0.02/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.13 % Command : run_E %s %d THM 0.09/0.33 % Computer : n022.cluster.edu 0.09/0.33 % Model : x86_64 x86_64 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.33 % Memory : 8042.1875MB 0.09/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.33 % CPULimit : 1440 0.09/0.33 % WCLimit : 180 0.09/0.33 % DateTime : Thu Jul 4 09:48:53 EDT 2024 0.09/0.33 % CPUTime : 0.16/0.47 Running higher-order theorem proving 0.16/0.50 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.GP9gm0QO99/E---3.1_13802.p 109.87/17.34 # Version: 3.2.0-ho 109.87/17.34 # Preprocessing class: HSLMSLSSLLLCHFA. 109.87/17.34 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 109.87/17.34 # Starting ehoh_best5 with 180s (1) cores 109.87/17.34 # Starting almost_fo_3_lam with 180s (1) cores 109.87/17.34 # Starting new_bool_5 with 180s (1) cores 109.87/17.34 # Starting pre_casc_3 with 180s (1) cores 109.87/17.34 # Starting ho_unfolding_8 with 180s (1) cores 109.87/17.34 # Starting new_ho_10_cnf2 with 180s (1) cores 109.87/17.34 # Starting new_bool_3 with 180s (1) cores 109.87/17.34 # Starting new_ho_5 with 180s (1) cores 109.87/17.34 # new_bool_5 with pid 13882 completed with status 0 109.87/17.34 # Result found by new_bool_5 109.87/17.34 # Preprocessing class: HSLMSLSSLLLCHFA. 109.87/17.34 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 109.87/17.34 # Starting ehoh_best5 with 180s (1) cores 109.87/17.34 # Starting almost_fo_3_lam with 180s (1) cores 109.87/17.34 # Starting new_bool_5 with 180s (1) cores 109.87/17.34 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 109.87/17.34 # Search class: HGHSM-FSLM31-MHFMMSBN 109.87/17.34 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 109.87/17.34 # Starting new_ho_10_cnf2 with 98s (1) cores 109.87/17.34 # new_ho_10_cnf2 with pid 13890 completed with status 0 109.87/17.34 # Result found by new_ho_10_cnf2 109.87/17.34 # Preprocessing class: HSLMSLSSLLLCHFA. 109.87/17.34 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 109.87/17.34 # Starting ehoh_best5 with 180s (1) cores 109.87/17.34 # Starting almost_fo_3_lam with 180s (1) cores 109.87/17.34 # Starting new_bool_5 with 180s (1) cores 109.87/17.34 # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0) 109.87/17.34 # Search class: HGHSM-FSLM31-MHFMMSBN 109.87/17.34 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 109.87/17.34 # Starting new_ho_10_cnf2 with 98s (1) cores 109.87/17.34 # Preprocessing time : 0.004 s 109.87/17.34 # Presaturation interreduction done 109.87/17.34 109.87/17.34 # Proof found! 109.87/17.34 # SZS status Theorem 109.87/17.34 # SZS output start CNFRefutation 109.87/17.34 thf(decl_22, type, in: $i > $i > $o). 109.87/17.34 thf(decl_23, type, exu: ($i > $o) > $o). 109.87/17.34 thf(decl_24, type, setextAx: $o). 109.87/17.34 thf(decl_25, type, emptyset: $i). 109.87/17.34 thf(decl_26, type, emptysetAx: $o). 109.87/17.34 thf(decl_27, type, setadjoin: $i > $i > $i). 109.87/17.34 thf(decl_28, type, setadjoinAx: $o). 109.87/17.34 thf(decl_29, type, powerset: $i > $i). 109.87/17.34 thf(decl_30, type, powersetAx: $o). 109.87/17.34 thf(decl_31, type, setunion: $i > $i). 109.87/17.34 thf(decl_32, type, setunionAx: $o). 109.87/17.34 thf(decl_33, type, omega: $i). 109.87/17.34 thf(decl_34, type, omega0Ax: $o). 109.87/17.34 thf(decl_35, type, omegaSAx: $o). 109.87/17.34 thf(decl_36, type, omegaIndAx: $o). 109.87/17.34 thf(decl_37, type, replAx: $o). 109.87/17.34 thf(decl_38, type, foundationAx: $o). 109.87/17.34 thf(decl_39, type, wellorderingAx: $o). 109.87/17.34 thf(decl_40, type, descr: ($i > $o) > $i). 109.87/17.34 thf(decl_41, type, descrp: $o). 109.87/17.34 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 109.87/17.34 thf(decl_43, type, dsetconstrI: $o). 109.87/17.34 thf(decl_44, type, dsetconstrEL: $o). 109.87/17.34 thf(decl_45, type, dsetconstrER: $o). 109.87/17.34 thf(decl_46, type, exuE1: $o). 109.87/17.34 thf(decl_47, type, prop2set: $o > $i). 109.87/17.34 thf(decl_48, type, prop2setE: $o). 109.87/17.34 thf(decl_49, type, emptysetE: $o). 109.87/17.34 thf(decl_50, type, emptysetimpfalse: $o). 109.87/17.34 thf(decl_51, type, notinemptyset: $o). 109.87/17.34 thf(decl_52, type, exuE3e: $o). 109.87/17.34 thf(decl_53, type, setext: $o). 109.87/17.34 thf(decl_54, type, emptyI: $o). 109.87/17.34 thf(decl_55, type, noeltsimpempty: $o). 109.87/17.34 thf(decl_56, type, setbeta: $o). 109.87/17.34 thf(decl_57, type, nonempty: $i > $o). 109.87/17.34 thf(decl_58, type, nonemptyE1: $o). 109.87/17.34 thf(decl_59, type, nonemptyI: $o). 109.87/17.34 thf(decl_60, type, nonemptyI1: $o). 109.87/17.34 thf(decl_61, type, setadjoinIL: $o). 109.87/17.34 thf(decl_62, type, emptyinunitempty: $o). 109.87/17.34 thf(decl_63, type, setadjoinIR: $o). 109.87/17.34 thf(decl_64, type, setadjoinE: $o). 109.87/17.34 thf(decl_65, type, setadjoinOr: $o). 109.87/17.34 thf(decl_66, type, setoftrueEq: $o). 109.87/17.34 thf(decl_67, type, powersetI: $o). 109.87/17.34 thf(decl_68, type, emptyinPowerset: $o). 109.87/17.34 thf(decl_69, type, emptyInPowerset: $o). 109.87/17.34 thf(decl_70, type, powersetE: $o). 109.87/17.34 thf(decl_71, type, setunionI: $o). 109.87/17.34 thf(decl_72, type, setunionE: $o). 109.87/17.34 thf(decl_73, type, subPowSU: $o). 109.87/17.34 thf(decl_74, type, exuE2: $o). 109.87/17.34 thf(decl_75, type, nonemptyImpWitness: $o). 109.87/17.34 thf(decl_76, type, uniqinunit: $o). 109.87/17.34 thf(decl_77, type, notinsingleton: $o). 109.87/17.34 thf(decl_78, type, eqinunit: $o). 109.87/17.34 thf(decl_79, type, singletonsswitch: $o). 109.87/17.34 thf(decl_80, type, upairsetE: $o). 109.87/17.34 thf(decl_81, type, upairsetIL: $o). 109.87/17.34 thf(decl_82, type, upairsetIR: $o). 109.87/17.34 thf(decl_83, type, emptyE1: $o). 109.87/17.34 thf(decl_84, type, vacuousDall: $o). 109.87/17.34 thf(decl_85, type, quantDeMorgan1: $o). 109.87/17.34 thf(decl_86, type, quantDeMorgan2: $o). 109.87/17.34 thf(decl_87, type, quantDeMorgan3: $o). 109.87/17.34 thf(decl_88, type, quantDeMorgan4: $o). 109.87/17.34 thf(decl_89, type, prop2setI: $o). 109.87/17.34 thf(decl_91, type, prop2set2propI: $o). 109.87/17.34 thf(decl_92, type, notdexE: $o). 109.87/17.34 thf(decl_93, type, notdallE: $o). 109.87/17.34 thf(decl_94, type, exuI1: $o). 109.87/17.34 thf(decl_95, type, exuI3: $o). 109.87/17.34 thf(decl_96, type, exuI2: $o). 109.87/17.34 thf(decl_97, type, inCongP: $o). 109.87/17.34 thf(decl_98, type, in__Cong: $o). 109.87/17.34 thf(decl_99, type, exuE3u: $o). 109.87/17.34 thf(decl_100, type, exu__Cong: $o). 109.87/17.34 thf(decl_101, type, emptyset__Cong: $o). 109.87/17.34 thf(decl_102, type, setadjoin__Cong: $o). 109.87/17.34 thf(decl_103, type, powerset__Cong: $o). 109.87/17.34 thf(decl_104, type, setunion__Cong: $o). 109.87/17.34 thf(decl_105, type, omega__Cong: $o). 109.87/17.34 thf(decl_106, type, exuEu: $o). 109.87/17.34 thf(decl_107, type, descr__Cong: $o). 109.87/17.34 thf(decl_108, type, dsetconstr__Cong: $o). 109.87/17.34 thf(decl_109, type, subset: $i > $i > $o). 109.87/17.34 thf(decl_112, type, subsetI1: $o). 109.87/17.34 thf(decl_113, type, eqimpsubset2: $o). 109.87/17.34 thf(decl_114, type, eqimpsubset1: $o). 109.87/17.34 thf(decl_115, type, subsetI2: $o). 109.87/17.34 thf(decl_116, type, emptysetsubset: $o). 109.87/17.34 thf(decl_117, type, subsetE: $o). 109.87/17.34 thf(decl_118, type, subsetE2: $o). 109.87/17.34 thf(decl_119, type, notsubsetI: $o). 109.87/17.34 thf(decl_120, type, notequalI1: $o). 109.87/17.34 thf(decl_121, type, notequalI2: $o). 109.87/17.34 thf(decl_122, type, subsetRefl: $o). 109.87/17.34 thf(decl_123, type, subsetTrans: $o). 109.87/17.34 thf(decl_124, type, setadjoinSub: $o). 109.87/17.34 thf(decl_125, type, setadjoinSub2: $o). 109.87/17.34 thf(decl_126, type, subset2powerset: $o). 109.87/17.34 thf(decl_127, type, setextsub: $o). 109.87/17.34 thf(decl_128, type, subsetemptysetimpeq: $o). 109.87/17.34 thf(decl_129, type, powersetI1: $o). 109.87/17.34 thf(decl_130, type, powersetE1: $o). 109.87/17.34 thf(decl_131, type, inPowerset: $o). 109.87/17.34 thf(decl_132, type, powersetsubset: $o). 109.87/17.34 thf(decl_133, type, sepInPowerset: $o). 109.87/17.34 thf(decl_134, type, sepSubset: $o). 109.87/17.34 thf(decl_135, type, binunion: $i > $i > $i). 109.87/17.34 thf(decl_136, type, binunionIL: $o). 109.87/17.34 thf(decl_137, type, upairset2IR: $o). 109.87/17.34 thf(decl_138, type, binunionIR: $o). 109.87/17.34 thf(decl_139, type, binunionEcases: $o). 109.87/17.34 thf(decl_140, type, binunionE: $o). 109.87/17.34 thf(decl_141, type, binunionLsub: $o). 109.87/17.34 thf(decl_142, type, binunionRsub: $o). 109.87/17.34 thf(decl_143, type, binintersect: $i > $i > $i). 109.87/17.34 thf(decl_144, type, binintersectI: $o). 109.87/17.34 thf(decl_145, type, binintersectSubset5: $o). 109.87/17.34 thf(decl_146, type, binintersectEL: $o). 109.87/17.34 thf(decl_147, type, binintersectLsub: $o). 109.87/17.34 thf(decl_148, type, binintersectSubset2: $o). 109.87/17.34 thf(decl_149, type, binintersectSubset3: $o). 109.87/17.34 thf(decl_150, type, binintersectER: $o). 109.87/17.34 thf(decl_151, type, disjointsetsI1: $o). 109.87/17.34 thf(decl_152, type, binintersectRsub: $o). 109.87/17.34 thf(decl_153, type, binintersectSubset4: $o). 109.87/17.34 thf(decl_154, type, binintersectSubset1: $o). 109.87/17.34 thf(decl_155, type, bs114d: $o). 109.87/17.34 thf(decl_157, type, setminus: $i > $i > $i). 109.87/17.34 thf(decl_158, type, setminusI: $o). 109.87/17.34 thf(decl_159, type, setminusEL: $o). 109.87/17.34 thf(decl_160, type, setminusER: $o). 109.87/17.34 thf(decl_161, type, setminusSubset2: $o). 109.87/17.34 thf(decl_162, type, setminusERneg: $o). 109.87/17.34 thf(decl_163, type, setminusELneg: $o). 109.87/17.34 thf(decl_164, type, setminusILneg: $o). 109.87/17.34 thf(decl_165, type, setminusIRneg: $o). 109.87/17.34 thf(decl_166, type, setminusLsub: $o). 109.87/17.34 thf(decl_167, type, setminusSubset1: $o). 109.87/17.34 thf(decl_168, type, symdiff: $i > $i > $i). 109.87/17.34 thf(decl_169, type, symdiffE: $o). 109.87/17.34 thf(decl_170, type, symdiffI1: $o). 109.87/17.34 thf(decl_171, type, symdiffI2: $o). 109.87/17.34 thf(decl_172, type, symdiffIneg1: $o). 109.87/17.34 thf(decl_173, type, symdiffIneg2: $o). 109.87/17.34 thf(decl_174, type, iskpair: $i > $o). 109.87/17.34 thf(decl_175, type, secondinupair: $o). 109.87/17.34 thf(decl_176, type, setukpairIL: $o). 109.87/17.34 thf(decl_177, type, setukpairIR: $o). 109.87/17.34 thf(decl_178, type, kpairiskpair: $o). 109.87/17.34 thf(decl_179, type, kpair: $i > $i > $i). 109.87/17.34 thf(decl_180, type, kpairp: $o). 109.87/17.34 thf(decl_181, type, cartprod: $i > $i > $i). 109.87/17.34 thf(decl_182, type, singletonsubset: $o). 109.87/17.34 thf(decl_183, type, singletoninpowerset: $o). 109.87/17.34 thf(decl_184, type, singletoninpowunion: $o). 109.87/17.34 thf(decl_185, type, upairset2E: $o). 109.87/17.34 thf(decl_186, type, upairsubunion: $o). 109.87/17.34 thf(decl_187, type, upairinpowunion: $o). 109.87/17.34 thf(decl_188, type, ubforcartprodlem1: $o). 109.87/17.34 thf(decl_189, type, ubforcartprodlem2: $o). 109.87/17.34 thf(decl_190, type, ubforcartprodlem3: $o). 109.87/17.34 thf(decl_191, type, epred1_0: $o). 109.87/17.34 thf(decl_192, type, esk1_2: $i > $i > $i). 109.87/17.34 thf(decl_193, type, esk2_2: $i > $i > $i). 109.87/17.34 thf(decl_194, type, esk3_2: $i > $i > $i). 109.87/17.34 thf(decl_195, type, esk4_1: $i > $i). 109.87/17.34 thf(decl_196, type, esk5_2: ($i > $i > $o) > $i > $i). 109.87/17.34 thf(decl_197, type, esk6_2: ($i > $i > $o) > $i > $i). 109.87/17.34 thf(decl_198, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 109.87/17.34 thf(decl_199, type, esk8_1: $i > $i). 109.87/17.34 thf(decl_200, type, esk9_1: ($i > $o) > $i). 109.87/17.34 thf(decl_201, type, esk10_1: ($i > $o) > $i). 109.87/17.34 thf(decl_202, type, esk11_2: $i > $i > $i). 109.87/17.34 thf(decl_203, type, esk12_2: $i > $i > $i). 109.87/17.34 thf(decl_204, type, esk13_1: $i > $i). 109.87/17.34 thf(decl_205, type, esk14_1: $i > $i). 109.87/17.34 thf(decl_206, type, esk15_1: $i > $i). 109.87/17.34 thf(decl_207, type, esk16_2: $i > $i > $i). 109.87/17.34 thf(decl_208, type, esk17_3: $i > $i > $o > $i). 109.87/17.34 thf(decl_209, type, esk18_1: ($i > $o) > $i). 109.87/17.34 thf(decl_210, type, esk19_1: $i > $i). 109.87/17.34 thf(decl_211, type, esk20_2: $i > ($i > $o) > $i). 109.87/17.34 thf(decl_212, type, esk21_2: $i > ($i > $o) > $i). 109.87/17.34 thf(decl_213, type, esk22_2: $i > ($i > $o) > $i). 109.87/17.34 thf(decl_214, type, esk23_2: $i > ($i > $o) > $i). 109.87/17.34 thf(decl_215, type, esk24_2: $i > ($i > $o) > $i). 109.87/17.34 thf(decl_216, type, esk25_2: $i > ($i > $o) > $i). 109.87/17.34 thf(decl_217, type, esk26_2: ($i > $o) > $i > $i). 109.87/17.34 thf(decl_218, type, esk27_1: ($i > $o) > $i). 109.87/17.34 thf(decl_219, type, esk28_1: ($i > $o) > $i). 109.87/17.34 thf(decl_220, type, esk29_2: ($i > $o) > $i > $i). 109.87/17.34 thf(decl_221, type, esk30_2: ($i > $o) > ($i > $o) > $i). 109.87/17.34 thf(decl_222, type, esk31_2: ($i > $o) > ($i > $o) > $i). 109.87/17.34 thf(decl_223, type, esk32_2: ($i > $o) > ($i > $o) > $i). 109.87/17.34 thf(decl_224, type, esk33_2: ($i > $o) > ($i > $o) > $i). 109.87/17.34 thf(decl_225, type, esk34_4: $i > $i > ($i > $o) > ($i > $o) > $i). 109.87/17.34 thf(decl_226, type, esk35_4: $i > $i > ($i > $o) > ($i > $o) > $i). 109.87/17.34 thf(decl_227, type, esk36_2: $i > $i > $i). 109.87/17.34 thf(decl_228, type, esk37_2: $i > $i > $i). 109.87/17.34 thf(decl_229, type, esk38_2: $i > $i > $i). 109.87/17.34 thf(decl_230, type, esk39_0: $i). 109.87/17.34 thf(decl_231, type, esk40_0: $i). 109.87/17.34 thf(decl_232, type, esk41_0: $i). 109.87/17.34 thf(decl_233, type, esk42_0: $i). 109.87/17.34 thf(decl_240, type, epred3_2: $i > $i > $i > $o). 109.87/17.34 thf(decl_241, type, esk48_3: $i > $i > $i > $i). 109.87/17.34 thf(decl_242, type, esk49_3: $i > $i > $i > $i). 109.87/17.34 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', sepInPowerset)). 109.87/17.34 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.GP9gm0QO99/E---3.1_13802.p', exuE1)). 109.87/17.34 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', dsetconstrI)). 109.87/17.34 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', descrp)). 109.87/17.34 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', sepSubset)). 109.87/17.34 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', dsetconstr__Cong)). 109.87/17.34 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', descr__Cong)). 109.87/17.34 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', exuEu)). 109.87/17.34 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', exu__Cong)). 109.87/17.34 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', exuI3)). 109.87/17.34 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', exuE2)). 109.87/17.34 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.GP9gm0QO99/E---3.1_13802.p', exuE3u)). 109.87/17.34 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.GP9gm0QO99/E---3.1_13802.p', exuI2)). 109.87/17.34 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.GP9gm0QO99/E---3.1_13802.p', exuI1)). 109.87/17.34 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.GP9gm0QO99/E---3.1_13802.p', emptyE1)). 109.87/17.34 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setoftrueEq)). 109.87/17.34 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', nonemptyI)). 109.87/17.34 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setbeta)). 109.87/17.34 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', exuE3e)). 109.87/17.34 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', dsetconstrER)). 109.87/17.34 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', dsetconstrEL)). 109.87/17.34 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', replAx)). 109.87/17.34 thf(cartprodpairin, conjecture, ((setextAx)=>(((((setunionAx)=>(((omegaSAx)=>((omegaIndAx)=>((replAx)=>((((((dsetconstrEL)=>((dsetconstrER)=>(((((((exuE3e)=>(((((setbeta)=>(((nonemptyI)=>((((((((setoftrueEq)=>(((emptyinPowerset)=>(((powersetE)=>((((subPowSU)=>(((nonemptyImpWitness)=>(((((singletonsswitch)=>((upairsetE)=>((((emptyE1)=>((vacuousDall)=>((((((prop2setI)=>(((notdexE)=>((notdallE)=>((exuI1)=>(((exuI2)=>((((exuE3u)=>((((setadjoin__Cong)=>((powerset__Cong)=>((((((((eqimpsubset2)=>(((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>(((((((setadjoinSub)=>((((setextsub)=>(((powersetI1)=>(((inPowerset)=>(((sepInPowerset)=>(((binunionIL)=>(((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>(((binintersectEL)=>((binintersectLsub)=>((((((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>(((setminusERneg)=>(((setminusILneg)=>((((((symdiffI1)=>((symdiffI2)=>(((symdiffIneg2)=>(((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>(((singletonsubset)=>((((upairset2E)=>(((((ubforcartprodlem2)=>(![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))<=(in @ X3 @ X5)))))<=(ubforcartprodlem3)))<=(ubforcartprodlem1))<=(upairinpowunion))<=(upairsubunion)))<=(singletoninpowunion))<=(singletoninpowerset)))<=(kpairp)))))<=(secondinupair)))<=(symdiffIneg1))))<=(symdiffE))<=(setminusSubset1))<=(setminusLsub))<=(setminusIRneg)))<=(setminusELneg)))<=(setminusSubset2)))))))))<=(disjointsetsI1))<=(binintersectER))<=(binintersectSubset3))<=(binintersectSubset2))))<=(binintersectSubset5))))))))<=(upairset2IR)))<=(sepSubset)))<=(powersetsubset)))<=(powersetE1)))<=(subsetemptysetimpeq)))<=(subset2powerset))<=(setadjoinSub2)))<=(subsetTrans))<=(subsetRefl))<=(notequalI2))<=(notequalI1))<=(notsubsetI))))))<=(eqimpsubset1)))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong))<=(exuEu))<=(omega__Cong))<=(setunion__Cong))))<=(emptyset__Cong))<=(exu__Cong)))<=(in__Cong))<=(inCongP)))<=(exuI3)))))<=(prop2set2propI)))<=(quantDeMorgan4))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1))))<=(upairsetIR))<=(upairsetIL))))<=(eqinunit))<=(notinsingleton))<=(uniqinunit)))<=(exuE2)))<=(setunionE))<=(setunionI)))<=(emptyInPowerset)))<=(powersetI)))<=(setadjoinOr))<=(setadjoinE))<=(setadjoinIR))<=(emptyinunitempty))<=(setadjoinIL))<=(nonemptyI1)))<=(nonemptyE1)))<=(noeltsimpempty))<=(emptyI))<=(setext)))<=(notinemptyset))<=(emptysetimpfalse))<=(emptysetE))<=(prop2setE))<=(exuE1))))<=(dsetconstrI))<=(descrp))<=(wellorderingAx))<=(foundationAx)))))<=(omega0Ax)))<=(powersetAx))<=(setadjoinAx))<=(emptysetAx))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', cartprodpairin)). 109.87/17.34 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setadjoinSub)). 109.87/17.34 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.GP9gm0QO99/E---3.1_13802.p', wellorderingAx)). 109.87/17.34 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', emptysetAx)). 109.87/17.34 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setunionE)). 109.87/17.34 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setunionI)). 109.87/17.34 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', powersetI1)). 109.87/17.34 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', emptyInPowerset)). 109.87/17.34 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', powersetI)). 109.87/17.34 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', inPowerset)). 109.87/17.34 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setadjoinOr)). 109.87/17.34 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.GP9gm0QO99/E---3.1_13802.p', setadjoinE)). 109.87/17.34 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setadjoinIR)). 109.87/17.34 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', emptyinunitempty)). 109.87/17.34 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setadjoinIL)). 109.87/17.34 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', binunionIL)). 109.87/17.34 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', nonemptyI1)). 109.87/17.34 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', nonemptyE1)). 109.87/17.34 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', noeltsimpempty)). 109.87/17.34 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', binunionIR)). 109.87/17.34 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', emptyI)). 109.87/17.34 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setext)). 109.87/17.34 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', binunionEcases)). 109.87/17.34 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', notinemptyset)). 109.87/17.34 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', subsetE2)). 109.87/17.34 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', emptysetimpfalse)). 109.87/17.34 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', emptysetE)). 109.87/17.34 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', prop2setE)). 109.87/17.34 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', binunionE)). 109.87/17.34 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', binunionLsub)). 109.87/17.34 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', symdiffIneg2)). 109.87/17.34 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', foundationAx)). 109.87/17.34 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', omega0Ax)). 109.87/17.34 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', binunionRsub)). 109.87/17.34 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', powersetAx)). 109.87/17.34 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setadjoinAx)). 109.87/17.34 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', binintersectI)). 109.87/17.34 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', binintersectEL)). 109.87/17.34 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', binintersectLsub)). 109.87/17.34 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', binintersectRsub)). 109.87/17.34 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', binintersectSubset4)). 109.87/17.34 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', binintersectSubset1)). 109.87/17.34 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', bs114d)). 109.87/17.34 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setminusI)). 109.87/17.34 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setminusEL)). 109.87/17.34 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setminusER)). 109.87/17.34 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setminusERneg)). 109.87/17.34 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setminusILneg)). 109.87/17.34 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', symdiffI1)). 109.87/17.34 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', symdiffI2)). 109.87/17.34 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', subset2powerset)). 109.87/17.34 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setadjoinSub2)). 109.87/17.34 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', subsetTrans)). 109.87/17.34 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', subsetRefl)). 109.87/17.34 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', notequalI2)). 109.87/17.34 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setukpairIL)). 109.87/17.34 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setukpairIR)). 109.87/17.34 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', kpairiskpair)). 109.87/17.34 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', singletonsubset)). 109.87/17.34 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', upairset2E)). 109.87/17.34 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.GP9gm0QO99/E---3.1_13802.p', ubforcartprodlem2)). 109.87/17.34 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.GP9gm0QO99/E---3.1_13802.p', ubforcartprodlem3)). 109.87/17.34 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.GP9gm0QO99/E---3.1_13802.p', ubforcartprodlem1)). 109.87/17.34 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setextsub)). 109.87/17.34 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.GP9gm0QO99/E---3.1_13802.p', upairinpowunion)). 109.87/17.34 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.GP9gm0QO99/E---3.1_13802.p', upairsubunion)). 109.87/17.34 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', singletoninpowunion)). 109.87/17.34 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', singletoninpowerset)). 109.87/17.34 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', kpairp)). 109.87/17.34 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', secondinupair)). 109.87/17.34 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', symdiffIneg1)). 109.87/17.34 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.GP9gm0QO99/E---3.1_13802.p', symdiffE)). 109.87/17.34 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setminusSubset1)). 109.87/17.34 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setminusLsub)). 109.87/17.34 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setminusIRneg)). 109.87/17.34 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setminusELneg)). 109.87/17.34 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setminusSubset2)). 109.87/17.34 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', disjointsetsI1)). 109.87/17.34 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', binintersectER)). 109.87/17.34 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', binintersectSubset3)). 109.87/17.34 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', binintersectSubset2)). 109.87/17.34 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', binintersectSubset5)). 109.87/17.34 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', upairset2IR)). 109.87/17.34 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', powersetsubset)). 109.87/17.34 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', powersetE1)). 109.87/17.34 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', subsetemptysetimpeq)). 109.87/17.34 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', notequalI1)). 109.87/17.34 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', notsubsetI)). 109.87/17.34 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', eqimpsubset1)). 109.87/17.34 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', subsetI1)). 109.87/17.34 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', omega__Cong)). 109.87/17.34 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setunion__Cong)). 109.87/17.34 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', emptyset__Cong)). 109.87/17.34 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.GP9gm0QO99/E---3.1_13802.p', in__Cong)). 109.87/17.34 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.GP9gm0QO99/E---3.1_13802.p', inCongP)). 109.87/17.34 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', quantDeMorgan4)). 109.87/17.34 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', quantDeMorgan3)). 109.87/17.34 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', quantDeMorgan2)). 109.87/17.34 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', quantDeMorgan1)). 109.87/17.34 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', upairsetIR)). 109.87/17.34 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', upairsetIL)). 109.87/17.34 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', eqinunit)). 109.87/17.34 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', notinsingleton)). 109.87/17.34 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', uniqinunit)). 109.87/17.34 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', subsetE)). 109.87/17.34 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', emptysetsubset)). 109.87/17.34 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', subsetI2)). 109.87/17.34 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', eqimpsubset2)). 109.87/17.34 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', powerset__Cong)). 109.87/17.34 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.GP9gm0QO99/E---3.1_13802.p', setadjoin__Cong)). 109.87/17.34 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', notdallE)). 109.87/17.34 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', notdexE)). 109.87/17.34 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', prop2setI)). 109.87/17.34 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', vacuousDall)). 109.87/17.34 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', upairsetE)). 109.87/17.34 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', singletonsswitch)). 109.87/17.34 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', nonemptyImpWitness)). 109.87/17.34 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', subPowSU)). 109.87/17.34 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', powersetE)). 109.87/17.34 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', emptyinPowerset)). 109.87/17.34 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', omegaIndAx)). 109.87/17.34 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', omegaSAx)). 109.87/17.34 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setunionAx)). 109.87/17.34 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', setextAx)). 109.87/17.34 thf(cartprod, axiom, ((cartprod)=(^[X4:$i, X5:$i]:(dsetconstr @ (powerset @ (powerset @ (binunion @ X4 @ X5))) @ (^[X2:$i]:(?[X3:$i]:(((in @ X3 @ X4)&?[X14:$i]:(((in @ X14 @ X5)&((X2)=(kpair @ X3 @ X14))))))))))), file('/export/starexec/sandbox/tmp/tmp.GP9gm0QO99/E---3.1_13802.p', cartprod)). 109.87/17.34 thf(c_0_147, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 109.87/17.34 thf(c_0_148, 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])). 109.87/17.34 thf(c_0_149, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 109.87/17.34 thf(c_0_150, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 109.87/17.34 thf(c_0_151, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 109.87/17.34 thf(c_0_152, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 109.87/17.34 thf(c_0_153, plain, ((descr__Cong)<=>![X1:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 109.87/17.34 thf(c_0_154, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 109.87/17.34 thf(c_0_155, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 109.87/17.34 thf(c_0_156, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 109.87/17.34 thf(c_0_157, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 109.87/17.34 thf(c_0_158, 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])). 109.87/17.34 thf(c_0_159, 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])). 109.87/17.34 thf(c_0_160, 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])). 109.87/17.34 thf(c_0_161, 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])). 109.87/17.34 thf(c_0_162, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 109.87/17.34 thf(c_0_163, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 109.87/17.34 thf(c_0_164, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 109.87/17.34 thf(c_0_165, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 109.87/17.34 thf(c_0_166, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 109.87/17.34 thf(c_0_167, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 109.87/17.34 thf(c_0_168, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 109.87/17.34 thf(c_0_169, plain, ((epred1_0)<=>![X781:$i]:(?[X782:$i]:((((![X783:$i]:(((in @ X783 @ X782)=>![X784:$i]:(((in @ X784 @ X783)=>(in @ X784 @ X781)))))&![X785:$i, X786:$i]:((((in @ X785 @ X781)&(in @ X786 @ X781))=>(![X787:$i]:(((in @ X787 @ X782)=>((in @ X785 @ X787)<=>(in @ X786 @ X787))))=>((X785)=(X786))))))&![X788:$i, X789:$i]:((((in @ X788 @ X782)&(in @ X789 @ X782))=>(![X790:$i]:(((in @ X790 @ X788)=>(in @ X790 @ X789)))|![X791:$i]:(((in @ X791 @ X789)=>(in @ X791 @ X788)))))))&![X792:$i]:(((![X793:$i]:(((in @ X793 @ X792)=>(in @ X793 @ X781)))&?[X794:$i]:((in @ X794 @ X792)))=>?[X795:$i, X796:$i]:(((((in @ X795 @ X782)&(in @ X796 @ X792))&~(?[X797:$i]:(((in @ X797 @ X795)&(in @ X797 @ X792)))))&![X798:$i]:(((in @ X798 @ X782)=>(![X799:$i]:(((in @ X799 @ X798)=>(in @ X799 @ X795)))|(in @ X796 @ X798)))))))))))), introduced(definition)). 109.87/17.34 thf(c_0_170, negated_conjecture, ~((![X418:$i, X419:$i]:((![X420:$i]:(((in @ X420 @ X418)<=>(in @ X420 @ X419)))=>((X418)=(X419))))=>(![X810:$i]:(~(in @ X810 @ emptyset))=>(![X807:$i, X808:$i, X809:$i]:(((in @ X809 @ (setadjoin @ X807 @ X808))<=>(((X809)=(X807))|(in @ X809 @ X808))))=>(![X804:$i, X805:$i]:(((in @ X805 @ (powerset @ X804))<=>![X806:$i]:(((in @ X806 @ X805)=>(in @ X806 @ X804)))))=>(![X421:$i, X422:$i]:(((in @ X422 @ (setunion @ X421))<=>?[X423:$i]:(((in @ X422 @ X423)&(in @ X423 @ X421)))))=>((in @ emptyset @ omega)=>(![X424:$i]:(((in @ X424 @ omega)=>(in @ (setadjoin @ X424 @ X424) @ omega)))=>(![X425:$i]:((((in @ emptyset @ X425)&![X426:$i]:((((in @ X426 @ omega)&(in @ X426 @ X425))=>(in @ (setadjoin @ X426 @ X426) @ X425))))=>![X427:$i]:(((in @ X427 @ omega)=>(in @ X427 @ X425)))))=>(![X428:$i > $i > $o, X429:$i]:((![X430:$i]:(((in @ X430 @ X429)=>(exu @ (X428 @ X430))))=>?[X431:$i]:(![X432:$i]:(((in @ X432 @ X431)<=>?[X433:$i]:(((in @ X433 @ X429)&(X428 @ X433 @ X432))))))))=>(![X800:$i]:((?[X801:$i]:((in @ X801 @ X800))=>?[X802:$i]:(((in @ X802 @ X800)&~(?[X803:$i]:(((in @ X803 @ X802)&(in @ X803 @ X800))))))))=>((epred1_0)=>(![X780:$i > $o]:(((exu @ X780)=>(X780 @ (descr @ (^[Z0/* 17 */:$i]:(X780 @ Z0))))))=>(![X777:$i, X778:$i > $o, X779:$i]:(((in @ X779 @ X777)=>((X778 @ X779)=>(in @ X779 @ (dsetconstr @ X777 @ X778)))))=>(![X434:$i, X435:$i > $o, X436:$i]:(((in @ X436 @ (dsetconstr @ X434 @ X435))=>(in @ X436 @ X434)))=>(![X437:$i, X438:$i > $o, 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emptyset @ (prop2set @ ((X467))))))=>((prop2set2propI)=>(![X468:$i, X469:$i > $o]:((~(?[X470:$i]:(((in @ X470 @ X468)&(X469 @ X470))))=>![X471:$i]:(((in @ X471 @ X468)=>~((X469 @ X471))))))=>(![X472:$i, X473:$i > $o]:((~(![X474:$i]:(((in @ X474 @ X472)=>(X473 @ X474))))=>?[X475:$i]:(((in @ X475 @ X472)&~((X473 @ X475))))))=>(![X476:$i > $o]:((?[X477:$i]:(((X476 @ X477)&![X478:$i]:(((X476 @ X478)=>((X477)=(X478))))))=>(exu @ X476)))=>(![X700:$i > $o]:((?[X701:$i]:((X700 @ X701))=>(![X702:$i, X703:$i]:(((X700 @ X702)=>((X700 @ X703)=>((X702)=(X703)))))=>(exu @ X700))))=>(![X479:$i > $o]:((?[X480:$i]:(![X481:$i]:(((X479 @ X481)<=>((X481)=(X480)))))=>(exu @ X479)))=>(![X696:$i, X697:$i]:((((X696)=(X697))=>![X698:$i, X699:$i]:((((X698)=(X699))=>((in @ X698 @ X696)=>(in @ X699 @ X697))))))=>(![X692:$i, X693:$i]:((((X692)=(X693))=>![X694:$i, X695:$i]:((((X694)=(X695))=>((in @ X694 @ X692)<=>(in @ X695 @ X693))))))=>(![X482:$i > $o]:(((exu @ X482)=>![X483:$i, X484:$i]:(((X482 @ X483)=>((X482 @ 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def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setadjoinSub]), wellorderingAx]), emptysetAx]), setunionE]), setunionI]), powersetI1]), emptyInPowerset]), powersetI]), inPowerset]), setadjoinOr]), setadjoinE]), setadjoinIR]), c_0_147]), emptyinunitempty]), setadjoinIL]), binunionIL]), nonemptyI1]), nonemptyE1]), noeltsimpempty]), binunionIR]), emptyI]), setext]), binunionEcases]), notinemptyset]), subsetE2]), emptysetimpfalse]), emptysetE]), prop2setE]), binunionE]), c_0_148]), c_0_149]), binunionLsub]), c_0_150]), symdiffIneg2]), foundationAx]), omega0Ax]), binunionRsub]), powersetAx]), setadjoinAx]), binintersectI]), binintersectEL]), binintersectLsub]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusERneg]), setminusILneg]), symdiffI1]), symdiffI2]), subset2powerset]), setadjoinSub2]), subsetTrans]), subsetRefl]), notequalI2]), setukpairIL]), setukpairIR]), kpairiskpair]), singletonsubset]), upairset2E]), ubforcartprodlem2]), ubforcartprodlem3]), ubforcartprodlem1]), setextsub]), upairinpowunion]), upairsubunion]), singletoninpowunion]), singletoninpowerset]), kpairp]), secondinupair]), symdiffIneg1]), symdiffE]), setminusSubset1]), setminusLsub]), setminusIRneg]), setminusELneg]), setminusSubset2]), disjointsetsI1]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectSubset5]), upairset2IR]), c_0_151]), powersetsubset]), powersetE1]), subsetemptysetimpeq]), notequalI1]), notsubsetI]), eqimpsubset1]), subsetI1]), c_0_152]), c_0_153]), c_0_154]), omega__Cong]), setunion__Cong]), emptyset__Cong]), c_0_155]), in__Cong]), inCongP]), c_0_156]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), upairsetIR]), upairsetIL]), eqinunit]), notinsingleton]), uniqinunit]), c_0_157]), subsetE]), emptysetsubset]), subsetI2]), eqimpsubset2]), powerset__Cong]), setadjoin__Cong]), c_0_158]), c_0_159]), c_0_160]), notdallE]), notdexE]), prop2setI]), vacuousDall]), c_0_161]), upairsetE]), singletonsswitch]), nonemptyImpWitness]), subPowSU]), powersetE]), emptyinPowerset]), c_0_162]), c_0_163]), c_0_164]), c_0_165]), c_0_166]), c_0_167]), c_0_168]), omegaIndAx]), omegaSAx]), setunionAx]), setextAx])])]), c_0_169])). 109.87/17.34 thf(c_0_171, plain, ![X811:$i, X812:$i]:(((cartprod @ X811 @ X812)=(dsetconstr @ (powerset @ (powerset @ (binunion @ X811 @ X812))) @ (^[Z0/* 5 */:$i]:(?[X3:$i]:(((in @ X3 @ X811)&?[X14:$i]:(((in @ X14 @ X812)&((Z0)=(kpair @ X3 @ X14))))))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[cartprod])])). 109.87/17.34 thf(c_0_172, negated_conjecture, ![X815:$i, X816:$i, X818:$i, X819:$i, X820:$i, X821:$i, X822:$i, X823:$i, X824:$i, X825:$i, X826:$i, X828:$i, X829:$i, X831:$i, X832:$i, X833:$i, X834:$i, X835:$i, X837:$i, X838:$i > $i > $o, X839:$i, X842:$i, X844:$i, X845:$i, X846:$i, X847:$i, X849:$i, X850:$i > $o, X851:$i, X852:$i > $o, X853:$i, X854:$i, X855:$i > $o, X856:$i, X857:$i, X858:$i > $o, X859:$i, X860:$i > $o, X862:$i, X863:$o, X864:$i, X865:$i, X866:$o, X867:$i, X868:$i, X869:$i > $o, X871:$i, X872:$i, X875:$i, X877:$i, X879:$i, X880:$i > $o, X881:$i, X882:$i, X884:$i, X885:$i > $o, X886:$i, X887:$i, X888:$i, X889:$i, X890:$i, X891:$i, X892:$i, X893:$i, X894:$i, X895:$i, X896:$i, X897:$o, X898:$i, X899:$i, X900:$i, X901:$i, X902:$i, X903:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X911:$i, X912:$i, X913:$i, X914:$i, X915:$o, X917:$i, X918:$i, X919:$i > $o, X921:$i, X922:$i, X923:$i, X925:$i, X926:$i, X927:$i, X928:$i, X929:$i, X930:$i, X931:$i, X932:$i, X933:$i, X934:$i, X935:$i, X936:$i, X937:$i, X938:$i, X939:$i, X940:$i, X941:$i > $o, X942:$i, X943:$i > $o, X944:$i, X945:$i, X946:$i > $o, X947:$i, X949:$i, X950:$i > $o, X952:$i, X953:$i, X954:$i > $o, X956:$i, X957:$i, X958:$i > $o, X959:$i, X961:$o, X962:$i, X963:$i > $o, X965:$i, X966:$i, X967:$i > $o, X968:$i, X970:$i > $o, X971:$i, X973:$i > $o, X974:$i, X977:$i > $o, X978:$i, X980:$i, X981:$i, X982:$i, X983:$i, X984:$i, X985:$i, X986:$i, X987:$i, X988:$i > $o, X989:$i, X990:$i, X991:$i > $o, X992:$i > $o, X995:$i, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1003:$i > $o, X1004:$i, X1005:$i, X1006:$i > $o, X1007:$i > $o, X1010:$i, X1011:$i, X1012:$i > $o, X1013:$i > $o, X1016:$i, X1017:$i, X1019:$i, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1026:$i, X1027:$i, X1028:$i, X1029:$i, X1030:$i, X1031:$i, X1032:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$i, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i, X1043:$i, X1044:$i, X1045:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i, X1054:$i, X1055:$i, X1056:$i, X1057:$i, X1058:$i, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i > $o, X1064:$i, X1065:$i > $o, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$i, X1071:$i, X1072:$i, X1073:$i, X1074:$i, X1075:$i, X1076:$i, X1077:$o, X1078:$i, X1079:$i, X1080:$i, X1081:$i, X1082:$i, X1083:$i, X1084:$i, X1085:$i, X1086:$i, X1087:$i, X1088:$i, X1089:$i, X1090:$i, X1091:$i, X1092:$i, X1093:$i, X1094:$i, X1095:$i, X1096:$i, X1097:$i, X1098:$i, X1099:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$i, X1125:$i, X1126:$i, X1127:$i, X1128:$i, X1129:$i, X1130:$i, X1131:$i, X1132:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1137:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$o, 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, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$i, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i]:((((~(in @ (esk1_2 @ X815 @ X816) @ X815)|~(in @ (esk1_2 @ X815 @ X816) @ X816)|((X815)=(X816)))&((in @ (esk1_2 @ X815 @ X816) @ X815)|(in @ (esk1_2 @ X815 @ X816) @ X816)|((X815)=(X816))))&(~(in @ X818 @ emptyset)&(((~(in @ X821 @ (setadjoin @ X819 @ X820))|(((X821)=(X819))|(in @ X821 @ X820)))&((((X821)!=(X819))|(in @ X821 @ (setadjoin @ X819 @ X820)))&(~(in @ X821 @ X820)|(in @ X821 @ (setadjoin @ X819 @ X820)))))&(((~(in @ X823 @ (powerset @ X822))|(~(in @ X824 @ X823)|(in @ X824 @ X822)))&(((in @ (esk2_2 @ X825 @ X826) @ X826)|(in @ X826 @ (powerset @ X825)))&(~(in @ (esk2_2 @ X825 @ X826) @ X825)|(in @ X826 @ (powerset @ X825)))))&(((((in @ X829 @ (esk3_2 @ X828 @ X829))|~(in @ X829 @ (setunion @ X828)))&((in @ (esk3_2 @ X828 @ X829) @ X828)|~(in @ X829 @ (setunion @ X828))))&(~(in @ X832 @ X833)|~(in @ X833 @ X831)|(in @ X832 @ (setunion @ X831))))&((in @ emptyset @ 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X872) @ X871)))&(((in @ (esk12_2 @ X871 @ X872) @ X872)|((X871)=(X872))|~(in @ (esk11_2 @ X871 @ X872) @ X872))&(~(in @ (esk12_2 @ X871 @ X872) @ X871)|((X871)=(X872))|~(in @ (esk11_2 @ X871 @ X872) @ X872))))&(((in @ (esk13_1 @ X875) @ X875)|((X875)=(emptyset)))&(((in @ (esk14_1 @ X877) @ X877)|((X877)=(emptyset)))&(((~(in @ X881 @ (dsetconstr @ X879 @ X880))|(X880 @ X881)|~(in @ X881 @ X879))&(~(X880 @ X881)|(in @ X881 @ (dsetconstr @ X879 @ X880))|~(in @ X881 @ X879)))&((~(nonempty @ X882)|(in @ (esk15_1 @ X882) @ X882))&((~(in @ X886 @ X884)|(~(X885 @ X886)|(nonempty @ (dsetconstr @ X884 @ X885))))&((~(in @ X888 @ X887)|(nonempty @ X887))&((in @ X889 @ (setadjoin @ X889 @ X890))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X893 @ X892)|(in @ X893 @ (setadjoin @ X891 @ X892)))&(((((in @ X896 @ X895)|(X897)|((X896)=(X894))|~(in @ X896 @ (setadjoin @ X894 @ X895)))&(~(X897)|(X897)|((X896)=(X894))|~(in @ X896 @ (setadjoin @ X894 @ X895))))&(((in @ X896 @ X895)|(X897)|~(X897)|~(in @ X896 @ (setadjoin @ X894 @ X895)))&(~(X897)|(X897)|~(X897)|~(in @ X896 @ (setadjoin @ X894 @ X895)))))&((~(in @ X900 @ (setadjoin @ X898 @ X899))|(((X900)=(X898))|(in @ X900 @ X899)))&(((dsetconstr @ X901 @ (^[Z0/* 1 */:$i]:($true)))=(X901))&((((in @ (esk16_2 @ X902 @ X903) @ X903)|(in @ X903 @ (powerset @ X902)))&(~(in @ (esk16_2 @ X902 @ X903) @ X902)|(in @ X903 @ (powerset @ X902))))&((in @ emptyset @ (powerset @ X905))&((in @ emptyset @ (powerset @ X906))&((~(in @ X908 @ (powerset @ X907))|(~(in @ X909 @ X908)|(in @ X909 @ X907)))&((~(in @ X911 @ X912)|(~(in @ X912 @ X910)|(in @ X911 @ (setunion @ X910))))&((((in @ X914 @ (esk17_3 @ X913 @ X914 @ X915))|(X915)|~(in @ X914 @ (setunion @ X913)))&(((in @ (esk17_3 @ X913 @ X914 @ X915) @ X913)|(X915)|~(in @ X914 @ (setunion @ X913)))&(~(X915)|(X915)|~(in @ X914 @ (setunion @ X913)))))&((~(in @ X918 @ X917)|(in @ X918 @ (powerset @ (setunion @ X917))))&(((~(X919 @ X921)|((X921)=(esk18_1 @ X919))|~(exu @ X919))&(((X922)!=(esk18_1 @ X919))|(X919 @ X922)|~(exu @ X919)))&((((in @ (esk19_1 @ X923) @ X923)|~(nonempty @ X923))&(($true)|~(nonempty @ X923)))&((~(in @ X925 @ (setadjoin @ X926 @ emptyset))|((X925)=(X926)))&((((X927)=(X928))|~(in @ X928 @ (setadjoin @ X927 @ emptyset)))&((((X929)!=(X930))|(in @ X929 @ (setadjoin @ X930 @ emptyset)))&((~(in @ X931 @ (setadjoin @ X932 @ emptyset))|(in @ X932 @ (setadjoin @ X931 @ emptyset)))&((~(in @ X935 @ (setadjoin @ X933 @ (setadjoin @ X934 @ emptyset)))|(((X935)=(X933))|((X935)=(X934))))&((in @ X936 @ (setadjoin @ X936 @ (setadjoin @ X937 @ emptyset)))&((in @ X939 @ (setadjoin @ X938 @ (setadjoin @ X939 @ emptyset)))&((~(in @ X942 @ X940)|~(X941 @ X942)|(((dsetconstr @ X940 @ X941)!=(emptyset))|~($true)))&((~(in @ X944 @ emptyset)|(X943 @ X944))&((((in @ (esk20_2 @ X945 @ X946) @ X945)|(~(in @ X947 @ X945)|(X946 @ X947)))&(~(X946 @ (esk20_2 @ X945 @ X946))|(~(in @ X947 @ X945)|(X946 @ X947))))&((((in @ (esk21_2 @ X949 @ X950) @ X949)|(~(in @ X952 @ X949)|~(X950 @ X952)))&((X950 @ (esk21_2 @ X949 @ X950))|(~(in @ X952 @ X949)|~(X950 @ X952))))&((((in @ (esk22_2 @ X953 @ X954) @ X953)|(~(in @ X956 @ X953)|~(X954 @ X956)))&((X954 @ (esk22_2 @ X953 @ X954))|(~(in @ X956 @ X953)|~(X954 @ X956))))&((((in @ (esk23_2 @ X957 @ X958) @ X957)|(~(in @ X959 @ X957)|(X958 @ X959)))&(~(X958 @ (esk23_2 @ X957 @ X958))|(~(in @ X959 @ X957)|(X958 @ X959))))&((~(X961)|(in @ emptyset @ (prop2set @ ((X961)))))&((prop2set2propI)&((((in @ (esk24_2 @ X962 @ X963) @ X962)|(~(in @ X965 @ X962)|~(X963 @ X965)))&((X963 @ (esk24_2 @ X962 @ X963))|(~(in @ X965 @ X962)|~(X963 @ X965))))&((((in @ (esk25_2 @ X966 @ X967) @ X966)|(~(in @ X968 @ X966)|(X967 @ X968)))&(~(X967 @ (esk25_2 @ X966 @ X967))|(~(in @ X968 @ X966)|(X967 @ X968))))&((((X970 @ (esk26_2 @ X970 @ X971))|~(X970 @ X971)|(exu @ X970))&(((X971)!=(esk26_2 @ X970 @ X971))|~(X970 @ X971)|(exu @ X970)))&((((X973 @ (esk27_1 @ X973))|(exu @ X973)|~(X973 @ X974))&(((X973 @ (esk28_1 @ X973))|(exu @ X973)|~(X973 @ X974))&(((esk27_1 @ X973)!=(esk28_1 @ X973))|(exu @ X973)|~(X973 @ X974))))&(((~(X977 @ (esk29_2 @ X977 @ X978))|((esk29_2 @ X977 @ X978)!=(X978))|(exu @ X977))&((X977 @ (esk29_2 @ X977 @ X978))|((esk29_2 @ X977 @ X978)=(X978))|(exu @ X977)))&((((X980)!=(X981))|(((X982)!=(X983))|(~(in @ X982 @ X980)|(in @ X983 @ X981))))&(((~(in @ X986 @ X984)|(in @ X987 @ X985)|((X986)!=(X987))|((X984)!=(X985)))&(~(in @ X987 @ X985)|(in @ X986 @ X984)|((X986)!=(X987))|((X984)!=(X985))))&((~(exu @ X988)|(~(X988 @ X989)|(~(X988 @ X990)|((X989)=(X990)))))&((((~(exu @ X991)|(exu @ X992)|((esk30_2 @ X991 @ X992)=(esk31_2 @ X991 @ X992)))&(~(exu @ X992)|(exu @ X991)|((esk30_2 @ X991 @ X992)=(esk31_2 @ X991 @ X992))))&(((~(exu @ X991)|(exu @ X992)|(~(X991 @ (esk30_2 @ X991 @ X992))|~(X992 @ (esk31_2 @ X991 @ X992))))&(~(exu @ X992)|(exu @ X991)|(~(X991 @ (esk30_2 @ X991 @ X992))|~(X992 @ (esk31_2 @ X991 @ X992)))))&((~(exu @ X991)|(exu @ X992)|((X991 @ (esk30_2 @ X991 @ X992))|(X992 @ (esk31_2 @ X991 @ X992))))&(~(exu @ X992)|(exu @ X991)|((X991 @ (esk30_2 @ X991 @ X992))|(X992 @ (esk31_2 @ X991 @ X992)))))))&(((emptyset)=(emptyset))&((((X995)!=(X996))|(((X997)!=(X998))|((setadjoin @ X995 @ X997)=(setadjoin @ X996 @ X998))))&((((X999)!=(X1000))|((powerset @ X999)=(powerset @ X1000)))&((((X1001)!=(X1002))|((setunion @ X1001)=(setunion @ X1002)))&(((omega)=(omega))&((~(exu @ X1003)|(~(X1003 @ X1004)|(~(X1003 @ X1005)|((X1004)=(X1005)))))&(((((esk32_2 @ X1006 @ X1007)=(esk33_2 @ X1006 @ X1007))|(~(exu @ X1006)|(~(exu @ X1007)|((descr @ X1006)=(descr @ X1007)))))&((~(X1006 @ (esk32_2 @ X1006 @ X1007))|~(X1007 @ (esk33_2 @ X1006 @ X1007))|(~(exu @ X1006)|(~(exu @ X1007)|((descr @ X1006)=(descr @ X1007)))))&((X1006 @ (esk32_2 @ X1006 @ X1007))|(X1007 @ (esk33_2 @ X1006 @ X1007))|(~(exu @ X1006)|(~(exu @ X1007)|((descr @ X1006)=(descr @ X1007)))))))&((((in @ (esk34_4 @ X1010 @ X1011 @ X1012 @ X1013) @ X1010)|((dsetconstr @ X1010 @ X1012)=(dsetconstr @ X1011 @ X1013))|((X1010)!=(X1011)))&(((in @ (esk35_4 @ X1010 @ X1011 @ X1012 @ X1013) @ X1011)|((dsetconstr @ X1010 @ X1012)=(dsetconstr @ X1011 @ X1013))|((X1010)!=(X1011)))&((((esk34_4 @ X1010 @ X1011 @ X1012 @ X1013)=(esk35_4 @ X1010 @ X1011 @ X1012 @ X1013))|((dsetconstr @ X1010 @ X1012)=(dsetconstr @ X1011 @ X1013))|((X1010)!=(X1011)))&((~(X1012 @ (esk34_4 @ X1010 @ X1011 @ X1012 @ X1013))|~(X1013 @ (esk35_4 @ X1010 @ X1011 @ X1012 @ X1013))|((dsetconstr @ X1010 @ X1012)=(dsetconstr @ X1011 @ X1013))|((X1010)!=(X1011)))&((X1012 @ (esk34_4 @ X1010 @ X1011 @ X1012 @ X1013))|(X1013 @ (esk35_4 @ X1010 @ X1011 @ X1012 @ X1013))|((dsetconstr @ X1010 @ X1012)=(dsetconstr @ X1011 @ X1013))|((X1010)!=(X1011)))))))&((((in @ (esk36_2 @ X1016 @ X1017) @ X1016)|(subset @ X1016 @ X1017))&(~(in @ (esk36_2 @ X1016 @ X1017) @ X1017)|(subset @ X1016 @ X1017)))&((((X1019)!=(X1020))|(subset @ X1020 @ X1019))&((((X1021)!=(X1022))|(subset @ X1021 @ X1022))&((((in @ (esk37_2 @ X1023 @ X1024) @ X1023)|(subset @ X1023 @ X1024))&(~(in @ (esk37_2 @ X1023 @ X1024) @ X1024)|(subset @ X1023 @ X1024)))&((subset @ emptyset @ X1026)&((~(subset @ X1027 @ X1028)|(~(in @ X1029 @ X1027)|(in @ X1029 @ X1028)))&((~(subset @ X1030 @ X1031)|((in @ X1032 @ X1031)|~(in @ X1032 @ X1030)))&((~(in @ X1035 @ X1033)|((in @ X1035 @ X1034)|~(subset @ X1033 @ X1034)))&(((subset @ X1036 @ X1037)|((X1036)!=(X1037)))&((~(in @ X1040 @ X1038)|((in @ X1040 @ X1039)|((X1038)!=(X1039))))&((subset @ X1041 @ X1041)&((~(subset @ X1042 @ X1043)|(~(subset @ X1043 @ X1044)|(subset @ X1042 @ X1044)))&((subset @ X1046 @ (setadjoin @ X1045 @ X1046))&((~(subset @ X1047 @ X1049)|(subset @ X1047 @ (setadjoin @ X1048 @ X1049)))&((~(subset @ X1050 @ X1051)|(in @ X1050 @ (powerset @ X1051)))&((~(subset @ X1052 @ X1053)|(~(subset @ X1053 @ X1052)|((X1052)=(X1053))))&((~(subset @ X1054 @ emptyset)|((X1054)=(emptyset)))&((~(subset @ X1056 @ X1055)|(in @ X1056 @ (powerset @ X1055)))&((~(in @ X1058 @ (powerset @ X1057))|(subset @ X1058 @ X1057))&((in @ X1059 @ (powerset @ X1059))&((~(subset @ X1060 @ X1061)|(subset @ (powerset @ X1060) @ (powerset @ X1061)))&((in @ (dsetconstr @ X1062 @ X1063) @ (powerset @ X1062))&((subset @ (dsetconstr @ X1064 @ X1065) @ X1064)&((~(in @ X1068 @ X1066)|(in @ X1068 @ (binunion @ X1066 @ X1067)))&((in @ X1070 @ (setadjoin @ X1069 @ (setadjoin @ X1070 @ emptyset)))&((~(in @ X1073 @ X1072)|(in @ X1073 @ (binunion @ X1071 @ X1072)))&(((((in @ X1076 @ X1075)|(X1077)|(in @ X1076 @ X1074)|~(in @ X1076 @ (binunion @ X1074 @ X1075)))&(~(X1077)|(X1077)|(in @ X1076 @ X1074)|~(in @ X1076 @ (binunion @ X1074 @ X1075))))&(((in @ X1076 @ X1075)|(X1077)|~(X1077)|~(in @ X1076 @ (binunion @ X1074 @ X1075)))&(~(X1077)|(X1077)|~(X1077)|~(in @ X1076 @ (binunion @ X1074 @ X1075)))))&((~(in @ X1080 @ (binunion @ X1078 @ X1079))|((in @ X1080 @ X1078)|(in @ X1080 @ X1079)))&((subset @ X1081 @ (binunion @ X1081 @ X1082))&((subset @ X1084 @ (binunion @ X1083 @ X1084))&((~(in @ X1087 @ X1085)|(~(in @ X1087 @ X1086)|(in @ X1087 @ (binintersect @ X1085 @ X1086))))&((~(subset @ X1090 @ X1088)|(~(subset @ X1090 @ X1089)|(subset @ X1090 @ (binintersect @ X1088 @ X1089))))&((~(in @ X1093 @ (binintersect @ X1091 @ X1092))|(in @ X1093 @ X1091))&((subset @ (binintersect @ X1094 @ X1095) @ X1094)&((~(subset @ X1096 @ X1097)|((binintersect @ X1096 @ X1097)=(X1096)))&((((binintersect @ X1098 @ X1099)!=(X1099))|(subset @ X1099 @ X1098))&((~(in @ X1102 @ (binintersect @ X1100 @ X1101))|(in @ X1102 @ X1101))&((((in @ (esk38_2 @ X1103 @ X1104) @ X1103)|((binintersect @ X1103 @ X1104)=(emptyset)))&((in @ (esk38_2 @ X1103 @ X1104) @ X1104)|((binintersect @ X1103 @ X1104)=(emptyset))))&((subset @ (binintersect @ X1106 @ X1107) @ X1107)&((~(subset @ X1109 @ X1108)|((binintersect @ X1108 @ X1109)=(X1109)))&((((binintersect @ X1110 @ X1111)!=(X1110))|(subset @ X1110 @ X1111))&(((binintersect @ X1112 @ (binunion @ X1113 @ X1114))=(binunion @ (binintersect @ X1112 @ X1113) @ (binintersect @ X1112 @ X1114)))&((~(in @ X1117 @ X1115)|((in @ X1117 @ X1116)|(in @ X1117 @ (setminus @ X1115 @ X1116))))&((~(in @ X1120 @ (setminus @ X1118 @ X1119))|(in @ X1120 @ X1118))&((~(in @ X1123 @ (setminus @ X1121 @ X1122))|~(in @ X1123 @ X1122))&((~(subset @ X1124 @ X1125)|((setminus @ X1124 @ X1125)=(emptyset)))&(((in @ X1128 @ (setminus @ X1126 @ X1127))|(~(in @ X1128 @ X1126)|(in @ X1128 @ X1127)))&(((in @ X1131 @ (setminus @ X1129 @ X1130))|((in @ X1131 @ X1130)|~(in @ X1131 @ X1129)))&(((in @ X1134 @ X1132)|~(in @ X1134 @ (setminus @ X1132 @ X1133)))&((~(in @ X1137 @ X1136)|~(in @ X1137 @ (setminus @ X1135 @ X1136)))&((subset @ (setminus @ X1138 @ X1139) @ X1138)&((((setminus @ X1140 @ X1141)!=(emptyset))|(subset @ X1140 @ X1141))&((((~(in @ X1144 @ X1142)|(X1145)|(in @ X1144 @ X1142)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(((in @ X1144 @ X1143)|(X1145)|(in @ X1144 @ X1142)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(~(X1145)|(X1145)|(in @ X1144 @ X1142)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))))&(((~(in @ X1144 @ X1142)|(X1145)|~(in @ X1144 @ X1143)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(((in @ X1144 @ X1143)|(X1145)|~(in @ X1144 @ X1143)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(~(X1145)|(X1145)|~(in @ X1144 @ X1143)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))))&((~(in @ X1144 @ X1142)|(X1145)|~(X1145)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(((in @ X1144 @ X1143)|(X1145)|~(X1145)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))&(~(X1145)|(X1145)|~(X1145)|~(in @ X1144 @ (symdiff @ X1142 @ X1143)))))))&((~(in @ X1148 @ X1146)|((in @ X1148 @ X1147)|(in @ X1148 @ (symdiff @ X1146 @ X1147))))&(((in @ X1151 @ X1149)|(~(in @ X1151 @ X1150)|(in @ X1151 @ (symdiff @ X1149 @ X1150))))&((~(in @ X1154 @ X1152)|(~(in @ X1154 @ X1153)|~(in @ X1154 @ (symdiff @ X1152 @ X1153))))&(((in @ X1157 @ X1155)|((in @ X1157 @ X1156)|~(in @ X1157 @ (symdiff @ X1155 @ X1156))))&((in @ X1159 @ (setadjoin @ X1158 @ (setadjoin @ X1159 @ emptyset)))&((in @ X1160 @ (setunion @ (setadjoin @ (setadjoin @ X1160 @ emptyset) @ (setadjoin @ (setadjoin @ X1160 @ (setadjoin @ X1161 @ emptyset)) @ emptyset))))&((in @ X1163 @ (setunion @ (setadjoin @ (setadjoin @ X1162 @ emptyset) @ (setadjoin @ (setadjoin @ X1162 @ (setadjoin @ X1163 @ emptyset)) @ emptyset))))&((iskpair @ (setadjoin @ (setadjoin @ X1164 @ emptyset) @ (setadjoin @ (setadjoin @ X1164 @ (setadjoin @ X1165 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X1166 @ X1167))&((~(in @ X1169 @ X1168)|(subset @ (setadjoin @ X1169 @ emptyset) @ X1168))&((~(in @ X1171 @ X1170)|(in @ (setadjoin @ X1171 @ emptyset) @ (powerset @ X1170)))&((~(in @ X1174 @ X1172)|(in @ (setadjoin @ X1174 @ emptyset) @ (powerset @ (binunion @ X1172 @ X1173))))&((~(in @ X1177 @ (setadjoin @ X1175 @ (setadjoin @ X1176 @ emptyset)))|(((X1177)=(X1175))|((X1177)=(X1176))))&((~(in @ X1180 @ X1178)|(~(in @ X1181 @ X1179)|(subset @ (setadjoin @ X1180 @ (setadjoin @ X1181 @ emptyset)) @ (binunion @ X1178 @ X1179))))&((~(in @ X1184 @ X1182)|(~(in @ X1185 @ X1183)|(in @ (setadjoin @ X1184 @ (setadjoin @ X1185 @ emptyset)) @ (powerset @ (binunion @ X1182 @ X1183)))))&((~(in @ X1188 @ X1186)|(~(in @ X1189 @ X1187)|(subset @ (setadjoin @ (setadjoin @ X1188 @ emptyset) @ (setadjoin @ (setadjoin @ X1188 @ (setadjoin @ X1189 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1186 @ X1187)))))&((~(in @ X1192 @ X1190)|(~(in @ X1193 @ X1191)|(in @ (setadjoin @ (setadjoin @ X1192 @ emptyset) @ (setadjoin @ (setadjoin @ X1192 @ (setadjoin @ X1193 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1190 @ X1191))))))&((~(in @ X1196 @ X1194)|(~(in @ X1197 @ X1195)|(in @ (kpair @ X1196 @ X1197) @ (powerset @ (powerset @ (binunion @ X1194 @ X1195))))))&((in @ esk41_0 @ esk39_0)&((in @ esk42_0 @ esk40_0)&~(in @ (kpair @ esk41_0 @ esk42_0) @ (cartprod @ esk39_0 @ esk40_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_170])])])])])])])). 109.87/17.34 thf(c_0_173, plain, ![X1202:$i, X1203:$i]:(((cartprod @ X1202 @ X1203)=(dsetconstr @ (powerset @ (powerset @ (binunion @ X1202 @ X1203))) @ (^[Z0/* 5 */:$i]:(?[X3:$i]:(((in @ X3 @ X1202)&?[X14:$i]:(((in @ X14 @ X1203)&((Z0)=(kpair @ X3 @ X14))))))))))), inference(variable_rename,[status(thm)],[c_0_171])). 109.87/17.34 thf(c_0_174, plain, ![X1228:$i, X2:$i, X3:$i]:(((epred3_2 @ X3 @ X2 @ X1228)<=>?[X1226:$i]:(((in @ X1226 @ X2)&?[X1227:$i]:(((in @ X1227 @ X3)&((X1228)=(kpair @ X1226 @ X1227)))))))), introduced(definition)). 109.87/17.34 thf(c_0_175, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ X2 @ (dsetconstr @ X3 @ X1))|~((X1 @ X2))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_172])). 109.87/17.34 thf(c_0_176, plain, ![X3:$i, X2:$i]:(((cartprod @ X2 @ X3)=(dsetconstr @ (powerset @ (powerset @ (binunion @ X2 @ X3))) @ (epred3_2 @ X3 @ X2)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_173]), c_0_174])). 109.87/17.34 thf(c_0_177, negated_conjecture, ~((in @ (kpair @ esk41_0 @ esk42_0) @ (cartprod @ esk39_0 @ esk40_0))), inference(split_conjunct,[status(thm)],[c_0_172])). 109.87/17.34 thf(c_0_178, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X2 @ (cartprod @ X3 @ X4))|~((in @ X2 @ (powerset @ (powerset @ (binunion @ X3 @ X4)))))|~((epred3_2 @ X4 @ X3 @ X2)))), inference(spm,[status(thm)],[c_0_175, c_0_176])). 109.87/17.34 thf(c_0_179, plain, ![X1230:$i, X1231:$i, X1232:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i]:(((((in @ (esk48_3 @ X1230 @ X1231 @ X1232) @ X1231)|~(epred3_2 @ X1232 @ X1231 @ X1230))&(((in @ (esk49_3 @ X1230 @ X1231 @ X1232) @ X1232)|~(epred3_2 @ X1232 @ X1231 @ X1230))&(((X1230)=(kpair @ (esk48_3 @ X1230 @ X1231 @ X1232) @ (esk49_3 @ X1230 @ X1231 @ X1232)))|~(epred3_2 @ X1232 @ X1231 @ X1230))))&(~(in @ X1238 @ X1236)|(~(in @ X1239 @ X1237)|((X1235)!=(kpair @ X1238 @ X1239)))|(epred3_2 @ X1237 @ X1236 @ X1235)))), 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)],[])])])])])])])). 109.87/17.34 thf(c_0_180, negated_conjecture, (~((in @ (kpair @ esk41_0 @ esk42_0) @ (powerset @ (powerset @ (binunion @ esk39_0 @ esk40_0)))))|~((epred3_2 @ esk40_0 @ esk39_0 @ (kpair @ esk41_0 @ esk42_0)))), inference(spm,[status(thm)],[c_0_177, c_0_178])). 109.87/17.34 thf(c_0_181, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i]:(((in @ (kpair @ X2 @ X4) @ (powerset @ (powerset @ (binunion @ X3 @ X5))))|~((in @ X2 @ X3))|~((in @ X4 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_172])). 109.87/17.34 thf(c_0_182, negated_conjecture, (in @ esk42_0 @ esk40_0), inference(split_conjunct,[status(thm)],[c_0_172])). 109.87/17.34 thf(c_0_183, negated_conjecture, (in @ esk41_0 @ esk39_0), inference(split_conjunct,[status(thm)],[c_0_172])). 109.87/17.34 thf(c_0_184, plain, ![X3:$i, X2:$i, X7:$i, X5:$i, X4:$i]:(((epred3_2 @ X5 @ X3 @ X7)|~((in @ X2 @ X3))|~((in @ X4 @ X5))|((X7)!=(kpair @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_179])). 109.87/17.34 thf(c_0_185, negated_conjecture, ~((epred3_2 @ esk40_0 @ esk39_0 @ (kpair @ esk41_0 @ esk42_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180, c_0_181]), c_0_182]), c_0_183])])). 109.87/17.34 thf(c_0_186, plain, ![X2:$i, X5:$i, X4:$i, X3:$i]:(((epred3_2 @ X2 @ X3 @ (kpair @ X4 @ X5))|~((in @ X5 @ X2))|~((in @ X4 @ X3)))), inference(er,[status(thm)],[c_0_184])). 109.87/17.34 thf(c_0_187, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185, c_0_186]), c_0_182]), c_0_183])]), ['proof']). 109.87/17.34 # SZS output end CNFRefutation 109.87/17.34 # Parsed axioms : 321 109.87/17.34 # Removed by relevancy pruning/SinE : 173 109.87/17.34 # Initial clauses : 234 109.87/17.34 # Removed in clause preprocessing : 25 109.87/17.34 # Initial clauses in saturation : 209 109.87/17.34 # Processed clauses : 4727 109.87/17.34 # ...of these trivial : 118 109.87/17.34 # ...subsumed : 1554 109.87/17.34 # ...remaining for further processing : 3055 109.87/17.34 # Other redundant clauses eliminated : 90 109.87/17.34 # Clauses deleted for lack of memory : 0 109.87/17.34 # Backward-subsumed : 439 109.87/17.34 # Backward-rewritten : 47 109.87/17.34 # Generated clauses : 497325 109.87/17.34 # ...of the previous two non-redundant : 492917 109.87/17.34 # ...aggressively subsumed : 0 109.87/17.34 # Contextual simplify-reflections : 11 109.87/17.34 # Paramodulations : 497114 109.87/17.34 # Factorizations : 110 109.87/17.34 # NegExts : 0 109.87/17.34 # Equation resolutions : 90 109.87/17.34 # Disequality decompositions : 0 109.87/17.34 # Total rewrite steps : 8994 109.87/17.34 # ...of those cached : 8018 109.87/17.34 # Propositional unsat checks : 0 109.87/17.34 # Propositional check models : 0 109.87/17.34 # Propositional check unsatisfiable : 0 109.87/17.34 # Propositional clauses : 0 109.87/17.34 # Propositional clauses after purity: 0 109.87/17.34 # Propositional unsat core size : 0 109.87/17.34 # Propositional preprocessing time : 0.000 109.87/17.34 # Propositional encoding time : 0.000 109.87/17.34 # Propositional solver time : 0.000 109.87/17.34 # Success case prop preproc time : 0.000 109.87/17.34 # Success case prop encoding time : 0.000 109.87/17.34 # Success case prop solver time : 0.000 109.87/17.34 # Current number of processed clauses : 2373 109.87/17.34 # Positive orientable unit clauses : 171 109.87/17.34 # Positive unorientable unit clauses: 0 109.87/17.34 # Negative unit clauses : 125 109.87/17.34 # Non-unit-clauses : 2077 109.87/17.34 # Current number of unprocessed clauses: 486962 109.87/17.34 # ...number of literals in the above : 2114786 109.87/17.34 # Current number of archived formulas : 0 109.87/17.34 # Current number of archived clauses : 670 109.87/17.34 # Clause-clause subsumption calls (NU) : 600208 109.87/17.34 # Rec. Clause-clause subsumption calls : 304320 109.87/17.34 # Non-unit clause-clause subsumptions : 711 109.87/17.34 # Unit Clause-clause subsumption calls : 21333 109.87/17.34 # Rewrite failures with RHS unbound : 0 109.87/17.34 # BW rewrite match attempts : 270 109.87/17.34 # BW rewrite match successes : 44 109.87/17.34 # Condensation attempts : 4727 109.87/17.34 # Condensation successes : 26 109.87/17.34 # Termbank termtop insertions : 9984119 109.87/17.34 # Search garbage collected termcells : 12954 109.87/17.34 109.87/17.34 # ------------------------------------------------- 109.87/17.34 # User time : 15.198 s 109.87/17.34 # System time : 0.457 s 109.87/17.34 # Total time : 15.655 s 109.87/17.34 # Maximum resident set size: 5028 pages 109.87/17.34 109.87/17.34 # ------------------------------------------------- 109.87/17.34 # User time : 15.207 s 109.87/17.34 # System time : 0.461 s 109.87/17.34 # Total time : 15.668 s 109.87/17.34 # Maximum resident set size: 2120 pages 109.87/17.34 % E---3.1 exiting 109.87/17.34 % E exiting 109.87/17.34 EOF