0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.12 % Command : run_E %s %d THM 0.12/0.32 % Computer : n008.cluster.edu 0.12/0.32 % Model : x86_64 x86_64 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.32 % Memory : 8042.1875MB 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.32 % CPULimit : 1440 0.12/0.32 % WCLimit : 180 0.12/0.32 % DateTime : Thu Jul 4 07:13:53 EDT 2024 0.12/0.33 % CPUTime : 0.19/0.46 Running higher-order theorem proving 0.19/0.49 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=180 /export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p 619.55/78.70 # Version: 3.2.0-ho 619.55/78.70 # Preprocessing class: HSLMSLSSLLLCHFA. 619.55/78.70 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 619.55/78.70 # Starting ehoh_best5 with 180s (1) cores 619.55/78.70 # Starting almost_fo_3_lam with 180s (1) cores 619.55/78.70 # Starting new_bool_5 with 180s (1) cores 619.55/78.70 # Starting pre_casc_3 with 180s (1) cores 619.55/78.70 # Starting ho_unfolding_8 with 180s (1) cores 619.55/78.70 # Starting new_ho_10_cnf2 with 180s (1) cores 619.55/78.70 # Starting new_bool_3 with 180s (1) cores 619.55/78.70 # Starting new_ho_5 with 180s (1) cores 619.55/78.70 # ho_unfolding_8 with pid 7189 completed with status 0 619.55/78.70 # Result found by ho_unfolding_8 619.55/78.70 # Preprocessing class: HSLMSLSSLLLCHFA. 619.55/78.70 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 619.55/78.70 # Starting ehoh_best5 with 180s (1) cores 619.55/78.70 # Starting almost_fo_3_lam with 180s (1) cores 619.55/78.70 # Starting new_bool_5 with 180s (1) cores 619.55/78.70 # Starting pre_casc_3 with 180s (1) cores 619.55/78.70 # Starting ho_unfolding_8 with 180s (1) cores 619.55/78.70 # No SInE strategy applied 619.55/78.70 # Search class: HGHSM-FSLM31-MHFMMSBN 619.55/78.70 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 619.55/78.70 # Starting new_ho_10_cnf2 with 98s (1) cores 619.55/78.70 # new_ho_10_cnf2 with pid 7197 completed with status 0 619.55/78.70 # Result found by new_ho_10_cnf2 619.55/78.70 # Preprocessing class: HSLMSLSSLLLCHFA. 619.55/78.70 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 619.55/78.70 # Starting ehoh_best5 with 180s (1) cores 619.55/78.70 # Starting almost_fo_3_lam with 180s (1) cores 619.55/78.70 # Starting new_bool_5 with 180s (1) cores 619.55/78.70 # Starting pre_casc_3 with 180s (1) cores 619.55/78.70 # Starting ho_unfolding_8 with 180s (1) cores 619.55/78.70 # No SInE strategy applied 619.55/78.70 # Search class: HGHSM-FSLM31-MHFMMSBN 619.55/78.70 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 619.55/78.70 # Starting new_ho_10_cnf2 with 98s (1) cores 619.55/78.70 # Preprocessing time : 0.005 s 619.55/78.70 # Presaturation interreduction done 619.55/78.70 619.55/78.70 # Proof found! 619.55/78.70 # SZS status Theorem 619.55/78.70 # SZS output start CNFRefutation 619.55/78.70 thf(decl_22, type, in: $i > $i > $o). 619.55/78.70 thf(decl_23, type, exu: ($i > $o) > $o). 619.55/78.70 thf(decl_24, type, setextAx: $o). 619.55/78.70 thf(decl_25, type, emptyset: $i). 619.55/78.70 thf(decl_26, type, emptysetAx: $o). 619.55/78.70 thf(decl_27, type, setadjoin: $i > $i > $i). 619.55/78.70 thf(decl_28, type, setadjoinAx: $o). 619.55/78.70 thf(decl_29, type, powerset: $i > $i). 619.55/78.70 thf(decl_30, type, powersetAx: $o). 619.55/78.70 thf(decl_31, type, setunion: $i > $i). 619.55/78.70 thf(decl_32, type, setunionAx: $o). 619.55/78.70 thf(decl_33, type, omega: $i). 619.55/78.70 thf(decl_34, type, omega0Ax: $o). 619.55/78.70 thf(decl_35, type, omegaSAx: $o). 619.55/78.70 thf(decl_36, type, omegaIndAx: $o). 619.55/78.70 thf(decl_37, type, replAx: $o). 619.55/78.70 thf(decl_38, type, foundationAx: $o). 619.55/78.70 thf(decl_39, type, wellorderingAx: $o). 619.55/78.70 thf(decl_40, type, descr: ($i > $o) > $i). 619.55/78.70 thf(decl_41, type, descrp: $o). 619.55/78.70 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 619.55/78.70 thf(decl_43, type, dsetconstrI: $o). 619.55/78.70 thf(decl_44, type, dsetconstrEL: $o). 619.55/78.70 thf(decl_45, type, dsetconstrER: $o). 619.55/78.70 thf(decl_46, type, exuE1: $o). 619.55/78.70 thf(decl_47, type, prop2set: $o > $i). 619.55/78.70 thf(decl_48, type, prop2setE: $o). 619.55/78.70 thf(decl_49, type, emptysetE: $o). 619.55/78.70 thf(decl_50, type, emptysetimpfalse: $o). 619.55/78.70 thf(decl_51, type, notinemptyset: $o). 619.55/78.70 thf(decl_52, type, exuE3e: $o). 619.55/78.70 thf(decl_53, type, setext: $o). 619.55/78.70 thf(decl_54, type, emptyI: $o). 619.55/78.70 thf(decl_55, type, noeltsimpempty: $o). 619.55/78.70 thf(decl_56, type, setbeta: $o). 619.55/78.70 thf(decl_57, type, nonempty: $i > $o). 619.55/78.70 thf(decl_58, type, nonemptyE1: $o). 619.55/78.70 thf(decl_59, type, nonemptyI: $o). 619.55/78.70 thf(decl_60, type, nonemptyI1: $o). 619.55/78.70 thf(decl_61, type, setadjoinIL: $o). 619.55/78.70 thf(decl_62, type, emptyinunitempty: $o). 619.55/78.70 thf(decl_63, type, setadjoinIR: $o). 619.55/78.70 thf(decl_64, type, setadjoinE: $o). 619.55/78.70 thf(decl_65, type, setadjoinOr: $o). 619.55/78.70 thf(decl_66, type, setoftrueEq: $o). 619.55/78.70 thf(decl_67, type, powersetI: $o). 619.55/78.70 thf(decl_68, type, emptyinPowerset: $o). 619.55/78.70 thf(decl_69, type, emptyInPowerset: $o). 619.55/78.70 thf(decl_70, type, powersetE: $o). 619.55/78.70 thf(decl_71, type, setunionI: $o). 619.55/78.70 thf(decl_72, type, setunionE: $o). 619.55/78.70 thf(decl_73, type, subPowSU: $o). 619.55/78.70 thf(decl_74, type, exuE2: $o). 619.55/78.70 thf(decl_75, type, nonemptyImpWitness: $o). 619.55/78.70 thf(decl_76, type, uniqinunit: $o). 619.55/78.70 thf(decl_77, type, notinsingleton: $o). 619.55/78.70 thf(decl_78, type, eqinunit: $o). 619.55/78.70 thf(decl_79, type, singletonsswitch: $o). 619.55/78.70 thf(decl_80, type, upairsetE: $o). 619.55/78.70 thf(decl_81, type, upairsetIL: $o). 619.55/78.70 thf(decl_82, type, upairsetIR: $o). 619.55/78.70 thf(decl_83, type, emptyE1: $o). 619.55/78.70 thf(decl_84, type, vacuousDall: $o). 619.55/78.70 thf(decl_85, type, quantDeMorgan1: $o). 619.55/78.70 thf(decl_86, type, quantDeMorgan2: $o). 619.55/78.70 thf(decl_87, type, quantDeMorgan3: $o). 619.55/78.70 thf(decl_88, type, quantDeMorgan4: $o). 619.55/78.70 thf(decl_89, type, prop2setI: $o). 619.55/78.70 thf(decl_90, type, set2prop: $i > $o). 619.55/78.70 thf(decl_91, type, prop2set2propI: $o). 619.55/78.70 thf(decl_92, type, notdexE: $o). 619.55/78.70 thf(decl_93, type, notdallE: $o). 619.55/78.70 thf(decl_94, type, exuI1: $o). 619.55/78.70 thf(decl_95, type, exuI3: $o). 619.55/78.70 thf(decl_96, type, exuI2: $o). 619.55/78.70 thf(decl_97, type, inCongP: $o). 619.55/78.70 thf(decl_98, type, in__Cong: $o). 619.55/78.70 thf(decl_99, type, exuE3u: $o). 619.55/78.70 thf(decl_100, type, exu__Cong: $o). 619.55/78.70 thf(decl_101, type, emptyset__Cong: $o). 619.55/78.70 thf(decl_102, type, setadjoin__Cong: $o). 619.55/78.70 thf(decl_103, type, powerset__Cong: $o). 619.55/78.70 thf(decl_104, type, setunion__Cong: $o). 619.55/78.70 thf(decl_105, type, omega__Cong: $o). 619.55/78.70 thf(decl_106, type, exuEu: $o). 619.55/78.70 thf(decl_107, type, descr__Cong: $o). 619.55/78.70 thf(decl_108, type, dsetconstr__Cong: $o). 619.55/78.70 thf(decl_109, type, subset: $i > $i > $o). 619.55/78.70 thf(decl_112, type, subsetI1: $o). 619.55/78.70 thf(decl_113, type, eqimpsubset2: $o). 619.55/78.70 thf(decl_114, type, eqimpsubset1: $o). 619.55/78.70 thf(decl_115, type, subsetI2: $o). 619.55/78.70 thf(decl_116, type, emptysetsubset: $o). 619.55/78.70 thf(decl_117, type, subsetE: $o). 619.55/78.70 thf(decl_118, type, subsetE2: $o). 619.55/78.70 thf(decl_119, type, notsubsetI: $o). 619.55/78.70 thf(decl_120, type, notequalI1: $o). 619.55/78.70 thf(decl_121, type, notequalI2: $o). 619.55/78.70 thf(decl_122, type, subsetRefl: $o). 619.55/78.70 thf(decl_123, type, subsetTrans: $o). 619.55/78.70 thf(decl_124, type, setadjoinSub: $o). 619.55/78.70 thf(decl_125, type, setadjoinSub2: $o). 619.55/78.70 thf(decl_126, type, subset2powerset: $o). 619.55/78.70 thf(decl_127, type, setextsub: $o). 619.55/78.70 thf(decl_128, type, subsetemptysetimpeq: $o). 619.55/78.70 thf(decl_129, type, powersetI1: $o). 619.55/78.70 thf(decl_130, type, powersetE1: $o). 619.55/78.70 thf(decl_131, type, inPowerset: $o). 619.55/78.70 thf(decl_132, type, powersetsubset: $o). 619.55/78.70 thf(decl_133, type, sepInPowerset: $o). 619.55/78.70 thf(decl_134, type, sepSubset: $o). 619.55/78.70 thf(decl_135, type, binunion: $i > $i > $i). 619.55/78.70 thf(decl_136, type, binunionIL: $o). 619.55/78.70 thf(decl_137, type, upairset2IR: $o). 619.55/78.70 thf(decl_138, type, binunionIR: $o). 619.55/78.70 thf(decl_139, type, binunionEcases: $o). 619.55/78.70 thf(decl_140, type, binunionE: $o). 619.55/78.70 thf(decl_141, type, binunionLsub: $o). 619.55/78.70 thf(decl_142, type, binunionRsub: $o). 619.55/78.70 thf(decl_143, type, binintersect: $i > $i > $i). 619.55/78.70 thf(decl_144, type, binintersectI: $o). 619.55/78.70 thf(decl_145, type, binintersectSubset5: $o). 619.55/78.70 thf(decl_146, type, binintersectEL: $o). 619.55/78.70 thf(decl_147, type, binintersectLsub: $o). 619.55/78.70 thf(decl_148, type, binintersectSubset2: $o). 619.55/78.70 thf(decl_149, type, binintersectSubset3: $o). 619.55/78.70 thf(decl_150, type, binintersectER: $o). 619.55/78.70 thf(decl_151, type, disjointsetsI1: $o). 619.55/78.70 thf(decl_152, type, binintersectRsub: $o). 619.55/78.70 thf(decl_153, type, binintersectSubset4: $o). 619.55/78.70 thf(decl_154, type, binintersectSubset1: $o). 619.55/78.70 thf(decl_155, type, bs114d: $o). 619.55/78.70 thf(decl_157, type, setminus: $i > $i > $i). 619.55/78.70 thf(decl_158, type, setminusI: $o). 619.55/78.70 thf(decl_159, type, setminusEL: $o). 619.55/78.70 thf(decl_160, type, setminusER: $o). 619.55/78.70 thf(decl_161, type, setminusSubset2: $o). 619.55/78.70 thf(decl_162, type, setminusERneg: $o). 619.55/78.70 thf(decl_163, type, setminusELneg: $o). 619.55/78.70 thf(decl_164, type, setminusILneg: $o). 619.55/78.70 thf(decl_165, type, setminusIRneg: $o). 619.55/78.70 thf(decl_166, type, setminusLsub: $o). 619.55/78.70 thf(decl_167, type, setminusSubset1: $o). 619.55/78.70 thf(decl_168, type, symdiff: $i > $i > $i). 619.55/78.70 thf(decl_169, type, symdiffE: $o). 619.55/78.70 thf(decl_170, type, symdiffI1: $o). 619.55/78.70 thf(decl_171, type, symdiffI2: $o). 619.55/78.70 thf(decl_172, type, symdiffIneg1: $o). 619.55/78.70 thf(decl_173, type, symdiffIneg2: $o). 619.55/78.70 thf(decl_174, type, iskpair: $i > $o). 619.55/78.70 thf(decl_175, type, secondinupair: $o). 619.55/78.70 thf(decl_176, type, setukpairIL: $o). 619.55/78.70 thf(decl_177, type, setukpairIR: $o). 619.55/78.70 thf(decl_178, type, kpairiskpair: $o). 619.55/78.70 thf(decl_179, type, kpair: $i > $i > $i). 619.55/78.70 thf(decl_180, type, kpairp: $o). 619.55/78.70 thf(decl_181, type, cartprod: $i > $i > $i). 619.55/78.70 thf(decl_182, type, singletonsubset: $o). 619.55/78.70 thf(decl_183, type, singletoninpowerset: $o). 619.55/78.70 thf(decl_184, type, singletoninpowunion: $o). 619.55/78.70 thf(decl_185, type, upairset2E: $o). 619.55/78.70 thf(decl_186, type, upairsubunion: $o). 619.55/78.70 thf(decl_187, type, upairinpowunion: $o). 619.55/78.70 thf(decl_188, type, ubforcartprodlem1: $o). 619.55/78.70 thf(decl_189, type, ubforcartprodlem2: $o). 619.55/78.70 thf(decl_190, type, ubforcartprodlem3: $o). 619.55/78.70 thf(decl_191, type, cartprodpairin: $o). 619.55/78.70 thf(decl_192, type, cartprodmempair1: $o). 619.55/78.70 thf(decl_193, type, epred1_0: $o). 619.55/78.70 thf(decl_194, type, esk1_2: $i > $i > $i). 619.55/78.70 thf(decl_195, type, esk2_2: $i > $i > $i). 619.55/78.70 thf(decl_196, type, esk3_2: $i > $i > $i). 619.55/78.70 thf(decl_197, type, esk4_1: $i > $i). 619.55/78.70 thf(decl_198, type, esk5_2: ($i > $i > $o) > $i > $i). 619.55/78.70 thf(decl_199, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 619.55/78.70 thf(decl_200, type, esk7_2: ($i > $i > $o) > $i > $i). 619.55/78.70 thf(decl_201, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 619.55/78.70 thf(decl_202, type, esk9_1: $i > $i). 619.55/78.70 thf(decl_203, type, esk10_2: ($i > $o) > $i > $i). 619.55/78.70 thf(decl_204, type, esk11_2: ($i > $o) > $i > $i). 619.55/78.70 thf(decl_205, type, esk12_1: ($i > $o) > $i). 619.55/78.70 thf(decl_206, type, esk13_2: ($i > $o) > $i > $i). 619.55/78.70 thf(decl_207, type, esk14_1: ($i > $o) > $i). 619.55/78.70 thf(decl_208, type, esk15_2: $i > $i > $i). 619.55/78.70 thf(decl_209, type, esk16_2: $i > $i > $i). 619.55/78.70 thf(decl_210, type, esk17_1: $i > $i). 619.55/78.70 thf(decl_211, type, esk18_1: $i > $i). 619.55/78.70 thf(decl_212, type, esk19_1: $i > $i). 619.55/78.70 thf(decl_213, type, esk20_2: $i > $i > $i). 619.55/78.70 thf(decl_214, type, esk21_3: $i > $i > $o > $i). 619.55/78.70 thf(decl_215, type, esk22_2: ($i > $o) > $i > $i). 619.55/78.70 thf(decl_216, type, esk23_1: ($i > $o) > $i). 619.55/78.70 thf(decl_217, type, esk24_1: $i > $i). 619.55/78.70 thf(decl_218, type, esk25_2: $i > ($i > $o) > $i). 619.55/78.70 thf(decl_219, type, esk26_2: $i > ($i > $o) > $i). 619.55/78.70 thf(decl_220, type, esk27_2: $i > ($i > $o) > $i). 619.55/78.70 thf(decl_221, type, esk28_2: $i > ($i > $o) > $i). 619.55/78.70 thf(decl_222, type, esk29_2: $i > ($i > $o) > $i). 619.55/78.70 thf(decl_223, type, esk30_2: $i > ($i > $o) > $i). 619.55/78.70 thf(decl_224, type, esk31_2: ($i > $o) > $i > $i). 619.55/78.70 thf(decl_225, type, esk32_1: ($i > $o) > $i). 619.55/78.70 thf(decl_226, type, esk33_1: ($i > $o) > $i). 619.55/78.70 thf(decl_227, type, esk34_1: ($i > $o) > $i). 619.55/78.70 thf(decl_228, type, esk35_1: ($i > $o) > $i). 619.55/78.70 thf(decl_229, type, esk36_2: ($i > $o) > $i > $i). 619.55/78.70 thf(decl_230, type, esk37_1: ($i > $o) > $i). 619.55/78.70 thf(decl_231, type, esk38_2: ($i > $o) > $i > $i). 619.55/78.70 thf(decl_232, type, esk39_2: ($i > $o) > ($i > $o) > $i). 619.55/78.70 thf(decl_233, type, esk40_2: ($i > $o) > ($i > $o) > $i). 619.55/78.70 thf(decl_234, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 619.55/78.70 thf(decl_235, type, esk42_2: ($i > $o) > ($i > $o) > $i). 619.55/78.70 thf(decl_236, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 619.55/78.70 thf(decl_237, type, esk44_2: ($i > $o) > ($i > $o) > $i). 619.55/78.70 thf(decl_238, type, esk45_2: ($i > $o) > $i > $i). 619.55/78.70 thf(decl_239, type, esk46_2: ($i > $o) > ($i > $o) > $i). 619.55/78.70 thf(decl_240, type, esk47_2: ($i > $o) > ($i > $o) > $i). 619.55/78.70 thf(decl_241, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 619.55/78.70 thf(decl_242, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 619.55/78.70 thf(decl_243, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 619.55/78.70 thf(decl_244, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 619.55/78.70 thf(decl_245, type, esk52_2: $i > $i > $i). 619.55/78.70 thf(decl_246, type, esk53_2: $i > $i > $i). 619.55/78.70 thf(decl_247, type, esk54_2: $i > $i > $i). 619.55/78.70 thf(decl_248, type, esk55_2: $i > $i > $i). 619.55/78.70 thf(decl_249, type, esk56_2: $i > $i > $i). 619.55/78.70 thf(decl_250, type, esk57_2: $i > $i > $i). 619.55/78.70 thf(decl_251, type, esk58_2: $i > $i > $i). 619.55/78.70 thf(decl_252, type, esk59_3: $i > $i > $i > $i). 619.55/78.70 thf(decl_253, type, esk60_3: $i > $i > $i > $i). 619.55/78.70 thf(decl_254, type, esk61_0: $i). 619.55/78.70 thf(decl_255, type, esk62_0: $i). 619.55/78.70 thf(decl_256, type, esk63_0: $i). 619.55/78.70 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', replAx)). 619.55/78.70 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', exu)). 619.55/78.70 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', descrp)). 619.55/78.70 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', exuE1)). 619.55/78.70 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', exuE3e)). 619.55/78.70 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', nonempty)). 619.55/78.70 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', nonemptyI)). 619.55/78.70 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', exuE2)). 619.55/78.70 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.oACHQ9NSgc/E---3.1_7107.p', exuI1)). 619.55/78.70 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', exuI3)). 619.55/78.70 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', exuI2)). 619.55/78.70 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.oACHQ9NSgc/E---3.1_7107.p', exuE3u)). 619.55/78.70 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', exu__Cong)). 619.55/78.70 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', exuEu)). 619.55/78.70 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', descr__Cong)). 619.55/78.70 thf(iskpair, axiom, ((iskpair)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ (setunion @ X4))&?[X3:$i]:(((in @ X3 @ (setunion @ X4))&((X4)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', iskpair)). 619.55/78.70 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', dsetconstrI)). 619.55/78.70 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', dsetconstrEL)). 619.55/78.70 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', dsetconstrER)). 619.55/78.70 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setbeta)). 619.55/78.70 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', nonemptyE1)). 619.55/78.70 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', nonemptyI1)). 619.55/78.70 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setoftrueEq)). 619.55/78.70 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', nonemptyImpWitness)). 619.55/78.70 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.oACHQ9NSgc/E---3.1_7107.p', emptyE1)). 619.55/78.70 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', dsetconstr__Cong)). 619.55/78.70 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', sepInPowerset)). 619.55/78.70 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', sepSubset)). 619.55/78.70 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.oACHQ9NSgc/E---3.1_7107.p', kpairiskpair)). 619.55/78.70 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', kpairp)). 619.55/78.70 thf(cartprodmempair, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>(((((omegaSAx)=>(((replAx)=>((foundationAx)=>(((descrp)=>(((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((((exuE3e)=>((setext)=>(((noeltsimpempty)=>(((nonemptyE1)=>(((nonemptyI1)=>((((setadjoinIR)=>(((((powersetI)=>((((powersetE)=>((setunionI)=>((setunionE)=>((((((notinsingleton)=>((eqinunit)=>((((upairsetIL)=>(((emptyE1)=>(((((((prop2setI)=>((prop2set2propI)=>(((notdallE)=>(((((inCongP)=>((in__Cong)=>((exuE3u)=>((((((setunion__Cong)=>((omega__Cong)=>((exuEu)=>(((dsetconstr__Cong)=>((((eqimpsubset1)=>((((((notsubsetI)=>((notequalI1)=>((notequalI2)=>((((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((((powersetI1)=>((powersetE1)=>((inPowerset)=>((((sepSubset)=>((binunionIL)=>(((binunionIR)=>(((binunionE)=>(((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((((disjointsetsI1)=>((binintersectRsub)=>(((binintersectSubset1)=>((((((setminusSubset2)=>((setminusERneg)=>(((((setminusLsub)=>(((symdiffE)=>((symdiffI1)=>((((((setukpairIL)=>((setukpairIR)=>((((singletonsubset)=>(((((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>(((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>![X4:$i, X5:$i, X18:$i]:(((iskpair @ X18)<=(in @ X18 @ (cartprod @ X4 @ X5)))))))<=(ubforcartprodlem2)))))<=(upairset2E))<=(singletoninpowunion))<=(singletoninpowerset)))<=(kpairp))<=(kpairiskpair))))<=(secondinupair))<=(symdiffIneg2))<=(symdiffIneg1))<=(symdiffI2))))<=(setminusSubset1)))<=(setminusIRneg))<=(setminusILneg))<=(setminusELneg))))<=(setminusER))<=(setminusEL))<=(setminusI))<=(bs114d)))<=(binintersectSubset4))))<=(binintersectER))<=(binintersectSubset3))))))))<=(binunionLsub)))<=(binunionEcases)))<=(upairset2IR))))<=(sepInPowerset))<=(powersetsubset)))))<=(subsetemptysetimpeq))<=(setextsub)))))<=(subsetTrans))<=(subsetRefl)))))<=(subsetE2))<=(subsetE))<=(emptysetsubset))<=(subsetI2)))<=(eqimpsubset2))<=(subsetI1)))<=(descr__Cong)))))<=(powerset__Cong))<=(setadjoin__Cong))<=(emptyset__Cong))<=(exu__Cong)))))<=(exuI2))<=(exuI3))<=(exuI1)))<=(notdexE))))<=(quantDeMorgan4))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1))<=(vacuousDall)))<=(upairsetIR)))<=(upairsetE))<=(singletonsswitch))))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU)))))<=(emptyInPowerset))<=(emptyinPowerset)))<=(setoftrueEq))<=(setadjoinOr))<=(setadjoinE)))<=(emptyinunitempty))<=(setadjoinIL)))<=(nonemptyI)))<=(setbeta)))<=(emptyI))))<=(notinemptyset))<=(emptysetimpfalse)))))))<=(dsetconstrI)))<=(wellorderingAx))))<=(omegaIndAx)))<=(omega0Ax))<=(setunionAx))<=(powersetAx))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', cartprodmempair)). 619.55/78.70 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setextAx)). 619.55/78.70 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', emptysetAx)). 619.55/78.70 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setadjoinAx)). 619.55/78.70 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', powersetAx)). 619.55/78.70 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setunionAx)). 619.55/78.70 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', omega0Ax)). 619.55/78.70 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', omegaSAx)). 619.55/78.70 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.oACHQ9NSgc/E---3.1_7107.p', omegaIndAx)). 619.55/78.70 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.oACHQ9NSgc/E---3.1_7107.p', foundationAx)). 619.55/78.70 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', wellorderingAx)). 619.55/78.70 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', prop2setE)). 619.55/78.70 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', emptysetE)). 619.55/78.70 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', emptysetimpfalse)). 619.55/78.70 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', notinemptyset)). 619.55/78.70 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.oACHQ9NSgc/E---3.1_7107.p', setext)). 619.55/78.70 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', emptyI)). 619.55/78.70 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', noeltsimpempty)). 619.55/78.70 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setadjoinIL)). 619.55/78.70 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', emptyinunitempty)). 619.55/78.70 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setadjoinIR)). 619.55/78.70 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setadjoinE)). 619.55/78.70 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setadjoinOr)). 619.55/78.70 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', powersetI)). 619.55/78.70 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', emptyinPowerset)). 619.55/78.70 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', emptyInPowerset)). 619.55/78.70 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', powersetE)). 619.55/78.70 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setunionI)). 619.55/78.70 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setunionE)). 619.55/78.70 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', subPowSU)). 619.55/78.70 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', uniqinunit)). 619.55/78.70 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', notinsingleton)). 619.55/78.70 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', eqinunit)). 619.55/78.70 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', singletonsswitch)). 619.55/78.70 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', upairsetE)). 619.55/78.70 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', upairsetIL)). 619.55/78.70 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', upairsetIR)). 619.55/78.70 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', vacuousDall)). 619.55/78.70 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', quantDeMorgan1)). 619.55/78.70 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', quantDeMorgan2)). 619.55/78.70 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', quantDeMorgan3)). 619.55/78.70 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', quantDeMorgan4)). 619.55/78.70 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', prop2setI)). 619.55/78.70 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', prop2set2propI)). 619.55/78.70 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', notdexE)). 619.55/78.70 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', notdallE)). 619.55/78.70 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', inCongP)). 619.55/78.70 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', in__Cong)). 619.55/78.70 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', emptyset__Cong)). 619.55/78.70 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setadjoin__Cong)). 619.55/78.70 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', powerset__Cong)). 619.55/78.70 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setunion__Cong)). 619.55/78.70 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', omega__Cong)). 619.55/78.70 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', subsetI1)). 619.55/78.70 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', eqimpsubset2)). 619.55/78.70 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', eqimpsubset1)). 619.55/78.70 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', subsetI2)). 619.55/78.70 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', emptysetsubset)). 619.55/78.70 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', subsetE)). 619.55/78.70 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', subsetE2)). 619.55/78.70 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', notsubsetI)). 619.55/78.70 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', notequalI1)). 619.55/78.70 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', notequalI2)). 619.55/78.70 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', subsetRefl)). 619.55/78.70 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', subsetTrans)). 619.55/78.70 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setadjoinSub)). 619.55/78.70 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setadjoinSub2)). 619.55/78.70 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', subset2powerset)). 619.55/78.70 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setextsub)). 619.55/78.70 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', subsetemptysetimpeq)). 619.55/78.70 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', powersetI1)). 619.55/78.70 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', powersetE1)). 619.55/78.70 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', inPowerset)). 619.55/78.70 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', powersetsubset)). 619.55/78.70 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', binunionIL)). 619.55/78.70 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', upairset2IR)). 619.55/78.70 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', binunionIR)). 619.55/78.70 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', binunionEcases)). 619.55/78.70 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', binunionE)). 619.55/78.70 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', binunionLsub)). 619.55/78.70 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', binunionRsub)). 619.55/78.70 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', binintersectI)). 619.55/78.70 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', binintersectSubset5)). 619.55/78.70 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', binintersectEL)). 619.55/78.70 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', binintersectLsub)). 619.55/78.70 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', binintersectSubset2)). 619.55/78.70 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', binintersectSubset3)). 619.55/78.70 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', binintersectER)). 619.55/78.70 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', disjointsetsI1)). 619.55/78.70 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', binintersectRsub)). 619.55/78.70 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', binintersectSubset4)). 619.55/78.70 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', binintersectSubset1)). 619.55/78.70 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', bs114d)). 619.55/78.70 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setminusI)). 619.55/78.70 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setminusEL)). 619.55/78.70 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setminusER)). 619.55/78.70 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setminusSubset2)). 619.55/78.70 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setminusERneg)). 619.55/78.70 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setminusELneg)). 619.55/78.70 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setminusILneg)). 619.55/78.70 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setminusIRneg)). 619.55/78.70 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setminusLsub)). 619.55/78.70 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setminusSubset1)). 619.55/78.70 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', symdiffE)). 619.55/78.70 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', symdiffI1)). 619.55/78.70 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', symdiffI2)). 619.55/78.70 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', symdiffIneg1)). 619.55/78.70 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', symdiffIneg2)). 619.55/78.70 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', secondinupair)). 619.55/78.70 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setukpairIL)). 619.55/78.70 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', setukpairIR)). 619.55/78.70 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', singletonsubset)). 619.55/78.70 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', singletoninpowerset)). 619.55/78.70 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', singletoninpowunion)). 619.55/78.70 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', upairset2E)). 619.55/78.70 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', upairsubunion)). 619.55/78.70 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', upairinpowunion)). 619.55/78.70 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', ubforcartprodlem1)). 619.55/78.70 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', ubforcartprodlem2)). 619.55/78.70 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', ubforcartprodlem3)). 619.55/78.70 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', cartprodpairin)). 619.55/78.70 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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.oACHQ9NSgc/E---3.1_7107.p', cartprodmempair1)). 619.55/78.70 thf(kpair, axiom, ((kpair)=(^[X2:$i, X3:$i]:(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.oACHQ9NSgc/E---3.1_7107.p', kpair)). 619.55/78.70 thf(c_0_153, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 619.55/78.70 thf(c_0_154, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 619.55/78.70 thf(c_0_155, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 619.55/78.70 thf(c_0_156, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 619.55/78.70 thf(c_0_157, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 619.55/78.70 thf(c_0_158, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 619.55/78.70 thf(c_0_159, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 619.55/78.70 thf(c_0_160, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 619.55/78.70 thf(c_0_161, 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])). 619.55/78.70 thf(c_0_162, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 619.55/78.70 thf(c_0_163, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 619.55/78.70 thf(c_0_164, 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])). 619.55/78.70 thf(c_0_165, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 619.55/78.70 thf(c_0_166, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 619.55/78.70 thf(c_0_167, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 619.55/78.70 thf(c_0_168, plain, ((iskpair)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ (setunion @ Z0))&?[X3:$i]:(((in @ X3 @ (setunion @ Z0))&((Z0)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))))))), inference(fof_simplification,[status(thm)],[iskpair])). 619.55/78.70 thf(c_0_169, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X427:$i]:((((X6 @ X2 @ X427))&![X428:$i]:((((X6 @ X2 @ X428))=>((X427)=(X428)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_153, c_0_154])). 619.55/78.70 thf(c_0_170, plain, ((descrp)=(![X1:$i > $o]:(((?[X429:$i]:((((X1 @ X429))&![X430:$i]:((((X1 @ X430))=>((X429)=(X430)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_155, c_0_154])). 619.55/78.70 thf(c_0_171, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 619.55/78.70 thf(c_0_172, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 619.55/78.70 thf(c_0_173, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 619.55/78.70 thf(c_0_174, plain, ((exuE1)=(![X1:$i > $o]:(((?[X431:$i]:((((X1 @ X431))&![X432:$i]:((((X1 @ X432))=>((X431)=(X432)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_156, c_0_154])). 619.55/78.70 thf(c_0_175, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X433:$i]:((((X1 @ X433))&![X434:$i]:((((X1 @ X434))=>((X433)=(X434)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_157, c_0_154])). 619.55/78.70 thf(c_0_176, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 619.55/78.70 thf(c_0_177, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_158])). 619.55/78.70 thf(c_0_178, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_159, c_0_158])). 619.55/78.70 thf(c_0_179, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_158])). 619.55/78.70 thf(c_0_180, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 619.55/78.70 thf(c_0_181, plain, ((exuE2)=(![X1:$i > $o]:(((?[X435:$i]:((((X1 @ X435))&![X436:$i]:((((X1 @ X436))=>((X435)=(X436)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_160, c_0_154])). 619.55/78.70 thf(c_0_182, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_158])). 619.55/78.70 thf(c_0_183, 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])). 619.55/78.70 thf(c_0_184, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X437:$i]:((((X1 @ X437))&![X438:$i]:((((X1 @ X438))=>((X437)=(X438))))))))))), inference(apply_def,[status(thm)],[c_0_161, c_0_154])). 619.55/78.70 thf(c_0_185, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X439:$i]:((((X1 @ X439))&![X440:$i]:((((X1 @ X440))=>((X439)=(X440)))))))))))), inference(apply_def,[status(thm)],[c_0_162, c_0_154])). 619.55/78.70 thf(c_0_186, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X441:$i]:((((X1 @ X441))&![X442:$i]:((((X1 @ X442))=>((X441)=(X442))))))))))), inference(apply_def,[status(thm)],[c_0_163, c_0_154])). 619.55/78.70 thf(c_0_187, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X443:$i]:((((X1 @ X443))&![X444:$i]:((((X1 @ X444))=>((X443)=(X444)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_164, c_0_154])). 619.55/78.70 thf(c_0_188, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X445:$i]:((((X1 @ X445))&![X446:$i]:((((X1 @ X446))=>((X445)=(X446)))))))<=>(?[X447:$i]:((((X17 @ X447))&![X448:$i]:((((X17 @ X448))=>((X447)=(X448)))))))))))), inference(apply_def,[status(thm)],[c_0_165, c_0_154])). 619.55/78.70 thf(c_0_189, plain, ((exuEu)=(![X1:$i > $o]:(((?[X449:$i]:((((X1 @ X449))&![X450:$i]:((((X1 @ X450))=>((X449)=(X450)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_166, c_0_154])). 619.55/78.70 thf(c_0_190, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X451:$i]:((((X1 @ X451))&![X452:$i]:((((X1 @ X452))=>((X451)=(X452)))))))=>((?[X453:$i]:((((X17 @ X453))&![X454:$i]:((((X17 @ X454))=>((X453)=(X454)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_167, c_0_154])). 619.55/78.70 thf(c_0_191, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 619.55/78.70 thf(c_0_192, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 619.55/78.70 thf(c_0_193, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 619.55/78.70 thf(c_0_194, axiom, ((kpairiskpair)=(![X2:$i, X3:$i]:((?[X455:$i]:(((in @ X455 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&?[X456:$i]:(((in @ X456 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X455 @ emptyset) @ (setadjoin @ (setadjoin @ X455 @ (setadjoin @ X456 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[kpairiskpair, c_0_168])). 619.55/78.70 thf(c_0_195, axiom, ((kpairp)=(![X2:$i, X3:$i]:((?[X457:$i]:(((in @ X457 @ (setunion @ (kpair @ X2 @ X3)))&?[X458:$i]:(((in @ X458 @ (setunion @ (kpair @ X2 @ X3)))&((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X457 @ emptyset) @ (setadjoin @ (setadjoin @ X457 @ (setadjoin @ X458 @ emptyset)) @ emptyset))))))))))), inference(apply_def,[status(thm)],[kpairp, c_0_168])). 619.55/78.70 thf(c_0_196, plain, ((epred1_0)<=>![X868:$i]:(?[X869:$i]:((((![X870:$i]:(((in @ X870 @ X869)=>![X871:$i]:(((in @ X871 @ X870)=>(in @ X871 @ X868)))))&![X872:$i, X873:$i]:((((in @ X872 @ X868)&(in @ X873 @ X868))=>(![X874:$i]:(((in @ X874 @ X869)=>((in @ X872 @ X874)<=>(in @ X873 @ X874))))=>((X872)=(X873))))))&![X875:$i, X876:$i]:((((in @ X875 @ X869)&(in @ X876 @ X869))=>(![X877:$i]:(((in @ X877 @ X875)=>(in @ X877 @ X876)))|![X878:$i]:(((in @ X878 @ X876)=>(in @ X878 @ X875)))))))&![X879:$i]:(((![X880:$i]:(((in @ X880 @ X879)=>(in @ X880 @ X868)))&?[X881:$i]:((in @ X881 @ X879)))=>?[X882:$i, X883:$i]:(((((in @ X882 @ X869)&(in @ X883 @ X879))&~(?[X884:$i]:(((in @ X884 @ X882)&(in @ X884 @ X879)))))&![X885:$i]:(((in @ X885 @ X869)=>(![X886:$i]:(((in @ X886 @ X885)=>(in @ X886 @ X882)))|(in @ X883 @ X885)))))))))))), introduced(definition)). 619.55/78.70 thf(c_0_197, negated_conjecture, ~((![X459:$i, X460:$i]:((![X461:$i]:(((in @ X461 @ X459)<=>(in @ X461 @ X460)))=>((X459)=(X460))))=>(![X462:$i]:(~(in @ X462 @ emptyset))=>(![X463:$i, X464:$i, X465:$i]:(((in @ X465 @ (setadjoin @ X463 @ X464))<=>(((X465)=(X463))|(in @ X465 @ X464))))=>(![X893:$i, X894:$i]:(((in @ X894 @ (powerset @ X893))<=>![X895:$i]:(((in @ X895 @ X894)=>(in @ X895 @ X893)))))=>(![X890:$i, X891:$i]:(((in @ X891 @ (setunion @ X890))<=>?[X892:$i]:(((in @ X891 @ X892)&(in @ X892 @ X890)))))=>((in @ emptyset @ omega)=>(![X466:$i]:(((in @ X466 @ omega)=>(in @ (setadjoin @ X466 @ X466) @ omega)))=>(![X887:$i]:((((in @ emptyset @ X887)&![X888:$i]:((((in @ X888 @ omega)&(in @ X888 @ X887))=>(in @ (setadjoin @ X888 @ X888) @ X887))))=>![X889:$i]:(((in @ X889 @ omega)=>(in @ X889 @ X887)))))=>(![X467:$i > $i > $o, X468:$i]:((![X469:$i]:(((in @ X469 @ X468)=>?[X470:$i]:(((X467 @ X469 @ X470)&![X471:$i]:(((X467 @ X469 @ X471)=>((X470)=(X471))))))))=>?[X472:$i]:(![X473:$i]:(((in @ X473 @ X472)<=>?[X474:$i]:(((in @ X474 @ X468)&(X467 @ X474 @ X473))))))))=>(![X475:$i]:((?[X476:$i]:((in @ X476 @ X475))=>?[X477:$i]:(((in @ X477 @ X475)&~(?[X478:$i]:(((in @ X478 @ X477)&(in @ X478 @ X475))))))))=>((epred1_0)=>(![X479:$i > $o]:((?[X480:$i]:(((X479 @ X480)&![X481:$i]:(((X479 @ X481)=>((X480)=(X481))))))=>(X479 @ (descr @ (^[Z0/* 17 */:$i]:(X479 @ Z0))))))=>(![X865:$i, X866:$i > $o, X867:$i]:(((in @ X867 @ X865)=>((X866 @ X867)=>(in @ X867 @ (dsetconstr @ X865 @ X866)))))=>(![X482:$i, X483:$i > $o, X484:$i]:(((in @ X484 @ (dsetconstr @ X482 @ X483))=>(in @ X484 @ X482)))=>(![X485:$i, X486:$i > $o, X487:$i]:(((in @ X487 @ (dsetconstr @ X485 @ X486))=>(X486 @ X487)))=>(![X488:$i > $o]:((?[X489:$i]:(((X488 @ X489)&![X490:$i]:(((X488 @ X490)=>((X489)=(X490))))))=>?[X491:$i]:(((X488 @ X491)&![X492:$i]:(((X488 @ X492)=>((X491)=(X492))))))))=>(![X493:$o, X494:$i]:(((in @ X494 @ (prop2set @ ((X493))))=>(X493)))=>(![X495:$i]:(((in @ X495 @ emptyset)=>![X496:$o]:((X496))))=>(![X864:$i]:(((in @ X864 @ emptyset)=>~($true)))=>(![X863:$i]:(~(in @ X863 @ emptyset))=>(![X497:$i > $o]:((?[X498:$i]:(((X497 @ X498)&![X499:$i]:(((X497 @ X499)=>((X498)=(X499))))))=>?[X500:$i]:((X497 @ X500))))=>(![X501:$i, X502:$i]:((![X503:$i]:(((in @ X503 @ X501)=>(in @ X503 @ X502)))=>(![X504:$i]:(((in @ X504 @ X502)=>(in @ X504 @ X501)))=>((X501)=(X502)))))=>(![X861:$i]:((![X862:$i]:(~(in @ X862 @ X861))=>((X861)=(emptyset))))=>(![X505:$i]:((![X506:$i]:(~(in @ X506 @ X505))=>((X505)=(emptyset))))=>(![X858:$i, X859:$i > $o, X860:$i]:(((in @ X860 @ X858)=>((in @ X860 @ (dsetconstr @ X858 @ X859))<=>(X859 @ X860))))=>(![X507:$i]:((((X507)!=(emptyset))=>?[X508:$i]:((in @ X508 @ X507))))=>(![X855:$i, X856:$i > $o, X857:$i]:(((in @ X857 @ X855)=>((X856 @ X857)=>((dsetconstr @ X855 @ X856)!=(emptyset)))))=>(![X509:$i]:((?[X510:$i]:((in @ X510 @ X509))=>((X509)!=(emptyset))))=>(![X853:$i, X854:$i]:((in @ X853 @ (setadjoin @ X853 @ X854)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X511:$i, X512:$i, X513:$i]:(((in @ X513 @ X512)=>(in @ X513 @ (setadjoin @ X511 @ X512))))=>(![X849:$i, X850:$i, X851:$i]:(((in @ X851 @ (setadjoin @ X849 @ X850))=>![X852:$o]:(((((X851)=(X849))=>(X852))=>(((in @ X851 @ X850)=>(X852))=>(X852))))))=>(![X846:$i, X847:$i, X848:$i]:(((in @ X848 @ (setadjoin @ X846 @ X847))=>(((X848)=(X846))|(in @ X848 @ X847))))=>(![X845:$i]:(((dsetconstr @ X845 @ (^[Z0/* 1 */:$i]:($true)))=(X845)))=>(![X514:$i, X515:$i]:((![X516:$i]:(((in @ X516 @ X515)=>(in @ X516 @ X514)))=>(in @ X515 @ (powerset @ X514))))=>(![X844:$i]:((in @ emptyset @ (powerset @ X844)))=>(![X843:$i]:((in @ emptyset @ (powerset @ X843)))=>(![X517:$i, X518:$i, X519:$i]:(((in @ X518 @ (powerset @ X517))=>((in @ X519 @ X518)=>(in @ X519 @ X517))))=>(![X520:$i, X521:$i, X522:$i]:(((in @ X521 @ X522)=>((in @ X522 @ X520)=>(in @ X521 @ (setunion @ X520)))))=>(![X523:$i, X524:$i]:(((in @ X524 @ (setunion @ X523))=>![X525:$o]:((![X526:$i]:(((in @ X524 @ X526)=>((in @ X526 @ X523)=>(X525))))=>(X525)))))=>(![X841:$i, X842:$i]:(((in @ X842 @ X841)=>(in @ X842 @ (powerset @ (setunion @ X841)))))=>(![X836:$i > $o]:((?[X837:$i]:(((X836 @ X837)&![X838:$i]:(((X836 @ X838)=>((X837)=(X838))))))=>?[X839:$i]:(![X840:$i]:(((X836 @ X840)<=>((X840)=(X839)))))))=>(![X834:$i]:((((X834)!=(emptyset))=>?[X835:$i]:(((in @ X835 @ X834)&$true))))=>(![X832:$i, X833:$i]:(((in @ X832 @ (setadjoin @ X833 @ emptyset))=>((X832)=(X833))))=>(![X527:$i, X528:$i]:((((X527)!=(X528))=>~(in @ X528 @ (setadjoin @ X527 @ emptyset))))=>(![X529:$i, X530:$i]:((((X529)=(X530))=>(in @ X529 @ (setadjoin @ X530 @ emptyset))))=>(![X830:$i, X831:$i]:(((in @ X830 @ (setadjoin @ X831 @ emptyset))=>(in @ X831 @ (setadjoin @ X830 @ emptyset))))=>(![X827:$i, X828:$i, X829:$i]:(((in @ X829 @ (setadjoin @ X827 @ (setadjoin @ X828 @ emptyset)))=>(((X829)=(X827))|((X829)=(X828)))))=>(![X531:$i, X532:$i]:((in @ X531 @ (setadjoin @ X531 @ (setadjoin @ X532 @ emptyset))))=>(![X825:$i, X826:$i]:((in @ X826 @ (setadjoin @ X825 @ (setadjoin @ X826 @ emptyset))))=>(![X533:$i, X534:$i > $o]:((?[X535:$i]:(((in @ X535 @ X533)&(X534 @ 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[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(assume_negation,[status(cth)],[cartprodmempair]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_169]), foundationAx]), wellorderingAx]), c_0_170]), c_0_171]), c_0_172]), c_0_173]), c_0_174]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_175]), setext]), emptyI]), noeltsimpempty]), c_0_176]), c_0_177]), c_0_178]), c_0_179]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_180]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_181]), c_0_182]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_183]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_184]), c_0_185]), c_0_186]), inCongP]), in__Cong]), c_0_187]), c_0_188]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_189]), c_0_190]), c_0_191]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_192]), c_0_193]), 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]), c_0_168]), secondinupair]), setukpairIL]), setukpairIR]), c_0_194]), c_0_195]), singletonsubset]), singletoninpowerset]), singletoninpowunion]), upairset2E]), upairsubunion]), upairinpowunion]), ubforcartprodlem1]), ubforcartprodlem2]), ubforcartprodlem3]), cartprodpairin]), cartprodmempair1])])]), c_0_196])). 619.55/78.70 thf(c_0_198, plain, ![X896:$i, X897:$i]:(((kpair @ X896 @ X897)=(setadjoin @ (setadjoin @ X896 @ emptyset) @ (setadjoin @ (setadjoin @ X896 @ (setadjoin @ X897 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])])). 619.55/78.70 thf(c_0_199, negated_conjecture, ![X900:$i, X901:$i, X903:$i, X904:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X911:$i, X913:$i, X914:$i, X916:$i, X917:$i, X918:$i, X919:$i, X920:$i, X922:$i, X923:$i > $i > $o, X924:$i, X926:$i, X929:$i, X931:$i, X932:$i, X933:$i, X934:$i, X936:$i, X937:$i > $o, X938:$i, X940:$i, X941:$i > $o, X942:$i, X943:$i, X944:$i > $o, X945:$i, X946:$i, X947:$i > $o, X948:$i, X949:$i > $o, X950:$i, X953:$i, X954:$o, X955:$i, X956:$i, X957:$o, X958:$i, X959:$i, X960:$i > $o, X961:$i, X964:$i, X965:$i, X968:$i, X970:$i, X972:$i, X973:$i > $o, X974:$i, X975:$i, X977:$i, X978:$i > $o, X979:$i, X980:$i, X981:$i, X982:$i, X983:$i, X984:$i, X985:$i, X986:$i, X987:$i, X988:$i, X989:$i, X990:$o, X991:$i, X992:$i, X993:$i, X994:$i, X995:$i, X996:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1003:$i, X1004:$i, X1005:$i, X1006:$i, X1007:$i, X1008:$o, X1010:$i, X1011:$i, X1012:$i > $o, X1013:$i, X1016:$i, X1017:$i, X1018:$i, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1025:$i, X1026:$i, X1027:$i, X1028:$i, X1029:$i, X1030:$i, X1031:$i, X1032:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$i > $o, X1037:$i, X1038:$i > $o, X1039:$i, X1040:$i, X1041:$i > $o, X1042:$i, X1044:$i, X1045:$i > $o, X1047:$i, X1048:$i, X1049:$i > $o, X1051:$i, X1052:$i, X1053:$i > $o, X1054:$i, X1056:$o, X1057:$o, X1058:$i, X1059:$i > $o, X1061:$i, X1062:$i, X1063:$i > $o, X1064:$i, X1066:$i > $o, X1067:$i, X1070:$i, X1071:$i > $o, X1072:$i, X1076:$i, X1077:$i > $o, X1078:$i, X1081:$i, X1082:$i, X1083:$i, X1084:$i, X1085:$i, X1086:$i, X1087:$i, X1088:$i, X1089:$i, X1090:$i > $o, X1091:$i, X1093:$i, X1094:$i, X1095:$i > $o, X1096:$i > $o, X1099:$i, X1102:$i, X1103:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i > $o, X1116:$i, X1118:$i, X1119:$i, X1120:$i > $o, X1121:$i > $o, X1124:$i, X1126:$i, X1128:$i, X1129:$i, X1130:$i > $o, X1131:$i > $o, X1134:$i, X1135:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1144:$i, X1145:$i, X1146:$i, X1147:$i, X1148:$i, X1149:$i, X1150:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1162:$i, X1163:$i, X1164:$i, X1165:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1171:$i, X1172:$i, X1173:$i, X1174:$i, X1175:$i, X1176:$i, X1177:$i, X1178:$i, X1179:$i, X1180:$i, X1181:$i > $o, X1182:$i, X1183:$i > $o, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$o, X1196:$i, X1197:$i, X1198:$i, X1199:$i, X1200:$i, X1201:$i, X1202:$i, X1203:$i, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$i, X1210:$i, X1211:$i, X1212:$i, X1213:$i, X1214:$i, X1215:$i, X1216:$i, X1217:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1222:$i, X1224:$i, X1225:$i, X1226:$i, X1227:$i, X1228:$i, X1229:$i, X1230:$i, X1231:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$i, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1247:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i, X1253:$i, X1254:$i, X1255:$i, X1256:$i, X1257:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1262:$i, X1263:$o, X1264:$i, X1265:$i, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, X1278:$i, X1279:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1286:$i, X1287:$i, X1290:$i, X1291:$i, X1292:$i, X1293:$i, X1294:$i, X1295:$i, X1296:$i, X1297:$i, X1298:$i, X1299:$i, X1300:$i, X1301:$i, X1302:$i, X1303:$i, X1304:$i, X1305:$i, X1306:$i, X1307:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i, X1326:$i, X1332:$i, X1333:$i]:((((~(in @ (esk1_2 @ X900 @ X901) @ X900)|~(in @ (esk1_2 @ X900 @ X901) @ X901)|((X900)=(X901)))&((in @ (esk1_2 @ X900 @ X901) @ X900)|(in @ (esk1_2 @ X900 @ X901) @ X901)|((X900)=(X901))))&(~(in @ X903 @ emptyset)&(((~(in @ X906 @ (setadjoin @ X904 @ X905))|(((X906)=(X904))|(in @ X906 @ X905)))&((((X906)!=(X904))|(in @ X906 @ (setadjoin @ X904 @ X905)))&(~(in @ X906 @ X905)|(in @ X906 @ (setadjoin @ X904 @ X905)))))&(((~(in @ X908 @ (powerset @ X907))|(~(in @ X909 @ X908)|(in @ X909 @ X907)))&(((in @ (esk2_2 @ X910 @ X911) @ X911)|(in @ X911 @ (powerset @ X910)))&(~(in @ (esk2_2 @ X910 @ X911) @ X910)|(in @ X911 @ (powerset @ X910)))))&(((((in @ X914 @ (esk3_2 @ X913 @ X914))|~(in @ X914 @ (setunion @ X913)))&((in @ (esk3_2 @ X913 @ X914) @ X913)|~(in @ X914 @ (setunion @ X913))))&(~(in @ X917 @ X918)|~(in @ X918 @ X916)|(in @ X917 @ (setunion @ X916))))&((in @ emptyset @ omega)&((~(in @ X919 @ omega)|(in @ (setadjoin @ X919 @ X919) @ omega))&(((((in @ (esk4_1 @ X920) @ omega)|~(in @ emptyset @ X920)|(~(in @ X922 @ omega)|(in @ X922 @ X920)))&((in @ (esk4_1 @ X920) @ X920)|~(in @ emptyset @ X920)|(~(in @ X922 @ omega)|(in @ X922 @ X920))))&(~(in @ (setadjoin @ (esk4_1 @ X920) @ (esk4_1 @ X920)) @ X920)|~(in @ emptyset @ X920)|(~(in @ X922 @ omega)|(in @ X922 @ X920))))&((((((in @ (esk8_3 @ X923 @ X924 @ X929) @ X924)|~(in @ X929 @ (esk7_2 @ X923 @ X924))|(in @ (esk5_2 @ X923 @ X924) @ X924))&((X923 @ (esk8_3 @ X923 @ X924 @ X929) @ X929)|~(in @ X929 @ (esk7_2 @ X923 @ X924))|(in @ (esk5_2 @ X923 @ X924) @ X924)))&(~(in @ X932 @ X924)|~(X923 @ X932 @ X931)|(in @ X931 @ (esk7_2 @ X923 @ X924))|(in @ (esk5_2 @ X923 @ X924) @ X924)))&(((((in @ (esk8_3 @ X923 @ X924 @ X929) @ X924)|~(in @ X929 @ (esk7_2 @ X923 @ X924))|((X923 @ (esk5_2 @ X923 @ X924) @ (esk6_3 @ X923 @ X924 @ X926))|~(X923 @ (esk5_2 @ X923 @ X924) @ X926)))&((X923 @ (esk8_3 @ X923 @ X924 @ X929) @ X929)|~(in @ X929 @ (esk7_2 @ X923 @ X924))|((X923 @ (esk5_2 @ X923 @ X924) @ (esk6_3 @ X923 @ X924 @ X926))|~(X923 @ (esk5_2 @ X923 @ X924) @ X926))))&(~(in @ X932 @ X924)|~(X923 @ X932 @ X931)|(in @ X931 @ (esk7_2 @ X923 @ X924))|((X923 @ (esk5_2 @ X923 @ X924) @ (esk6_3 @ X923 @ X924 @ X926))|~(X923 @ (esk5_2 @ X923 @ X924) @ X926))))&((((in @ (esk8_3 @ X923 @ X924 @ X929) @ X924)|~(in @ X929 @ (esk7_2 @ X923 @ X924))|(((X926)!=(esk6_3 @ X923 @ X924 @ X926))|~(X923 @ (esk5_2 @ X923 @ X924) @ X926)))&((X923 @ (esk8_3 @ X923 @ X924 @ X929) @ X929)|~(in @ X929 @ (esk7_2 @ X923 @ X924))|(((X926)!=(esk6_3 @ X923 @ X924 @ X926))|~(X923 @ (esk5_2 @ X923 @ X924) @ X926))))&(~(in @ 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@ X1128 @ X1129 @ X1130 @ X1131))|((dsetconstr @ X1128 @ X1130)=(dsetconstr @ X1129 @ X1131))|((X1128)!=(X1129)))))))&((((in @ (esk52_2 @ X1134 @ X1135) @ X1134)|(subset @ X1134 @ X1135))&(~(in @ (esk52_2 @ X1134 @ X1135) @ X1135)|(subset @ X1134 @ X1135)))&((((X1137)!=(X1138))|(subset @ X1138 @ X1137))&((((X1139)!=(X1140))|(subset @ X1139 @ X1140))&((((in @ (esk53_2 @ X1141 @ X1142) @ X1141)|(subset @ X1141 @ X1142))&(~(in @ (esk53_2 @ X1141 @ X1142) @ X1142)|(subset @ X1141 @ X1142)))&((subset @ emptyset @ X1144)&((~(subset @ X1145 @ X1146)|(~(in @ X1147 @ X1145)|(in @ X1147 @ X1146)))&((~(subset @ X1148 @ X1149)|((in @ X1150 @ X1149)|~(in @ X1150 @ X1148)))&((~(in @ X1153 @ X1151)|((in @ X1153 @ X1152)|~(subset @ X1151 @ X1152)))&(((subset @ X1154 @ X1155)|((X1154)!=(X1155)))&((~(in @ X1158 @ X1156)|((in @ X1158 @ X1157)|((X1156)!=(X1157))))&((subset @ X1159 @ X1159)&((~(subset @ X1160 @ X1161)|(~(subset @ X1161 @ X1162)|(subset @ X1160 @ X1162)))&((subset @ X1164 @ (setadjoin @ X1163 @ X1164))&((~(subset @ X1165 @ X1167)|(subset @ X1165 @ (setadjoin @ X1166 @ X1167)))&((~(subset @ X1168 @ X1169)|(in @ X1168 @ (powerset @ X1169)))&((~(subset @ X1170 @ X1171)|(~(subset @ X1171 @ X1170)|((X1170)=(X1171))))&((~(subset @ X1172 @ emptyset)|((X1172)=(emptyset)))&((~(subset @ X1174 @ X1173)|(in @ X1174 @ (powerset @ X1173)))&((~(in @ X1176 @ (powerset @ X1175))|(subset @ X1176 @ X1175))&((in @ X1177 @ (powerset @ X1177))&((~(subset @ X1178 @ X1179)|(subset @ (powerset @ X1178) @ (powerset @ X1179)))&((in @ (dsetconstr @ X1180 @ X1181) @ (powerset @ X1180))&((subset @ (dsetconstr @ X1182 @ X1183) @ X1182)&((~(in @ X1186 @ X1184)|(in @ X1186 @ (binunion @ X1184 @ X1185)))&((in @ X1188 @ (setadjoin @ X1187 @ (setadjoin @ X1188 @ emptyset)))&((~(in @ X1191 @ X1190)|(in @ X1191 @ (binunion @ X1189 @ X1190)))&(((((in @ X1194 @ X1193)|(X1195)|(in @ X1194 @ X1192)|~(in @ X1194 @ (binunion @ X1192 @ X1193)))&(~(X1195)|(X1195)|(in @ X1194 @ X1192)|~(in @ X1194 @ (binunion @ X1192 @ X1193))))&(((in @ X1194 @ X1193)|(X1195)|~(X1195)|~(in @ X1194 @ (binunion @ X1192 @ X1193)))&(~(X1195)|(X1195)|~(X1195)|~(in @ X1194 @ (binunion @ X1192 @ X1193)))))&((~(in @ X1198 @ (binunion @ X1196 @ X1197))|((in @ X1198 @ X1196)|(in @ X1198 @ X1197)))&((subset @ X1199 @ (binunion @ X1199 @ X1200))&((subset @ X1202 @ (binunion @ X1201 @ X1202))&((~(in @ X1205 @ X1203)|(~(in @ X1205 @ X1204)|(in @ X1205 @ (binintersect @ X1203 @ X1204))))&((~(subset @ X1208 @ X1206)|(~(subset @ X1208 @ X1207)|(subset @ X1208 @ (binintersect @ X1206 @ X1207))))&((~(in @ X1211 @ (binintersect @ X1209 @ X1210))|(in @ X1211 @ X1209))&((subset @ (binintersect @ X1212 @ X1213) @ X1212)&((~(subset @ X1214 @ X1215)|((binintersect @ X1214 @ X1215)=(X1214)))&((((binintersect @ X1216 @ X1217)!=(X1217))|(subset @ X1217 @ X1216))&((~(in @ X1220 @ (binintersect @ X1218 @ X1219))|(in @ X1220 @ X1219))&((((in @ (esk54_2 @ X1221 @ X1222) @ X1221)|((binintersect @ X1221 @ X1222)=(emptyset)))&((in @ (esk54_2 @ X1221 @ X1222) @ X1222)|((binintersect @ X1221 @ X1222)=(emptyset))))&((subset @ (binintersect @ X1224 @ X1225) @ X1225)&((~(subset @ X1227 @ X1226)|((binintersect @ X1226 @ X1227)=(X1227)))&((((binintersect @ X1228 @ X1229)!=(X1228))|(subset @ X1228 @ X1229))&(((binintersect @ X1230 @ (binunion @ X1231 @ X1232))=(binunion @ (binintersect @ X1230 @ X1231) @ (binintersect @ X1230 @ X1232)))&((~(in @ X1235 @ X1233)|((in @ X1235 @ X1234)|(in @ X1235 @ (setminus @ X1233 @ X1234))))&((~(in @ X1238 @ (setminus @ X1236 @ X1237))|(in @ X1238 @ X1236))&((~(in @ X1241 @ (setminus @ X1239 @ X1240))|~(in @ X1241 @ X1240))&((~(subset @ X1242 @ X1243)|((setminus @ X1242 @ X1243)=(emptyset)))&(((in @ X1246 @ (setminus @ X1244 @ X1245))|(~(in @ X1246 @ X1244)|(in @ X1246 @ X1245)))&(((in @ X1249 @ (setminus @ X1247 @ X1248))|((in @ X1249 @ X1248)|~(in @ X1249 @ X1247)))&(((in @ X1252 @ X1250)|~(in @ X1252 @ (setminus @ X1250 @ X1251)))&((~(in @ X1255 @ X1254)|~(in @ X1255 @ (setminus @ X1253 @ X1254)))&((subset @ (setminus @ X1256 @ X1257) @ X1256)&((((setminus @ X1258 @ X1259)!=(emptyset))|(subset @ X1258 @ X1259))&((((~(in @ X1262 @ X1260)|(X1263)|(in @ X1262 @ X1260)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))&(((in @ X1262 @ X1261)|(X1263)|(in @ X1262 @ X1260)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))&(~(X1263)|(X1263)|(in @ X1262 @ X1260)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))))&(((~(in @ X1262 @ X1260)|(X1263)|~(in @ X1262 @ X1261)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))&(((in @ X1262 @ X1261)|(X1263)|~(in @ X1262 @ X1261)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))&(~(X1263)|(X1263)|~(in @ X1262 @ X1261)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))))&((~(in @ X1262 @ X1260)|(X1263)|~(X1263)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))&(((in @ X1262 @ X1261)|(X1263)|~(X1263)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))&(~(X1263)|(X1263)|~(X1263)|~(in @ X1262 @ (symdiff @ X1260 @ X1261)))))))&((~(in @ X1266 @ X1264)|((in @ X1266 @ X1265)|(in @ X1266 @ (symdiff @ X1264 @ X1265))))&(((in @ X1269 @ X1267)|(~(in @ X1269 @ X1268)|(in @ X1269 @ (symdiff @ X1267 @ X1268))))&((~(in @ X1272 @ X1270)|(~(in @ X1272 @ X1271)|~(in @ X1272 @ (symdiff @ X1270 @ X1271))))&(((in @ X1275 @ X1273)|((in @ X1275 @ X1274)|~(in @ X1275 @ (symdiff @ X1273 @ X1274))))&((in @ X1277 @ (setadjoin @ X1276 @ (setadjoin @ X1277 @ emptyset)))&((in @ X1278 @ (setunion @ (setadjoin @ (setadjoin @ X1278 @ emptyset) @ (setadjoin @ (setadjoin @ X1278 @ (setadjoin @ X1279 @ emptyset)) @ emptyset))))&((in @ X1281 @ (setunion @ (setadjoin @ (setadjoin @ X1280 @ emptyset) @ (setadjoin @ (setadjoin @ X1280 @ (setadjoin @ X1281 @ emptyset)) @ emptyset))))&(((in @ (esk55_2 @ X1282 @ X1283) @ (setunion @ (setadjoin @ (setadjoin @ X1282 @ emptyset) @ (setadjoin @ (setadjoin @ X1282 @ (setadjoin @ X1283 @ emptyset)) @ emptyset))))&((in @ (esk56_2 @ X1282 @ X1283) @ (setunion @ (setadjoin @ (setadjoin @ X1282 @ emptyset) @ (setadjoin @ (setadjoin @ X1282 @ (setadjoin @ X1283 @ emptyset)) @ emptyset))))&((setadjoin @ (setadjoin @ X1282 @ emptyset) @ (setadjoin @ (setadjoin @ X1282 @ (setadjoin @ X1283 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ (esk55_2 @ X1282 @ X1283) @ emptyset) @ (setadjoin @ (setadjoin @ (esk55_2 @ X1282 @ X1283) @ (setadjoin @ (esk56_2 @ X1282 @ X1283) @ emptyset)) @ emptyset)))))&(((in @ (esk57_2 @ X1286 @ X1287) @ (setunion @ (kpair @ X1286 @ X1287)))&((in @ (esk58_2 @ X1286 @ X1287) @ (setunion @ (kpair @ X1286 @ X1287)))&((kpair @ X1286 @ X1287)=(setadjoin @ (setadjoin @ (esk57_2 @ X1286 @ X1287) @ emptyset) @ (setadjoin @ (setadjoin @ (esk57_2 @ X1286 @ X1287) @ (setadjoin @ (esk58_2 @ X1286 @ X1287) @ emptyset)) @ emptyset)))))&((~(in @ X1291 @ X1290)|(subset @ (setadjoin @ X1291 @ emptyset) @ X1290))&((~(in @ X1293 @ X1292)|(in @ (setadjoin @ X1293 @ emptyset) @ (powerset @ X1292)))&((~(in @ X1296 @ X1294)|(in @ (setadjoin @ X1296 @ emptyset) @ (powerset @ (binunion @ X1294 @ X1295))))&((~(in @ X1299 @ (setadjoin @ X1297 @ (setadjoin @ X1298 @ emptyset)))|(((X1299)=(X1297))|((X1299)=(X1298))))&((~(in @ X1302 @ X1300)|(~(in @ X1303 @ X1301)|(subset @ (setadjoin @ X1302 @ (setadjoin @ X1303 @ emptyset)) @ (binunion @ X1300 @ X1301))))&((~(in @ X1306 @ X1304)|(~(in @ X1307 @ X1305)|(in @ (setadjoin @ X1306 @ (setadjoin @ X1307 @ emptyset)) @ (powerset @ (binunion @ X1304 @ X1305)))))&((~(in @ X1310 @ X1308)|(~(in @ X1311 @ X1309)|(subset @ (setadjoin @ (setadjoin @ X1310 @ emptyset) @ (setadjoin @ (setadjoin @ X1310 @ (setadjoin @ X1311 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1308 @ X1309)))))&((~(in @ X1314 @ X1312)|(~(in @ X1315 @ X1313)|(in @ (setadjoin @ (setadjoin @ X1314 @ emptyset) @ (setadjoin @ (setadjoin @ X1314 @ (setadjoin @ X1315 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1312 @ X1313))))))&((~(in @ X1318 @ X1316)|(~(in @ X1319 @ X1317)|(in @ (kpair @ X1318 @ X1319) @ (powerset @ (powerset @ (binunion @ X1316 @ X1317))))))&((~(in @ X1322 @ X1320)|(~(in @ X1323 @ X1321)|(in @ (kpair @ X1322 @ X1323) @ (cartprod @ X1320 @ X1321))))&((((in @ (esk59_3 @ X1324 @ X1325 @ X1326) @ X1324)|~(in @ X1326 @ (cartprod @ X1324 @ X1325)))&(((in @ (esk60_3 @ X1324 @ X1325 @ X1326) @ X1325)|~(in @ X1326 @ (cartprod @ X1324 @ X1325)))&(((X1326)=(kpair @ (esk59_3 @ X1324 @ X1325 @ X1326) @ (esk60_3 @ X1324 @ X1325 @ X1326)))|~(in @ X1326 @ (cartprod @ X1324 @ X1325)))))&((in @ esk63_0 @ (cartprod @ esk61_0 @ esk62_0))&(~(in @ X1332 @ (setunion @ esk63_0))|(~(in @ X1333 @ (setunion @ esk63_0))|((esk63_0)!=(setadjoin @ (setadjoin @ X1332 @ emptyset) @ (setadjoin @ (setadjoin @ X1332 @ (setadjoin @ X1333 @ emptyset)) @ 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_197])])])])])])])). 619.55/78.70 thf(c_0_200, plain, ![X898:$i, X899:$i]:(((kpair @ X898 @ X899)=(setadjoin @ (setadjoin @ X898 @ emptyset) @ (setadjoin @ (setadjoin @ X898 @ (setadjoin @ X899 @ emptyset)) @ emptyset)))), inference(variable_rename,[status(thm)],[c_0_198])). 619.55/78.70 thf(c_0_201, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((((X2)=(kpair @ (esk59_3 @ X3 @ X4 @ X2) @ (esk60_3 @ X3 @ X4 @ X2)))|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_199])). 619.55/78.70 thf(c_0_202, plain, ![X2:$i, X3:$i]:(((kpair @ X2 @ X3)=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_200])). 619.55/78.70 thf(c_0_203, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_199])). 619.55/78.70 thf(c_0_204, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:((((X2)=(setadjoin @ (setadjoin @ (esk59_3 @ X3 @ X4 @ X2) @ emptyset) @ (setadjoin @ (setadjoin @ (esk59_3 @ X3 @ X4 @ X2) @ (setadjoin @ (esk60_3 @ X3 @ X4 @ X2) @ emptyset)) @ emptyset)))|~((in @ X2 @ (cartprod @ X3 @ X4))))), inference(rw,[status(thm)],[c_0_201, c_0_202])). 619.55/78.70 thf(c_0_205, negated_conjecture, ![X3:$i, X2:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_199])). 619.55/78.70 thf(c_0_206, negated_conjecture, ![X2:$i, X3:$i]:((~((in @ X2 @ (setunion @ esk63_0)))|~((in @ X3 @ (setunion @ esk63_0)))|((esk63_0)!=(setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), inference(split_conjunct,[status(thm)],[c_0_199])). 619.55/78.70 thf(c_0_207, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ (esk59_3 @ X2 @ X3 @ X4) @ (setunion @ X4))|~((in @ X4 @ (cartprod @ X2 @ X3))))), inference(spm,[status(thm)],[c_0_203, c_0_204])). 619.55/78.70 thf(c_0_208, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ (esk60_3 @ X2 @ X3 @ X4) @ (setunion @ X4))|~((in @ X4 @ (cartprod @ X2 @ X3))))), inference(spm,[status(thm)],[c_0_205, c_0_204])). 619.55/78.70 thf(c_0_209, negated_conjecture, (in @ esk63_0 @ (cartprod @ esk61_0 @ esk62_0)), inference(split_conjunct,[status(thm)],[c_0_199])). 619.55/78.70 thf(c_0_210, negated_conjecture, ![X2:$i, X3:$i]:(~((in @ esk63_0 @ (cartprod @ X2 @ X3)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_206, c_0_204])]), c_0_207]), c_0_208])). 619.55/78.70 thf(c_0_211, negated_conjecture, ($false), inference(sr,[status(thm)],[c_0_209, c_0_210]), ['proof']). 619.55/78.70 # SZS output end CNFRefutation 619.55/78.70 # Parsed axioms : 324 619.55/78.70 # Removed by relevancy pruning/SinE : 0 619.55/78.70 # Initial clauses : 450 619.55/78.70 # Removed in clause preprocessing : 196 619.55/78.70 # Initial clauses in saturation : 254 619.55/78.70 # Processed clauses : 9885 619.55/78.70 # ...of these trivial : 107 619.55/78.70 # ...subsumed : 3919 619.55/78.70 # ...remaining for further processing : 5859 619.55/78.70 # Other redundant clauses eliminated : 409 619.55/78.70 # Clauses deleted for lack of memory : 9511 619.55/78.70 # Backward-subsumed : 130 619.55/78.70 # Backward-rewritten : 211 619.55/78.70 # Generated clauses : 2775664 619.55/78.70 # ...of the previous two non-redundant : 2767032 619.55/78.70 # ...aggressively subsumed : 0 619.55/78.70 # Contextual simplify-reflections : 12 619.55/78.70 # Paramodulations : 2775117 619.55/78.70 # Factorizations : 137 619.55/78.70 # NegExts : 0 619.55/78.70 # Equation resolutions : 409 619.55/78.70 # Disequality decompositions : 0 619.55/78.70 # Total rewrite steps : 19791 619.55/78.70 # ...of those cached : 18919 619.55/78.70 # Propositional unsat checks : 0 619.55/78.70 # Propositional check models : 0 619.55/78.70 # Propositional check unsatisfiable : 0 619.55/78.70 # Propositional clauses : 0 619.55/78.70 # Propositional clauses after purity: 0 619.55/78.70 # Propositional unsat core size : 0 619.55/78.70 # Propositional preprocessing time : 0.000 619.55/78.70 # Propositional encoding time : 0.000 619.55/78.70 # Propositional solver time : 0.000 619.55/78.70 # Success case prop preproc time : 0.000 619.55/78.70 # Success case prop encoding time : 0.000 619.55/78.70 # Success case prop solver time : 0.000 619.55/78.70 # Current number of processed clauses : 5286 619.55/78.70 # Positive orientable unit clauses : 122 619.55/78.70 # Positive unorientable unit clauses: 0 619.55/78.70 # Negative unit clauses : 221 619.55/78.70 # Non-unit-clauses : 4943 619.55/78.70 # Current number of unprocessed clauses: 1862443 619.55/78.70 # ...number of literals in the above : 9872287 619.55/78.70 # Current number of archived formulas : 0 619.55/78.70 # Current number of archived clauses : 561 619.55/78.70 # Clause-clause subsumption calls (NU) : 3099521 619.55/78.70 # Rec. Clause-clause subsumption calls : 765928 619.55/78.70 # Non-unit clause-clause subsumptions : 2535 619.55/78.70 # Unit Clause-clause subsumption calls : 117942 619.55/78.70 # Rewrite failures with RHS unbound : 0 619.55/78.70 # BW rewrite match attempts : 74 619.55/78.70 # BW rewrite match successes : 29 619.55/78.70 # Condensation attempts : 9885 619.55/78.70 # Condensation successes : 137 619.55/78.70 # Termbank termtop insertions : 98991731 619.55/78.70 # Search garbage collected termcells : 1317756 619.55/78.70 619.55/78.70 # ------------------------------------------------- 619.55/78.70 # User time : 75.823 s 619.55/78.70 # System time : 1.366 s 619.55/78.70 # Total time : 77.189 s 619.55/78.70 # Maximum resident set size: 5172 pages 619.55/78.70 619.55/78.70 # ------------------------------------------------- 619.55/78.70 # User time : 75.831 s 619.55/78.70 # System time : 1.372 s 619.55/78.70 # Total time : 77.203 s 619.55/78.70 # Maximum resident set size: 2104 pages 619.55/78.70 % E---3.1 exiting 619.55/78.70 % E exiting 619.55/78.70 EOF