0.04/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.09 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM 0.09/0.29 % Computer : n014.cluster.edu 0.09/0.29 % Model : x86_64 x86_64 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.29 % Memory : 8042.1875MB 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.29 % CPULimit : 1920 0.09/0.29 % WCLimit : 240 0.09/0.29 % DateTime : Wed Jul 30 10:38:49 EDT 2025 0.09/0.29 % CPUTime : 0.15/0.41 Running higher-order theorem proving 0.15/0.45 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p 1194.21/150.62 # Version: 3.0.0-ho 1194.21/150.62 # Preprocessing class: HSLMSLSSLLLCHSA. 1194.21/150.62 # Scheduled 5 strats onto 8 cores with 240 seconds (1920 total) 1194.21/150.62 # Starting ho_unfolding_5 with 960s (4) cores 1194.21/150.62 # Starting pre_casc_3 with 240s (1) cores 1194.21/150.62 # Starting new_ho_10_cnf2 with 240s (1) cores 1194.21/150.62 # Starting full_lambda_10 with 240s (1) cores 1194.21/150.62 # Starting ehoh_best_nonlift_rwall with 240s (1) cores 1194.21/150.62 # ho_unfolding_5 with pid 22361 completed with status 0 1194.21/150.62 # Result found by ho_unfolding_5 1194.21/150.62 # Preprocessing class: HSLMSLSSLLLCHSA. 1194.21/150.62 # Scheduled 5 strats onto 8 cores with 240 seconds (1920 total) 1194.21/150.62 # Starting ho_unfolding_5 with 960s (4) cores 1194.21/150.62 # No SInE strategy applied 1194.21/150.62 # Search class: HGHSM-FSLM32-MHSMMSBN 1194.21/150.62 # Scheduled 12 strats onto 4 cores with 960 seconds (960 total) 1194.21/150.62 # Starting full_lambda_5 with 79s (1) cores 1194.21/150.62 # Starting ho_unfolding_5 with 97s (1) cores 1194.21/150.62 # Starting pre_casc_4 with 79s (1) cores 1194.21/150.62 # Starting pre_casc_3 with 79s (1) cores 1194.21/150.62 # full_lambda_5 with pid 22370 completed with status 8 1194.21/150.62 # Starting almost_fo_4 with 79s (1) cores 1194.21/150.62 # pre_casc_4 with pid 22372 completed with status 8 1194.21/150.62 # Starting post_as_ho9 with 79s (1) cores 1194.21/150.62 # pre_casc_3 with pid 22373 completed with status 8 1194.21/150.62 # Starting new_ho_9 with 79s (1) cores 1194.21/150.62 # ho_unfolding_5 with pid 22371 completed with status 8 1194.21/150.62 # Starting ho_unfolding_8 with 79s (1) cores 1194.21/150.62 # almost_fo_4 with pid 22442 completed with status 0 1194.21/150.62 # Result found by almost_fo_4 1194.21/150.62 # Preprocessing class: HSLMSLSSLLLCHSA. 1194.21/150.62 # Scheduled 5 strats onto 8 cores with 240 seconds (1920 total) 1194.21/150.62 # Starting ho_unfolding_5 with 960s (4) cores 1194.21/150.62 # No SInE strategy applied 1194.21/150.62 # Search class: HGHSM-FSLM32-MHSMMSBN 1194.21/150.62 # Scheduled 12 strats onto 4 cores with 960 seconds (960 total) 1194.21/150.62 # Starting full_lambda_5 with 79s (1) cores 1194.21/150.62 # Starting ho_unfolding_5 with 97s (1) cores 1194.21/150.62 # Starting pre_casc_4 with 79s (1) cores 1194.21/150.62 # Starting pre_casc_3 with 79s (1) cores 1194.21/150.62 # full_lambda_5 with pid 22370 completed with status 8 1194.21/150.62 # Starting almost_fo_4 with 79s (1) cores 1194.21/150.62 # Preprocessing time : 0.077 s 1194.21/150.62 # Presaturation interreduction done 1194.21/150.62 1194.21/150.62 # Proof found! 1194.21/150.62 # SZS status Theorem 1194.21/150.62 # SZS output start CNFRefutation 1194.21/150.62 thf(decl_23, type, in: $i > $i > $o). 1194.21/150.62 thf(decl_24, type, exu: ($i > $o) > $o). 1194.21/150.62 thf(decl_25, type, setextAx: $o). 1194.21/150.62 thf(decl_26, type, emptyset: $i). 1194.21/150.62 thf(decl_27, type, emptysetAx: $o). 1194.21/150.62 thf(decl_28, type, setadjoin: $i > $i > $i). 1194.21/150.62 thf(decl_29, type, setadjoinAx: $o). 1194.21/150.62 thf(decl_30, type, powerset: $i > $i). 1194.21/150.62 thf(decl_31, type, powersetAx: $o). 1194.21/150.62 thf(decl_32, type, setunion: $i > $i). 1194.21/150.62 thf(decl_33, type, setunionAx: $o). 1194.21/150.62 thf(decl_34, type, omega: $i). 1194.21/150.62 thf(decl_35, type, omega0Ax: $o). 1194.21/150.62 thf(decl_36, type, omegaSAx: $o). 1194.21/150.62 thf(decl_37, type, omegaIndAx: $o). 1194.21/150.62 thf(decl_38, type, replAx: $o). 1194.21/150.62 thf(decl_39, type, foundationAx: $o). 1194.21/150.62 thf(decl_40, type, wellorderingAx: $o). 1194.21/150.62 thf(decl_41, type, descr: ($i > $o) > $i). 1194.21/150.62 thf(decl_42, type, descrp: $o). 1194.21/150.62 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_44, type, dsetconstrI: $o). 1194.21/150.62 thf(decl_45, type, dsetconstrEL: $o). 1194.21/150.62 thf(decl_46, type, dsetconstrER: $o). 1194.21/150.62 thf(decl_47, type, exuE1: $o). 1194.21/150.62 thf(decl_48, type, prop2set: $o > $i). 1194.21/150.62 thf(decl_49, type, prop2setE: $o). 1194.21/150.62 thf(decl_50, type, emptysetE: $o). 1194.21/150.62 thf(decl_51, type, emptysetimpfalse: $o). 1194.21/150.62 thf(decl_52, type, notinemptyset: $o). 1194.21/150.62 thf(decl_53, type, exuE3e: $o). 1194.21/150.62 thf(decl_54, type, setext: $o). 1194.21/150.62 thf(decl_55, type, emptyI: $o). 1194.21/150.62 thf(decl_56, type, noeltsimpempty: $o). 1194.21/150.62 thf(decl_57, type, setbeta: $o). 1194.21/150.62 thf(decl_58, type, nonempty: $i > $o). 1194.21/150.62 thf(decl_59, type, nonemptyE1: $o). 1194.21/150.62 thf(decl_60, type, nonemptyI: $o). 1194.21/150.62 thf(decl_61, type, nonemptyI1: $o). 1194.21/150.62 thf(decl_62, type, setadjoinIL: $o). 1194.21/150.62 thf(decl_63, type, emptyinunitempty: $o). 1194.21/150.62 thf(decl_64, type, setadjoinIR: $o). 1194.21/150.62 thf(decl_65, type, setadjoinE: $o). 1194.21/150.62 thf(decl_66, type, setadjoinOr: $o). 1194.21/150.62 thf(decl_67, type, setoftrueEq: $o). 1194.21/150.62 thf(decl_68, type, powersetI: $o). 1194.21/150.62 thf(decl_69, type, emptyinPowerset: $o). 1194.21/150.62 thf(decl_70, type, emptyInPowerset: $o). 1194.21/150.62 thf(decl_71, type, powersetE: $o). 1194.21/150.62 thf(decl_72, type, setunionI: $o). 1194.21/150.62 thf(decl_73, type, setunionE: $o). 1194.21/150.62 thf(decl_74, type, subPowSU: $o). 1194.21/150.62 thf(decl_75, type, exuE2: $o). 1194.21/150.62 thf(decl_76, type, nonemptyImpWitness: $o). 1194.21/150.62 thf(decl_77, type, uniqinunit: $o). 1194.21/150.62 thf(decl_78, type, notinsingleton: $o). 1194.21/150.62 thf(decl_79, type, eqinunit: $o). 1194.21/150.62 thf(decl_80, type, singletonsswitch: $o). 1194.21/150.62 thf(decl_81, type, upairsetE: $o). 1194.21/150.62 thf(decl_82, type, upairsetIL: $o). 1194.21/150.62 thf(decl_83, type, upairsetIR: $o). 1194.21/150.62 thf(decl_84, type, emptyE1: $o). 1194.21/150.62 thf(decl_85, type, vacuousDall: $o). 1194.21/150.62 thf(decl_86, type, quantDeMorgan1: $o). 1194.21/150.62 thf(decl_87, type, quantDeMorgan2: $o). 1194.21/150.62 thf(decl_88, type, quantDeMorgan3: $o). 1194.21/150.62 thf(decl_89, type, quantDeMorgan4: $o). 1194.21/150.62 thf(decl_90, type, prop2setI: $o). 1194.21/150.62 thf(decl_91, type, set2prop: $i > $o). 1194.21/150.62 thf(decl_92, type, prop2set2propI: $o). 1194.21/150.62 thf(decl_93, type, notdexE: $o). 1194.21/150.62 thf(decl_94, type, notdallE: $o). 1194.21/150.62 thf(decl_95, type, exuI1: $o). 1194.21/150.62 thf(decl_96, type, exuI3: $o). 1194.21/150.62 thf(decl_97, type, exuI2: $o). 1194.21/150.62 thf(decl_98, type, inCongP: $o). 1194.21/150.62 thf(decl_99, type, in__Cong: $o). 1194.21/150.62 thf(decl_100, type, exuE3u: $o). 1194.21/150.62 thf(decl_101, type, exu__Cong: $o). 1194.21/150.62 thf(decl_102, type, emptyset__Cong: $o). 1194.21/150.62 thf(decl_103, type, setadjoin__Cong: $o). 1194.21/150.62 thf(decl_104, type, powerset__Cong: $o). 1194.21/150.62 thf(decl_105, type, setunion__Cong: $o). 1194.21/150.62 thf(decl_106, type, omega__Cong: $o). 1194.21/150.62 thf(decl_107, type, exuEu: $o). 1194.21/150.62 thf(decl_108, type, descr__Cong: $o). 1194.21/150.62 thf(decl_109, type, dsetconstr__Cong: $o). 1194.21/150.62 thf(decl_110, type, subset: $i > $i > $o). 1194.21/150.62 thf(decl_113, type, subsetI1: $o). 1194.21/150.62 thf(decl_114, type, eqimpsubset2: $o). 1194.21/150.62 thf(decl_115, type, eqimpsubset1: $o). 1194.21/150.62 thf(decl_116, type, subsetI2: $o). 1194.21/150.62 thf(decl_117, type, emptysetsubset: $o). 1194.21/150.62 thf(decl_118, type, subsetE: $o). 1194.21/150.62 thf(decl_119, type, subsetE2: $o). 1194.21/150.62 thf(decl_120, type, notsubsetI: $o). 1194.21/150.62 thf(decl_121, type, notequalI1: $o). 1194.21/150.62 thf(decl_122, type, notequalI2: $o). 1194.21/150.62 thf(decl_123, type, subsetRefl: $o). 1194.21/150.62 thf(decl_124, type, subsetTrans: $o). 1194.21/150.62 thf(decl_125, type, setadjoinSub: $o). 1194.21/150.62 thf(decl_126, type, setadjoinSub2: $o). 1194.21/150.62 thf(decl_127, type, subset2powerset: $o). 1194.21/150.62 thf(decl_128, type, setextsub: $o). 1194.21/150.62 thf(decl_129, type, subsetemptysetimpeq: $o). 1194.21/150.62 thf(decl_130, type, powersetI1: $o). 1194.21/150.62 thf(decl_131, type, powersetE1: $o). 1194.21/150.62 thf(decl_132, type, inPowerset: $o). 1194.21/150.62 thf(decl_133, type, powersetsubset: $o). 1194.21/150.62 thf(decl_134, type, sepInPowerset: $o). 1194.21/150.62 thf(decl_135, type, sepSubset: $o). 1194.21/150.62 thf(decl_136, type, binunion: $i > $i > $i). 1194.21/150.62 thf(decl_137, type, binunionIL: $o). 1194.21/150.62 thf(decl_138, type, upairset2IR: $o). 1194.21/150.62 thf(decl_139, type, binunionIR: $o). 1194.21/150.62 thf(decl_140, type, binunionEcases: $o). 1194.21/150.62 thf(decl_141, type, binunionE: $o). 1194.21/150.62 thf(decl_142, type, binunionLsub: $o). 1194.21/150.62 thf(decl_143, type, binunionRsub: $o). 1194.21/150.62 thf(decl_144, type, binintersect: $i > $i > $i). 1194.21/150.62 thf(decl_145, type, binintersectI: $o). 1194.21/150.62 thf(decl_146, type, binintersectSubset5: $o). 1194.21/150.62 thf(decl_147, type, binintersectEL: $o). 1194.21/150.62 thf(decl_148, type, binintersectLsub: $o). 1194.21/150.62 thf(decl_149, type, binintersectSubset2: $o). 1194.21/150.62 thf(decl_150, type, binintersectSubset3: $o). 1194.21/150.62 thf(decl_151, type, binintersectER: $o). 1194.21/150.62 thf(decl_152, type, disjointsetsI1: $o). 1194.21/150.62 thf(decl_153, type, binintersectRsub: $o). 1194.21/150.62 thf(decl_154, type, binintersectSubset4: $o). 1194.21/150.62 thf(decl_155, type, binintersectSubset1: $o). 1194.21/150.62 thf(decl_156, type, bs114d: $o). 1194.21/150.62 thf(decl_158, type, setminus: $i > $i > $i). 1194.21/150.62 thf(decl_159, type, setminusI: $o). 1194.21/150.62 thf(decl_160, type, setminusEL: $o). 1194.21/150.62 thf(decl_161, type, setminusER: $o). 1194.21/150.62 thf(decl_162, type, setminusSubset2: $o). 1194.21/150.62 thf(decl_163, type, setminusERneg: $o). 1194.21/150.62 thf(decl_164, type, setminusELneg: $o). 1194.21/150.62 thf(decl_165, type, setminusILneg: $o). 1194.21/150.62 thf(decl_166, type, setminusIRneg: $o). 1194.21/150.62 thf(decl_167, type, setminusLsub: $o). 1194.21/150.62 thf(decl_168, type, setminusSubset1: $o). 1194.21/150.62 thf(decl_169, type, symdiff: $i > $i > $i). 1194.21/150.62 thf(decl_170, type, symdiffE: $o). 1194.21/150.62 thf(decl_171, type, symdiffI1: $o). 1194.21/150.62 thf(decl_172, type, symdiffI2: $o). 1194.21/150.62 thf(decl_173, type, symdiffIneg1: $o). 1194.21/150.62 thf(decl_174, type, symdiffIneg2: $o). 1194.21/150.62 thf(decl_175, type, iskpair: $i > $o). 1194.21/150.62 thf(decl_176, type, secondinupair: $o). 1194.21/150.62 thf(decl_177, type, setukpairIL: $o). 1194.21/150.62 thf(decl_178, type, setukpairIR: $o). 1194.21/150.62 thf(decl_179, type, kpairiskpair: $o). 1194.21/150.62 thf(decl_180, type, kpair: $i > $i > $i). 1194.21/150.62 thf(decl_181, type, kpairp: $o). 1194.21/150.62 thf(decl_182, type, cartprod: $i > $i > $i). 1194.21/150.62 thf(decl_183, type, singletonsubset: $o). 1194.21/150.62 thf(decl_184, type, singletoninpowerset: $o). 1194.21/150.62 thf(decl_185, type, singletoninpowunion: $o). 1194.21/150.62 thf(decl_186, type, upairset2E: $o). 1194.21/150.62 thf(decl_187, type, upairsubunion: $o). 1194.21/150.62 thf(decl_188, type, upairinpowunion: $o). 1194.21/150.62 thf(decl_189, type, ubforcartprodlem1: $o). 1194.21/150.62 thf(decl_190, type, ubforcartprodlem2: $o). 1194.21/150.62 thf(decl_191, type, ubforcartprodlem3: $o). 1194.21/150.62 thf(decl_192, type, cartprodpairin: $o). 1194.21/150.62 thf(decl_193, type, cartprodmempair1: $o). 1194.21/150.62 thf(decl_194, type, cartprodmempair: $o). 1194.21/150.62 thf(decl_195, type, setunionE2: $o). 1194.21/150.62 thf(decl_196, type, setunionsingleton1: $o). 1194.21/150.62 thf(decl_197, type, setunionsingleton2: $o). 1194.21/150.62 thf(decl_198, type, setunionsingleton: $o). 1194.21/150.62 thf(decl_199, type, singleton: $i > $o). 1194.21/150.62 thf(decl_200, type, singletonprop: $o). 1194.21/150.62 thf(decl_201, type, ex1: $i > ($i > $o) > $o). 1194.21/150.62 thf(decl_202, type, ex1E1: $o). 1194.21/150.62 thf(decl_203, type, ex1I: $o). 1194.21/150.62 thf(decl_204, type, ex1I2: $o). 1194.21/150.62 thf(decl_205, type, singletonsuniq: $o). 1194.21/150.62 thf(decl_210, type, setukpairinjL1: $o). 1194.21/150.62 thf(decl_211, type, kfstsingleton: $o). 1194.21/150.62 thf(decl_212, type, theprop: $o). 1194.21/150.62 thf(decl_213, type, kfst: $i > $i). 1194.21/150.62 thf(decl_214, type, kfstpairEq: $o). 1194.21/150.62 thf(decl_215, type, cartprodfstin: $o). 1194.21/150.62 thf(decl_216, type, setukpairinjL2: $o). 1194.21/150.62 thf(decl_217, type, setukpairinjL: $o). 1194.21/150.62 thf(decl_218, type, setukpairinjR11: $o). 1194.21/150.62 thf(decl_219, type, setukpairinjR12: $o). 1194.21/150.62 thf(decl_220, type, setukpairinjR1: $o). 1194.21/150.62 thf(decl_221, type, upairequniteq: $o). 1194.21/150.62 thf(decl_222, type, setukpairinjR2: $o). 1194.21/150.62 thf(decl_223, type, setukpairinjR: $o). 1194.21/150.62 thf(decl_224, type, ksndsingleton: $o). 1194.21/150.62 thf(decl_225, type, ksnd: $i > $i). 1194.21/150.62 thf(decl_226, type, ksndpairEq: $o). 1194.21/150.62 thf(decl_227, type, kpairsurjEq: $o). 1194.21/150.62 thf(decl_228, type, cartprodsndin: $o). 1194.21/150.62 thf(decl_229, type, cartprodpairmemEL: $o). 1194.21/150.62 thf(decl_230, type, cartprodpairmemER: $o). 1194.21/150.62 thf(decl_231, type, cartprodmempaircEq: $o). 1194.21/150.62 thf(decl_232, type, cartprodfstpairEq: $o). 1194.21/150.62 thf(decl_233, type, cartprodsndpairEq: $o). 1194.21/150.62 thf(decl_234, type, cartprodpairsurjEq: $o). 1194.21/150.62 thf(decl_235, type, breln: $i > $i > $i > $o). 1194.21/150.62 thf(decl_236, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 1194.21/150.62 thf(decl_237, type, dpsetconstrI: $o). 1194.21/150.62 thf(decl_238, type, dpsetconstrSub: $o). 1194.21/150.62 thf(decl_239, type, setOfPairsIsBReln: $o). 1194.21/150.62 thf(decl_240, type, dpsetconstrERa: $o). 1194.21/150.62 thf(decl_241, type, dpsetconstrEL1: $o). 1194.21/150.62 thf(decl_242, type, dpsetconstrEL2: $o). 1194.21/150.62 thf(decl_243, type, dpsetconstrER: $o). 1194.21/150.62 thf(decl_244, type, func: $i > $i > $i > $o). 1194.21/150.62 thf(decl_245, type, funcSet: $i > $i > $i). 1194.21/150.62 thf(decl_246, type, funcImageSingleton: $o). 1194.21/150.62 thf(decl_247, type, apProp: $o). 1194.21/150.62 thf(decl_248, type, ap: $i > $i > $i > $i > $i). 1194.21/150.62 thf(decl_249, type, app: $o). 1194.21/150.62 thf(decl_250, type, infuncsetfunc: $o). 1194.21/150.62 thf(decl_251, type, ap2p: $o). 1194.21/150.62 thf(decl_252, type, funcinfuncset: $o). 1194.21/150.62 thf(decl_253, type, lamProp: $o). 1194.21/150.62 thf(decl_254, type, lam: $i > $i > ($i > $i) > $i). 1194.21/150.62 thf(decl_255, type, lamp: $o). 1194.21/150.62 thf(decl_256, type, lam2p: $o). 1194.21/150.62 thf(decl_257, type, brelnall1: $o). 1194.21/150.62 thf(decl_258, type, brelnall2: $o). 1194.21/150.62 thf(decl_259, type, ex1E2: $o). 1194.21/150.62 thf(decl_260, type, funcGraphProp1: $o). 1194.21/150.62 thf(decl_261, type, funcGraphProp3: $o). 1194.21/150.62 thf(decl_262, type, funcGraphProp2: $o). 1194.21/150.62 thf(decl_263, type, funcextLem: $o). 1194.21/150.62 thf(decl_264, type, funcGraphProp4: $o). 1194.21/150.62 thf(decl_265, type, subbreln: $o). 1194.21/150.62 thf(decl_266, type, eqbreln: $o). 1194.21/150.62 thf(decl_267, type, funcext: $o). 1194.21/150.62 thf(decl_268, type, funcext2: $o). 1194.21/150.62 thf(decl_269, type, ap2apEq1: $o). 1194.21/150.62 thf(decl_270, type, ap2apEq2: $o). 1194.21/150.62 thf(decl_271, type, beta1: $o). 1194.21/150.62 thf(decl_272, type, eta1: $o). 1194.21/150.62 thf(decl_273, type, lam2lamEq: $o). 1194.21/150.62 thf(decl_274, type, beta2: $o). 1194.21/150.62 thf(decl_275, type, eta2: $o). 1194.21/150.62 thf(decl_276, type, iffalseProp1: $o). 1194.21/150.62 thf(decl_277, type, epred1_0: $o). 1194.21/150.62 thf(decl_278, type, esk1_2: $i > $i > $i). 1194.21/150.62 thf(decl_279, type, esk2_2: $i > $i > $i). 1194.21/150.62 thf(decl_280, type, esk3_2: $i > $i > $i). 1194.21/150.62 thf(decl_281, type, esk4_1: $i > $i). 1194.21/150.62 thf(decl_282, type, esk5_2: ($i > $i > $o) > $i > $i). 1194.21/150.62 thf(decl_283, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 1194.21/150.62 thf(decl_284, type, esk7_2: ($i > $i > $o) > $i > $i). 1194.21/150.62 thf(decl_285, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 1194.21/150.62 thf(decl_286, type, esk9_1: $i > $i). 1194.21/150.62 thf(decl_287, type, esk10_2: ($i > $o) > $i > $i). 1194.21/150.62 thf(decl_288, type, esk11_2: ($i > $o) > $i > $i). 1194.21/150.62 thf(decl_289, type, esk12_1: ($i > $o) > $i). 1194.21/150.62 thf(decl_290, type, esk13_2: ($i > $o) > $i > $i). 1194.21/150.62 thf(decl_291, type, esk14_1: ($i > $o) > $i). 1194.21/150.62 thf(decl_292, type, esk15_2: $i > $i > $i). 1194.21/150.62 thf(decl_293, type, esk16_2: $i > $i > $i). 1194.21/150.62 thf(decl_294, type, esk17_1: $i > $i). 1194.21/150.62 thf(decl_295, type, esk18_1: $i > $i). 1194.21/150.62 thf(decl_296, type, esk19_1: $i > $i). 1194.21/150.62 thf(decl_297, type, esk20_2: $i > $i > $i). 1194.21/150.62 thf(decl_298, type, esk21_3: $i > $i > $o > $i). 1194.21/150.62 thf(decl_299, type, esk22_2: ($i > $o) > $i > $i). 1194.21/150.62 thf(decl_300, type, esk23_1: ($i > $o) > $i). 1194.21/150.62 thf(decl_301, type, esk24_1: $i > $i). 1194.21/150.62 thf(decl_302, type, esk25_2: $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_303, type, esk26_2: $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_304, type, esk27_2: $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_305, type, esk28_2: $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_306, type, esk29_2: $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_307, type, esk30_2: $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_308, type, esk31_2: ($i > $o) > $i > $i). 1194.21/150.62 thf(decl_309, type, esk32_1: ($i > $o) > $i). 1194.21/150.62 thf(decl_310, type, esk33_1: ($i > $o) > $i). 1194.21/150.62 thf(decl_311, type, esk34_1: ($i > $o) > $i). 1194.21/150.62 thf(decl_312, type, esk35_1: ($i > $o) > $i). 1194.21/150.62 thf(decl_313, type, esk36_2: ($i > $o) > $i > $i). 1194.21/150.62 thf(decl_314, type, esk37_1: ($i > $o) > $i). 1194.21/150.62 thf(decl_315, type, esk38_2: ($i > $o) > $i > $i). 1194.21/150.62 thf(decl_316, type, esk39_2: ($i > $o) > ($i > $o) > $i). 1194.21/150.62 thf(decl_317, type, esk40_2: ($i > $o) > ($i > $o) > $i). 1194.21/150.62 thf(decl_318, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 1194.21/150.62 thf(decl_319, type, esk42_2: ($i > $o) > ($i > $o) > $i). 1194.21/150.62 thf(decl_320, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 1194.21/150.62 thf(decl_321, type, esk44_2: ($i > $o) > ($i > $o) > $i). 1194.21/150.62 thf(decl_322, type, esk45_2: ($i > $o) > $i > $i). 1194.21/150.62 thf(decl_323, type, esk46_2: ($i > $o) > ($i > $o) > $i). 1194.21/150.62 thf(decl_324, type, esk47_2: ($i > $o) > ($i > $o) > $i). 1194.21/150.62 thf(decl_325, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 1194.21/150.62 thf(decl_326, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 1194.21/150.62 thf(decl_327, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 1194.21/150.62 thf(decl_328, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 1194.21/150.62 thf(decl_329, type, esk52_2: $i > $i > $i). 1194.21/150.62 thf(decl_330, type, esk53_2: $i > $i > $i). 1194.21/150.62 thf(decl_331, type, esk54_2: $i > $i > $i). 1194.21/150.62 thf(decl_332, type, esk55_3: $i > $i > $i > $i). 1194.21/150.62 thf(decl_333, type, esk56_3: $i > $i > $i > $i). 1194.21/150.62 thf(decl_334, type, esk57_2: $i > $i > $i). 1194.21/150.62 thf(decl_335, type, esk58_2: $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_336, type, esk59_2: $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_337, type, esk60_2: $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_338, type, esk61_2: $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_339, type, esk62_3: $i > ($i > $o) > $i > $i). 1194.21/150.62 thf(decl_340, type, esk63_3: $i > ($i > $o) > $i > $i). 1194.21/150.62 thf(decl_341, type, esk64_2: $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_342, type, esk65_2: $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_343, type, esk66_2: $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_344, type, esk67_1: $i > $i). 1194.21/150.62 thf(decl_345, type, esk68_1: $i > $i). 1194.21/150.62 thf(decl_346, type, esk69_4: $i > $i > $i > $i > $i). 1194.21/150.62 thf(decl_347, type, esk70_3: $i > $i > ($i > $i) > $i). 1194.21/150.62 thf(decl_348, type, esk71_3: $i > $i > ($i > $i) > $i). 1194.21/150.62 thf(decl_349, type, esk72_3: $i > $i > ($i > $i) > $i). 1194.21/150.62 thf(decl_350, type, esk73_4: $i > $i > $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_351, type, esk74_4: $i > $i > $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_352, type, esk75_4: $i > $i > $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_353, type, esk76_4: $i > $i > $i > ($i > $o) > $i). 1194.21/150.62 thf(decl_354, type, esk77_4: $i > $i > $i > $i > $i). 1194.21/150.62 thf(decl_355, type, esk78_4: $i > $i > $i > $i > $i). 1194.21/150.62 thf(decl_356, type, esk79_4: $i > $i > $i > $i > $i). 1194.21/150.62 thf(decl_357, type, esk80_4: $i > $i > $i > $i > $i). 1194.21/150.62 thf(decl_358, type, esk81_4: $i > $i > $i > $i > $i). 1194.21/150.62 thf(decl_359, type, esk82_4: $i > $i > $i > $i > $i). 1194.21/150.62 thf(decl_360, type, esk83_4: $i > $i > $i > $i > $i). 1194.21/150.62 thf(decl_361, type, esk84_4: $i > $i > $i > $i > $i). 1194.21/150.62 thf(decl_362, type, esk85_4: $i > $i > $i > $i > $i). 1194.21/150.62 thf(decl_363, type, esk86_3: $i > $i > ($i > $i) > $i). 1194.21/150.62 thf(decl_364, type, esk87_3: $i > $i > ($i > $i) > $i). 1194.21/150.62 thf(decl_365, type, esk88_3: $i > $i > ($i > $i) > $i). 1194.21/150.62 thf(decl_366, type, esk89_0: $i). 1194.21/150.62 thf(decl_367, type, epred2_0: $o). 1194.21/150.62 thf(decl_368, type, esk90_0: $i). 1194.21/150.62 thf(decl_369, type, esk91_0: $i). 1194.21/150.62 thf(decl_375, type, epred3_0: $i > $o). 1194.21/150.62 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', ex1)). 1194.21/150.62 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', singleton)). 1194.21/150.62 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', replAx)). 1194.21/150.62 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', exu)). 1194.21/150.62 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', descrp)). 1194.21/150.62 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', exuE1)). 1194.21/150.62 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', exuE3e)). 1194.21/150.62 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', nonempty)). 1194.21/150.62 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', nonemptyI)). 1194.21/150.62 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', exuE2)). 1194.21/150.62 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', exuI1)). 1194.21/150.62 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', exuI3)). 1194.21/150.62 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', exuI2)). 1194.21/150.62 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', exuE3u)). 1194.21/150.62 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', exu__Cong)). 1194.21/150.62 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', exuEu)). 1194.21/150.62 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', descr__Cong)). 1194.21/150.62 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', singletonprop)). 1194.21/150.62 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', ex1E1)). 1194.21/150.62 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', ex1I)). 1194.21/150.62 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', ex1I2)). 1194.21/150.62 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', kfstsingleton)). 1194.21/150.62 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', ksndsingleton)). 1194.21/150.62 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setOfPairsIsBReln)). 1194.21/150.62 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', breln)). 1194.21/150.62 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', funcImageSingleton)). 1194.21/150.62 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', ex1E2)). 1194.21/150.62 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', dsetconstrI)). 1194.21/150.62 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', dsetconstrEL)). 1194.21/150.62 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', dsetconstrER)). 1194.21/150.62 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setbeta)). 1194.21/150.62 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', nonemptyE1)). 1194.21/150.62 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', nonemptyI1)). 1194.21/150.62 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setoftrueEq)). 1194.21/150.62 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', nonemptyImpWitness)). 1194.21/150.62 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', emptyE1)). 1194.21/150.62 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', dsetconstr__Cong)). 1194.21/150.62 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', sepInPowerset)). 1194.21/150.62 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', sepSubset)). 1194.21/150.62 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', theprop)). 1194.21/150.62 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', dpsetconstrI)). 1194.21/150.62 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', dpsetconstrSub)). 1194.21/150.62 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', dpsetconstrERa)). 1194.21/150.62 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', dpsetconstrEL1)). 1194.21/150.62 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', dpsetconstrEL2)). 1194.21/150.62 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', dpsetconstrER)). 1194.21/150.62 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', apProp)). 1194.21/150.62 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', lamProp)). 1194.21/150.62 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', lamp)). 1194.21/150.62 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', lam2p)). 1194.21/150.62 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', brelnall1)). 1194.21/150.62 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', brelnall2)). 1194.21/150.62 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', subbreln)). 1194.21/150.62 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', eqbreln)). 1194.21/150.62 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', beta1)). 1194.21/150.62 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', eta1)). 1194.21/150.62 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', lam2lamEq)). 1194.21/150.62 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', beta2)). 1194.21/150.62 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', eta2)). 1194.21/150.62 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', iffalseProp1)). 1194.21/150.62 thf(iffalseProp2, conjecture, (((((powersetAx)=>((setunionAx)=>(((omegaSAx)=>(((replAx)=>(((wellorderingAx)=>(((((dsetconstrER)=>((((emptysetE)=>(((((((noeltsimpempty)=>((((nonemptyI)=>((((emptyinunitempty)=>(((((setoftrueEq)=>(((((((((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>(((quantDeMorgan3)=>(((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((((exuI2)=>((inCongP)=>(((exuE3u)=>((((setadjoin__Cong)=>(((((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((((eqimpsubset1)=>(((emptysetsubset)=>((subsetE)=>(((notsubsetI)=>((notequalI1)=>(((subsetRefl)=>(((setadjoinSub)=>((setadjoinSub2)=>(((setextsub)=>(((powersetI1)=>((powersetE1)=>((inPowerset)=>(((sepInPowerset)=>((sepSubset)=>((binunionIL)=>(((((binunionE)=>(((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>(((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((((binintersectRsub)=>((((((setminusEL)=>((((setminusERneg)=>(((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((((((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((((kpairp)=>((singletonsubset)=>(((singletoninpowunion)=>((upairset2E)=>(((upairinpowunion)=>((ubforcartprodlem1)=>(((ubforcartprodlem3)=>(((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>(((setunionsingleton)=>(((((ex1I2)=>(((setukpairinjL1)=>((((kfstpairEq)=>((((((setukpairinjR12)=>((setukpairinjR1)=>((((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>(((cartprodfstpairEq)=>(((cartprodpairsurjEq)=>(((((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>(((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>(((funcinfuncset)=>((lamProp)=>((((((((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>(((eqbreln)=>(((((((eta1)=>(((beta2)=>((![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:(((~((X40))&((X14)=(X3)))|(((X14)=(X2))&(X40))))))=(setadjoin @ X3 @ emptyset)))))))<=(iffalseProp1))<=(eta2)))<=(lam2lamEq)))<=(beta1))<=(ap2apEq2))<=(ap2apEq1))<=(funcext2))<=(funcext)))<=(subbreln))))))<=(funcGraphProp1))<=(ex1E2))<=(brelnall2))<=(brelnall1))<=(lam2p))<=(lamp))))<=(ap2p))))))<=(dpsetconstrER)))))<=(setOfPairsIsBReln))<=(dpsetconstrSub))<=(dpsetconstrI)))<=(cartprodsndpairEq)))<=(cartprodmempaircEq)))))))))<=(setukpairinjR2))<=(upairequniteq))))<=(setukpairinjR11))<=(setukpairinjL))<=(setukpairinjL2))<=(cartprodfstin)))<=(theprop))<=(kfstsingleton)))<=(singletonsuniq)))<=(ex1I))<=(ex1E1))<=(singletonprop)))<=(setunionsingleton2))))))<=(cartprodpairin)))<=(ubforcartprodlem2))))<=(upairsubunion))))<=(singletoninpowerset))))<=(kpairiskpair))<=(setukpairIR))))))<=(symdiffI2))<=(symdiffI1))<=(symdiffE))<=(setminusSubset1)))))<=(setminusELneg)))<=(setminusSubset2))<=(setminusER)))<=(setminusI))<=(bs114d))<=(binintersectSubset1))<=(binintersectSubset4)))<=(disjointsetsI1))<=(binintersectER)))))<=(binintersectEL)))))<=(binunionLsub)))<=(binunionEcases))<=(binunionIR))<=(upairset2IR)))))<=(powersetsubset)))))<=(subsetemptysetimpeq)))<=(subset2powerset))))<=(subsetTrans)))<=(notequalI2))))<=(subsetE2))))<=(subsetI2)))<=(eqimpsubset2))<=(subsetI1)))))<=(omega__Cong))<=(setunion__Cong))<=(powerset__Cong)))<=(emptyset__Cong))<=(exu__Cong)))<=(in__Cong))))<=(exuI3))<=(exuI1))))))<=(quantDeMorgan4)))<=(quantDeMorgan2))))))<=(upairsetIL))<=(upairsetE))))))))<=(subPowSU))<=(setunionE))<=(setunionI))<=(powersetE))<=(emptyInPowerset))<=(emptyinPowerset))<=(powersetI)))<=(setadjoinOr))<=(setadjoinE))<=(setadjoinIR)))<=(setadjoinIL))<=(nonemptyI1)))<=(nonemptyE1))<=(setbeta)))<=(emptyI))<=(setext))<=(exuE3e))<=(notinemptyset))<=(emptysetimpfalse)))<=(prop2setE))<=(exuE1)))<=(dsetconstrEL))<=(dsetconstrI))<=(descrp)))<=(foundationAx)))<=(omegaIndAx)))<=(omega0Ax))))<=(setadjoinAx))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', iffalseProp2)). 1194.21/150.62 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setextAx)). 1194.21/150.62 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', emptysetAx)). 1194.21/150.62 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setadjoinAx)). 1194.21/150.62 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', powersetAx)). 1194.21/150.62 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setunionAx)). 1194.21/150.62 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', omega0Ax)). 1194.21/150.62 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', omegaSAx)). 1194.21/150.62 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', omegaIndAx)). 1194.21/150.62 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', foundationAx)). 1194.21/150.62 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', wellorderingAx)). 1194.21/150.62 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', prop2setE)). 1194.21/150.62 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', emptysetE)). 1194.21/150.62 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', emptysetimpfalse)). 1194.21/150.62 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', notinemptyset)). 1194.21/150.62 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setext)). 1194.21/150.62 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', emptyI)). 1194.21/150.62 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', noeltsimpempty)). 1194.21/150.62 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setadjoinIL)). 1194.21/150.62 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', emptyinunitempty)). 1194.21/150.62 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setadjoinIR)). 1194.21/150.62 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setadjoinE)). 1194.21/150.62 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setadjoinOr)). 1194.21/150.62 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', powersetI)). 1194.21/150.62 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', emptyinPowerset)). 1194.21/150.62 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', emptyInPowerset)). 1194.21/150.62 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', powersetE)). 1194.21/150.62 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setunionI)). 1194.21/150.62 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setunionE)). 1194.21/150.62 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', subPowSU)). 1194.21/150.62 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', uniqinunit)). 1194.21/150.62 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', notinsingleton)). 1194.21/150.62 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', eqinunit)). 1194.21/150.62 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', singletonsswitch)). 1194.21/150.62 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', upairsetE)). 1194.21/150.62 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', upairsetIL)). 1194.21/150.62 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', upairsetIR)). 1194.21/150.62 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', vacuousDall)). 1194.21/150.62 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', quantDeMorgan1)). 1194.21/150.62 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', quantDeMorgan2)). 1194.21/150.62 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', quantDeMorgan3)). 1194.21/150.62 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', quantDeMorgan4)). 1194.21/150.62 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', prop2setI)). 1194.21/150.62 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', prop2set2propI)). 1194.21/150.62 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', notdexE)). 1194.21/150.62 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', notdallE)). 1194.21/150.62 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', inCongP)). 1194.21/150.62 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', in__Cong)). 1194.21/150.62 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', emptyset__Cong)). 1194.21/150.62 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setadjoin__Cong)). 1194.21/150.62 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', powerset__Cong)). 1194.21/150.62 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setunion__Cong)). 1194.21/150.62 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', omega__Cong)). 1194.21/150.62 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', subsetI1)). 1194.21/150.62 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', eqimpsubset2)). 1194.21/150.62 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', eqimpsubset1)). 1194.21/150.62 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', subsetI2)). 1194.21/150.62 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', emptysetsubset)). 1194.21/150.62 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', subsetE)). 1194.21/150.62 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', subsetE2)). 1194.21/150.62 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', notsubsetI)). 1194.21/150.62 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', notequalI1)). 1194.21/150.62 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', notequalI2)). 1194.21/150.62 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', subsetRefl)). 1194.21/150.62 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', subsetTrans)). 1194.21/150.62 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setadjoinSub)). 1194.21/150.62 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setadjoinSub2)). 1194.21/150.62 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', subset2powerset)). 1194.21/150.62 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setextsub)). 1194.21/150.62 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', subsetemptysetimpeq)). 1194.21/150.62 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', powersetI1)). 1194.21/150.62 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', powersetE1)). 1194.21/150.62 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', inPowerset)). 1194.21/150.62 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', powersetsubset)). 1194.21/150.62 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', binunionIL)). 1194.21/150.62 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', upairset2IR)). 1194.21/150.62 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', binunionIR)). 1194.21/150.62 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', binunionEcases)). 1194.21/150.62 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', binunionE)). 1194.21/150.62 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', binunionLsub)). 1194.21/150.62 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', binunionRsub)). 1194.21/150.62 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', binintersectI)). 1194.21/150.62 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', binintersectSubset5)). 1194.21/150.62 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', binintersectEL)). 1194.21/150.62 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', binintersectLsub)). 1194.21/150.62 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', binintersectSubset2)). 1194.21/150.62 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', binintersectSubset3)). 1194.21/150.62 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', binintersectER)). 1194.21/150.62 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', disjointsetsI1)). 1194.21/150.62 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', binintersectRsub)). 1194.21/150.62 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', binintersectSubset4)). 1194.21/150.62 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', binintersectSubset1)). 1194.21/150.62 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', bs114d)). 1194.21/150.62 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setminusI)). 1194.21/150.62 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setminusEL)). 1194.21/150.62 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setminusER)). 1194.21/150.62 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setminusSubset2)). 1194.21/150.62 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setminusERneg)). 1194.21/150.62 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setminusELneg)). 1194.21/150.62 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setminusILneg)). 1194.21/150.62 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setminusIRneg)). 1194.21/150.62 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setminusLsub)). 1194.21/150.62 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setminusSubset1)). 1194.21/150.62 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', symdiffE)). 1194.21/150.62 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', symdiffI1)). 1194.21/150.62 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', symdiffI2)). 1194.21/150.62 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', symdiffIneg1)). 1194.21/150.62 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', symdiffIneg2)). 1194.21/150.62 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', secondinupair)). 1194.21/150.62 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setukpairIL)). 1194.21/150.62 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setukpairIR)). 1194.21/150.62 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', kpairiskpair)). 1194.21/150.62 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', kpairp)). 1194.21/150.62 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', singletonsubset)). 1194.21/150.62 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', singletoninpowerset)). 1194.21/150.62 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', singletoninpowunion)). 1194.21/150.62 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', upairset2E)). 1194.21/150.62 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', upairsubunion)). 1194.21/150.62 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', upairinpowunion)). 1194.21/150.62 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', ubforcartprodlem1)). 1194.21/150.62 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', ubforcartprodlem2)). 1194.21/150.62 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', ubforcartprodlem3)). 1194.21/150.62 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', cartprodpairin)). 1194.21/150.62 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', cartprodmempair1)). 1194.21/150.62 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', cartprodmempair)). 1194.21/150.62 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setunionE2)). 1194.21/150.62 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setunionsingleton1)). 1194.21/150.62 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setunionsingleton2)). 1194.21/150.62 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setunionsingleton)). 1194.21/150.62 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', singletonsuniq)). 1194.21/150.62 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setukpairinjL1)). 1194.21/150.62 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', kfstpairEq)). 1194.21/150.62 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', cartprodfstin)). 1194.21/150.62 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setukpairinjL2)). 1194.21/150.62 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setukpairinjL)). 1194.21/150.62 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setukpairinjR11)). 1194.21/150.62 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setukpairinjR12)). 1194.21/150.62 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setukpairinjR1)). 1194.21/150.62 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', upairequniteq)). 1194.21/150.62 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setukpairinjR2)). 1194.21/150.62 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', setukpairinjR)). 1194.21/150.62 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', ksndpairEq)). 1194.21/150.62 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', kpairsurjEq)). 1194.21/150.62 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', cartprodsndin)). 1194.21/150.62 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', cartprodpairmemEL)). 1194.21/150.62 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', cartprodpairmemER)). 1194.21/150.62 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', cartprodmempaircEq)). 1194.21/150.62 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', cartprodfstpairEq)). 1194.21/150.62 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', cartprodsndpairEq)). 1194.21/150.62 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', cartprodpairsurjEq)). 1194.21/150.62 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', app)). 1194.21/150.62 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', infuncsetfunc)). 1194.21/150.62 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', ap2p)). 1194.21/150.62 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', funcinfuncset)). 1194.21/150.62 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', funcGraphProp1)). 1194.21/150.62 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', funcGraphProp3)). 1194.21/150.62 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', funcGraphProp2)). 1194.21/150.62 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', funcextLem)). 1194.21/150.62 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', funcGraphProp4)). 1194.21/150.62 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', funcext)). 1194.21/150.62 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', funcext2)). 1194.21/150.62 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', ap2apEq1)). 1194.21/150.62 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.n3nXOaXkGe/E---3.1_22281.p', ap2apEq2)). 1194.21/150.62 thf(c_0_223, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X736:$i]:(((in @ X736 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X736 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])). 1194.21/150.62 thf(c_0_224, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])). 1194.21/150.62 thf(c_0_225, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 1194.21/150.62 thf(c_0_226, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 1194.21/150.62 thf(c_0_227, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 1194.21/150.62 thf(c_0_228, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 1194.21/150.62 thf(c_0_229, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 1194.21/150.62 thf(c_0_230, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 1194.21/150.62 thf(c_0_231, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 1194.21/150.62 thf(c_0_232, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 1194.21/150.62 thf(c_0_233, 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])). 1194.21/150.62 thf(c_0_234, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 1194.21/150.62 thf(c_0_235, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 1194.21/150.62 thf(c_0_236, 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])). 1194.21/150.62 thf(c_0_237, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 1194.21/150.62 thf(c_0_238, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 1194.21/150.62 thf(c_0_239, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 1194.21/150.62 thf(c_0_240, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])). 1194.21/150.62 thf(c_0_241, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])). 1194.21/150.62 thf(c_0_242, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X736:$i]:(((in @ X736 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X736 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_223, c_0_224])). 1194.21/150.62 thf(c_0_243, 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])). 1194.21/150.62 thf(c_0_244, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])). 1194.21/150.62 thf(c_0_245, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])). 1194.21/150.62 thf(c_0_246, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])). 1194.21/150.62 thf(c_0_247, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])). 1194.21/150.62 thf(c_0_248, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])). 1194.21/150.62 thf(c_0_249, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])). 1194.21/150.62 thf(c_0_250, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])). 1194.21/150.62 thf(c_0_251, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X707:$i]:((((X6 @ X2 @ X707))&![X708:$i]:((((X6 @ X2 @ X708))=>((X707)=(X708)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_225, c_0_226])). 1194.21/150.62 thf(c_0_252, plain, ((descrp)=(![X1:$i > $o]:(((?[X709:$i]:((((X1 @ X709))&![X710:$i]:((((X1 @ X710))=>((X709)=(X710)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_227, c_0_226])). 1194.21/150.62 thf(c_0_253, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 1194.21/150.62 thf(c_0_254, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 1194.21/150.62 thf(c_0_255, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 1194.21/150.62 thf(c_0_256, plain, ((exuE1)=(![X1:$i > $o]:(((?[X711:$i]:((((X1 @ X711))&![X712:$i]:((((X1 @ X712))=>((X711)=(X712)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_228, c_0_226])). 1194.21/150.62 thf(c_0_257, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X713:$i]:((((X1 @ X713))&![X714:$i]:((((X1 @ X714))=>((X713)=(X714)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_229, c_0_226])). 1194.21/150.62 thf(c_0_258, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 1194.21/150.62 thf(c_0_259, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_230])). 1194.21/150.62 thf(c_0_260, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_231, c_0_230])). 1194.21/150.62 thf(c_0_261, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_230])). 1194.21/150.62 thf(c_0_262, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 1194.21/150.62 thf(c_0_263, plain, ((exuE2)=(![X1:$i > $o]:(((?[X715:$i]:((((X1 @ X715))&![X716:$i]:((((X1 @ X716))=>((X715)=(X716)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_232, c_0_226])). 1194.21/150.62 thf(c_0_264, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_230])). 1194.21/150.62 thf(c_0_265, 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])). 1194.21/150.62 thf(c_0_266, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X717:$i]:((((X1 @ X717))&![X718:$i]:((((X1 @ X718))=>((X717)=(X718))))))))))), inference(apply_def,[status(thm)],[c_0_233, c_0_226])). 1194.21/150.62 thf(c_0_267, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X719:$i]:((((X1 @ X719))&![X720:$i]:((((X1 @ X720))=>((X719)=(X720)))))))))))), inference(apply_def,[status(thm)],[c_0_234, c_0_226])). 1194.21/150.62 thf(c_0_268, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X721:$i]:((((X1 @ X721))&![X722:$i]:((((X1 @ X722))=>((X721)=(X722))))))))))), inference(apply_def,[status(thm)],[c_0_235, c_0_226])). 1194.21/150.62 thf(c_0_269, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X723:$i]:((((X1 @ X723))&![X724:$i]:((((X1 @ X724))=>((X723)=(X724)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_236, c_0_226])). 1194.21/150.62 thf(c_0_270, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X725:$i]:((((X1 @ X725))&![X726:$i]:((((X1 @ X726))=>((X725)=(X726)))))))<=>(?[X727:$i]:((((X17 @ X727))&![X728:$i]:((((X17 @ X728))=>((X727)=(X728)))))))))))), inference(apply_def,[status(thm)],[c_0_237, c_0_226])). 1194.21/150.62 thf(c_0_271, plain, ((exuEu)=(![X1:$i > $o]:(((?[X729:$i]:((((X1 @ X729))&![X730:$i]:((((X1 @ X730))=>((X729)=(X730)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_238, c_0_226])). 1194.21/150.62 thf(c_0_272, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X731:$i]:((((X1 @ X731))&![X732:$i]:((((X1 @ X732))=>((X731)=(X732)))))))=>((?[X733:$i]:((((X17 @ X733))&![X734:$i]:((((X17 @ X734))=>((X733)=(X734)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_239, c_0_226])). 1194.21/150.62 thf(c_0_273, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 1194.21/150.62 thf(c_0_274, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 1194.21/150.62 thf(c_0_275, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 1194.21/150.62 thf(c_0_276, 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)))=>(?[X735:$i]:(((in @ X735 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X735 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_240, c_0_224])). 1194.21/150.62 thf(c_0_277, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X737:$i]:(((in @ X737 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X737 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_241, c_0_242])). 1194.21/150.62 thf(c_0_278, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X738:$i]:(((in @ X738 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X738 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_243, c_0_242])). 1194.21/150.62 thf(c_0_279, 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)))=>(?[X739:$i]:(((in @ X739 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X739 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_244, c_0_242])). 1194.21/150.62 thf(c_0_280, plain, ((kfstsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X740:$i]:(((in @ X740 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X740 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_245, c_0_224])). 1194.21/150.62 thf(c_0_281, axiom, ((theprop)=(![X21:$i]:(((?[X741:$i]:(((in @ X741 @ X21)&((X21)=(setadjoin @ X741 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_224])). 1194.21/150.62 thf(c_0_282, plain, ((ksndsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X742:$i]:(((in @ X742 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X742 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_246, c_0_224])). 1194.21/150.62 thf(c_0_283, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])). 1194.21/150.62 thf(c_0_284, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])). 1194.21/150.62 thf(c_0_285, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_247, c_0_248])). 1194.21/150.62 thf(c_0_286, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])). 1194.21/150.62 thf(c_0_287, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])). 1194.21/150.62 thf(c_0_288, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])). 1194.21/150.62 thf(c_0_289, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])). 1194.21/150.62 thf(c_0_290, plain, ((funcImageSingleton)=(![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(?[X743:$i]:(((in @ X743 @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))&((dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))=(setadjoin @ X743 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_249, c_0_224])). 1194.21/150.62 thf(c_0_291, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])). 1194.21/150.62 thf(c_0_292, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])). 1194.21/150.62 thf(c_0_293, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])). 1194.21/150.62 thf(c_0_294, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])). 1194.21/150.62 thf(c_0_295, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_248])). 1194.21/150.62 thf(c_0_296, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_248])). 1194.21/150.62 thf(c_0_297, plain, ((ex1E2)=(![X4:$i, X1:$i > $o]:(((?[X744:$i]:(((in @ X744 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X744 @ emptyset)))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_250, c_0_242])). 1194.21/150.62 thf(c_0_298, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_248])). 1194.21/150.62 thf(c_0_299, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_248])). 1194.21/150.62 thf(c_0_300, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])). 1194.21/150.62 thf(c_0_301, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 248 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])). 1194.21/150.62 thf(c_0_302, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])). 1194.21/150.62 thf(c_0_303, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])). 1194.21/150.62 thf(c_0_304, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 248 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])). 1194.21/150.62 thf(c_0_305, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])). 1194.21/150.62 thf(c_0_306, plain, ((epred1_0)<=>![X760:$i]:(?[X761:$i]:((((![X762:$i]:(((in @ X762 @ X761)=>![X763:$i]:(((in @ X763 @ X762)=>(in @ X763 @ X760)))))&![X764:$i, X765:$i]:((((in @ X764 @ X760)&(in @ X765 @ X760))=>(![X766:$i]:(((in @ X766 @ X761)=>((in @ X764 @ X766)<=>(in @ X765 @ X766))))=>((X764)=(X765))))))&![X767:$i, X768:$i]:((((in @ X767 @ X761)&(in @ X768 @ X761))=>(![X769:$i]:(((in @ X769 @ X767)=>(in @ X769 @ X768)))|![X770:$i]:(((in @ X770 @ X768)=>(in @ X770 @ X767)))))))&![X771:$i]:(((![X772:$i]:(((in @ X772 @ X771)=>(in @ X772 @ X760)))&?[X773:$i]:((in @ X773 @ X771)))=>?[X774:$i, X775:$i]:(((((in @ X774 @ X761)&(in @ X775 @ X771))&~(?[X776:$i]:(((in @ X776 @ X774)&(in @ X776 @ X771)))))&![X777:$i]:(((in @ X777 @ X761)=>(![X778:$i]:(((in @ X778 @ X777)=>(in @ X778 @ X774)))|(in @ X775 @ X777)))))))))))), introduced(definition)). 1194.21/150.62 thf(c_0_307, negated_conjecture, ~((![X1441:$i, X1442:$i]:((![X1443:$i]:(((in @ X1443 @ X1441)<=>(in @ X1443 @ X1442)))=>((X1441)=(X1442))))=>(![X1440:$i]:(~(in @ X1440 @ emptyset))=>(![X1437:$i, X1438:$i, X1439:$i]:(((in @ X1439 @ (setadjoin @ X1437 @ X1438))<=>(((X1439)=(X1437))|(in @ X1439 @ X1438))))=>(![X745:$i, X746:$i]:(((in @ X746 @ (powerset @ X745))<=>![X747:$i]:(((in @ X747 @ X746)=>(in @ X747 @ X745)))))=>(![X748:$i, X749:$i]:(((in @ X749 @ (setunion @ X748))<=>?[X750:$i]:(((in @ X749 @ X750)&(in @ X750 @ X748)))))=>((in @ emptyset @ omega)=>(![X751:$i]:(((in @ X751 @ omega)=>(in @ (setadjoin @ X751 @ X751) @ omega)))=>(![X1434:$i]:((((in @ emptyset @ X1434)&![X1435:$i]:((((in @ X1435 @ omega)&(in @ X1435 @ X1434))=>(in @ (setadjoin @ X1435 @ X1435) @ X1434))))=>![X1436:$i]:(((in @ X1436 @ omega)=>(in @ X1436 @ X1434)))))=>(![X752:$i > $i > $o, X753:$i]:((![X754:$i]:(((in @ X754 @ X753)=>?[X755:$i]:(((X752 @ X754 @ X755)&![X756:$i]:(((X752 @ X754 @ X756)=>((X755)=(X756))))))))=>?[X757:$i]:(![X758:$i]:(((in @ X758 @ X757)<=>?[X759:$i]:(((in @ X759 @ X753)&(X752 @ X759 @ X758))))))))=>(![X1430:$i]:((?[X1431:$i]:((in @ X1431 @ X1430))=>?[X1432:$i]:(((in @ X1432 @ X1430)&~(?[X1433:$i]:(((in @ X1433 @ X1432)&(in @ X1433 @ X1430))))))))=>((epred1_0)=>(![X1427:$i > $o]:((?[X1428:$i]:(((X1427 @ X1428)&![X1429:$i]:(((X1427 @ X1429)=>((X1428)=(X1429))))))=>(X1427 @ (descr @ (^[Z0/* 17 */:$i]:(X1427 @ Z0))))))=>(![X1424:$i, X1425:$i > $o, X1426:$i]:(((in @ X1426 @ X1424)=>((X1425 @ X1426)=>(in @ X1426 @ (dsetconstr @ X1424 @ X1425)))))=>(![X1421:$i, X1422:$i > $o, X1423:$i]:(((in @ X1423 @ (dsetconstr @ X1421 @ X1422))=>(in @ X1423 @ X1421)))=>(![X779:$i, X780:$i > $o, X781:$i]:(((in @ X781 @ (dsetconstr @ X779 @ X780))=>(X780 @ X781)))=>(![X1416:$i > $o]:((?[X1417:$i]:(((X1416 @ X1417)&![X1418:$i]:(((X1416 @ X1418)=>((X1417)=(X1418))))))=>?[X1419:$i]:(((X1416 @ X1419)&![X1420:$i]:(((X1416 @ X1420)=>((X1419)=(X1420))))))))=>(![X1414:$o, X1415:$i]:(((in @ X1415 @ (prop2set @ ((X1414))))=>(X1414)))=>(![X782:$i]:(((in @ X782 @ emptyset)=>![X783:$o]:((X783))))=>(![X1413:$i]:(((in @ X1413 @ emptyset)=>~($true)))=>(![X1412:$i]:(~(in @ X1412 @ emptyset))=>(![X1408:$i > $o]:((?[X1409:$i]:(((X1408 @ X1409)&![X1410:$i]:(((X1408 @ X1410)=>((X1409)=(X1410))))))=>?[X1411:$i]:((X1408 @ X1411))))=>(![X1404:$i, X1405:$i]:((![X1406:$i]:(((in @ X1406 @ X1404)=>(in @ X1406 @ X1405)))=>(![X1407:$i]:(((in @ X1407 @ X1405)=>(in @ X1407 @ X1404)))=>((X1404)=(X1405)))))=>(![X1402:$i]:((![X1403:$i]:(~(in @ X1403 @ X1402))=>((X1402)=(emptyset))))=>(![X784:$i]:((![X785:$i]:(~(in @ X785 @ X784))=>((X784)=(emptyset))))=>(![X1399:$i, X1400:$i > $o, X1401:$i]:(((in @ X1401 @ X1399)=>((in @ X1401 @ (dsetconstr @ X1399 @ X1400))<=>(X1400 @ X1401))))=>(![X1397:$i]:((((X1397)!=(emptyset))=>?[X1398:$i]:((in @ X1398 @ X1397))))=>(![X786:$i, X787:$i > $o, X788:$i]:(((in @ X788 @ X786)=>((X787 @ X788)=>((dsetconstr @ X786 @ X787)!=(emptyset)))))=>(![X1395:$i]:((?[X1396:$i]:((in @ X1396 @ X1395))=>((X1395)!=(emptyset))))=>(![X1393:$i, X1394:$i]:((in @ X1393 @ (setadjoin @ X1393 @ X1394)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1390:$i, X1391:$i, X1392:$i]:(((in @ X1392 @ X1391)=>(in @ X1392 @ (setadjoin @ X1390 @ X1391))))=>(![X1386:$i, X1387:$i, X1388:$i]:(((in @ X1388 @ (setadjoin @ X1386 @ X1387))=>![X1389:$o]:(((((X1388)=(X1386))=>(X1389))=>(((in @ X1388 @ X1387)=>(X1389))=>(X1389))))))=>(![X1383:$i, X1384:$i, X1385:$i]:(((in @ X1385 @ (setadjoin @ X1383 @ X1384))=>(((X1385)=(X1383))|(in @ X1385 @ X1384))))=>(![X789:$i]:(((dsetconstr @ X789 @ (^[Z0/* 1 */:$i]:($true)))=(X789)))=>(![X1380:$i, X1381:$i]:((![X1382:$i]:(((in @ X1382 @ X1381)=>(in @ X1382 @ X1380)))=>(in @ X1381 @ (powerset @ X1380))))=>(![X1379:$i]:((in @ emptyset @ (powerset @ X1379)))=>(![X1378:$i]:((in @ emptyset @ (powerset @ X1378)))=>(![X1375:$i, X1376:$i, X1377:$i]:(((in @ X1376 @ (powerset @ X1375))=>((in @ X1377 @ X1376)=>(in @ X1377 @ X1375))))=>(![X1372:$i, X1373:$i, X1374:$i]:(((in @ X1373 @ X1374)=>((in @ X1374 @ X1372)=>(in @ X1373 @ (setunion @ X1372)))))=>(![X1368:$i, X1369:$i]:(((in @ X1369 @ (setunion @ X1368))=>![X1370:$o]:((![X1371:$i]:(((in @ X1369 @ X1371)=>((in @ X1371 @ X1368)=>(X1370))))=>(X1370)))))=>(![X1366:$i, X1367:$i]:(((in @ X1367 @ X1366)=>(in @ X1367 @ (powerset @ (setunion @ X1366)))))=>(![X790:$i > $o]:((?[X791:$i]:(((X790 @ X791)&![X792:$i]:(((X790 @ X792)=>((X791)=(X792))))))=>?[X793:$i]:(![X794:$i]:(((X790 @ 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emptyset)=>(X810 @ X811)))=>(![X812:$i, X813:$i > $o]:((~(![X814:$i]:(((in @ X814 @ X812)=>(X813 @ X814))))=>?[X815:$i]:(((in @ X815 @ X812)&~((X813 @ X815))))))=>(![X1357:$i, X1358:$i > $o]:((![X1359:$i]:(((in @ X1359 @ X1357)=>~((X1358 @ X1359))))=>~(?[X1360:$i]:(((in @ X1360 @ X1357)&(X1358 @ X1360))))))=>(![X816:$i, X817:$i > $o]:((~(?[X818:$i]:(((in @ X818 @ X816)&(X817 @ X818))))=>![X819:$i]:(((in @ X819 @ X816)=>~((X817 @ X819))))))=>(![X1353:$i, X1354:$i > $o]:((?[X1355:$i]:(((in @ X1355 @ X1353)&~((X1354 @ X1355))))=>~(![X1356:$i]:(((in @ X1356 @ X1353)=>(X1354 @ X1356))))))=>(![X820:$o]:(((X820)=>(in @ emptyset @ (prop2set @ ((X820))))))=>(![X821:$o]:(((X821)=>(set2prop @ (prop2set @ ((X821))))))=>(![X822:$i, X823:$i > $o]:((~(?[X824:$i]:(((in @ X824 @ X822)&(X823 @ X824))))=>![X825:$i]:(((in @ X825 @ X822)=>~((X823 @ X825))))))=>(![X826:$i, X827:$i > $o]:((~(![X828:$i]:(((in @ X828 @ X826)=>(X827 @ X828))))=>?[X829:$i]:(((in @ X829 @ X826)&~((X827 @ X829))))))=>(![X1348:$i > 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X1098 @ X1095)=>(~(X1096)=>(in @ X1098 @ (dsetconstr @ X1095 @ (^[Z0/* 9 */:$i]:((((X1096)&((Z0)=(X1097)))|(~((X1096))&((Z0)=(X1098)))))))))))))=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~(X40)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:(((~((X40))&((Z0)=(X3)))|(((Z0)=(X2))&(X40))))))=(setadjoin @ X3 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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,[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(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[iffalseProp2])]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_251]), foundationAx]), wellorderingAx]), c_0_252]), c_0_253]), c_0_254]), c_0_255]), c_0_256]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_257]), setext]), emptyI]), noeltsimpempty]), c_0_258]), c_0_259]), c_0_260]), c_0_261]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_262]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_263]), c_0_264]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_265]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_266]), c_0_267]), c_0_268]), inCongP]), in__Cong]), c_0_269]), c_0_270]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_271]), c_0_272]), c_0_273]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_274]), c_0_275]), 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_276]), c_0_277]), c_0_278]), c_0_279]), singletonsuniq]), setukpairinjL1]), c_0_280]), c_0_281]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_282]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_283]), c_0_284]), c_0_285]), c_0_286]), c_0_287]), c_0_288]), c_0_289]), c_0_290]), c_0_291]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_292]), c_0_293]), c_0_294]), c_0_295]), c_0_296]), c_0_297]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), c_0_298]), c_0_299]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_300]), c_0_301]), c_0_302]), c_0_303]), c_0_304]), c_0_305])])]), c_0_306])). 1194.21/150.62 thf(c_0_308, plain, ![X2172:$i]:(((((((X2172)=(esk90_0))|~(epred2_0)|~(epred3_0 @ X2172))&((epred2_0)|~(epred2_0)|~(epred3_0 @ X2172)))&((((X2172)=(esk90_0))|((X2172)=(esk91_0))|~(epred3_0 @ X2172))&((epred2_0)|((X2172)=(esk91_0))|~(epred3_0 @ X2172))))&(((epred2_0)|((X2172)!=(esk91_0))|(epred3_0 @ X2172))&(((X2172)!=(esk90_0))|~(epred2_0)|(epred3_0 @ X2172))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[])])])])])). 1194.21/150.62 thf(c_0_309, negated_conjecture, ![X1444:$i, X1445:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1457:$i, X1458:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1466:$i, X1467:$i > $i > $o, X1468:$i, X1470:$i, X1473:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1480:$i, X1481:$i > $o, X1482:$i, X1484:$i, X1485:$i > $o, X1486:$i, X1487:$i, X1488:$i > $o, X1489:$i, X1490:$i, X1491:$i > $o, X1492:$i, X1493:$i > $o, X1494:$i, X1497:$i, X1498:$o, X1499:$i, X1500:$i, X1501:$o, X1502:$i, X1503:$i, X1504:$i > $o, X1505:$i, X1508:$i, X1509:$i, X1512:$i, X1514:$i, X1516:$i, X1517:$i > $o, X1518:$i, X1519:$i, X1521:$i, X1522:$i > $o, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$o, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$o, X1554:$i, X1555:$i, X1556:$i > $o, X1557:$i, X1560:$i, X1561:$i, X1562:$i, X1564:$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 > $o, X1581:$i, X1582:$i > $o, X1583:$i, X1584:$i, X1585:$i > $o, X1586:$i, X1588:$i, X1589:$i > $o, X1591:$i, X1592:$i, X1593:$i > $o, X1595:$i, X1596:$i, X1597:$i > $o, X1598:$i, X1600:$o, X1601:$o, X1602:$i, X1603:$i > $o, X1605:$i, X1606:$i, X1607:$i > $o, X1608:$i, X1610:$i > $o, X1611:$i, X1614:$i, X1615:$i > $o, X1616:$i, X1620:$i, X1621:$i > $o, X1622:$i, X1625:$i, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$i, X1634:$i > $o, X1635:$i, X1637:$i, X1638:$i, X1639:$i > $o, X1640:$i > $o, X1643:$i, X1646:$i, X1647:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i > $o, X1660:$i, X1662:$i, X1663:$i, X1664:$i > $o, X1665:$i > $o, X1668:$i, X1670:$i, X1672:$i, X1673:$i, X1674:$i > $o, X1675:$i > $o, X1678:$i, X1679:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i, X1685:$i, X1686:$i, X1688:$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, X1717:$i, X1718:$i, X1719:$i, X1720:$i, X1721:$i, X1722:$i, X1723:$i, X1724:$i, X1725:$i > $o, X1726:$i, X1727:$i > $o, X1728:$i, X1729:$i, X1730:$i, X1731:$i, X1732:$i, X1733:$i, X1734:$i, X1735:$i, X1736:$i, X1737:$i, X1738:$i, X1739:$o, X1740:$i, X1741:$i, X1742:$i, X1743:$i, X1744:$i, X1745:$i, X1746:$i, X1747:$i, X1748:$i, X1749:$i, X1750:$i, X1751:$i, X1752:$i, X1753:$i, X1754:$i, X1755:$i, X1756:$i, X1757:$i, X1758:$i, X1759:$i, X1760:$i, X1761:$i, X1762:$i, X1763:$i, X1764:$i, X1765:$i, X1766:$i, X1768:$i, X1769:$i, X1770:$i, X1771:$i, X1772:$i, X1773:$i, X1774:$i, X1775:$i, X1776:$i, X1777:$i, X1778:$i, X1779:$i, X1780:$i, X1781:$i, X1782:$i, X1783:$i, X1784:$i, X1785:$i, X1786:$i, X1787:$i, X1788:$i, X1789:$i, X1790:$i, X1791:$i, X1792:$i, X1793:$i, X1794:$i, X1795:$i, X1796:$i, X1797:$i, X1798:$i, X1799:$i, X1800:$i, X1801:$i, X1802:$i, X1803:$i, X1804:$i, X1805:$i, X1806:$i, X1807:$o, X1808:$i, X1809:$i, X1810:$i, X1811:$i, X1812:$i, X1813:$i, X1814:$i, X1815:$i, X1816:$i, X1817:$i, X1818:$i, X1819:$i, X1820:$i, X1821:$i, X1822:$i, X1823:$i, X1824:$i, X1825:$i, X1826:$i, X1827:$i, X1828:$i, X1829:$i, X1830:$i, X1831:$i, X1832:$i, X1833:$i, X1834:$i, X1835:$i, X1836:$i, X1837:$i, X1838:$i, X1839:$i, X1840:$i, X1841:$i, X1842:$i, X1843:$i, X1844:$i, X1845:$i, X1846:$i, X1847:$i, X1848:$i, X1849:$i, X1850:$i, X1851:$i, X1852:$i, X1853:$i, X1854:$i, X1855:$i, X1856:$i, X1857:$i, X1858:$i, X1859:$i, X1860:$i, X1861:$i, X1862:$i, X1863:$i, X1864:$i, X1865:$i, X1866:$i, X1869:$i, X1870:$i, X1871:$i, X1872:$i, X1873:$i, X1875:$i, X1876:$i, X1877:$i, X1878:$i, X1879:$i > $o, X1882:$i, X1884:$i, X1885:$i > $o, X1886:$i, X1888:$i, X1889:$i > $o, X1890:$i, X1893:$i, X1894:$i > $o, X1897:$i, X1899:$i, X1900:$i, X1901:$i, X1902:$i, X1903:$i, X1904:$i, X1906:$i, X1907:$i, X1908:$i, X1909:$i, X1910:$i, X1911:$i, X1912:$i, X1913:$i, X1914:$i, X1915:$i, X1916:$i, X1917:$i, X1918:$i, X1919:$i, X1920:$i, X1921:$i, X1922:$i, X1923:$i, X1924:$i, X1925:$i, X1926:$i, X1927:$i, X1928:$i, X1929:$i, X1930:$i, X1931:$i, X1932:$i, X1933:$i, X1934:$i, X1935:$i, X1936:$i, X1937:$i, X1938:$i, X1939:$i, X1940:$i, X1942:$i, X1943:$i, X1944:$i, X1945:$i, X1946:$i, X1947:$i, X1948:$i, X1949:$i, X1950:$i, X1951:$i, X1952:$i, X1953:$i, X1954:$i, X1955:$i, X1956:$i, X1957:$i, X1958:$i, X1959:$i, X1960:$i, X1961:$i, X1962:$i, X1963:$i, X1964:$i, X1965:$i, X1966:$i, X1967:$i, X1968:$i, X1969:$i, X1970:$i, X1971:$i, X1972:$i, X1973:$i > $i > $o, X1974:$i, X1975:$i, X1976:$i, X1977:$i, X1978:$i > $i > $o, X1979:$i, X1980:$i, X1981:$i > $i > $o, X1982:$i, X1983:$i, X1984:$i > $i > $o, X1985:$i, X1986:$i, X1987:$i, X1988:$i, X1989:$i > $i > $o, X1990:$i, X1991:$i, X1992:$i, X1993:$i, X1994:$i > $i > $o, X1995:$i, X1996:$i, X1997:$i, X1998:$i, X1999:$i > $i > $o, X2000:$i, X2001:$i, X2002:$i, X2003:$i, X2004:$i, X2005:$i, X2007:$i, X2008:$i, X2009:$i, X2010:$i, X2011:$i, X2012:$i, X2013:$i, X2014:$i, X2015:$i, X2016:$i, X2017:$i, X2018:$i, X2019:$i, X2020:$i, X2021:$i, X2022:$i, X2023:$i, X2024:$i, X2025:$i, X2026:$i, X2027:$i > $i, X2029:$i, X2030:$i, X2031:$i > $i, X2033:$i, X2034:$i, X2035:$i > $i, X2037:$i, X2038:$i, X2039:$i, X2040:$i > $o, X2043:$i, X2044:$i, X2045:$i, X2046:$i, X2047:$i > $o, X2050:$i, X2051:$i, X2052:$i > $o, X2053:$i, X2054:$i, X2055:$i, X2056:$i, X2057:$i, X2058:$i, X2059:$i, X2060:$i, X2061:$i, X2062:$i, X2063:$i, X2064:$i, X2065:$i, X2066:$i, X2067:$i, X2068:$i, X2069:$i, X2070:$i, X2071:$i, X2072:$i, X2074:$i, X2075:$i, X2076:$i, X2077:$i, X2078:$i, X2079:$i, X2080:$i, X2081:$i, X2082:$i, X2083:$i, X2084:$i, X2087:$i, X2088:$i, X2089:$i, X2090:$i, X2095:$i, X2096:$i, X2097:$i, X2098:$i, X2100:$i, X2101:$i, X2102:$i, X2103:$i, X2105:$i, X2106:$i, X2107:$i, X2108:$i, X2109:$i, X2110:$i, 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@ X2071 @ X2072)))|(~(in @ X2074 @ X2069)|(~(in @ X2075 @ X2070)|(~(in @ (kpair @ X2074 @ X2075) @ X2072)|(in @ (kpair @ X2074 @ X2075) @ X2071))))|~(func @ X2069 @ X2070 @ X2072)|~(func @ X2069 @ X2070 @ X2071)))&((~(in @ X2078 @ (funcSet @ X2076 @ X2077))|(~(in @ X2079 @ X2076)|(~(in @ X2080 @ X2077)|(~(in @ (kpair @ X2079 @ X2080) @ X2078)|((ap @ X2076 @ X2077 @ X2078 @ X2079)=(X2080))))))&((((in @ (esk78_4 @ X2081 @ X2082 @ X2083 @ X2084) @ X2081)|(subset @ X2083 @ X2084)|~(subset @ X2084 @ (cartprod @ X2081 @ X2082))|~(subset @ X2083 @ (cartprod @ X2081 @ X2082)))&(((in @ (esk79_4 @ X2081 @ X2082 @ X2083 @ X2084) @ X2082)|(subset @ X2083 @ X2084)|~(subset @ X2084 @ (cartprod @ X2081 @ X2082))|~(subset @ X2083 @ (cartprod @ X2081 @ X2082)))&(((in @ (kpair @ (esk78_4 @ X2081 @ X2082 @ X2083 @ X2084) @ (esk79_4 @ X2081 @ X2082 @ X2083 @ X2084)) @ X2083)|(subset @ X2083 @ X2084)|~(subset @ X2084 @ (cartprod @ X2081 @ X2082))|~(subset @ X2083 @ (cartprod @ X2081 @ X2082)))&(~(in @ (kpair @ (esk78_4 @ X2081 @ X2082 @ X2083 @ X2084) @ (esk79_4 @ X2081 @ X2082 @ X2083 @ X2084)) @ X2084)|(subset @ X2083 @ X2084)|~(subset @ X2084 @ (cartprod @ X2081 @ X2082))|~(subset @ X2083 @ (cartprod @ X2081 @ X2082))))))&(((((in @ (esk82_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2087)|((X2089)=(X2090))|(in @ (esk80_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2087)|~(subset @ X2090 @ (cartprod @ X2087 @ X2088))|~(subset @ X2089 @ (cartprod @ X2087 @ X2088)))&(((in @ (esk83_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2088)|((X2089)=(X2090))|(in @ (esk80_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2087)|~(subset @ X2090 @ (cartprod @ X2087 @ X2088))|~(subset @ X2089 @ (cartprod @ X2087 @ X2088)))&(((in @ (kpair @ (esk82_4 @ X2087 @ X2088 @ X2089 @ X2090) @ (esk83_4 @ X2087 @ X2088 @ X2089 @ X2090)) @ X2090)|((X2089)=(X2090))|(in @ (esk80_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2087)|~(subset @ X2090 @ (cartprod @ X2087 @ X2088))|~(subset @ X2089 @ (cartprod @ X2087 @ X2088)))&(~(in @ (kpair @ (esk82_4 @ X2087 @ X2088 @ X2089 @ X2090) @ (esk83_4 @ X2087 @ X2088 @ X2089 @ X2090)) @ X2089)|((X2089)=(X2090))|(in @ (esk80_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2087)|~(subset @ X2090 @ (cartprod @ X2087 @ X2088))|~(subset @ X2089 @ (cartprod @ X2087 @ X2088))))))&((((in @ (esk82_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2087)|((X2089)=(X2090))|(in @ (esk81_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2088)|~(subset @ X2090 @ (cartprod @ X2087 @ X2088))|~(subset @ X2089 @ (cartprod @ X2087 @ X2088)))&(((in @ (esk83_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2088)|((X2089)=(X2090))|(in @ (esk81_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2088)|~(subset @ X2090 @ (cartprod @ X2087 @ X2088))|~(subset @ X2089 @ (cartprod @ X2087 @ X2088)))&(((in @ (kpair @ (esk82_4 @ X2087 @ X2088 @ X2089 @ X2090) @ (esk83_4 @ X2087 @ X2088 @ X2089 @ X2090)) @ X2090)|((X2089)=(X2090))|(in @ (esk81_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2088)|~(subset @ X2090 @ (cartprod @ X2087 @ X2088))|~(subset @ X2089 @ (cartprod @ X2087 @ X2088)))&(~(in @ (kpair @ (esk82_4 @ X2087 @ X2088 @ X2089 @ X2090) @ (esk83_4 @ X2087 @ X2088 @ X2089 @ X2090)) @ X2089)|((X2089)=(X2090))|(in @ (esk81_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2088)|~(subset @ X2090 @ (cartprod @ X2087 @ X2088))|~(subset @ X2089 @ (cartprod @ X2087 @ X2088))))))&((((in @ (esk82_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2087)|((X2089)=(X2090))|(in @ (kpair @ (esk80_4 @ X2087 @ X2088 @ X2089 @ X2090) @ (esk81_4 @ X2087 @ X2088 @ X2089 @ X2090)) @ X2089)|~(subset @ X2090 @ (cartprod @ X2087 @ X2088))|~(subset @ X2089 @ (cartprod @ X2087 @ X2088)))&(((in @ (esk83_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2088)|((X2089)=(X2090))|(in @ (kpair @ (esk80_4 @ X2087 @ X2088 @ X2089 @ X2090) @ (esk81_4 @ X2087 @ X2088 @ X2089 @ X2090)) @ X2089)|~(subset @ X2090 @ (cartprod @ X2087 @ X2088))|~(subset @ X2089 @ (cartprod @ X2087 @ X2088)))&(((in @ (kpair @ (esk82_4 @ X2087 @ X2088 @ X2089 @ X2090) @ (esk83_4 @ X2087 @ X2088 @ X2089 @ X2090)) @ X2090)|((X2089)=(X2090))|(in @ (kpair @ (esk80_4 @ X2087 @ X2088 @ X2089 @ X2090) @ (esk81_4 @ X2087 @ X2088 @ X2089 @ X2090)) @ X2089)|~(subset @ X2090 @ (cartprod @ X2087 @ X2088))|~(subset @ X2089 @ (cartprod @ X2087 @ X2088)))&(~(in @ (kpair @ (esk82_4 @ X2087 @ X2088 @ X2089 @ X2090) @ (esk83_4 @ X2087 @ X2088 @ X2089 @ X2090)) @ X2089)|((X2089)=(X2090))|(in @ (kpair @ (esk80_4 @ X2087 @ X2088 @ X2089 @ X2090) @ (esk81_4 @ X2087 @ X2088 @ X2089 @ X2090)) @ X2089)|~(subset @ X2090 @ (cartprod @ X2087 @ X2088))|~(subset @ X2089 @ (cartprod @ X2087 @ X2088))))))&(((in @ (esk82_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2087)|((X2089)=(X2090))|~(in @ (kpair @ (esk80_4 @ X2087 @ X2088 @ X2089 @ X2090) @ (esk81_4 @ X2087 @ X2088 @ X2089 @ X2090)) @ X2090)|~(subset @ X2090 @ (cartprod @ X2087 @ X2088))|~(subset @ X2089 @ (cartprod @ X2087 @ X2088)))&(((in @ (esk83_4 @ X2087 @ X2088 @ X2089 @ X2090) @ X2088)|((X2089)=(X2090))|~(in @ (kpair @ (esk80_4 @ X2087 @ X2088 @ X2089 @ X2090) @ (esk81_4 @ X2087 @ X2088 @ X2089 @ X2090)) @ X2090)|~(subset @ X2090 @ (cartprod @ X2087 @ X2088))|~(subset @ X2089 @ (cartprod @ X2087 @ X2088)))&(((in @ (kpair @ (esk82_4 @ X2087 @ X2088 @ X2089 @ X2090) @ (esk83_4 @ X2087 @ X2088 @ X2089 @ X2090)) @ X2090)|((X2089)=(X2090))|~(in @ (kpair @ (esk80_4 @ X2087 @ X2088 @ X2089 @ X2090) @ (esk81_4 @ X2087 @ X2088 @ X2089 @ X2090)) @ X2090)|~(subset @ X2090 @ (cartprod @ X2087 @ X2088))|~(subset @ X2089 @ (cartprod @ X2087 @ X2088)))&(~(in @ (kpair @ (esk82_4 @ X2087 @ X2088 @ X2089 @ X2090) @ (esk83_4 @ X2087 @ X2088 @ X2089 @ X2090)) @ X2089)|((X2089)=(X2090))|~(in @ (kpair @ (esk80_4 @ X2087 @ X2088 @ X2089 @ X2090) @ (esk81_4 @ X2087 @ X2088 @ X2089 @ X2090)) @ X2090)|~(subset @ X2090 @ (cartprod @ X2087 @ X2088))|~(subset @ X2089 @ (cartprod @ X2087 @ X2088)))))))))&((((in @ (esk84_4 @ X2095 @ X2096 @ X2097 @ X2098) @ X2095)|((X2097)=(X2098))|~(func @ X2095 @ X2096 @ X2098)|~(func @ X2095 @ X2096 @ X2097))&(((ap @ X2095 @ X2096 @ X2097 @ (esk84_4 @ X2095 @ X2096 @ X2097 @ X2098))!=(ap @ X2095 @ X2096 @ X2098 @ (esk84_4 @ X2095 @ X2096 @ X2097 @ X2098)))|((X2097)=(X2098))|~(func @ X2095 @ X2096 @ X2098)|~(func @ X2095 @ X2096 @ X2097)))&((((in @ (esk85_4 @ X2100 @ X2101 @ X2102 @ X2103) @ X2100)|((X2102)=(X2103))|~(in @ X2103 @ (funcSet @ X2100 @ X2101))|~(in @ X2102 @ (funcSet @ X2100 @ X2101)))&(((ap @ X2100 @ X2101 @ X2102 @ (esk85_4 @ X2100 @ X2101 @ X2102 @ X2103))!=(ap @ X2100 @ X2101 @ X2103 @ (esk85_4 @ X2100 @ X2101 @ X2102 @ X2103)))|((X2102)=(X2103))|~(in @ X2103 @ (funcSet @ X2100 @ X2101))|~(in @ X2102 @ (funcSet @ X2100 @ X2101))))&((~(in @ X2107 @ (funcSet @ X2105 @ X2106))|(~(in @ X2108 @ X2105)|((ap @ X2105 @ X2106 @ X2107 @ X2108)=(ap @ X2105 @ X2106 @ X2107 @ X2108))))&((~(func @ X2109 @ X2110 @ X2111)|(~(in @ X2112 @ X2109)|((ap @ X2109 @ X2110 @ X2111 @ X2112)=(ap @ X2109 @ X2110 @ X2111 @ X2112))))&((((in @ (esk86_3 @ X2113 @ X2114 @ X2115) @ X2113)|(~(in @ X2117 @ X2113)|((ap @ X2113 @ X2114 @ (lam @ X2113 @ X2114 @ X2115) @ X2117)=(X2115 @ X2117))))&(~(in @ (X2115 @ (esk86_3 @ X2113 @ X2114 @ X2115)) @ X2114)|(~(in @ X2117 @ X2113)|((ap @ X2113 @ X2114 @ (lam @ X2113 @ X2114 @ X2115) @ X2117)=(X2115 @ X2117)))))&((~(func @ X2118 @ X2119 @ X2120)|((lam @ X2118 @ X2119 @ (ap @ X2118 @ X2119 @ X2120))=(X2120)))&((((in @ (esk87_3 @ X2121 @ X2122 @ X2123) @ X2121)|((lam @ X2121 @ X2122 @ X2123)=(lam @ X2121 @ X2122 @ X2123)))&(~(in @ (X2123 @ (esk87_3 @ X2121 @ X2122 @ X2123)) @ X2122)|((lam @ X2121 @ X2122 @ X2123)=(lam @ X2121 @ X2122 @ X2123))))&((((in @ (esk88_3 @ X2125 @ X2126 @ X2127) @ X2125)|(~(in @ X2129 @ X2125)|((ap @ X2125 @ X2126 @ (lam @ X2125 @ X2126 @ X2127) @ X2129)=(X2127 @ X2129))))&(~(in @ (X2127 @ (esk88_3 @ X2125 @ X2126 @ X2127)) @ X2126)|(~(in @ X2129 @ X2125)|((ap @ X2125 @ X2126 @ (lam @ X2125 @ X2126 @ X2127) @ X2129)=(X2127 @ X2129)))))&((~(in @ X2132 @ (funcSet @ X2130 @ X2131))|((lam @ X2130 @ X2131 @ (ap @ X2130 @ X2131 @ X2132))=(X2132)))&((~(in @ X2135 @ X2133)|(~(in @ X2136 @ X2133)|((X2134)|(in @ X2136 @ (dsetconstr @ X2133 @ (^[Z0/* 9 */:$i]:((((X2134)&((Z0)=(X2135)))|(~((X2134))&((Z0)=(X2136)))))))))))&((in @ esk90_0 @ esk89_0)&((in @ esk91_0 @ esk89_0)&(~(epred2_0)&((dsetconstr @ esk89_0 @ (^[Z0/* 9 */:$i]:(((~((epred2_0))&((Z0)=(esk91_0)))|(((Z0)=(esk90_0))&(epred2_0))))))!=(setadjoin @ esk91_0 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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_307])])])])])])])). 1194.21/150.62 thf(c_0_310, plain, ![X2:$i]:(((epred2_0)|((X2)=(esk91_0))|~((epred3_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_308])). 1194.21/150.62 thf(c_0_311, negated_conjecture, ~((epred2_0)), inference(split_conjunct,[status(thm)],[c_0_309])). 1194.21/150.62 thf(c_0_312, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:((((dsetconstr @ X2 @ X1)=(setadjoin @ (esk60_2 @ X2 @ X1) @ emptyset))|(X1 @ (esk59_2 @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_309])). 1194.21/150.62 thf(c_0_313, negated_conjecture, (in @ esk91_0 @ esk89_0), inference(split_conjunct,[status(thm)],[c_0_309])). 1194.21/150.62 thf(c_0_314, plain, ![X2:$i]:(((epred2_0)|(epred3_0 @ X2)|((X2)!=(esk91_0)))), inference(split_conjunct,[status(thm)],[c_0_308])). 1194.21/150.62 thf(c_0_315, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:((((dsetconstr @ X2 @ X1)=(setadjoin @ (esk60_2 @ X2 @ X1) @ emptyset))|(X1 @ (esk58_2 @ X2 @ X1))|~((in @ X3 @ X2))|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_309])). 1194.21/150.62 thf(c_0_316, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:((((dsetconstr @ X2 @ X1)=(setadjoin @ (esk60_2 @ X2 @ X1) @ emptyset))|~((in @ X3 @ X2))|~((X1 @ X3))|((esk58_2 @ X2 @ X1)!=(esk59_2 @ X2 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_309])). 1194.21/150.62 thf(c_0_317, plain, ![X2:$i]:((((X2)=(esk91_0))|~((epred3_0 @ X2)))), inference(sr,[status(thm)],[c_0_310, c_0_311])). 1194.21/150.62 thf(c_0_318, negated_conjecture, ![X1:$i > $o]:((((setadjoin @ (esk60_2 @ esk89_0 @ X1) @ emptyset)=(dsetconstr @ esk89_0 @ X1))|(X1 @ (esk59_2 @ esk89_0 @ X1))|~((X1 @ esk91_0)))), inference(spm,[status(thm)],[c_0_312, c_0_313])). 1194.21/150.62 thf(c_0_319, plain, (epred3_0 @ esk91_0), inference(er,[status(thm)],[inference(sr,[status(thm)],[c_0_314, c_0_311])])). 1194.21/150.62 thf(c_0_320, negated_conjecture, ![X1:$i > $o]:((((setadjoin @ (esk60_2 @ esk89_0 @ X1) @ emptyset)=(dsetconstr @ esk89_0 @ X1))|(X1 @ (esk58_2 @ esk89_0 @ X1))|~((X1 @ esk91_0)))), inference(spm,[status(thm)],[c_0_315, c_0_313])). 1194.21/150.62 thf(c_0_321, negated_conjecture, ![X1:$i > $o]:((((setadjoin @ (esk60_2 @ esk89_0 @ X1) @ emptyset)=(dsetconstr @ esk89_0 @ X1))|((esk59_2 @ esk89_0 @ X1)!=(esk58_2 @ esk89_0 @ X1))|~((X1 @ esk91_0)))), inference(spm,[status(thm)],[c_0_316, c_0_313])). 1194.21/150.62 thf(c_0_322, plain, (((setadjoin @ (esk60_2 @ esk89_0 @ epred3_0) @ emptyset)=(dsetconstr @ esk89_0 @ epred3_0))|((esk59_2 @ esk89_0 @ epred3_0)=(esk91_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_317, c_0_318]), c_0_319])])). 1194.21/150.62 thf(c_0_323, plain, (((setadjoin @ (esk60_2 @ esk89_0 @ epred3_0) @ emptyset)=(dsetconstr @ esk89_0 @ epred3_0))|((esk58_2 @ esk89_0 @ epred3_0)=(esk91_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_317, c_0_320]), c_0_319])])). 1194.21/150.62 thf(c_0_324, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_309])). 1194.21/150.62 thf(c_0_325, negated_conjecture, ((setadjoin @ (esk60_2 @ esk89_0 @ epred3_0) @ emptyset)=(dsetconstr @ esk89_0 @ epred3_0)), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_321, c_0_322]), c_0_319])]), c_0_323])). 1194.21/150.62 thf(c_0_326, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((X1 @ X2)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_309])). 1194.21/150.62 thf(c_0_327, negated_conjecture, (in @ (esk60_2 @ esk89_0 @ epred3_0) @ (dsetconstr @ esk89_0 @ epred3_0)), inference(spm,[status(thm)],[c_0_324, c_0_325])). 1194.21/150.62 thf(c_0_328, negated_conjecture, (epred3_0 @ (esk60_2 @ esk89_0 @ epred3_0)), inference(spm,[status(thm)],[c_0_326, c_0_327])). 1194.21/150.62 thf(c_0_329, plain, ![X2160:$i]:(((epred3_0 @ X2160)<=>((~((epred2_0))&((X2160)=(esk91_0)))|(((X2160)=(esk90_0))&(epred2_0))))), introduced(definition)). 1194.21/150.62 thf(c_0_330, plain, ((esk60_2 @ esk89_0 @ epred3_0)=(esk91_0)), inference(spm,[status(thm)],[c_0_317, c_0_328])). 1194.21/150.62 thf(c_0_331, negated_conjecture, ((dsetconstr @ esk89_0 @ epred3_0)!=(setadjoin @ esk91_0 @ emptyset)), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_309]), c_0_329])). 1194.21/150.62 thf(c_0_332, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_325, c_0_330]), c_0_331]), ['proof']). 1194.21/150.62 # SZS output end CNFRefutation 1194.21/150.62 # Parsed axioms : 477 1194.21/150.62 # Removed by relevancy pruning/SinE : 0 1194.21/150.62 # Initial clauses : 681 1194.21/150.62 # Removed in clause preprocessing : 290 1194.21/150.62 # Initial clauses in saturation : 391 1194.21/150.62 # Processed clauses : 16006 1194.21/150.62 # ...of these trivial : 68 1194.21/150.62 # ...subsumed : 8881 1194.21/150.62 # ...remaining for further processing : 7057 1194.21/150.62 # Other redundant clauses eliminated : 138 1194.21/150.62 # Clauses deleted for lack of memory : 29627 1194.21/150.62 # Backward-subsumed : 257 1194.21/150.62 # Backward-rewritten : 60 1194.21/150.62 # Generated clauses : 1950971 1194.21/150.62 # ...of the previous two non-redundant : 1940400 1194.21/150.62 # ...aggressively subsumed : 0 1194.21/150.62 # Contextual simplify-reflections : 526 1194.21/150.62 # Paramodulations : 1949631 1194.21/150.62 # Factorizations : 139 1194.21/150.62 # NegExts : 429 1194.21/150.62 # Equation resolutions : 147 1194.21/150.62 # Disequality decompositions : 0 1194.21/150.62 # Total rewrite steps : 110876 1194.21/150.62 # ...of those cached : 109892 1194.21/150.62 # Propositional unsat checks : 1 1194.21/150.62 # Propositional check models : 0 1194.21/150.62 # Propositional check unsatisfiable : 0 1194.21/150.62 # Propositional clauses : 0 1194.21/150.62 # Propositional clauses after purity: 0 1194.21/150.62 # Propositional unsat core size : 0 1194.21/150.62 # Propositional preprocessing time : 0.000 1194.21/150.62 # Propositional encoding time : 3.673 1194.21/150.62 # Propositional solver time : 0.901 1194.21/150.62 # Success case prop preproc time : 0.000 1194.21/150.62 # Success case prop encoding time : 0.000 1194.21/150.62 # Success case prop solver time : 0.000 1194.21/150.62 # Current number of processed clauses : 6080 1194.21/150.62 # Positive orientable unit clauses : 81 1194.21/150.62 # Positive unorientable unit clauses: 0 1194.21/150.62 # Negative unit clauses : 43 1194.21/150.62 # Non-unit-clauses : 5956 1194.21/150.62 # Current number of unprocessed clauses: 1175075 1194.21/150.62 # ...number of literals in the above : 5875977 1194.21/150.62 # Current number of archived formulas : 0 1194.21/150.62 # Current number of archived clauses : 961 1194.21/150.62 # Clause-clause subsumption calls (NU) : 4627710 1194.21/150.62 # Rec. Clause-clause subsumption calls : 810954 1194.21/150.62 # Non-unit clause-clause subsumptions : 6352 1194.21/150.62 # Unit Clause-clause subsumption calls : 16748 1194.21/150.62 # Rewrite failures with RHS unbound : 0 1194.21/150.62 # BW rewrite match attempts : 51 1194.21/150.62 # BW rewrite match successes : 21 1194.21/150.62 # Condensation attempts : 0 1194.21/150.62 # Condensation successes : 0 1194.21/150.62 # Termbank termtop insertions : 86645325 1194.21/150.62 # Search garbage collected termcells : 2267281 1194.21/150.62 1194.21/150.62 # ------------------------------------------------- 1194.21/150.62 # User time : 396.213 s 1194.21/150.62 # System time : 8.569 s 1194.21/150.62 # Total time : 404.782 s 1194.21/150.62 # Maximum resident set size: 7336 pages 1194.21/150.62 1194.21/150.62 # ------------------------------------------------- 1194.21/150.62 # User time : 585.051 s 1194.21/150.62 # System time : 12.621 s 1194.21/150.62 # Total time : 597.673 s 1194.21/150.62 # Maximum resident set size: 2344 pages 1194.21/150.62 % E exiting 1194.21/150.62 % E exiting 1194.21/150.62 EOF