0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.16 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.zCNujRh3BD true 0.16/0.37 % Computer : n014.cluster.edu 0.16/0.37 % Model : x86_64 x86_64 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.37 % Memory : 8042.1875MB 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.37 % CPULimit : 1440 0.16/0.37 % WCLimit : 180 0.16/0.37 % DateTime : Thu Jul 4 11:20:54 EDT 2024 0.16/0.37 % CPUTime : 0.16/0.37 % Running portfolio for 1440 s 0.16/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.16/0.37 % Number of cores: 8 0.16/0.38 % Python version: Python 3.6.8 0.16/0.38 % Running in HO mode 0.56/0.68 % Total configuration time : 828 0.56/0.68 % Estimated wc time : 1656 0.56/0.68 % Estimated cpu time (8 cpus) : 207.0 0.58/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.58/0.75 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.58/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.58/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.58/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.58/0.80 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.58/0.81 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 97.42/12.98 % Solved by lams/40_c_ic.sh. 97.42/12.98 % done 5360 iterations in 12.140s 97.42/12.98 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 97.42/12.98 % SZS output start Refutation 97.42/12.98 thf(setadjoinAx_type, type, setadjoinAx: $o). 97.42/12.98 thf(notdexE_type, type, notdexE: $o). 97.42/12.98 thf(setukpairinjL2_type, type, setukpairinjL2: $o). 97.42/12.98 thf(setunionAx_type, type, setunionAx: $o). 97.42/12.98 thf(setminusELneg_type, type, setminusELneg: $o). 97.42/12.98 thf(cartprodsndin_type, type, cartprodsndin: $o). 97.42/12.98 thf(ex1E1_type, type, ex1E1: $o). 97.42/12.98 thf(powersetE_type, type, powersetE: $o). 97.42/12.98 thf(omegaSAx_type, type, omegaSAx: $o). 97.42/12.98 thf(exuI1_type, type, exuI1: $o). 97.42/12.98 thf(exuI2_type, type, exuI2: $o). 97.42/12.98 thf(notequalI2_type, type, notequalI2: $o). 97.42/12.98 thf(setukpairinjL_type, type, setukpairinjL: $o). 97.42/12.98 thf(kpairiskpair_type, type, kpairiskpair: $o). 97.42/12.98 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o). 97.42/12.98 thf(upairsubunion_type, type, upairsubunion: $o). 97.42/12.98 thf(funcGraphProp3_type, type, funcGraphProp3: $o). 97.42/12.98 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o). 97.42/12.98 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o). 97.42/12.98 thf(powerset__Cong_type, type, powerset__Cong: $o). 97.42/12.98 thf(setminusILneg_type, type, setminusILneg: $o). 97.42/12.98 thf(wellorderingAx_type, type, wellorderingAx: $o). 97.42/12.98 thf(ksndpairEq_type, type, ksndpairEq: $o). 97.42/12.98 thf(funcGraphProp2_type, type, funcGraphProp2: $o). 97.42/12.98 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 97.42/12.98 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 97.42/12.98 thf(iftrue_type, type, iftrue: $o). 97.42/12.98 thf(upairinpowunion_type, type, upairinpowunion: $o). 97.42/12.98 thf(ifSingleton_type, type, ifSingleton: $o). 97.42/12.98 thf(setoftrueEq_type, type, setoftrueEq: $o). 97.42/12.98 thf(sk__132_type, type, sk__132: $i). 97.42/12.98 thf(funcImageSingleton_type, type, funcImageSingleton: $o). 97.42/12.98 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o). 97.42/12.98 thf(lamProp_type, type, lamProp: $o). 97.42/12.98 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o). 97.42/12.98 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 97.42/12.98 thf(dpsetconstrER_type, type, dpsetconstrER: $o). 97.42/12.98 thf(sepInPowerset_type, type, sepInPowerset: $o). 97.42/12.98 thf(setukpairIR_type, type, setukpairIR: $o). 97.42/12.98 thf(setukpairinjR1_type, type, setukpairinjR1: $o). 97.42/12.98 thf(lam2p_type, type, lam2p: $o). 97.42/12.98 thf(binunionE_type, type, binunionE: $o). 97.42/12.98 thf(setext_type, type, setext: $o). 97.42/12.98 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 97.42/12.98 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o). 97.42/12.98 thf(descr__Cong_type, type, descr__Cong: $o). 97.42/12.98 thf(kfstsingleton_type, type, kfstsingleton: $o). 97.42/12.98 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o). 97.42/12.98 thf(eqbreln_type, type, eqbreln: $o). 97.42/12.98 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 97.42/12.98 thf(in_type, type, in: $i > $i > $o). 97.42/12.98 thf(binunionT_lem_type, type, binunionT_lem: $o). 97.42/12.98 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 97.42/12.98 thf(complementT_lem_type, type, complementT_lem: $o). 97.42/12.98 thf(kpairsurjEq_type, type, kpairsurjEq: $o). 97.42/12.98 thf(setadjoinIR_type, type, setadjoinIR: $o). 97.42/12.98 thf(beta1_type, type, beta1: $o). 97.42/12.98 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 97.42/12.98 thf(powersetTE1_type, type, powersetTE1: $o). 97.42/12.98 thf(symdiffI2_type, type, symdiffI2: $o). 97.42/12.98 thf(iftrueProp2_type, type, iftrueProp2: $o). 97.42/12.98 thf(upairset2IR_type, type, upairset2IR: $o). 97.42/12.98 thf(iffalseProp2_type, type, iffalseProp2: $o). 97.42/12.98 thf(subsetE_type, type, subsetE: $o). 97.42/12.98 thf(sk__133_type, type, sk__133: $i). 97.42/12.98 thf(prop2set2propI_type, type, prop2set2propI: $o). 97.42/12.98 thf(sk__131_type, type, sk__131: $i). 97.42/12.98 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 97.42/12.98 thf(setbeta_type, type, setbeta: $o). 97.42/12.98 thf(eqinunit_type, type, eqinunit: $o). 97.42/12.98 thf(upairsetIL_type, type, upairsetIL: $o). 97.42/12.98 thf(powersetI1_type, type, powersetI1: $o). 97.42/12.98 thf(kfstpairEq_type, type, kfstpairEq: $o). 97.42/12.98 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 97.42/12.98 thf(setminusIRneg_type, type, setminusIRneg: $o). 97.42/12.98 thf(ap2apEq1_type, type, ap2apEq1: $o). 97.42/12.98 thf(powersetAx_type, type, powersetAx: $o). 97.42/12.98 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 97.42/12.98 thf(singletoninpowunion_type, type, singletoninpowunion: $o). 97.42/12.98 thf(powersetI_type, type, powersetI: $o). 97.42/12.98 thf(cartprodmempair_type, type, cartprodmempair: $o). 97.42/12.98 thf(upairsetIR_type, type, upairsetIR: $o). 97.42/12.98 thf(lamp_type, type, lamp: $o). 97.42/12.98 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o). 97.42/12.98 thf(inCongP_type, type, inCongP: $o). 97.42/12.98 thf(setadjoinSub_type, type, setadjoinSub: $o). 97.42/12.98 thf(exuE3e_type, type, exuE3e: $o). 97.42/12.98 thf(emptysetE_type, type, emptysetE: $o). 97.42/12.98 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 97.42/12.98 thf(setunionI_type, type, setunionI: $o). 97.42/12.98 thf(setunion__Cong_type, type, setunion__Cong: $o). 97.42/12.98 thf(prop2setI_type, type, prop2setI: $o). 97.42/12.98 thf(singletonsuniq_type, type, singletonsuniq: $o). 97.42/12.98 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 97.42/12.98 thf(setminusER_type, type, setminusER: $o). 97.42/12.98 thf(exuE2_type, type, exuE2: $o). 97.42/12.98 thf(emptyset_type, type, emptyset: $i). 97.42/12.98 thf(setukpairinjR11_type, type, setukpairinjR11: $o). 97.42/12.98 thf(ex1I_type, type, ex1I: $o). 97.42/12.98 thf(ex1E2_type, type, ex1E2: $o). 97.42/12.98 thf(setminus_type, type, setminus: $i > $i > $i). 97.42/12.98 thf(setukpairinjL1_type, type, setukpairinjL1: $o). 97.42/12.98 thf(powersetsubset_type, type, powersetsubset: $o). 97.42/12.98 thf(subPowSU_type, type, subPowSU: $o). 97.42/12.98 thf(notequalI1_type, type, notequalI1: $o). 97.42/12.98 thf(contrasubsetT_type, type, contrasubsetT: $o). 97.42/12.98 thf(notinemptyset_type, type, notinemptyset: $o). 97.42/12.98 thf(lam2lamEq_type, type, lam2lamEq: $o). 97.42/12.98 thf(nonemptyI1_type, type, nonemptyI1: $o). 97.42/12.98 thf(subsetTrans_type, type, subsetTrans: $o). 97.42/12.98 thf(kpairp_type, type, kpairp: $o). 97.42/12.98 thf(setukpairinjR12_type, type, setukpairinjR12: $o). 97.42/12.98 thf(setminusI_type, type, setminusI: $o). 97.42/12.98 thf(binunionIL_type, type, binunionIL: $o). 97.42/12.98 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o). 97.42/12.98 thf(setunionsingleton_type, type, setunionsingleton: $o). 97.42/12.98 thf(subsetE2_type, type, subsetE2: $o). 97.42/12.98 thf(singletonsswitch_type, type, singletonsswitch: $o). 97.42/12.98 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o). 97.42/12.98 thf(beta2_type, type, beta2: $o). 97.42/12.98 thf(dpsetconstrI_type, type, dpsetconstrI: $o). 97.42/12.98 thf(setextsub_type, type, setextsub: $o). 97.42/12.98 thf(binunionLsub_type, type, binunionLsub: $o). 97.42/12.98 thf(setunionsingleton1_type, type, setunionsingleton1: $o). 97.42/12.98 thf(iftrueorfalse_type, type, iftrueorfalse: $o). 97.42/12.98 thf(emptysetsubset_type, type, emptysetsubset: $o). 97.42/12.98 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 97.42/12.98 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o). 97.42/12.98 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o). 97.42/12.98 thf(setunionE_type, type, setunionE: $o). 97.42/12.98 thf(ksndsingleton_type, type, ksndsingleton: $o). 97.42/12.98 thf(setminusSubset1_type, type, setminusSubset1: $o). 97.42/12.98 thf(powersetT_lem_type, type, powersetT_lem: $o). 97.42/12.98 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 97.42/12.98 thf(binunionIR_type, type, binunionIR: $o). 97.42/12.98 thf(theeq_type, type, theeq: $o). 97.42/12.98 thf(setadjoinE_type, type, setadjoinE: $o). 97.42/12.98 thf(infuncsetfunc_type, type, infuncsetfunc: $o). 97.42/12.98 thf(sk__127_type, type, sk__127: $i > $i > $i). 97.42/12.98 thf(ap2apEq2_type, type, ap2apEq2: $o). 97.42/12.98 thf(ap2p_type, type, ap2p: $o). 97.42/12.98 thf(setadjoinIL_type, type, setadjoinIL: $o). 97.42/12.98 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o). 97.42/12.98 thf(exuE1_type, type, exuE1: $o). 97.42/12.98 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o). 97.42/12.98 thf(binintersectRsub_type, type, binintersectRsub: $o). 97.42/12.98 thf(setminusLsub_type, type, setminusLsub: $o). 97.42/12.98 thf(funcextLem_type, type, funcextLem: $o). 97.42/12.98 thf(setukpairinjR_type, type, setukpairinjR: $o). 97.42/12.98 thf(notinsingleton_type, type, notinsingleton: $o). 97.42/12.98 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 97.42/12.98 thf(exuEu_type, type, exuEu: $o). 97.42/12.98 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 97.42/12.98 thf(upairsetE_type, type, upairsetE: $o). 97.42/12.98 thf(omega0Ax_type, type, omega0Ax: $o). 97.42/12.98 thf(subsetTI_type, type, subsetTI: $o). 97.42/12.98 thf(notsubsetI_type, type, notsubsetI: $o). 97.42/12.98 thf(iffalseProp1_type, type, iffalseProp1: $o). 97.42/12.98 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 97.42/12.98 thf(setextAx_type, type, setextAx: $o). 97.42/12.98 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o). 97.42/12.98 thf(powersetE1_type, type, powersetE1: $o). 97.42/12.98 thf(bs114d_type, type, bs114d: $o). 97.42/12.98 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 97.42/12.98 thf(ifp_type, type, ifp: $o). 97.42/12.98 thf(powersetTI1_type, type, powersetTI1: $o). 97.42/12.98 thf(binintersectLsub_type, type, binintersectLsub: $o). 97.42/12.98 thf(subsetI1_type, type, subsetI1: $o). 97.42/12.98 thf(symdiffE_type, type, symdiffE: $o). 97.42/12.98 thf(descrp_type, type, descrp: $o). 97.42/12.98 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 97.42/12.98 thf(foundationAx_type, type, foundationAx: $o). 97.42/12.98 thf(emptysetAx_type, type, emptysetAx: $o). 97.42/12.98 thf(emptyI_type, type, emptyI: $o). 97.42/12.98 thf(setadjoinOr_type, type, setadjoinOr: $o). 97.42/12.98 thf(eta2_type, type, eta2: $o). 97.42/12.98 thf(binintersectEL_type, type, binintersectEL: $o). 97.42/12.98 thf(emptyE1_type, type, emptyE1: $o). 97.42/12.98 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 97.42/12.98 thf(complementTI1_type, type, complementTI1: $o). 97.42/12.98 thf(vacuousDall_type, type, vacuousDall: $o). 97.42/12.98 thf(dsetconstrER_type, type, dsetconstrER: $o). 97.42/12.98 thf(binintersectI_type, type, binintersectI: $o). 97.42/12.98 thf(funcext_type, type, funcext: $o). 97.42/12.98 thf(funcGraphProp4_type, type, funcGraphProp4: $o). 97.42/12.98 thf(cartprodpairin_type, type, cartprodpairin: $o). 97.42/12.98 thf(cartprodmempair1_type, type, cartprodmempair1: $o). 97.42/12.98 thf(brelnall2_type, type, brelnall2: $o). 97.42/12.98 thf(setextT_type, type, setextT: $o). 97.42/12.98 thf(ex1I2_type, type, ex1I2: $o). 97.42/12.98 thf(symdiffI1_type, type, symdiffI1: $o). 97.42/12.98 thf(setukpairinjR2_type, type, setukpairinjR2: $o). 97.42/12.98 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o). 97.42/12.98 thf(theprop_type, type, theprop: $o). 97.42/12.98 thf(subsetI2_type, type, subsetI2: $o). 97.42/12.98 thf(setminusT_lem_type, type, setminusT_lem: $o). 97.42/12.98 thf(symdiffIneg1_type, type, symdiffIneg1: $o). 97.42/12.98 thf(setminusERneg_type, type, setminusERneg: $o). 97.42/12.98 thf(symdiffIneg2_type, type, symdiffIneg2: $o). 97.42/12.98 thf(omega__Cong_type, type, omega__Cong: $o). 97.42/12.98 thf(subsetRefl_type, type, subsetRefl: $o). 97.42/12.98 thf(uniqinunit_type, type, uniqinunit: $o). 97.42/12.98 thf(setminusSubset2_type, type, setminusSubset2: $o). 97.42/12.98 thf(prop2setE_type, type, prop2setE: $o). 97.42/12.98 thf(binunionEcases_type, type, binunionEcases: $o). 97.42/12.98 thf(funcinfuncset_type, type, funcinfuncset: $o). 97.42/12.98 thf(complementTE1_type, type, complementTE1: $o). 97.42/12.98 thf(nonemptyI_type, type, nonemptyI: $o). 97.42/12.98 thf(app_type, type, app: $o). 97.42/12.98 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 97.42/12.98 thf(exuE3u_type, type, exuE3u: $o). 97.42/12.98 thf(eta1_type, type, eta1: $o). 97.42/12.98 thf(setminusEL_type, type, setminusEL: $o). 97.42/12.98 thf(cartprodfstin_type, type, cartprodfstin: $o). 97.42/12.98 thf(setunionsingleton2_type, type, setunionsingleton2: $o). 97.42/12.98 thf(sepSubset_type, type, sepSubset: $o). 97.42/12.98 thf(upairset2E_type, type, upairset2E: $o). 97.42/12.98 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 97.42/12.98 thf(exuI3_type, type, exuI3: $o). 97.42/12.98 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o). 97.42/12.98 thf(apProp_type, type, apProp: $o). 97.42/12.98 thf(notdallE_type, type, notdallE: $o). 97.42/12.98 thf(iftrueProp1_type, type, iftrueProp1: $o). 97.42/12.98 thf(binintersectER_type, type, binintersectER: $o). 97.42/12.98 thf(brelnall1_type, type, brelnall1: $o). 97.42/12.98 thf(powerset_type, type, powerset: $i > $i). 97.42/12.98 thf(dsetconstrI_type, type, dsetconstrI: $o). 97.42/12.98 thf(funcGraphProp1_type, type, funcGraphProp1: $o). 97.42/12.98 thf(binintersectT_lem_type, type, binintersectT_lem: $o). 97.42/12.98 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 97.42/12.98 thf(exu__Cong_type, type, exu__Cong: $o). 97.42/12.98 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 97.42/12.98 thf(secondinupair_type, type, secondinupair: $o). 97.42/12.98 thf(singletonprop_type, type, singletonprop: $o). 97.42/12.98 thf(singletonsubset_type, type, singletonsubset: $o). 97.42/12.98 thf(contrasubsetT1_type, type, contrasubsetT1: $o). 97.42/12.98 thf(singletoninpowerset_type, type, singletoninpowerset: $o). 97.42/12.98 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 97.42/12.98 thf(replAx_type, type, replAx: $o). 97.42/12.98 thf(upairequniteq_type, type, upairequniteq: $o). 97.42/12.98 thf(nonemptyE1_type, type, nonemptyE1: $o). 97.42/12.98 thf(omegaIndAx_type, type, omegaIndAx: $o). 97.42/12.98 thf(setukpairIL_type, type, setukpairIL: $o). 97.42/12.98 thf(setunionE2_type, type, setunionE2: $o). 97.42/12.98 thf(inPowerset_type, type, inPowerset: $o). 97.42/12.98 thf(iffalse_type, type, iffalse: $o). 97.42/12.98 thf(funcext2_type, type, funcext2: $o). 97.42/12.98 thf(subset_type, type, subset: $i > $i > $o). 97.42/12.98 thf(subbreln_type, type, subbreln: $o). 97.42/12.98 thf(in__Cong_type, type, in__Cong: $o). 97.42/12.98 thf(binunionRsub_type, type, binunionRsub: $o). 97.42/12.98 thf(subset2powerset_type, type, subset2powerset: $o). 97.42/12.98 thf(contrasubsetT1, axiom, contrasubsetT1 = 97.42/12.98 (![A:$i,X:$i]: 97.42/12.98 ( ( in @ X @ ( powerset @ A ) ) => 97.42/12.98 ( ![Y:$i]: 97.42/12.98 ( ( in @ Y @ ( powerset @ A ) ) => 97.42/12.98 ( ![Xx:$i]: 97.42/12.98 ( ( in @ Xx @ A ) => 97.42/12.98 ( ( subset @ X @ Y ) => 97.42/12.98 ( ( ~( in @ Xx @ Y ) ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))). 97.42/12.98 thf('0', plain, 97.42/12.98 (( contrasubsetT1 ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) => 97.42/12.98 ( ![X8:$i]: 97.42/12.98 ( ( in @ X8 @ ( powerset @ X4 ) ) => 97.42/12.98 ( ![X10:$i]: 97.42/12.98 ( ( in @ X10 @ X4 ) => 97.42/12.98 ( ( subset @ X6 @ X8 ) => 97.42/12.98 ( ( ~( in @ X10 @ X8 ) ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(contrasubsetT, axiom, contrasubsetT = 97.42/12.98 (![A:$i,X:$i]: 97.42/12.98 ( ( in @ X @ ( powerset @ A ) ) => 97.42/12.98 ( ![Y:$i]: 97.42/12.98 ( ( in @ Y @ ( powerset @ A ) ) => 97.42/12.98 ( ![Xx:$i]: 97.42/12.98 ( ( in @ Xx @ A ) => 97.42/12.98 ( ( subset @ X @ ( setminus @ A @ Y ) ) => 97.42/12.98 ( ( in @ Xx @ Y ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))). 97.42/12.98 thf('1', plain, 97.42/12.98 (( contrasubsetT ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) => 97.42/12.98 ( ![X8:$i]: 97.42/12.98 ( ( in @ X8 @ ( powerset @ X4 ) ) => 97.42/12.98 ( ![X10:$i]: 97.42/12.98 ( ( in @ X10 @ X4 ) => 97.42/12.98 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) => 97.42/12.98 ( ( in @ X10 @ X8 ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(complementTE1, axiom, complementTE1 = 97.42/12.98 (![A:$i,X:$i]: 97.42/12.98 ( ( in @ X @ ( powerset @ A ) ) => 97.42/12.98 ( ![Xx:$i]: 97.42/12.98 ( ( in @ Xx @ A ) => 97.42/12.98 ( ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) => ( in @ Xx @ X ) ) ) ) ))). 97.42/12.98 thf('2', plain, 97.42/12.98 (( complementTE1 ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) => 97.42/12.98 ( ![X8:$i]: 97.42/12.98 ( ( in @ X8 @ X4 ) => 97.42/12.98 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) => ( in @ X8 @ X6 ) ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(complementTI1, axiom, complementTI1 = 97.42/12.98 (![A:$i,X:$i]: 97.42/12.98 ( ( in @ X @ ( powerset @ A ) ) => 97.42/12.98 ( ![Xx:$i]: 97.42/12.98 ( ( in @ Xx @ A ) => 97.42/12.98 ( ( in @ Xx @ X ) => ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ))). 97.42/12.98 thf('3', plain, 97.42/12.98 (( complementTI1 ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) => 97.42/12.98 ( ![X8:$i]: 97.42/12.98 ( ( in @ X8 @ X4 ) => 97.42/12.98 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(powersetTE1, axiom, powersetTE1 = 97.42/12.98 (![A:$i,X:$i]: 97.42/12.98 ( ( in @ X @ ( powerset @ A ) ) => 97.42/12.98 ( ![Y:$i]: 97.42/12.98 ( ( in @ Y @ ( powerset @ A ) ) => 97.42/12.98 ( ![Xx:$i]: 97.42/12.98 ( ( in @ Xx @ A ) => 97.42/12.98 ( ( in @ X @ ( powerset @ Y ) ) => 97.42/12.98 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))). 97.42/12.98 thf('4', plain, 97.42/12.98 (( powersetTE1 ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) => 97.42/12.98 ( ![X8:$i]: 97.42/12.98 ( ( in @ X8 @ ( powerset @ X4 ) ) => 97.42/12.98 ( ![X10:$i]: 97.42/12.98 ( ( in @ X10 @ X4 ) => 97.42/12.98 ( ( in @ X6 @ ( powerset @ X8 ) ) => 97.42/12.98 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(powersetTI1, axiom, powersetTI1 = 97.42/12.98 (![A:$i,X:$i]: 97.42/12.98 ( ( in @ X @ ( powerset @ A ) ) => 97.42/12.98 ( ![Y:$i]: 97.42/12.98 ( ( in @ Y @ ( powerset @ A ) ) => 97.42/12.98 ( ( ![Xx:$i]: 97.42/12.98 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) => 97.42/12.98 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))). 97.42/12.98 thf('5', plain, 97.42/12.98 (( powersetTI1 ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) => 97.42/12.98 ( ![X8:$i]: 97.42/12.98 ( ( in @ X8 @ ( powerset @ X4 ) ) => 97.42/12.98 ( ( ![X10:$i]: 97.42/12.98 ( ( in @ X10 @ X4 ) => 97.42/12.98 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) => 97.42/12.98 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(subsetTI, axiom, subsetTI = 97.42/12.98 (![A:$i,X:$i]: 97.42/12.98 ( ( in @ X @ ( powerset @ A ) ) => 97.42/12.98 ( ![Y:$i]: 97.42/12.98 ( ( in @ Y @ ( powerset @ A ) ) => 97.42/12.98 ( ( ![Xx:$i]: 97.42/12.98 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) => 97.42/12.98 ( subset @ X @ Y ) ) ) ) ))). 97.42/12.98 thf('6', plain, 97.42/12.98 (( subsetTI ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) => 97.42/12.98 ( ![X8:$i]: 97.42/12.98 ( ( in @ X8 @ ( powerset @ X4 ) ) => 97.42/12.98 ( ( ![X10:$i]: 97.42/12.98 ( ( in @ X10 @ X4 ) => 97.42/12.98 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) => 97.42/12.98 ( subset @ X6 @ X8 ) ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(setextT, axiom, setextT = 97.42/12.98 (![A:$i,X:$i]: 97.42/12.98 ( ( in @ X @ ( powerset @ A ) ) => 97.42/12.98 ( ![Y:$i]: 97.42/12.98 ( ( in @ Y @ ( powerset @ A ) ) => 97.42/12.98 ( ( ![Xx:$i]: 97.42/12.98 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) => 97.42/12.98 ( ( ![Xx:$i]: 97.42/12.98 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) => 97.42/12.98 ( ( X ) = ( Y ) ) ) ) ) ) ))). 97.42/12.98 thf('7', plain, 97.42/12.98 (( setextT ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) => 97.42/12.98 ( ![X8:$i]: 97.42/12.98 ( ( in @ X8 @ ( powerset @ X4 ) ) => 97.42/12.98 ( ( ![X10:$i]: 97.42/12.98 ( ( in @ X10 @ X4 ) => 97.42/12.98 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) => 97.42/12.98 ( ( ![X12:$i]: 97.42/12.98 ( ( in @ X12 @ X4 ) => 97.42/12.98 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) => 97.42/12.98 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(complementT_lem, axiom, complementT_lem = 97.42/12.98 (![A:$i,X:$i]: 97.42/12.98 ( ( in @ X @ ( powerset @ A ) ) => 97.42/12.98 ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ))). 97.42/12.98 thf('8', plain, 97.42/12.98 (( complementT_lem ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) => 97.42/12.98 ( in @ ( setminus @ X4 @ X6 ) @ ( powerset @ X4 ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(setminusT_lem, axiom, setminusT_lem = 97.42/12.98 (![A:$i,X:$i]: 97.42/12.98 ( ( in @ X @ ( powerset @ A ) ) => 97.42/12.98 ( ![Y:$i]: 97.42/12.98 ( ( in @ Y @ ( powerset @ A ) ) => 97.42/12.98 ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ))). 97.42/12.98 thf('9', plain, 97.42/12.98 (( setminusT_lem ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) => 97.42/12.98 ( ![X8:$i]: 97.42/12.98 ( ( in @ X8 @ ( powerset @ X4 ) ) => 97.42/12.98 ( in @ ( setminus @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(powersetT_lem, axiom, powersetT_lem = 97.42/12.98 (![A:$i,X:$i]: 97.42/12.98 ( ( in @ X @ ( powerset @ A ) ) => 97.42/12.98 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))). 97.42/12.98 thf('10', plain, 97.42/12.98 (( powersetT_lem ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) => 97.42/12.98 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(singletoninpowerset, axiom, singletoninpowerset = 97.42/12.98 (![A:$i,Xx:$i]: 97.42/12.98 ( ( in @ Xx @ A ) => 97.42/12.98 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))). 97.42/12.98 thf('11', plain, 97.42/12.98 (( singletoninpowerset ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ X4 ) => 97.42/12.98 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(singletonsubset, axiom, singletonsubset = 97.42/12.98 (![A:$i,Xx:$i]: 97.42/12.98 ( ( in @ Xx @ A ) => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ))). 97.42/12.98 thf('12', plain, 97.42/12.98 (( singletonsubset ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ X4 ) => ( subset @ ( setadjoin @ X6 @ emptyset ) @ X4 ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(setminusSubset1, axiom, setminusSubset1 = 97.42/12.98 (![A:$i,B:$i]: 97.42/12.98 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))). 97.42/12.98 thf('13', plain, 97.42/12.98 (( setminusSubset1 ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(setminusLsub, axiom, setminusLsub = 97.42/12.98 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))). 97.42/12.98 thf('14', plain, 97.42/12.98 (( setminusLsub ) = 97.42/12.98 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(setminusIRneg, axiom, setminusIRneg = 97.42/12.98 (![A:$i,B:$i,Xx:$i]: 97.42/12.98 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))). 97.42/12.98 thf('15', plain, 97.42/12.98 (( setminusIRneg ) = 97.42/12.98 ( ![X4:$i,X6:$i,X8:$i]: 97.42/12.98 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(setminusILneg, axiom, setminusILneg = 97.42/12.98 (![A:$i,B:$i,Xx:$i]: 97.42/12.98 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))). 97.42/12.98 thf('16', plain, 97.42/12.98 (( setminusILneg ) = 97.42/12.98 ( ![X4:$i,X6:$i,X8:$i]: 97.42/12.98 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(setminusELneg, axiom, setminusELneg = 97.42/12.98 (![A:$i,B:$i,Xx:$i]: 97.42/12.98 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) => 97.42/12.98 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))). 97.42/12.98 thf('17', plain, 97.42/12.98 (( setminusELneg ) = 97.42/12.98 ( ![X4:$i,X6:$i,X8:$i]: 97.42/12.98 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) => 97.42/12.98 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(setminusERneg, axiom, setminusERneg = 97.42/12.98 (![A:$i,B:$i,Xx:$i]: 97.42/12.98 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) => 97.42/12.98 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))). 97.42/12.98 thf('18', plain, 97.42/12.98 (( setminusERneg ) = 97.42/12.98 ( ![X4:$i,X6:$i,X8:$i]: 97.42/12.98 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) => 97.42/12.98 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(setminusSubset2, axiom, setminusSubset2 = 97.42/12.98 (![A:$i,B:$i]: 97.42/12.98 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))). 97.42/12.98 thf('19', plain, 97.42/12.98 (( setminusSubset2 ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(setminusER, axiom, setminusER = 97.42/12.98 (![A:$i,B:$i,Xx:$i]: 97.42/12.98 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))). 97.42/12.98 thf('20', plain, 97.42/12.98 (( setminusER ) = 97.42/12.98 ( ![X4:$i,X6:$i,X8:$i]: 97.42/12.98 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(setminusEL, axiom, setminusEL = 97.42/12.98 (![A:$i,B:$i,Xx:$i]: 97.42/12.98 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))). 97.42/12.98 thf('21', plain, 97.42/12.98 (( setminusEL ) = 97.42/12.98 ( ![X4:$i,X6:$i,X8:$i]: 97.42/12.98 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(setminusI, axiom, setminusI = 97.42/12.98 (![A:$i,B:$i,Xx:$i]: 97.42/12.98 ( ( in @ Xx @ A ) => 97.42/12.98 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))). 97.42/12.98 thf('22', plain, 97.42/12.98 (( setminusI ) = 97.42/12.98 ( ![X4:$i,X6:$i,X8:$i]: 97.42/12.98 ( ( in @ X8 @ X4 ) => 97.42/12.98 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(powersetsubset, axiom, powersetsubset = 97.42/12.98 (![A:$i,B:$i]: 97.42/12.98 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))). 97.42/12.98 thf('23', plain, 97.42/12.98 (( powersetsubset ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( subset @ X4 @ X6 ) => 97.42/12.98 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))). 97.42/12.98 thf('24', plain, 97.42/12.98 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(powersetE1, axiom, powersetE1 = 97.42/12.98 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))). 97.42/12.98 thf('25', plain, 97.42/12.98 (( powersetE1 ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(powersetI1, axiom, powersetI1 = 97.42/12.98 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))). 97.42/12.98 thf('26', plain, 97.42/12.98 (( powersetI1 ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq = 97.42/12.98 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))). 97.42/12.98 thf('27', plain, 97.42/12.98 (( subsetemptysetimpeq ) = 97.42/12.98 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(setextsub, axiom, setextsub = 97.42/12.98 (![A:$i,B:$i]: 97.42/12.98 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))). 97.42/12.98 thf('28', plain, 97.42/12.98 (( setextsub ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( subset @ X4 @ X6 ) => 97.42/12.98 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(subset2powerset, axiom, subset2powerset = 97.42/12.98 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))). 97.42/12.98 thf('29', plain, 97.42/12.98 (( subset2powerset ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(setadjoinSub2, axiom, setadjoinSub2 = 97.42/12.98 (![A:$i,Xx:$i,B:$i]: 97.42/12.98 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))). 97.42/12.98 thf('30', plain, 97.42/12.98 (( setadjoinSub2 ) = 97.42/12.98 ( ![X4:$i,X6:$i,X8:$i]: 97.42/12.98 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(setadjoinSub, axiom, setadjoinSub = 97.42/12.98 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))). 97.42/12.98 thf('31', plain, 97.42/12.98 (( setadjoinSub ) = 97.42/12.98 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(subsetTrans, axiom, subsetTrans = 97.42/12.98 (![A:$i,B:$i,C:$i]: 97.42/12.98 ( ( subset @ A @ B ) => ( ( subset @ B @ C ) => ( subset @ A @ C ) ) ))). 97.42/12.98 thf('32', plain, 97.42/12.98 (( subsetTrans ) = 97.42/12.98 ( ![X4:$i,X6:$i,X8:$i]: 97.42/12.98 ( ( subset @ X4 @ X6 ) => 97.42/12.98 ( ( subset @ X6 @ X8 ) => ( subset @ X4 @ X8 ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(subsetRefl, axiom, subsetRefl = (![A:$i]: ( subset @ A @ A ))). 97.42/12.98 thf('33', plain, (( subsetRefl ) = ( ![X4:$i]: ( subset @ X4 @ X4 ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(notequalI1, axiom, notequalI1 = 97.42/12.98 (![A:$i,B:$i]: ( ( ~( subset @ A @ B ) ) => ( ( A ) != ( B ) ) ))). 97.42/12.98 thf('34', plain, 97.42/12.98 (( notequalI1 ) = 97.42/12.98 ( ![X4:$i,X6:$i]: ( ( ~( subset @ X4 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(notsubsetI, axiom, notsubsetI = 97.42/12.98 (![A:$i,B:$i,Xx:$i]: 97.42/12.98 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ~( subset @ A @ B ) ) ) ))). 97.42/12.98 thf('35', plain, 97.42/12.98 (( notsubsetI ) = 97.42/12.98 ( ![X4:$i,X6:$i,X8:$i]: 97.42/12.98 ( ( in @ X8 @ X4 ) => 97.42/12.98 ( ( ~( in @ X8 @ X6 ) ) => ( ~( subset @ X4 @ X6 ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(subsetE2, axiom, subsetE2 = 97.42/12.98 (![A:$i,B:$i,Xx:$i]: 97.42/12.98 ( ( subset @ A @ B ) => ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))). 97.42/12.98 thf('36', plain, 97.42/12.98 (( subsetE2 ) = 97.42/12.98 ( ![X4:$i,X6:$i,X8:$i]: 97.42/12.98 ( ( subset @ X4 @ X6 ) => 97.42/12.98 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(subsetE, axiom, subsetE = 97.42/12.98 (![A:$i,B:$i,Xx:$i]: 97.42/12.98 ( ( subset @ A @ B ) => ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))). 97.42/12.98 thf('37', plain, 97.42/12.98 (( subsetE ) = 97.42/12.98 ( ![X4:$i,X6:$i,X8:$i]: 97.42/12.98 ( ( subset @ X4 @ X6 ) => ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(emptysetsubset, axiom, emptysetsubset = 97.42/12.98 (![A:$i]: ( subset @ emptyset @ A ))). 97.42/12.98 thf('38', plain, 97.42/12.98 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(subsetI2, axiom, subsetI2 = 97.42/12.98 (![A:$i,B:$i]: 97.42/12.98 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) => 97.42/12.98 ( subset @ A @ B ) ))). 97.42/12.98 thf('39', plain, 97.42/12.98 (( subsetI2 ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) => 97.42/12.98 ( subset @ X4 @ X6 ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(eqimpsubset1, axiom, eqimpsubset1 = 97.42/12.98 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ A @ B ) ))). 97.42/12.98 thf('40', plain, 97.42/12.98 (( eqimpsubset1 ) = 97.42/12.98 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X4 @ X6 ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(eqimpsubset2, axiom, eqimpsubset2 = 97.42/12.98 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ B @ A ) ))). 97.42/12.98 thf('41', plain, 97.42/12.98 (( eqimpsubset2 ) = 97.42/12.98 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(subsetI1, axiom, subsetI1 = 97.42/12.98 (![A:$i,B:$i]: 97.42/12.98 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) => 97.42/12.98 ( subset @ A @ B ) ))). 97.42/12.98 thf('42', plain, 97.42/12.98 (( subsetI1 ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) => 97.42/12.98 ( subset @ X4 @ X6 ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(powerset__Cong, axiom, powerset__Cong = 97.42/12.98 (![A:$i,B:$i]: 97.42/12.98 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))). 97.42/12.98 thf('43', plain, 97.42/12.98 (( powerset__Cong ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(powersetE, axiom, powersetE = 97.42/12.98 (![A:$i,B:$i,Xx:$i]: 97.42/12.98 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))). 97.42/12.98 thf('44', plain, 97.42/12.98 (( powersetE ) = 97.42/12.98 ( ![X4:$i,X6:$i,X8:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) => 97.42/12.98 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(emptyInPowerset, axiom, emptyInPowerset = 97.42/12.98 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))). 97.42/12.98 thf('45', plain, 97.42/12.98 (( emptyInPowerset ) = 97.42/12.98 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(emptyinPowerset, axiom, emptyinPowerset = 97.42/12.98 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))). 97.42/12.98 thf('46', plain, 97.42/12.98 (( emptyinPowerset ) = 97.42/12.98 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(powersetI, axiom, powersetI = 97.42/12.98 (![A:$i,B:$i]: 97.42/12.98 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) => 97.42/12.98 ( in @ B @ ( powerset @ A ) ) ))). 97.42/12.98 thf('47', plain, 97.42/12.98 (( powersetI ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) => 97.42/12.98 ( in @ X6 @ ( powerset @ X4 ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(powersetAx, axiom, powersetAx = 97.42/12.98 (![A:$i,B:$i]: 97.42/12.98 ( ( in @ B @ ( powerset @ A ) ) <=> 97.42/12.98 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))). 97.42/12.98 thf('48', plain, 97.42/12.98 (( powersetAx ) = 97.42/12.98 ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) <=> 97.42/12.98 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )), 97.42/12.98 define([status(thm)])). 97.42/12.98 thf(contrasubsetT2, conjecture, 97.42/12.98 (( setextAx ) => 97.42/12.98 ( ( emptysetAx ) => 97.42/12.98 ( ( setadjoinAx ) => 97.42/12.98 ( ( powersetAx ) => 97.42/12.98 ( ( setunionAx ) => 97.42/12.98 ( ( omega0Ax ) => 97.42/12.98 ( ( omegaSAx ) => 97.42/12.98 ( ( omegaIndAx ) => 97.42/12.98 ( ( replAx ) => 97.42/12.98 ( ( foundationAx ) => 97.42/12.98 ( ( wellorderingAx ) => 97.42/12.98 ( ( descrp ) => 97.42/12.98 ( ( dsetconstrI ) => 97.42/12.98 ( ( dsetconstrEL ) => 97.42/12.98 ( ( dsetconstrER ) => 97.42/12.98 ( ( exuE1 ) => 97.42/12.98 ( ( prop2setE ) => 97.42/12.98 ( ( emptysetE ) => 97.42/12.98 ( ( emptysetimpfalse ) => 97.42/12.98 ( ( notinemptyset ) => 97.42/12.98 ( ( exuE3e ) => 97.42/12.98 ( ( setext ) => 97.42/12.98 ( ( emptyI ) => 97.42/12.98 ( ( noeltsimpempty ) => 97.42/12.98 ( ( setbeta ) => 97.42/12.98 ( ( nonemptyE1 ) => 97.42/12.98 ( ( nonemptyI ) => 97.42/12.98 ( ( nonemptyI1 ) => 97.42/12.98 ( ( setadjoinIL ) => 97.42/12.98 ( ( emptyinunitempty ) => 97.42/12.98 ( ( setadjoinIR ) => 97.42/12.98 ( ( setadjoinE ) => 97.42/12.98 ( ( 97.42/12.98 setadjoinOr ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setoftrueEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 powersetI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 emptyinPowerset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 emptyInPowerset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 powersetE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subPowSU ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuE2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 nonemptyImpWitness ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 uniqinunit ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notinsingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 eqinunit ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 singletonsswitch ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairsetE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairsetIL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairsetIR ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 emptyE1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 vacuousDall ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 quantDeMorgan1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 quantDeMorgan2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 quantDeMorgan3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 quantDeMorgan4 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 prop2setI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 prop2set2propI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notdexE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notdallE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuI1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuI3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuI2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 inCongP ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuE3u ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exu__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 emptyset__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setadjoin__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 powerset__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunion__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 omega__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuEu ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 descr__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dsetconstr__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subsetI1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 eqimpsubset2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 eqimpsubset1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subsetI2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 emptysetsubset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subsetE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subsetE2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notsubsetI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notequalI1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notequalI2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subsetRefl ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subsetTrans ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setadjoinSub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setadjoinSub2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset2powerset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setextsub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subsetemptysetimpeq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 powersetI1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 powersetE1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 inPowerset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 powersetsubset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 sepInPowerset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 sepSubset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionIL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairset2IR ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionIR ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionEcases ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionLsub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionRsub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectSubset5 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectEL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectLsub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectSubset2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectSubset3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectER ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 disjointsetsI1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectRsub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectSubset4 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectSubset1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 bs114d ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setminusI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setminusEL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setminusER ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setminusSubset2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setminusERneg ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setminusELneg ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setminusILneg ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setminusIRneg ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setminusLsub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setminusSubset1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 symdiffE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 symdiffI1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 symdiffI2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 symdiffIneg1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 symdiffIneg2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 secondinupair ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairIL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairIR ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 kpairiskpair ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 kpairp ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 singletonsubset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 singletoninpowerset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 singletoninpowunion ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairset2E ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairsubunion ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairinpowunion ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ubforcartprodlem1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ubforcartprodlem2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ubforcartprodlem3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodpairin ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodmempair1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodmempair ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionE2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionsingleton1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionsingleton2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionsingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 singletonprop ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ex1E1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ex1I ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ex1I2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 singletonsuniq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjL1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 kfstsingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 theprop ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 kfstpairEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodfstin ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjL2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjR11 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjR12 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjR1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairequniteq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjR2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjR ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ksndsingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ksndpairEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 kpairsurjEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodsndin ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodpairmemEL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodpairmemER ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodmempaircEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodfstpairEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodsndpairEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodpairsurjEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrSub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setOfPairsIsBReln ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrERa ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrEL1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrEL2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrER ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcImageSingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 apProp ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 app ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 infuncsetfunc ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ap2p ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcinfuncset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 lamProp ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 lamp ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 lam2p ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 brelnall1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 brelnall2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ex1E2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcGraphProp1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcGraphProp3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcGraphProp2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcextLem ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcGraphProp4 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subbreln ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 eqbreln ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcext ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcext2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ap2apEq1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ap2apEq2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 beta1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 eta1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 lam2lamEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 beta2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 eta2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iffalseProp1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iffalseProp2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iftrueProp1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iftrueProp2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ifSingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ifp ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 theeq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iftrue ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iffalse ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iftrueorfalse ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectT_lem ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionT_lem ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 powersetT_lem ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setminusT_lem ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 complementT_lem ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setextT ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subsetTI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 powersetTI1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 powersetTE1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 complementTI1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 complementTE1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectTELcontra ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectTERcontra ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 contrasubsetT ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 contrasubsetT1 ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 A:$i,X:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 A ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 Y:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 Y @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 A ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X @ Y ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 A @ Y ) @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 A @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 97.42/12.98 thf(zf_stmt_0, conjecture, 97.42/12.98 (( setextAx ) => 97.42/12.98 ( ( emptysetAx ) => 97.42/12.98 ( ( setadjoinAx ) => 97.42/12.98 ( ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) <=> 97.42/12.98 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) => 97.42/12.98 ( ( setunionAx ) => 97.42/12.98 ( ( omega0Ax ) => 97.42/12.98 ( ( omegaSAx ) => 97.42/12.98 ( ( omegaIndAx ) => 97.42/12.98 ( ( replAx ) => 97.42/12.98 ( ( foundationAx ) => 97.42/12.98 ( ( wellorderingAx ) => 97.42/12.98 ( ( descrp ) => 97.42/12.98 ( ( dsetconstrI ) => 97.42/12.98 ( ( dsetconstrEL ) => 97.42/12.98 ( ( dsetconstrER ) => 97.42/12.98 ( ( exuE1 ) => 97.42/12.98 ( ( prop2setE ) => 97.42/12.98 ( ( emptysetE ) => 97.42/12.98 ( ( emptysetimpfalse ) => 97.42/12.98 ( ( notinemptyset ) => 97.42/12.98 ( ( exuE3e ) => 97.42/12.98 ( ( setext ) => 97.42/12.98 ( ( emptyI ) => 97.42/12.98 ( ( noeltsimpempty ) => 97.42/12.98 ( ( setbeta ) => 97.42/12.98 ( ( nonemptyE1 ) => 97.42/12.98 ( ( nonemptyI ) => 97.42/12.98 ( ( nonemptyI1 ) => 97.42/12.98 ( ( setadjoinIL ) => 97.42/12.98 ( ( emptyinunitempty ) => 97.42/12.98 ( ( setadjoinIR ) => 97.42/12.98 ( ( setadjoinE ) => 97.42/12.98 ( ( 97.42/12.98 setadjoinOr ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setoftrueEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X10:$i, 97.42/12.98 X12:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X14:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X14 @ X12 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X14 @ X10 ) ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X12 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X10 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X16:$i]: 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 emptyset @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X16 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X18:$i]: 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 emptyset @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X18 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X20:$i, 97.42/12.98 X22:$i, 97.42/12.98 X24:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X22 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X20 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X24 @ X22 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X24 @ X20 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subPowSU ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuE2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 nonemptyImpWitness ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 uniqinunit ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notinsingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 eqinunit ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 singletonsswitch ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairsetE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairsetIL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairsetIR ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 emptyE1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 vacuousDall ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 quantDeMorgan1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 quantDeMorgan2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 quantDeMorgan3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 quantDeMorgan4 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 prop2setI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 prop2set2propI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notdexE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notdallE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuI1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuI3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuI2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 inCongP ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuE3u ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exu__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 emptyset__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setadjoin__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X26:$i, 97.42/12.98 X28:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 X26 ) = 97.42/12.98 ( 97.42/12.98 X28 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X26 ) = 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X28 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunion__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 omega__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuEu ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 descr__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dsetconstr__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X30:$i, 97.42/12.98 X32:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X34:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X34 @ X30 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X34 @ X32 ) ) ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X30 @ X32 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X36:$i, 97.42/12.98 X38:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 X36 ) = 97.42/12.98 ( 97.42/12.98 X38 ) ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X38 @ X36 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X40:$i, 97.42/12.98 X42:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 X40 ) = 97.42/12.98 ( 97.42/12.98 X42 ) ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X40 @ X42 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X44:$i, 97.42/12.98 X46:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X48:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X48 @ X44 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X48 @ X46 ) ) ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X44 @ X46 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X50:$i]: 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 emptyset @ 97.42/12.98 X50 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X52:$i, 97.42/12.98 X54:$i, 97.42/12.98 X56:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X52 @ X54 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X56 @ X52 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X56 @ X54 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X58:$i, 97.42/12.98 X60:$i, 97.42/12.98 X62:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X58 @ X60 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X62 @ X60 ) ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X62 @ X58 ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X64:$i, 97.42/12.98 X66:$i, 97.42/12.98 X68:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X68 @ X64 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X68 @ X66 ) ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 subset @ 97.42/12.98 X64 @ X66 ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X70:$i, 97.42/12.98 X72:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 subset @ 97.42/12.98 X70 @ X72 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 X70 ) != 97.42/12.98 ( 97.42/12.98 X72 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notequalI2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X74:$i]: 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X74 @ X74 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X76:$i, 97.42/12.98 X78:$i, 97.42/12.98 X80:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X76 @ X78 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X78 @ X80 ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X76 @ X80 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X82:$i, 97.42/12.98 X84:$i]: 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X84 @ 97.42/12.98 ( 97.42/12.98 setadjoin 97.42/12.98 @ 97.42/12.98 X82 @ X84 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X86:$i, 97.42/12.98 X88:$i, 97.42/12.98 X90:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X86 @ X90 ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X86 @ 97.42/12.98 ( 97.42/12.98 setadjoin 97.42/12.98 @ 97.42/12.98 X88 @ X90 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X92:$i, 97.42/12.98 X94:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X92 @ X94 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X92 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X94 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X96:$i, 97.42/12.98 X98:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X96 @ X98 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X98 @ X96 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 X96 ) = 97.42/12.98 ( 97.42/12.98 X98 ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X100:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X100 @ 97.42/12.98 emptyset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 X100 ) = 97.42/12.98 ( 97.42/12.98 emptyset ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X102:$i, 97.42/12.98 X104:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X104 @ 97.42/12.98 X102 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X104 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X102 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X106:$i, 97.42/12.98 X108:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X108 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X106 ) ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X108 @ 97.42/12.98 X106 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X110:$i]: 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X110 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X110 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X112:$i, 97.42/12.98 X114:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X112 @ 97.42/12.98 X114 ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X112 ) @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X114 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 sepInPowerset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 sepSubset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionIL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairset2IR ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionIR ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionEcases ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionLsub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionRsub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectSubset5 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectEL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectLsub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectSubset2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectSubset3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectER ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 disjointsetsI1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectRsub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectSubset4 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectSubset1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 bs114d ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X116:$i, 97.42/12.98 X118:$i, 97.42/12.98 X120:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X120 @ 97.42/12.98 X116 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X120 @ 97.42/12.98 X118 ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X120 @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X116 @ 97.42/12.98 X118 ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X122:$i, 97.42/12.98 X124:$i, 97.42/12.98 X126:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X126 @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X122 @ 97.42/12.98 X124 ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X126 @ 97.42/12.98 X122 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X128:$i, 97.42/12.98 X130:$i, 97.42/12.98 X132:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X132 @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X128 @ 97.42/12.98 X130 ) ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X132 @ 97.42/12.98 X130 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X134:$i, 97.42/12.98 X136:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X134 @ 97.42/12.98 X136 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X134 @ 97.42/12.98 X136 ) = 97.42/12.98 ( 97.42/12.98 emptyset ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X138:$i, 97.42/12.98 X140:$i, 97.42/12.98 X142:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X142 @ 97.42/12.98 ( 97.42/12.98 setminus 97.42/12.98 @ 97.42/12.98 X138 @ 97.42/12.98 X140 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X142 @ 97.42/12.98 X138 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X142 @ 97.42/12.98 X140 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X144:$i, 97.42/12.98 X146:$i, 97.42/12.98 X148:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X148 @ 97.42/12.98 ( 97.42/12.98 setminus 97.42/12.98 @ 97.42/12.98 X144 @ 97.42/12.98 X146 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X148 @ 97.42/12.98 X146 ) ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X148 @ 97.42/12.98 X144 ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X150:$i, 97.42/12.98 X152:$i, 97.42/12.98 X154:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X154 @ 97.42/12.98 X150 ) ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X154 @ 97.42/12.98 ( 97.42/12.98 setminus 97.42/12.98 @ 97.42/12.98 X150 @ 97.42/12.98 X152 ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X156:$i, 97.42/12.98 X158:$i, 97.42/12.98 X160:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X160 @ 97.42/12.98 X158 ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X160 @ 97.42/12.98 ( 97.42/12.98 setminus 97.42/12.98 @ 97.42/12.98 X156 @ 97.42/12.98 X158 ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X162:$i, 97.42/12.98 X164:$i]: 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X162 @ 97.42/12.98 X164 ) @ 97.42/12.98 X162 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X166:$i, 97.42/12.98 X168:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X166 @ 97.42/12.98 X168 ) = 97.42/12.98 ( 97.42/12.98 emptyset ) ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X166 @ 97.42/12.98 X168 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 symdiffE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 symdiffI1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 symdiffI2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 symdiffIneg1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 symdiffIneg2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 secondinupair ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairIL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairIR ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 kpairiskpair ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 kpairp ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X170:$i, 97.42/12.98 X172:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X172 @ 97.42/12.98 X170 ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 ( 97.42/12.98 setadjoin 97.42/12.98 @ 97.42/12.98 X172 @ 97.42/12.98 emptyset ) @ 97.42/12.98 X170 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X174:$i, 97.42/12.98 X176:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X176 @ 97.42/12.98 X174 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 ( 97.42/12.98 setadjoin 97.42/12.98 @ 97.42/12.98 X176 @ 97.42/12.98 emptyset ) @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X174 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 singletoninpowunion ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairset2E ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairsubunion ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairinpowunion ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ubforcartprodlem1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ubforcartprodlem2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ubforcartprodlem3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodpairin ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodmempair1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodmempair ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionE2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionsingleton1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionsingleton2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionsingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 singletonprop ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ex1E1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ex1I ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ex1I2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 singletonsuniq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjL1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 kfstsingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 theprop ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 kfstpairEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodfstin ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjL2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjR11 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjR12 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjR1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairequniteq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjR2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjR ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ksndsingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ksndpairEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 kpairsurjEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodsndin ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodpairmemEL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodpairmemER ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodmempaircEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodfstpairEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodsndpairEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodpairsurjEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrSub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setOfPairsIsBReln ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrERa ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrEL1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrEL2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrER ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcImageSingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 apProp ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 app ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 infuncsetfunc ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ap2p ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcinfuncset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 lamProp ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 lamp ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 lam2p ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 brelnall1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 brelnall2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ex1E2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcGraphProp1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcGraphProp3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcGraphProp2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcextLem ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcGraphProp4 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subbreln ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 eqbreln ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcext ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcext2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ap2apEq1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ap2apEq2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 beta1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 eta1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 lam2lamEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 beta2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 eta2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iffalseProp1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iffalseProp2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iftrueProp1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iftrueProp2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ifSingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ifp ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 theeq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iftrue ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iffalse ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iftrueorfalse ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectT_lem ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionT_lem ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X178:$i, 97.42/12.98 X180:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X180 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X178 ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X180 ) @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X178 ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X182:$i, 97.42/12.98 X184:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X184 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X182 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X186:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X186 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X182 ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X184 @ 97.42/12.98 X186 ) @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X182 ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X188:$i, 97.42/12.98 X190:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X190 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X188 ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X188 @ 97.42/12.98 X190 ) @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X188 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X192:$i, 97.42/12.98 X194:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X194 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X192 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X196:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X196 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X192 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X198:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X198 @ 97.42/12.98 X192 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X198 @ 97.42/12.98 X194 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X198 @ 97.42/12.98 X196 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X200:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X200 @ 97.42/12.98 X192 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X200 @ 97.42/12.98 X196 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X200 @ 97.42/12.98 X194 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 X194 ) = 97.42/12.98 ( 97.42/12.98 X196 ) ) ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X202:$i, 97.42/12.98 X204:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X204 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X202 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X206:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X206 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X202 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X208:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X208 @ 97.42/12.98 X202 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X208 @ 97.42/12.98 X204 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X208 @ 97.42/12.98 X206 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X204 @ 97.42/12.98 X206 ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X210:$i, 97.42/12.98 X212:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X212 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X210 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X214:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X214 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X210 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X216:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X216 @ 97.42/12.98 X210 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X216 @ 97.42/12.98 X212 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X216 @ 97.42/12.98 X214 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X212 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X214 ) ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X218:$i, 97.42/12.98 X220:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X220 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X218 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X222:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X222 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X218 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X224:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X224 @ 97.42/12.98 X218 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X220 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X222 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X224 @ 97.42/12.98 X220 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X224 @ 97.42/12.98 X222 ) ) ) ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X226:$i, 97.42/12.98 X228:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X228 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X226 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X230:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X230 @ 97.42/12.98 X226 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X230 @ 97.42/12.98 X228 ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X230 @ 97.42/12.98 ( 97.42/12.98 setminus 97.42/12.98 @ 97.42/12.98 X226 @ 97.42/12.98 X228 ) ) ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X232:$i, 97.42/12.98 X234:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X234 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X232 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X236:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X236 @ 97.42/12.98 X232 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X236 @ 97.42/12.98 ( 97.42/12.98 setminus 97.42/12.98 @ 97.42/12.98 X232 @ 97.42/12.98 X234 ) ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X236 @ 97.42/12.98 X234 ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectTELcontra ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectTERcontra ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X238:$i, 97.42/12.98 X240:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X240 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X238 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X242:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X242 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X238 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X244:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X244 @ 97.42/12.98 X238 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X240 @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X238 @ 97.42/12.98 X242 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X244 @ 97.42/12.98 X242 ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X244 @ 97.42/12.98 X240 ) ) ) ) ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X246:$i, 97.42/12.98 X248:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X248 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X246 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X250:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X250 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X246 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X252:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X252 @ 97.42/12.98 X246 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X248 @ 97.42/12.98 X250 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X252 @ 97.42/12.98 X250 ) ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X252 @ 97.42/12.98 X248 ) ) ) ) ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X254:$i, 97.42/12.98 X256:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X256 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X254 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X258:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X258 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X254 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X256 @ 97.42/12.98 X258 ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X254 @ 97.42/12.98 X258 ) @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X254 @ 97.42/12.98 X256 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 97.42/12.98 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o). 97.42/12.98 thf(zf_stmt_2, axiom, 97.42/12.98 (![X8:$i,X6:$i,X4:$i]: 97.42/12.98 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=> 97.42/12.98 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))). 97.42/12.98 thf(zf_stmt_3, conjecture, 97.42/12.98 (( setextAx ) => 97.42/12.98 ( ( emptysetAx ) => 97.42/12.98 ( ( setadjoinAx ) => 97.42/12.98 ( ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) <=> 97.42/12.98 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) => 97.42/12.98 ( ( setunionAx ) => 97.42/12.98 ( ( omega0Ax ) => 97.42/12.98 ( ( omegaSAx ) => 97.42/12.98 ( ( omegaIndAx ) => 97.42/12.98 ( ( replAx ) => 97.42/12.98 ( ( foundationAx ) => 97.42/12.98 ( ( wellorderingAx ) => 97.42/12.98 ( ( descrp ) => 97.42/12.98 ( ( dsetconstrI ) => 97.42/12.98 ( ( dsetconstrEL ) => 97.42/12.98 ( ( dsetconstrER ) => 97.42/12.98 ( ( exuE1 ) => 97.42/12.98 ( ( prop2setE ) => 97.42/12.98 ( ( emptysetE ) => 97.42/12.98 ( ( emptysetimpfalse ) => 97.42/12.98 ( ( notinemptyset ) => 97.42/12.98 ( ( exuE3e ) => 97.42/12.98 ( ( setext ) => 97.42/12.98 ( ( emptyI ) => 97.42/12.98 ( ( noeltsimpempty ) => 97.42/12.98 ( ( setbeta ) => 97.42/12.98 ( ( nonemptyE1 ) => 97.42/12.98 ( ( nonemptyI ) => 97.42/12.98 ( ( nonemptyI1 ) => 97.42/12.98 ( ( setadjoinIL ) => 97.42/12.98 ( ( emptyinunitempty ) => 97.42/12.98 ( ( setadjoinIR ) => 97.42/12.98 ( ( setadjoinE ) => 97.42/12.98 ( ( 97.42/12.98 setadjoinOr ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setoftrueEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X10:$i, 97.42/12.98 X12:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X14:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X14 @ X12 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X14 @ X10 ) ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X12 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X10 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X16:$i]: 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 emptyset @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X16 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X18:$i]: 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 emptyset @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X18 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X20:$i, 97.42/12.98 X22:$i, 97.42/12.98 X24:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X22 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X20 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X24 @ X22 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X24 @ X20 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subPowSU ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuE2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 nonemptyImpWitness ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 uniqinunit ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notinsingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 eqinunit ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 singletonsswitch ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairsetE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairsetIL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairsetIR ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 emptyE1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 vacuousDall ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 quantDeMorgan1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 quantDeMorgan2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 quantDeMorgan3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 quantDeMorgan4 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 prop2setI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 prop2set2propI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notdexE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notdallE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuI1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuI3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuI2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 inCongP ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuE3u ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exu__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 emptyset__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setadjoin__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X26:$i, 97.42/12.98 X28:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 X26 ) = 97.42/12.98 ( 97.42/12.98 X28 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X26 ) = 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X28 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunion__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 omega__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuEu ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 descr__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dsetconstr__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X30:$i, 97.42/12.98 X32:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X34:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X34 @ X30 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X34 @ X32 ) ) ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X30 @ X32 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X36:$i, 97.42/12.98 X38:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 X36 ) = 97.42/12.98 ( 97.42/12.98 X38 ) ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X38 @ X36 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X40:$i, 97.42/12.98 X42:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 X40 ) = 97.42/12.98 ( 97.42/12.98 X42 ) ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X40 @ X42 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X44:$i, 97.42/12.98 X46:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X48:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X48 @ X44 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X48 @ X46 ) ) ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X44 @ X46 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X50:$i]: 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 emptyset @ 97.42/12.98 X50 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X52:$i, 97.42/12.98 X54:$i, 97.42/12.98 X56:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X52 @ X54 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X56 @ X52 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X56 @ X54 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X58:$i, 97.42/12.98 X60:$i, 97.42/12.98 X62:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X58 @ X60 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X62 @ X60 ) ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X62 @ X58 ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X64:$i, 97.42/12.98 X66:$i, 97.42/12.98 X68:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X68 @ X64 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X68 @ X66 ) ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 subset @ 97.42/12.98 X64 @ X66 ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X70:$i, 97.42/12.98 X72:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 subset @ 97.42/12.98 X70 @ X72 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 X70 ) != 97.42/12.98 ( 97.42/12.98 X72 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notequalI2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X74:$i]: 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X74 @ X74 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X76:$i, 97.42/12.98 X78:$i, 97.42/12.98 X80:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X76 @ X78 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X78 @ X80 ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X76 @ X80 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X82:$i, 97.42/12.98 X84:$i]: 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X84 @ 97.42/12.98 ( 97.42/12.98 setadjoin 97.42/12.98 @ 97.42/12.98 X82 @ X84 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X86:$i, 97.42/12.98 X88:$i, 97.42/12.98 X90:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X86 @ X90 ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X86 @ 97.42/12.98 ( 97.42/12.98 setadjoin 97.42/12.98 @ 97.42/12.98 X88 @ X90 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X92:$i, 97.42/12.98 X94:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X92 @ X94 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X92 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X94 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X96:$i, 97.42/12.98 X98:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X96 @ X98 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X98 @ X96 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 X96 ) = 97.42/12.98 ( 97.42/12.98 X98 ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X100:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X100 @ 97.42/12.98 emptyset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 X100 ) = 97.42/12.98 ( 97.42/12.98 emptyset ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X102:$i, 97.42/12.98 X104:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X104 @ 97.42/12.98 X102 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X104 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X102 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X106:$i, 97.42/12.98 X108:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X108 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X106 ) ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X108 @ 97.42/12.98 X106 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X110:$i]: 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X110 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X110 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X112:$i, 97.42/12.98 X114:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X112 @ 97.42/12.98 X114 ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X112 ) @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X114 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 sepInPowerset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 sepSubset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionIL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairset2IR ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionIR ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionEcases ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionLsub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionRsub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectSubset5 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectEL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectLsub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectSubset2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectSubset3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectER ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 disjointsetsI1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectRsub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectSubset4 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectSubset1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 bs114d ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X116:$i, 97.42/12.98 X118:$i, 97.42/12.98 X120:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X120 @ 97.42/12.98 X116 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X120 @ 97.42/12.98 X118 ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X120 @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X116 @ 97.42/12.98 X118 ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X122:$i, 97.42/12.98 X124:$i, 97.42/12.98 X126:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X126 @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X122 @ 97.42/12.98 X124 ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X126 @ 97.42/12.98 X122 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X128:$i, 97.42/12.98 X130:$i, 97.42/12.98 X132:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X132 @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X128 @ 97.42/12.98 X130 ) ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X132 @ 97.42/12.98 X130 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X134:$i, 97.42/12.98 X136:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X134 @ 97.42/12.98 X136 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X134 @ 97.42/12.98 X136 ) = 97.42/12.98 ( 97.42/12.98 emptyset ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X138:$i, 97.42/12.98 X140:$i, 97.42/12.98 X142:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X142 @ 97.42/12.98 ( 97.42/12.98 setminus 97.42/12.98 @ 97.42/12.98 X138 @ 97.42/12.98 X140 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X142 @ 97.42/12.98 X138 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X142 @ 97.42/12.98 X140 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X144:$i, 97.42/12.98 X146:$i, 97.42/12.98 X148:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X148 @ 97.42/12.98 ( 97.42/12.98 setminus 97.42/12.98 @ 97.42/12.98 X144 @ 97.42/12.98 X146 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X148 @ 97.42/12.98 X146 ) ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X148 @ 97.42/12.98 X144 ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X150:$i, 97.42/12.98 X152:$i, 97.42/12.98 X154:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X154 @ 97.42/12.98 X150 ) ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X154 @ 97.42/12.98 ( 97.42/12.98 setminus 97.42/12.98 @ 97.42/12.98 X150 @ 97.42/12.98 X152 ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X156:$i, 97.42/12.98 X158:$i, 97.42/12.98 X160:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X160 @ 97.42/12.98 X158 ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X160 @ 97.42/12.98 ( 97.42/12.98 setminus 97.42/12.98 @ 97.42/12.98 X156 @ 97.42/12.98 X158 ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X162:$i, 97.42/12.98 X164:$i]: 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X162 @ 97.42/12.98 X164 ) @ 97.42/12.98 X162 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X166:$i, 97.42/12.98 X168:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X166 @ 97.42/12.98 X168 ) = 97.42/12.98 ( 97.42/12.98 emptyset ) ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X166 @ 97.42/12.98 X168 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 symdiffE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 symdiffI1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 symdiffI2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 symdiffIneg1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 symdiffIneg2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 secondinupair ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairIL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairIR ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 kpairiskpair ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 kpairp ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X170:$i, 97.42/12.98 X172:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X172 @ 97.42/12.98 X170 ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 ( 97.42/12.98 setadjoin 97.42/12.98 @ 97.42/12.98 X172 @ 97.42/12.98 emptyset ) @ 97.42/12.98 X170 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X174:$i, 97.42/12.98 X176:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X176 @ 97.42/12.98 X174 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 ( 97.42/12.98 setadjoin 97.42/12.98 @ 97.42/12.98 X176 @ 97.42/12.98 emptyset ) @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X174 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 singletoninpowunion ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairset2E ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairsubunion ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairinpowunion ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ubforcartprodlem1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ubforcartprodlem2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ubforcartprodlem3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodpairin ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodmempair1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodmempair ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionE2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionsingleton1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionsingleton2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionsingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 singletonprop ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ex1E1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ex1I ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ex1I2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 singletonsuniq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjL1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 kfstsingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 theprop ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 kfstpairEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodfstin ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjL2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjR11 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjR12 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjR1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairequniteq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjR2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setukpairinjR ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ksndsingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ksndpairEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 kpairsurjEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodsndin ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodpairmemEL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodpairmemER ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodmempaircEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodfstpairEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodsndpairEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 cartprodpairsurjEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrSub ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setOfPairsIsBReln ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrERa ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrEL1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrEL2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 dpsetconstrER ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcImageSingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 apProp ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 app ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 infuncsetfunc ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ap2p ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcinfuncset ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 lamProp ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 lamp ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 lam2p ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 brelnall1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 brelnall2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ex1E2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcGraphProp1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcGraphProp3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcGraphProp2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcextLem ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcGraphProp4 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subbreln ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 eqbreln ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcext ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 funcext2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ap2apEq1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ap2apEq2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 beta1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 eta1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 lam2lamEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 beta2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 eta2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iffalseProp1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iffalseProp2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iftrueProp1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iftrueProp2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ifSingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ifp ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 theeq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iftrue ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iffalse ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 iftrueorfalse ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectT_lem ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binunionT_lem ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X178:$i, 97.42/12.98 X180:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X180 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X178 ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X180 ) @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X178 ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X182:$i, 97.42/12.98 X184:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X184 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X182 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X186:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X186 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X182 ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X184 @ 97.42/12.98 X186 ) @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X182 ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X188:$i, 97.42/12.98 X190:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X190 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X188 ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X188 @ 97.42/12.98 X190 ) @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X188 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X192:$i, 97.42/12.98 X194:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X194 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X192 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X196:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X196 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X192 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X198:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X198 @ 97.42/12.98 X192 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X198 @ 97.42/12.98 X194 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X198 @ 97.42/12.98 X196 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X200:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X200 @ 97.42/12.98 X192 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X200 @ 97.42/12.98 X196 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X200 @ 97.42/12.98 X194 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 X194 ) = 97.42/12.98 ( 97.42/12.98 X196 ) ) ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X202:$i, 97.42/12.98 X204:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X204 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X202 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X206:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X206 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X202 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X208:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X208 @ 97.42/12.98 X202 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X208 @ 97.42/12.98 X204 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X208 @ 97.42/12.98 X206 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X204 @ 97.42/12.98 X206 ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X210:$i, 97.42/12.98 X212:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X212 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X210 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X214:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X214 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X210 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X216:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X216 @ 97.42/12.98 X210 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X216 @ 97.42/12.98 X212 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X216 @ 97.42/12.98 X214 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X212 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X214 ) ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X218:$i, 97.42/12.98 X220:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X220 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X218 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X222:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X222 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X218 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X224:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X224 @ 97.42/12.98 X218 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X220 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X222 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X224 @ 97.42/12.98 X220 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X224 @ 97.42/12.98 X222 ) ) ) ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X226:$i, 97.42/12.98 X228:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X228 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X226 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X230:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X230 @ 97.42/12.98 X226 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X230 @ 97.42/12.98 X228 ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X230 @ 97.42/12.98 ( 97.42/12.98 setminus 97.42/12.98 @ 97.42/12.98 X226 @ 97.42/12.98 X228 ) ) ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X232:$i, 97.42/12.98 X234:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X234 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X232 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X236:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X236 @ 97.42/12.98 X232 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X236 @ 97.42/12.98 ( 97.42/12.98 setminus 97.42/12.98 @ 97.42/12.98 X232 @ 97.42/12.98 X234 ) ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X236 @ 97.42/12.98 X234 ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectTELcontra ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 binintersectTERcontra ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X238:$i, 97.42/12.98 X240:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X240 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X238 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X242:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X242 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X238 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X244:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X244 @ 97.42/12.98 X238 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X240 @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X238 @ 97.42/12.98 X242 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X244 @ 97.42/12.98 X242 ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X244 @ 97.42/12.98 X240 ) ) ) ) ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X246:$i, 97.42/12.98 X248:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X248 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X246 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X250:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X250 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X246 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X252:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X252 @ 97.42/12.98 X246 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X248 @ 97.42/12.98 X250 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X252 @ 97.42/12.98 X250 ) ) => 97.42/12.98 ( 97.42/12.98 ~( 97.42/12.98 in @ 97.42/12.98 X252 @ 97.42/12.98 X248 ) ) ) ) ) ) ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X254:$i, 97.42/12.98 X256:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X256 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X254 ) ) => 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X258:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X258 @ 97.42/12.98 ( 97.42/12.98 powerset @ 97.42/12.98 X254 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 X256 @ 97.42/12.98 X258 ) => 97.42/12.98 ( 97.42/12.98 subset @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X254 @ 97.42/12.98 X258 ) @ 97.42/12.98 ( 97.42/12.98 setminus @ 97.42/12.98 X254 @ 97.42/12.98 X256 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 97.42/12.98 thf(zf_stmt_4, negated_conjecture, 97.42/12.98 (~( ( setextAx ) => 97.42/12.98 ( ( emptysetAx ) => 97.42/12.98 ( ( setadjoinAx ) => 97.42/12.98 ( ( ![X4:$i,X6:$i]: 97.42/12.98 ( ( in @ X6 @ ( powerset @ X4 ) ) <=> 97.42/12.98 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) => 97.42/12.98 ( ( setunionAx ) => 97.42/12.98 ( ( omega0Ax ) => 97.42/12.98 ( ( omegaSAx ) => 97.42/12.98 ( ( omegaIndAx ) => 97.42/12.98 ( ( replAx ) => 97.42/12.98 ( ( foundationAx ) => 97.42/12.98 ( ( wellorderingAx ) => 97.42/12.98 ( ( descrp ) => 97.42/12.98 ( ( dsetconstrI ) => 97.42/12.98 ( ( dsetconstrEL ) => 97.42/12.98 ( ( dsetconstrER ) => 97.42/12.98 ( ( exuE1 ) => 97.42/12.98 ( ( prop2setE ) => 97.42/12.98 ( ( emptysetE ) => 97.42/12.98 ( ( emptysetimpfalse ) => 97.42/12.98 ( ( notinemptyset ) => 97.42/12.98 ( ( exuE3e ) => 97.42/12.98 ( ( setext ) => 97.42/12.98 ( ( emptyI ) => 97.42/12.98 ( ( noeltsimpempty ) => 97.42/12.98 ( ( setbeta ) => 97.42/12.98 ( ( nonemptyE1 ) => 97.42/12.98 ( ( nonemptyI ) => 97.42/12.98 ( ( nonemptyI1 ) => 97.42/12.98 ( ( setadjoinIL ) => 97.42/12.98 ( ( emptyinunitempty ) => 97.42/12.98 ( ( setadjoinIR ) => 97.42/12.98 ( ( 97.42/12.98 setadjoinE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setadjoinOr ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setoftrueEq ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X10:$i, 97.42/12.98 X12:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X14:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X14 @ X12 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X14 @ X10 ) ) ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X12 @ 97.42/12.98 ( 97.42/12.98 powerset 97.42/12.98 @ 97.42/12.98 X10 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X16:$i]: 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 emptyset @ 97.42/12.98 ( 97.42/12.98 powerset 97.42/12.98 @ 97.42/12.98 X16 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X18:$i]: 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 emptyset @ 97.42/12.98 ( 97.42/12.98 powerset 97.42/12.98 @ 97.42/12.98 X18 ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X20:$i, 97.42/12.98 X22:$i, 97.42/12.98 X24:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X22 @ 97.42/12.98 ( 97.42/12.98 powerset 97.42/12.98 @ 97.42/12.98 X20 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X24 @ X22 ) => 97.42/12.98 ( 97.42/12.98 in @ 97.42/12.98 X24 @ X20 ) ) ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setunionE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 subPowSU ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuE2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 nonemptyImpWitness ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 uniqinunit ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notinsingleton ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 eqinunit ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 singletonsswitch ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairsetE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairsetIL ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 upairsetIR ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 emptyE1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 vacuousDall ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 quantDeMorgan1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 quantDeMorgan2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 quantDeMorgan3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 quantDeMorgan4 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 prop2setI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 prop2set2propI ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notdexE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 notdallE ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuI1 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuI3 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuI2 ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 inCongP ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 in__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exuE3u ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 exu__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 emptyset__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 setadjoin__Cong ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ![ 97.42/12.98 X26:$i, 97.42/12.98 X28:$i]: 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 X26 ) = 97.42/12.98 ( 97.42/12.98 X28 ) ) => 97.42/12.98 ( 97.42/12.98 ( 97.42/12.98 powerset 97.42/12.98 @ 97.42/12.98 X26 ) = 97.42/12.98 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X28 ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setunion__Cong ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 omega__Cong ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 exuEu ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 descr__Cong ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 dsetconstr__Cong ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X30:$i, 97.42/12.99 X32:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X34:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X34 @ X30 ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X34 @ X32 ) ) ) => 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X30 @ X32 ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X36:$i, 97.42/12.99 X38:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 X36 ) = 97.42/12.99 ( 97.42/12.99 X38 ) ) => 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X38 @ X36 ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X40:$i, 97.42/12.99 X42:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 X40 ) = 97.42/12.99 ( 97.42/12.99 X42 ) ) => 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X40 @ X42 ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X44:$i, 97.42/12.99 X46:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X48:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X48 @ X44 ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X48 @ X46 ) ) ) => 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X44 @ X46 ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X50:$i]: 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 emptyset @ 97.42/12.99 X50 ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X52:$i, 97.42/12.99 X54:$i, 97.42/12.99 X56:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X52 @ X54 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X56 @ X52 ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X56 @ X54 ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X58:$i, 97.42/12.99 X60:$i, 97.42/12.99 X62:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X58 @ X60 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X62 @ X60 ) ) => 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X62 @ X58 ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X64:$i, 97.42/12.99 X66:$i, 97.42/12.99 X68:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X68 @ X64 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X68 @ X66 ) ) => 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X64 @ X66 ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X70:$i, 97.42/12.99 X72:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X70 @ X72 ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 X70 ) != 97.42/12.99 ( 97.42/12.99 X72 ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 notequalI2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X74:$i]: 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X74 @ X74 ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X76:$i, 97.42/12.99 X78:$i, 97.42/12.99 X80:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X76 @ X78 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X78 @ X80 ) => 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X76 @ X80 ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X82:$i, 97.42/12.99 X84:$i]: 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X84 @ 97.42/12.99 ( 97.42/12.99 setadjoin 97.42/12.99 @ 97.42/12.99 X82 @ X84 ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X86:$i, 97.42/12.99 X88:$i, 97.42/12.99 X90:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X86 @ X90 ) => 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X86 @ 97.42/12.99 ( 97.42/12.99 setadjoin 97.42/12.99 @ 97.42/12.99 X88 @ X90 ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X92:$i, 97.42/12.99 X94:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X92 @ X94 ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X92 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X94 ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X96:$i, 97.42/12.99 X98:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X96 @ X98 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X98 @ X96 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 X96 ) = 97.42/12.99 ( 97.42/12.99 X98 ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X100:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X100 @ 97.42/12.99 emptyset ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 X100 ) = 97.42/12.99 ( 97.42/12.99 emptyset ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X102:$i, 97.42/12.99 X104:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X104 @ 97.42/12.99 X102 ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X104 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X102 ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X106:$i, 97.42/12.99 X108:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X108 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X106 ) ) => 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X108 @ 97.42/12.99 X106 ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X110:$i]: 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X110 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X110 ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X112:$i, 97.42/12.99 X114:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X112 @ 97.42/12.99 X114 ) => 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X112 ) @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X114 ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 sepInPowerset ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 sepSubset ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binunionIL ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 upairset2IR ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binunionIR ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binunionEcases ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binunionE ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binunionLsub ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binunionRsub ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binintersectI ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binintersectSubset5 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binintersectEL ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binintersectLsub ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binintersectSubset2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binintersectSubset3 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binintersectER ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 disjointsetsI1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binintersectRsub ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binintersectSubset4 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binintersectSubset1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 bs114d ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X116:$i, 97.42/12.99 X118:$i, 97.42/12.99 X120:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X120 @ 97.42/12.99 X116 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X120 @ 97.42/12.99 X118 ) ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X120 @ 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X116 @ 97.42/12.99 X118 ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X122:$i, 97.42/12.99 X124:$i, 97.42/12.99 X126:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X126 @ 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X122 @ 97.42/12.99 X124 ) ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X126 @ 97.42/12.99 X122 ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X128:$i, 97.42/12.99 X130:$i, 97.42/12.99 X132:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X132 @ 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X128 @ 97.42/12.99 X130 ) ) => 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X132 @ 97.42/12.99 X130 ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X134:$i, 97.42/12.99 X136:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X134 @ 97.42/12.99 X136 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X134 @ 97.42/12.99 X136 ) = 97.42/12.99 ( 97.42/12.99 emptyset ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X138:$i, 97.42/12.99 X140:$i, 97.42/12.99 X142:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X142 @ 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X138 @ 97.42/12.99 X140 ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X142 @ 97.42/12.99 X138 ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X142 @ 97.42/12.99 X140 ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X144:$i, 97.42/12.99 X146:$i, 97.42/12.99 X148:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X148 @ 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X144 @ 97.42/12.99 X146 ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X148 @ 97.42/12.99 X146 ) ) => 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X148 @ 97.42/12.99 X144 ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X150:$i, 97.42/12.99 X152:$i, 97.42/12.99 X154:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X154 @ 97.42/12.99 X150 ) ) => 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X154 @ 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X150 @ 97.42/12.99 X152 ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X156:$i, 97.42/12.99 X158:$i, 97.42/12.99 X160:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X160 @ 97.42/12.99 X158 ) => 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X160 @ 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X156 @ 97.42/12.99 X158 ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X162:$i, 97.42/12.99 X164:$i]: 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X162 @ 97.42/12.99 X164 ) @ 97.42/12.99 X162 ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X166:$i, 97.42/12.99 X168:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X166 @ 97.42/12.99 X168 ) = 97.42/12.99 ( 97.42/12.99 emptyset ) ) => 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X166 @ 97.42/12.99 X168 ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 symdiffE ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 symdiffI1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 symdiffI2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 symdiffIneg1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 symdiffIneg2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 secondinupair ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setukpairIL ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setukpairIR ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 kpairiskpair ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 kpairp ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X170:$i, 97.42/12.99 X172:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X172 @ 97.42/12.99 X170 ) => 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 ( 97.42/12.99 setadjoin 97.42/12.99 @ 97.42/12.99 X172 @ 97.42/12.99 emptyset ) @ 97.42/12.99 X170 ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X174:$i, 97.42/12.99 X176:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X176 @ 97.42/12.99 X174 ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 ( 97.42/12.99 setadjoin 97.42/12.99 @ 97.42/12.99 X176 @ 97.42/12.99 emptyset ) @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X174 ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 singletoninpowunion ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 upairset2E ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 upairsubunion ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 upairinpowunion ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ubforcartprodlem1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ubforcartprodlem2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ubforcartprodlem3 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 cartprodpairin ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 cartprodmempair1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 cartprodmempair ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setunionE2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setunionsingleton1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setunionsingleton2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setunionsingleton ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 singletonprop ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ex1E1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ex1I ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ex1I2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 singletonsuniq ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setukpairinjL1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 kfstsingleton ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 theprop ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 kfstpairEq ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 cartprodfstin ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setukpairinjL2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setukpairinjL ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setukpairinjR11 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setukpairinjR12 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setukpairinjR1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 upairequniteq ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setukpairinjR2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setukpairinjR ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ksndsingleton ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ksndpairEq ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 kpairsurjEq ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 cartprodsndin ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 cartprodpairmemEL ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 cartprodpairmemER ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 cartprodmempaircEq ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 cartprodfstpairEq ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 cartprodsndpairEq ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 cartprodpairsurjEq ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 dpsetconstrI ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 dpsetconstrSub ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 setOfPairsIsBReln ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 dpsetconstrERa ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 dpsetconstrEL1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 dpsetconstrEL2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 dpsetconstrER ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 funcImageSingleton ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 apProp ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 app ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 infuncsetfunc ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ap2p ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 funcinfuncset ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 lamProp ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 lamp ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 lam2p ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 brelnall1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 brelnall2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ex1E2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 funcGraphProp1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 funcGraphProp3 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 funcGraphProp2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 funcextLem ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 funcGraphProp4 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 subbreln ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 eqbreln ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 funcext ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 funcext2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ap2apEq1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ap2apEq2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 beta1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 eta1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 lam2lamEq ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 beta2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 eta2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 iffalseProp1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 iffalseProp2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 iftrueProp1 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 iftrueProp2 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ifSingleton ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ifp ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 theeq ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 iftrue ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 iffalse ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 iftrueorfalse ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binintersectT_lem ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binunionT_lem ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X178:$i, 97.42/12.99 X180:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X180 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X178 ) ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X180 ) @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X178 ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X182:$i, 97.42/12.99 X184:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X184 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X182 ) ) => 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X186:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X186 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X182 ) ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X184 @ 97.42/12.99 X186 ) @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X182 ) ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X188:$i, 97.42/12.99 X190:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X190 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X188 ) ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X188 @ 97.42/12.99 X190 ) @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X188 ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X192:$i, 97.42/12.99 X194:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X194 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X192 ) ) => 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X196:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X196 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X192 ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X198:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X198 @ 97.42/12.99 X192 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X198 @ 97.42/12.99 X194 ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X198 @ 97.42/12.99 X196 ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X200:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X200 @ 97.42/12.99 X192 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X200 @ 97.42/12.99 X196 ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X200 @ 97.42/12.99 X194 ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 X194 ) = 97.42/12.99 ( 97.42/12.99 X196 ) ) ) ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X202:$i, 97.42/12.99 X204:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X204 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X202 ) ) => 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X206:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X206 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X202 ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X208:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X208 @ 97.42/12.99 X202 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X208 @ 97.42/12.99 X204 ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X208 @ 97.42/12.99 X206 ) ) ) ) => 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X204 @ 97.42/12.99 X206 ) ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X210:$i, 97.42/12.99 X212:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X212 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X210 ) ) => 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X214:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X214 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X210 ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X216:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X216 @ 97.42/12.99 X210 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X216 @ 97.42/12.99 X212 ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X216 @ 97.42/12.99 X214 ) ) ) ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X212 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X214 ) ) ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X218:$i, 97.42/12.99 X220:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X220 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X218 ) ) => 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X222:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X222 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X218 ) ) => 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X224:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X224 @ 97.42/12.99 X218 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X220 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X222 ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X224 @ 97.42/12.99 X220 ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X224 @ 97.42/12.99 X222 ) ) ) ) ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X226:$i, 97.42/12.99 X228:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X228 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X226 ) ) => 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X230:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X230 @ 97.42/12.99 X226 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X230 @ 97.42/12.99 X228 ) => 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X230 @ 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X226 @ 97.42/12.99 X228 ) ) ) ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X232:$i, 97.42/12.99 X234:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X234 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X232 ) ) => 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X236:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X236 @ 97.42/12.99 X232 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X236 @ 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X232 @ 97.42/12.99 X234 ) ) ) => 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X236 @ 97.42/12.99 X234 ) ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binintersectTELcontra ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 binintersectTERcontra ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X238:$i, 97.42/12.99 X240:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X240 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X238 ) ) => 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X242:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X242 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X238 ) ) => 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X244:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X244 @ 97.42/12.99 X238 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X240 @ 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X238 @ 97.42/12.99 X242 ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X244 @ 97.42/12.99 X242 ) => 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X244 @ 97.42/12.99 X240 ) ) ) ) ) ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X246:$i, 97.42/12.99 X248:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X248 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X246 ) ) => 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X250:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X250 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X246 ) ) => 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X252:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X252 @ 97.42/12.99 X246 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X248 @ 97.42/12.99 X250 ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X252 @ 97.42/12.99 X250 ) ) => 97.42/12.99 ( 97.42/12.99 ~ 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X252 @ 97.42/12.99 X248 ) ) ) ) ) ) ) ) ) ) => 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X254:$i, 97.42/12.99 X256:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X256 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X254 ) ) => 97.42/12.99 ( 97.42/12.99 ![ 97.42/12.99 X258:$i]: 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 in @ 97.42/12.99 X258 @ 97.42/12.99 ( 97.42/12.99 powerset 97.42/12.99 @ 97.42/12.99 X254 ) ) => 97.42/12.99 ( 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 X256 @ 97.42/12.99 X258 ) => 97.42/12.99 ( 97.42/12.99 subset @ 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X254 @ 97.42/12.99 X258 ) @ 97.42/12.99 ( 97.42/12.99 setminus 97.42/12.99 @ 97.42/12.99 X254 @ 97.42/12.99 X256 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 97.42/12.99 inference('cnf.neg', [status(esa)], [zf_stmt_3])). 97.42/12.99 thf(zip_derived_cl130, plain, ( (subset @ sk__132 @ sk__133)), 97.42/12.99 inference('cnf', [status(esa)], [zf_stmt_4])). 97.42/12.99 thf(zip_derived_cl45, plain, 97.42/12.99 (![X7 : $i, X8 : $i, X9 : $i]: 97.42/12.99 (~ (subset @ X7 @ X8) | (in @ X9 @ X8) | ~ (in @ X9 @ X7))), 97.42/12.99 inference('cnf', [status(esa)], [zf_stmt_4])). 97.42/12.99 thf(zip_derived_cl287, plain, 97.42/12.99 (![X0 : $i]: (~ (in @ X0 @ sk__132) | (in @ X0 @ sk__133))), 97.42/12.99 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl45])). 97.42/12.99 thf(zip_derived_cl225, plain, 97.42/12.99 (![X107 : $i, X108 : $i]: 97.42/12.99 ( (subset @ X107 @ X108) | (in @ (sk__127 @ X108 @ X107) @ X107))), 97.42/12.99 inference('cnf', [status(esa)], [zf_stmt_4])). 97.42/12.99 thf(zip_derived_cl67, plain, 97.42/12.99 (![X32 : $i, X33 : $i, X34 : $i]: 97.42/12.99 (~ (in @ X32 @ (setminus @ X33 @ X34)) | ~ (in @ X32 @ X34))), 97.42/12.99 inference('cnf', [status(esa)], [zf_stmt_4])). 97.42/12.99 thf(zip_derived_cl224, plain, 97.42/12.99 (![X107 : $i, X108 : $i]: 97.42/12.99 ( (subset @ X107 @ X108) | ~ (in @ (sk__127 @ X108 @ X107) @ X108))), 97.42/12.99 inference('cnf', [status(esa)], [zf_stmt_4])). 97.42/12.99 thf(zip_derived_cl225, plain, 97.42/12.99 (![X107 : $i, X108 : $i]: 97.42/12.99 ( (subset @ X107 @ X108) | (in @ (sk__127 @ X108 @ X107) @ X107))), 97.42/12.99 inference('cnf', [status(esa)], [zf_stmt_4])). 97.42/12.99 thf(zip_derived_cl64, plain, 97.42/12.99 (![X24 : $i, X25 : $i, X26 : $i]: 97.42/12.99 ( (in @ X24 @ X25) | ~ (in @ X24 @ (setminus @ X25 @ X26)))), 97.42/12.99 inference('cnf', [status(esa)], [zf_stmt_4])). 97.42/12.99 thf(zip_derived_cl624, plain, 97.42/12.99 (![X0 : $i, X1 : $i, X2 : $i]: 97.42/12.99 ( (subset @ (setminus @ X1 @ X0) @ X2) 97.42/12.99 | (in @ (sk__127 @ X2 @ (setminus @ X1 @ X0)) @ X1))), 97.42/12.99 inference('sup-', [status(thm)], [zip_derived_cl225, zip_derived_cl64])). 97.42/12.99 thf(zip_derived_cl129, plain, 97.42/12.99 (~ (subset @ (setminus @ sk__131 @ sk__133) @ 97.42/12.99 (setminus @ sk__131 @ sk__132))), 97.42/12.99 inference('cnf', [status(esa)], [zf_stmt_4])). 97.42/12.99 thf(zip_derived_cl201, plain, 97.42/12.99 (![X80 : $i, X81 : $i, X82 : $i]: 97.42/12.99 (~ (in @ X80 @ X81) 97.42/12.99 | (in @ X80 @ X82) 97.42/12.99 | (in @ X80 @ (setminus @ X81 @ X82)))), 97.42/12.99 inference('cnf', [status(esa)], [zf_stmt_4])). 97.42/12.99 thf(zip_derived_cl28736, plain, ($false), 97.42/12.99 inference('eprover', [status(thm)], 97.42/12.99 [zip_derived_cl287, zip_derived_cl225, zip_derived_cl67, 97.42/12.99 zip_derived_cl224, zip_derived_cl624, zip_derived_cl129, 97.42/12.99 zip_derived_cl201])). 97.42/12.99 97.42/12.99 % SZS output end Refutation 97.42/12.99 97.42/12.99 97.42/12.99 % Terminating... 97.42/13.07 % Runner terminated. 97.42/13.07 % Zipperpin 1.5 exiting 97.42/13.07 EOF