @ X638))=>![X640:$o]:(((((X639)=(X637))=>(X640))=>(((in @ X639 @ X638)=>(X640))=>(X640))))))=>(![X1109:$i, X1110:$i, X1111:$i]:(((in @ X1111 @ (setadjoin @ X1109 @ X1110))=>(((X1111)=(X1109))|(in @ X1111 @ X1110))))=>(![X641:$i]:(((dsetconstr @ X641 @ (^[Z0/* 1 */:$i]:($true)))=(X641)))=>(![X642:$i, X643:$i]:((![X644:$i]:(((in @ X644 @ X643)=>(in @ X644 @ X642)))=>(in @ X643 @ (powerset @ X642))))=>(![X1108:$i]:((in @ emptyset @ (powerset @ X1108)))=>(![X1107:$i]:((in @ emptyset @ (powerset @ X1107)))=>(![X645:$i, X646:$i, X647:$i]:(((in @ X646 @ (powerset @ X645))=>((in @ X647 @ X646)=>(in @ X647 @ X645))))=>(![X648:$i, X649:$i, X650:$i]:(((in @ X649 @ X650)=>((in @ X650 @ X648)=>(in @ X649 @ (setunion @ X648)))))=>(![X651:$i, X652:$i]:(((in @ X652 @ (setunion @ X651))=>![X653:$o]:((![X654:$i]:(((in @ X652 @ X654)=>((in @ X654 @ X651)=>(X653))))=>(X653)))))=>(![X1105:$i, X1106:$i]:(((in @ X1106 @ X1105)=>(in @ X1106 @ (powerset @ (setunion @ X1105)))))=>(![X1100:$i > $o]:((?[X1101:$i]:(((X1100 @ X1101)&![X1102:$i]:(((X1100 @ X1102)=>((X1101)=(X1102))))))=>?[X1103:$i]:(![X1104:$i]:(((X1100 @ X1104)<=>((X1104)=(X1103)))))))=>(![X655:$i]:((((X655)!=(emptyset))=>?[X656:$i]:(((in @ X656 @ X655)&$true))))=>(![X1098:$i, X1099:$i]:(((in @ X1098 @ (setadjoin @ X1099 @ emptyset))=>((X1098)=(X1099))))=>(![X657:$i, X658:$i]:((((X657)!=(X658))=>~(in @ X658 @ (setadjoin @ X657 @ emptyset))))=>(![X659:$i, X660:$i]:((((X659)=(X660))=>(in @ X659 @ (setadjoin @ X660 @ emptyset))))=>(![X1096:$i, X1097:$i]:(((in @ X1096 @ (setadjoin @ X1097 @ emptyset))=>(in @ X1097 @ (setadjoin @ X1096 @ emptyset))))=>(![X661:$i, X662:$i, X663:$i]:(((in @ X663 @ (setadjoin @ X661 @ (setadjoin @ X662 @ emptyset)))=>(((X663)=(X661))|((X663)=(X662)))))=>(![X664:$i, X665:$i]:((in @ X664 @ (setadjoin @ X664 @ (setadjoin @ X665 @ emptyset))))=>(![X666:$i, X667:$i]:((in @ X667 @ (setadjoin @ X666 @ (setadjoin @ X667 @ emptyset))))=>(![X1093:$i, X1094:$i > $o]:((?[X1095:$i]:(((in @ X1095 @ X1093)&(X1094 @ X1095)))=>(((dsetconstr @ X1093 @ X1094)=(emptyset))=>~($true))))=>(![X668:$i > $o, X669:$i]:(((in @ X669 @ emptyset)=>(X668 @ X669)))=>(![X1089:$i, X1090:$i > $o]:((~(![X1091:$i]:(((in @ X1091 @ X1089)=>(X1090 @ X1091))))=>?[X1092:$i]:(((in @ X1092 @ X1089)&~((X1090 @ X1092))))))=>(![X670:$i, X671:$i > $o]:((![X672:$i]:(((in @ X672 @ X670)=>~((X671 @ X672))))=>~(?[X673:$i]:(((in @ X673 @ X670)&(X671 @ X673))))))=>(![X674:$i, X675:$i > $o]:((~(?[X676:$i]:(((in @ X676 @ X674)&(X675 @ X676))))=>![X677:$i]:(((in @ X677 @ X674)=>~((X675 @ X677))))))=>(![X678:$i, X679:$i > $o]:((?[X680:$i]:(((in @ X680 @ X678)&~((X679 @ X680))))=>~(![X681:$i]:(((in @ X681 @ X678)=>(X679 @ X681))))))=>(![X1088:$o]:(((X1088)=>(in @ emptyset @ (prop2set @ ((X1088))))))=>(![X682:$o]:(((X682)=>(set2prop @ (prop2set @ ((X682))))))=>(![X683:$i, X684:$i > $o]:((~(?[X685:$i]:(((in @ X685 @ X683)&(X684 @ X685))))=>![X686:$i]:(((in @ X686 @ X683)=>~((X684 @ X686))))))=>(![X1084:$i, X1085:$i > $o]:((~(![X1086:$i]:(((in @ X1086 @ X1084)=>(X1085 @ X1086))))=>?[X1087:$i]:(((in @ X1087 @ X1084)&~((X1085 @ X1087))))))=>(![X1079:$i > $o]:((?[X1080:$i]:(((X1079 @ X1080)&![X1081:$i]:(((X1079 @ X1081)=>((X1080)=(X1081))))))=>?[X1082:$i]:(((X1079 @ X1082)&![X1083:$i]:(((X1079 @ X1083)=>((X1082)=(X1083))))))))=>(![X1073:$i > $o]:((?[X1074:$i]:((X1073 @ X1074))=>(![X1075:$i, X1076:$i]:(((X1073 @ X1075)=>((X1073 @ X1076)=>((X1075)=(X1076)))))=>?[X1077:$i]:(((X1073 @ X1077)&![X1078:$i]:(((X1073 @ X1078)=>((X1077)=(X1078)))))))))=>(![X1068:$i > $o]:((?[X1069:$i]:(![X1070:$i]:(((X1068 @ X1070)<=>((X1070)=(X1069)))))=>?[X1071:$i]:(((X1068 @ X1071)&![X1072:$i]:(((X1068 @ X1072)=>((X1071)=(X1072))))))))=>(![X1064:$i, X1065:$i]:((((X1064)=(X1065))=>![X1066:$i, X1067:$i]:((((X1066)=(X1067))=>((in @ X1066 @ X1064)=>(in @ X1067 @ X1065))))))=>(![X687:$i, X688:$i]:((((X687)=(X688))=>![X689:$i, X690:$i]:((((X689)=(X690))=>((in @ X689 @ X687)<=>(in @ X690 @ X688))))))=>(![X691:$i > $o]:((?[X692:$i]:(((X691 @ X692)&![X693:$i]:(((X691 @ X693)=>((X692)=(X693))))))=>![X694:$i, X695:$i]:(((X691 @ X694)=>((X691 @ X695)=>((X694)=(X695)))))))=>(![X1056:$i > $o, X1057:$i > $o]:((![X1058:$i, X1059:$i]:((((X1058)=(X1059))=>((X1056 @ X1058)<=>(X1057 @ X1059))))=>(?[X1060:$i]:(((X1056 @ X1060)&![X1061:$i]:(((X1056 @ X1061)=>((X1060)=(X1061))))))<=>?[X1062:$i]:(((X1057 @ X1062)&![X1063:$i]:(((X1057 @ X1063)=>((X1062)=(X1063)))))))))=>(((emptyset)=(emptyset))=>(![X1052:$i, X1053:$i]:((((X1052)=(X1053))=>![X1054:$i, X1055:$i]:((((X1054)=(X1055))=>((setadjoin @ X1052 @ X1054)=(setadjoin @ X1053 @ X1055))))))=>(![X696:$i, X697:$i]:((((X696)=(X697))=>((powerset @ X696)=(powerset @ X697))))=>(![X698:$i, X699:$i]:((((X698)=(X699))=>((setunion @ X698)=(setunion @ X699))))=>(((omega)=(omega))=>(![X1047:$i > $o]:((?[X1048:$i]:(((X1047 @ X1048)&![X1049:$i]:(((X1047 @ X1049)=>((X1048)=(X1049))))))=>![X1050:$i, X1051:$i]:(((X1047 @ X1050)=>((X1047 @ X1051)=>((X1050)=(X1051)))))))=>(![X700:$i > $o, X701:$i > $o]:((![X702:$i, X703:$i]:((((X702)=(X703))=>((X700 @ X702)<=>(X701 @ X703))))=>(?[X704:$i]:(((X700 @ X704)&![X705:$i]:(((X700 @ X705)=>((X704)=(X705))))))=>(?[X706:$i]:(((X701 @ X706)&![X707:$i]:(((X701 @ X707)=>((X706)=(X707))))))=>((descr @ X700)=(descr @ X701))))))=>(![X708:$i, X709:$i]:((((X708)=(X709))=>![X710:$i > $o, X711:$i > $o]:((![X712:$i]:(((in @ X712 @ X708)=>![X713:$i]:(((in @ X713 @ X709)=>(((X712)=(X713))=>((X710 @ X712)<=>(X711 @ X713)))))))=>((dsetconstr @ X708 @ X710)=(dsetconstr @ X709 @ X711))))))=>(![X714:$i, X715:$i]:((![X716:$i]:(((in @ X716 @ X714)=>(in @ X716 @ X715)))=>(subset @ X714 @ X715)))=>(![X717:$i, X718:$i]:((((X717)=(X718))=>(subset @ X718 @ X717)))=>(![X1045:$i, X1046:$i]:((((X1045)=(X1046))=>(subset @ X1045 @ X1046)))=>(![X1042:$i, X1043:$i]:((![X1044:$i]:(((in @ X1044 @ X1042)=>(in @ X1044 @ X1043)))=>(subset @ X1042 @ X1043)))=>(![X719:$i]:((subset @ emptyset @ X719))=>(![X1039:$i, X1040:$i, X1041:$i]:(((subset @ X1039 @ X1040)=>((in @ X1041 @ X1039)=>(in @ X1041 @ X1040))))=>(![X1036:$i, X1037:$i, X1038:$i]:(((subset @ X1036 @ X1037)=>(~(in @ X1038 @ X1037)=>~(in @ X1038 @ X1036))))=>(![X1033:$i, X1034:$i, X1035:$i]:(((in @ X1035 @ X1033)=>(~(in @ X1035 @ X1034)=>~(subset @ X1033 @ X1034))))=>(![X1031:$i, X1032:$i]:((~(subset @ X1031 @ X1032)=>((X1031)!=(X1032))))=>(![X1028:$i, X1029:$i, X1030:$i]:(((in @ X1030 @ X1028)=>(~(in @ X1030 @ X1029)=>((X1028)!=(X1029)))))=>(![X720:$i]:((subset @ X720 @ X720))=>(![X721:$i, X722:$i, X723:$i]:(((subset @ X721 @ X722)=>((subset @ X722 @ X723)=>(subset @ X721 @ X723))))=>(![X1026:$i, X1027:$i]:((subset @ X1027 @ (setadjoin @ X1026 @ 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def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setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_225]), foundationAx]), wellorderingAx]), c_0_226]), c_0_227]), c_0_228]), c_0_229]), c_0_230]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_231]), setext]), emptyI]), noeltsimpempty]), c_0_232]), c_0_233]), c_0_234]), c_0_235]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_236]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_237]), c_0_238]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_239]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_240]), c_0_241]), c_0_242]), inCongP]), in__Cong]), c_0_243]), c_0_244]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_245]), c_0_246]), c_0_247]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_248]), c_0_249]), 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_250]), c_0_251]), c_0_252]), c_0_253]), singletonsuniq]), setukpairinjL1]), c_0_254]), c_0_255]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_256]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_257]), c_0_258]), c_0_259]), c_0_260]), c_0_261]), c_0_262]), c_0_263]), c_0_224]), c_0_264])])]), c_0_265])). 1.15/0.73 thf(c_0_267, negated_conjecture, ![X1187:$i, X1188:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$i, X1200:$i, X1201:$i, X1203:$i, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1209:$i, X1210:$i > $i > $o, X1211:$i, X1213:$i, X1216:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1223:$i, X1224:$i > $o, X1225:$i, X1227:$i, X1228:$i > $o, X1229:$i, X1230:$i, X1231:$i > $o, X1232:$i, X1233:$i, X1234:$i > $o, X1235:$i, X1236:$i > $o, X1237:$i, X1240:$i, X1241:$o, X1242:$i, X1243:$i, X1244:$o, X1245:$i, X1246:$i, X1247:$i > $o, X1248:$i, X1251:$i, X1252:$i, X1255:$i, X1257:$i, X1259:$i, X1260:$i > $o, X1261:$i, X1262:$i, X1264:$i, X1265:$i > $o, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$o, X1278:$i, X1279:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$o, X1297:$i, X1298:$i, X1299:$i > $o, X1300:$i, X1303:$i, X1304:$i, X1305:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i > $o, X1324:$i, X1325:$i > $o, X1326:$i, X1327:$i, X1328:$i > $o, X1329:$i, X1331:$i, X1332:$i > $o, X1334:$i, X1335:$i, X1336:$i > $o, X1338:$i, X1339:$i, X1340:$i > $o, X1341:$i, X1343:$o, X1344:$o, X1345:$i, X1346:$i > $o, X1348:$i, X1349:$i, X1350:$i > $o, X1351:$i, X1353:$i > $o, X1354:$i, X1357:$i, X1358:$i > $o, X1359:$i, X1363:$i, X1364:$i > $o, X1365:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i > $o, X1378:$i, X1380:$i, X1381:$i, X1382:$i > $o, X1383:$i > $o, X1386:$i, X1389:$i, X1390:$i, X1393:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i > $o, X1403:$i, X1405:$i, X1406:$i, X1407:$i > $o, X1408:$i > $o, X1411:$i, X1413:$i, X1415:$i, X1416:$i, X1417:$i > $o, X1418:$i > $o, X1421:$i, X1422:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$i, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i > $o, X1469:$i, X1470:$i > $o, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$o, X1483:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$i, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$o, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i > $o, X1625:$i, X1627:$i, X1628:$i > $o, X1629:$i, X1631:$i, X1632:$i > $o, X1633:$i, X1636:$i, X1637:$i > $o, X1640:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1647:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1685:$i, X1686:$i, X1687:$i, X1688:$i, X1689:$i, X1690:$i, X1691:$i, X1692:$i, X1693:$i, X1694:$i, X1695:$i, X1696:$i, X1697:$i, X1698:$i, X1699:$i, X1700:$i, X1701:$i, X1702:$i, X1703:$i, X1704:$i, X1705:$i, X1706:$i, X1707:$i, X1708:$i, X1709:$i, X1710:$i, X1711:$i, X1712:$i, X1713:$i, X1714:$i, X1715:$i, X1716:$i > $i > $o, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i > $i > $o, X1722:$i, X1723:$i, X1724:$i > $i > $o, X1725:$i, X1726:$i, X1727:$i > $i > $o, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i > $i > $o, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i > $i > $o, X1738:$i, X1739:$i, X1740:$i, X1741:$i, X1742:$i > $i > $o, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1749:$i, X1750:$i, X1755:$i]:((((~(in @ (esk1_2 @ X1187 @ X1188) @ X1187)|~(in @ (esk1_2 @ X1187 @ X1188) @ X1188)|((X1187)=(X1188)))&((in @ (esk1_2 @ X1187 @ X1188) @ X1187)|(in @ (esk1_2 @ X1187 @ X1188) @ X1188)|((X1187)=(X1188))))&(~(in @ X1190 @ emptyset)&(((~(in @ X1193 @ (setadjoin @ X1191 @ X1192))|(((X1193)=(X1191))|(in @ X1193 @ X1192)))&((((X1193)!=(X1191))|(in @ X1193 @ (setadjoin @ X1191 @ X1192)))&(~(in @ X1193 @ X1192)|(in @ X1193 @ (setadjoin @ X1191 @ X1192)))))&(((~(in @ X1195 @ (powerset @ X1194))|(~(in @ X1196 @ X1195)|(in @ X1196 @ X1194)))&(((in @ (esk2_2 @ X1197 @ X1198) @ X1198)|(in @ X1198 @ (powerset @ X1197)))&(~(in @ (esk2_2 @ X1197 @ X1198) @ X1197)|(in @ X1198 @ (powerset @ X1197)))))&(((((in @ X1201 @ (esk3_2 @ X1200 @ X1201))|~(in @ X1201 @ (setunion @ X1200)))&((in @ (esk3_2 @ X1200 @ X1201) @ 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X1618)&((subset @ X1619 @ (setunion @ (setadjoin @ X1619 @ emptyset)))&(((setunion @ (setadjoin @ X1620 @ emptyset))=(X1620))&(((((in @ (esk60_2 @ X1621 @ X1622) @ (dsetconstr @ X1621 @ X1622))|(~(in @ X1625 @ X1621)|~(X1622 @ X1625))|(in @ (esk58_2 @ X1621 @ X1622) @ X1621))&(((dsetconstr @ X1621 @ X1622)=(setadjoin @ (esk60_2 @ X1621 @ X1622) @ emptyset))|(~(in @ X1625 @ X1621)|~(X1622 @ X1625))|(in @ (esk58_2 @ X1621 @ X1622) @ X1621)))&((((in @ (esk60_2 @ X1621 @ X1622) @ (dsetconstr @ X1621 @ X1622))|(~(in @ X1625 @ X1621)|~(X1622 @ X1625))|(in @ (esk59_2 @ X1621 @ X1622) @ X1621))&(((dsetconstr @ X1621 @ X1622)=(setadjoin @ (esk60_2 @ X1621 @ X1622) @ emptyset))|(~(in @ X1625 @ X1621)|~(X1622 @ X1625))|(in @ (esk59_2 @ X1621 @ X1622) @ X1621)))&((((in @ (esk60_2 @ X1621 @ X1622) @ (dsetconstr @ X1621 @ X1622))|(~(in @ X1625 @ X1621)|~(X1622 @ X1625))|(X1622 @ (esk58_2 @ X1621 @ X1622)))&(((dsetconstr @ X1621 @ X1622)=(setadjoin @ (esk60_2 @ X1621 @ X1622) @ emptyset))|(~(in @ X1625 @ X1621)|~(X1622 @ X1625))|(X1622 @ (esk58_2 @ X1621 @ X1622))))&((((in @ (esk60_2 @ X1621 @ X1622) @ (dsetconstr @ X1621 @ X1622))|(~(in @ X1625 @ X1621)|~(X1622 @ X1625))|(X1622 @ (esk59_2 @ X1621 @ X1622)))&(((dsetconstr @ X1621 @ X1622)=(setadjoin @ (esk60_2 @ X1621 @ X1622) @ emptyset))|(~(in @ X1625 @ X1621)|~(X1622 @ X1625))|(X1622 @ (esk59_2 @ X1621 @ X1622))))&(((in @ (esk60_2 @ X1621 @ X1622) @ (dsetconstr @ X1621 @ X1622))|(~(in @ X1625 @ X1621)|~(X1622 @ X1625))|((esk58_2 @ X1621 @ X1622)!=(esk59_2 @ X1621 @ X1622)))&(((dsetconstr @ X1621 @ X1622)=(setadjoin @ (esk60_2 @ X1621 @ X1622) @ emptyset))|(~(in @ X1625 @ X1621)|~(X1622 @ X1625))|((esk58_2 @ X1621 @ X1622)!=(esk59_2 @ X1621 @ X1622))))))))&((((in @ (esk61_2 @ X1627 @ X1628) @ X1627)|(~(in @ X1629 @ (dsetconstr @ X1627 @ X1628))|((dsetconstr @ X1627 @ X1628)!=(setadjoin @ X1629 @ emptyset))))&((X1628 @ (esk61_2 @ X1627 @ X1628))|(~(in @ X1629 @ (dsetconstr @ X1627 @ X1628))|((dsetconstr @ X1627 @ X1628)!=(setadjoin @ X1629 @ emptyset)))))&(((((in @ (esk63_3 @ X1631 @ X1632 @ X1633) @ (dsetconstr @ X1631 @ X1632))|(in @ (esk62_3 @ X1631 @ X1632 @ X1633) @ X1631)|~(X1632 @ X1633)|~(in @ X1633 @ X1631))&(((dsetconstr @ X1631 @ X1632)=(setadjoin @ (esk63_3 @ X1631 @ X1632 @ X1633) @ emptyset))|(in @ (esk62_3 @ X1631 @ X1632 @ X1633) @ X1631)|~(X1632 @ X1633)|~(in @ X1633 @ X1631)))&((((in @ (esk63_3 @ X1631 @ X1632 @ X1633) @ (dsetconstr @ X1631 @ X1632))|(X1632 @ (esk62_3 @ X1631 @ X1632 @ X1633))|~(X1632 @ X1633)|~(in @ X1633 @ X1631))&(((dsetconstr @ X1631 @ X1632)=(setadjoin @ (esk63_3 @ X1631 @ X1632 @ X1633) @ emptyset))|(X1632 @ (esk62_3 @ X1631 @ X1632 @ X1633))|~(X1632 @ X1633)|~(in @ X1633 @ X1631)))&(((in @ (esk63_3 @ X1631 @ X1632 @ X1633) @ (dsetconstr @ X1631 @ X1632))|((esk62_3 @ X1631 @ X1632 @ X1633)!=(X1633))|~(X1632 @ X1633)|~(in @ X1633 @ X1631))&(((dsetconstr @ X1631 @ X1632)=(setadjoin @ (esk63_3 @ X1631 @ X1632 @ X1633) @ emptyset))|((esk62_3 @ X1631 @ X1632 @ X1633)!=(X1633))|~(X1632 @ X1633)|~(in @ X1633 @ X1631)))))&(((((in @ (esk66_2 @ X1636 @ X1637) @ (dsetconstr @ X1636 @ X1637))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|(in @ (esk64_2 @ X1636 @ X1637) @ X1636))&(((dsetconstr @ X1636 @ X1637)=(setadjoin @ (esk66_2 @ X1636 @ X1637) @ emptyset))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|(in @ (esk64_2 @ X1636 @ X1637) @ X1636)))&((((in @ (esk66_2 @ X1636 @ X1637) @ (dsetconstr @ X1636 @ X1637))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|(in @ (esk65_2 @ X1636 @ X1637) @ X1636))&(((dsetconstr @ X1636 @ X1637)=(setadjoin @ (esk66_2 @ X1636 @ X1637) @ emptyset))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|(in @ (esk65_2 @ X1636 @ X1637) @ X1636)))&((((in @ (esk66_2 @ X1636 @ X1637) @ (dsetconstr @ X1636 @ X1637))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|(X1637 @ (esk64_2 @ X1636 @ X1637)))&(((dsetconstr @ X1636 @ X1637)=(setadjoin @ (esk66_2 @ X1636 @ X1637) @ emptyset))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|(X1637 @ (esk64_2 @ X1636 @ X1637))))&((((in @ (esk66_2 @ X1636 @ X1637) @ (dsetconstr @ X1636 @ X1637))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|(X1637 @ (esk65_2 @ X1636 @ X1637)))&(((dsetconstr @ X1636 @ X1637)=(setadjoin @ (esk66_2 @ X1636 @ X1637) @ emptyset))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|(X1637 @ (esk65_2 @ X1636 @ X1637))))&(((in @ (esk66_2 @ X1636 @ X1637) @ (dsetconstr @ X1636 @ X1637))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|((esk64_2 @ X1636 @ X1637)!=(esk65_2 @ X1636 @ X1637)))&(((dsetconstr @ X1636 @ X1637)=(setadjoin @ (esk66_2 @ X1636 @ X1637) @ emptyset))|(~(in @ X1640 @ X1636)|~(X1637 @ X1640))|((esk64_2 @ X1636 @ X1637)!=(esk65_2 @ X1636 @ X1637))))))))&((((setadjoin @ X1642 @ emptyset)!=(setadjoin @ X1643 @ emptyset))|((X1642)=(X1643)))&((~(in @ (setadjoin @ X1646 @ emptyset) @ (setadjoin @ (setadjoin @ X1644 @ emptyset) @ (setadjoin @ (setadjoin @ X1644 @ (setadjoin @ X1645 @ emptyset)) @ emptyset)))|((X1644)=(X1646)))&((((in @ (esk67_1 @ X1647) @ (dsetconstr @ (setunion @ X1647) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1647)))))|~(iskpair @ X1647))&(((dsetconstr @ (setunion @ X1647) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1647))))=(setadjoin @ (esk67_1 @ X1647) @ emptyset))|~(iskpair @ X1647)))&((~(in @ X1650 @ X1649)|((X1649)!=(setadjoin @ X1650 @ emptyset))|(in @ (setunion @ X1649) @ X1649))&(((kfst @ (kpair @ X1651 @ X1652))=(X1651))&((~(in @ X1655 @ (cartprod @ X1653 @ X1654))|(in @ (kfst @ X1655) @ X1653))&((((setadjoin @ (setadjoin @ X1656 @ emptyset) @ (setadjoin @ (setadjoin @ X1656 @ (setadjoin @ X1657 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1658 @ emptyset) @ (setadjoin @ (setadjoin @ X1658 @ (setadjoin @ X1659 @ emptyset)) @ emptyset)))|((X1656)=(X1658)))&((((kpair @ X1660 @ X1661)!=(kpair @ X1662 @ X1663))|((X1660)=(X1662)))&((((X1664)!=(X1665))|((setadjoin @ X1664 @ (setadjoin @ X1665 @ emptyset))=(setadjoin @ X1664 @ emptyset)))&((((X1666)!=(X1667))|((setadjoin @ (setadjoin @ X1666 @ emptyset) @ (setadjoin @ (setadjoin @ X1666 @ (setadjoin @ X1667 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1666 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1668 @ emptyset) @ (setadjoin @ (setadjoin @ X1668 @ (setadjoin @ X1669 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1670 @ emptyset) @ (setadjoin @ (setadjoin @ X1670 @ (setadjoin @ X1671 @ emptyset)) @ emptyset)))|(((X1670)!=(X1671))|((X1669)=(X1671))))&((((setadjoin @ X1672 @ (setadjoin @ X1673 @ emptyset))!=(setadjoin @ X1674 @ emptyset))|((X1672)=(X1673)))&((((setadjoin @ (setadjoin @ X1675 @ emptyset) @ (setadjoin @ (setadjoin @ X1675 @ (setadjoin @ X1676 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1677 @ emptyset) @ (setadjoin @ (setadjoin @ X1677 @ (setadjoin @ X1678 @ emptyset)) @ emptyset)))|((X1676)=(X1678)))&((((kpair @ X1679 @ X1680)!=(kpair @ X1681 @ X1682))|((X1680)=(X1682)))&((((in @ (esk68_1 @ X1683) @ (dsetconstr @ (setunion @ X1683) @ (^[Z0/* 3 */:$i]:(((X1683)=(kpair @ (kfst @ X1683) @ Z0))))))|~(iskpair @ X1683))&(((dsetconstr @ (setunion @ X1683) @ (^[Z0/* 3 */:$i]:(((X1683)=(kpair @ (kfst @ X1683) @ Z0)))))=(setadjoin @ (esk68_1 @ X1683) @ emptyset))|~(iskpair @ X1683)))&(((ksnd @ (kpair @ X1685 @ X1686))=(X1686))&((~(iskpair @ X1687)|((kpair @ (kfst @ X1687) @ (ksnd @ X1687))=(X1687)))&((~(in @ X1690 @ (cartprod @ X1688 @ X1689))|(in @ (ksnd @ X1690) @ X1689))&((~(in @ (kpair @ X1693 @ X1694) @ (cartprod @ X1691 @ X1692))|(in @ X1693 @ X1691))&((~(in @ (kpair @ X1697 @ X1698) @ (cartprod @ X1695 @ X1696))|(in @ X1698 @ X1696))&((~(in @ X1701 @ X1699)|(~(in @ X1702 @ X1700)|((kpair @ X1701 @ X1702)=(kpair @ X1701 @ X1702))))&((~(in @ X1705 @ X1703)|(~(in @ X1706 @ X1704)|((kfst @ (kpair @ X1705 @ X1706))=(X1705))))&((~(in @ X1709 @ X1707)|(~(in @ X1710 @ X1708)|((ksnd @ (kpair @ X1709 @ X1710))=(X1710))))&((~(in @ X1713 @ (cartprod @ X1711 @ X1712))|((kpair @ (kfst @ X1713) @ (ksnd @ X1713))=(X1713)))&((~(in @ X1717 @ X1714)|(~(in @ X1718 @ X1715)|(~(X1716 @ X1717 @ X1718)|(in @ (kpair @ X1717 @ X1718) @ (dpsetconstr @ X1714 @ X1715 @ X1716)))))&((subset @ (dpsetconstr @ X1719 @ X1720 @ X1721) @ (cartprod @ X1719 @ X1720))&((subset @ (dpsetconstr @ X1722 @ X1723 @ X1724) @ (cartprod @ X1722 @ X1723))&((~(in @ X1728 @ X1725)|(~(in @ X1729 @ X1726)|(~(in @ (kpair @ X1728 @ X1729) @ (dpsetconstr @ X1725 @ X1726 @ X1727))|(X1727 @ X1728 @ X1729))))&((~(in @ (kpair @ X1733 @ X1734) @ (dpsetconstr @ X1730 @ X1731 @ X1732))|(in @ X1733 @ X1730))&((~(in @ (kpair @ X1738 @ X1739) @ (dpsetconstr @ X1735 @ X1736 @ X1737))|(in @ X1739 @ X1736))&((~(in @ (kpair @ X1743 @ X1744) @ (dpsetconstr @ X1740 @ X1741 @ X1742))|(X1742 @ X1743 @ X1744))&(((((in @ (esk70_4 @ X1745 @ X1746 @ X1747 @ X1750) @ (dsetconstr @ X1746 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1750 @ Z0) @ X1747)))))|~(in @ X1750 @ X1745)|((in @ (esk69_3 @ X1745 @ X1746 @ X1747) @ X1745)|~(subset @ X1747 @ (cartprod @ X1745 @ X1746))))&(((dsetconstr @ X1746 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1750 @ Z0) @ X1747))))=(setadjoin @ (esk70_4 @ X1745 @ X1746 @ X1747 @ X1750) @ emptyset))|~(in @ X1750 @ X1745)|((in @ (esk69_3 @ X1745 @ X1746 @ X1747) @ X1745)|~(subset @ X1747 @ (cartprod @ X1745 @ X1746)))))&(((in @ (esk70_4 @ X1745 @ X1746 @ X1747 @ X1750) @ (dsetconstr @ X1746 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1750 @ Z0) @ X1747)))))|~(in @ X1750 @ X1745)|(~(in @ X1749 @ (dsetconstr @ X1746 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ (esk69_3 @ X1745 @ X1746 @ X1747) @ Z0) @ X1747)))))|((dsetconstr @ X1746 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ (esk69_3 @ X1745 @ X1746 @ X1747) @ Z0) @ X1747))))!=(setadjoin @ X1749 @ emptyset))|~(subset @ X1747 @ (cartprod @ X1745 @ X1746))))&(((dsetconstr @ X1746 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1750 @ Z0) @ X1747))))=(setadjoin @ (esk70_4 @ X1745 @ X1746 @ X1747 @ X1750) @ emptyset))|~(in @ X1750 @ X1745)|(~(in @ X1749 @ (dsetconstr @ X1746 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ (esk69_3 @ X1745 @ X1746 @ X1747) @ Z0) @ X1747)))))|((dsetconstr @ X1746 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ (esk69_3 @ X1745 @ X1746 @ X1747) @ Z0) @ X1747))))!=(setadjoin @ X1749 @ emptyset))|~(subset @ X1747 @ (cartprod @ X1745 @ X1746))))))&(((subset @ esk73_0 @ (cartprod @ esk71_0 @ esk72_0))&(((in @ (esk74_1 @ X1755) @ (dsetconstr @ esk72_0 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1755 @ Z0) @ esk73_0)))))|~(in @ X1755 @ esk71_0))&(((dsetconstr @ esk72_0 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X1755 @ Z0) @ esk73_0))))=(setadjoin @ (esk74_1 @ X1755) @ emptyset))|~(in @ X1755 @ esk71_0))))&((in @ esk75_0 @ esk71_0)&~(in @ (setunion @ (dsetconstr @ esk72_0 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ esk75_0 @ Z0) @ esk73_0))))) @ esk72_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_266])])])])])])])). 1.15/0.73 thf(c_0_268, plain, ![X1779:$i, X1780:$i, X1777:$i]:(((epred2_1 @ X1777 @ X1780 @ X1779)<=>(in @ (kpair @ X1777 @ X1779) @ X1780))), introduced(definition)). 1.15/0.73 thf(c_0_269, negated_conjecture, ![X2:$i]:((((dsetconstr @ esk72_0 @ (epred2_1 @ X2 @ esk73_0))=(setadjoin @ (esk74_1 @ X2) @ emptyset))|~((in @ X2 @ esk71_0)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_267]), c_0_268])). 1.15/0.73 thf(c_0_270, negated_conjecture, (in @ esk75_0 @ esk71_0), inference(split_conjunct,[status(thm)],[c_0_267])). 1.15/0.73 thf(c_0_271, negated_conjecture, ~((((in @ (setunion @ (dsetconstr @ esk72_0 @ (epred2_1 @ esk75_0 @ esk73_0))) @ esk72_0))=(($true)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_267]), c_0_268])). 1.15/0.73 thf(c_0_272, negated_conjecture, ![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2))), inference(split_conjunct,[status(thm)],[c_0_267])). 1.15/0.73 thf(c_0_273, negated_conjecture, ((setadjoin @ (esk74_1 @ esk75_0) @ emptyset)=(dsetconstr @ esk72_0 @ (epred2_1 @ esk75_0 @ esk73_0))), inference(spm,[status(thm)],[c_0_269, c_0_270])). 1.15/0.73 thf(c_0_274, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_267])). 1.15/0.73 thf(c_0_275, negated_conjecture, ~((in @ (setunion @ (dsetconstr @ esk72_0 @ (epred2_1 @ esk75_0 @ esk73_0))) @ esk72_0)), inference(cn,[status(thm)],[c_0_271])). 1.15/0.73 thf(c_0_276, negated_conjecture, ((setunion @ (dsetconstr @ esk72_0 @ (epred2_1 @ esk75_0 @ esk73_0)))=(esk74_1 @ esk75_0)), inference(spm,[status(thm)],[c_0_272, c_0_273])). 1.15/0.73 thf(c_0_277, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((in @ X2 @ X3)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_267])). 1.15/0.73 thf(c_0_278, negated_conjecture, (in @ (esk74_1 @ esk75_0) @ (dsetconstr @ esk72_0 @ (epred2_1 @ esk75_0 @ esk73_0))), inference(spm,[status(thm)],[c_0_274, c_0_273])). 1.15/0.73 thf(c_0_279, negated_conjecture, ~((in @ (esk74_1 @ esk75_0) @ esk72_0)), inference(rw,[status(thm)],[c_0_275, c_0_276])). 1.15/0.73 thf(c_0_280, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_277, c_0_278]), c_0_279]), ['proof']). 1.15/0.73 # SZS output end CNFRefutation 1.15/0.73 # Parsed axioms : 421 1.15/0.73 # Removed by relevancy pruning/SinE : 0 1.15/0.73 # Initial clauses : 586 1.15/0.73 # Removed in clause preprocessing : 252 1.15/0.73 # Initial clauses in saturation : 334 1.15/0.73 # Processed clauses : 394 1.15/0.73 # ...of these trivial : 9 1.15/0.73 # ...subsumed : 29 1.15/0.73 # ...remaining for further processing : 356 1.15/0.73 # Other redundant clauses eliminated : 20 1.15/0.73 # Clauses deleted for lack of memory : 0 1.15/0.73 # Backward-subsumed : 0 1.15/0.73 # Backward-rewritten : 2 1.15/0.73 # Generated clauses : 60 1.15/0.73 # ...of the previous two non-redundant : 42 1.15/0.73 # ...aggressively subsumed : 0 1.15/0.73 # Contextual simplify-reflections : 0 1.15/0.73 # Paramodulations : 24 1.15/0.73 # Factorizations : 0 1.15/0.73 # NegExts : 1 1.15/0.73 # Equation resolutions : 20 1.15/0.73 # Disequality decompositions : 0 1.15/0.73 # Total rewrite steps : 42 1.15/0.73 # ...of those cached : 22 1.15/0.73 # Propositional unsat checks : 0 1.15/0.73 # Propositional check models : 0 1.15/0.73 # Propositional check unsatisfiable : 0 1.15/0.73 # Propositional clauses : 0 1.15/0.73 # Propositional clauses after purity: 0 1.15/0.73 # Propositional unsat core size : 0 1.15/0.73 # Propositional preprocessing time : 0.000 1.15/0.73 # Propositional encoding time : 0.000 1.15/0.73 # Propositional solver time : 0.000 1.15/0.73 # Success case prop preproc time : 0.000 1.15/0.73 # Success case prop encoding time : 0.000 1.15/0.73 # Success case prop solver time : 0.000 1.15/0.73 # Current number of processed clauses : 48 1.15/0.73 # Positive orientable unit clauses : 23 1.15/0.73 # Positive unorientable unit clauses: 0 1.15/0.73 # Negative unit clauses : 10 1.15/0.73 # Non-unit-clauses : 15 1.15/0.73 # Current number of unprocessed clauses: 272 1.15/0.73 # ...number of literals in the above : 882 1.15/0.73 # Current number of archived formulas : 0 1.15/0.73 # Current number of archived clauses : 294 1.15/0.73 # Clause-clause subsumption calls (NU) : 14849 1.15/0.73 # Rec. Clause-clause subsumption calls : 6102 1.15/0.73 # Non-unit clause-clause subsumptions : 22 1.15/0.73 # Unit Clause-clause subsumption calls : 56 1.15/0.73 # Rewrite failures with RHS unbound : 0 1.15/0.73 # BW rewrite match attempts : 15 1.15/0.73 # BW rewrite match successes : 2 1.15/0.73 # Condensation attempts : 0 1.15/0.73 # Condensation successes : 0 1.15/0.73 # Termbank termtop insertions : 69423 1.15/0.73 # Search garbage collected termcells : 19487 1.15/0.73 1.15/0.73 # ------------------------------------------------- 1.15/0.73 # User time : 0.119 s 1.15/0.73 # System time : 0.013 s 1.15/0.73 # Total time : 0.132 s 1.15/0.73 # Maximum resident set size: 6496 pages 1.15/0.73 1.15/0.73 # ------------------------------------------------- 1.15/0.73 # User time : 0.295 s 1.15/0.73 # System time : 0.032 s 1.15/0.73 # Total time : 0.327 s 1.15/0.73 # Maximum resident set size: 2464 pages 1.15/0.73 % E---3.1 exiting 1.15/0.73 % E exiting 1.15/0.73 EOF