0.00/0.05 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.DZipM9mgBz true 0.24/0.51 % Computer : n029.cluster.edu 0.24/0.51 % Model : x86_64 x86_64 0.24/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.24/0.51 % Memory : 8046.5625MB 0.24/0.51 % OS : Linux 6.8.0-71-generic 0.24/0.51 % CPULimit : 1440 0.24/0.51 % WCLimit : 180 0.24/0.51 % DateTime : Mon Jul 27 13:19:16 UTC 2026 0.24/0.51 % CPUTime : 0.24/0.51 % Running portfolio for 1440 s 0.24/0.51 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.24/0.51 % Number of cores: 8 0.24/0.52 % Python version: Python 3.12.3 0.24/0.52 % Running in HO mode 0.49/0.96 % Total configuration time : 828 0.49/0.96 % Estimated wc time : 1656 0.49/0.96 % Estimated cpu time (8 cpus) : 207.0 0.49/1.07 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 1.97/1.16 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 1.97/1.17 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 1.97/1.18 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 1.97/1.18 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 1.97/1.18 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 1.97/1.18 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 2.39/1.23 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 119.84/17.06 % Solved by lams/40_c_ic.sh. 119.84/17.06 % done 2014 iterations in 15.644s 119.84/17.06 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 119.84/17.06 % SZS output start Refutation 119.84/17.06 thf(setadjoinAx_type, type, setadjoinAx: $o). 119.84/17.06 thf(notdexE_type, type, notdexE: $o). 119.84/17.06 thf(setukpairinjL2_type, type, setukpairinjL2: $o). 119.84/17.06 thf(doubleComplementI1_type, type, doubleComplementI1: $o). 119.84/17.06 thf(setunionAx_type, type, setunionAx: $o). 119.84/17.06 thf(setminusELneg_type, type, setminusELneg: $o). 119.84/17.06 thf(cartprodsndin_type, type, cartprodsndin: $o). 119.84/17.06 thf(ex1E1_type, type, ex1E1: $o). 119.84/17.06 thf(powersetE_type, type, powersetE: $o). 119.84/17.06 thf(omegaSAx_type, type, omegaSAx: $o). 119.84/17.06 thf(exuI1_type, type, exuI1: $o). 119.84/17.06 thf(exuI2_type, type, exuI2: $o). 119.84/17.06 thf(notequalI2_type, type, notequalI2: $o). 119.84/17.06 thf(setukpairinjL_type, type, setukpairinjL: $o). 119.84/17.06 thf(kpairiskpair_type, type, kpairiskpair: $o). 119.84/17.06 thf(upairsubunion_type, type, upairsubunion: $o). 119.84/17.06 thf(funcGraphProp3_type, type, funcGraphProp3: $o). 119.84/17.06 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o). 119.84/17.06 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o). 119.84/17.06 thf(powerset__Cong_type, type, powerset__Cong: $o). 119.84/17.06 thf(setminusILneg_type, type, setminusILneg: $o). 119.84/17.06 thf(wellorderingAx_type, type, wellorderingAx: $o). 119.84/17.06 thf(ksndpairEq_type, type, ksndpairEq: $o). 119.84/17.06 thf(funcGraphProp2_type, type, funcGraphProp2: $o). 119.84/17.06 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 119.84/17.06 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 119.84/17.06 thf(iftrue_type, type, iftrue: $o). 119.84/17.06 thf(upairinpowunion_type, type, upairinpowunion: $o). 119.84/17.06 thf(ifSingleton_type, type, ifSingleton: $o). 119.84/17.06 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o). 119.84/17.06 thf(setoftrueEq_type, type, setoftrueEq: $o). 119.84/17.06 thf(funcImageSingleton_type, type, funcImageSingleton: $o). 119.84/17.06 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o). 119.84/17.06 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o). 119.84/17.06 thf(lamProp_type, type, lamProp: $o). 119.84/17.06 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o). 119.84/17.06 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 119.84/17.06 thf(sk__156_type, type, sk__156: $i). 119.84/17.06 thf(dpsetconstrER_type, type, dpsetconstrER: $o). 119.84/17.06 thf(sepInPowerset_type, type, sepInPowerset: $o). 119.84/17.06 thf(setukpairIR_type, type, setukpairIR: $o). 119.84/17.06 thf(setukpairinjR1_type, type, setukpairinjR1: $o). 119.84/17.06 thf(lam2p_type, type, lam2p: $o). 119.84/17.06 thf(kpair_type, type, kpair: $i > $i > $i). 119.84/17.06 thf(binunionE_type, type, binunionE: $o). 119.84/17.06 thf(setext_type, type, setext: $o). 119.84/17.06 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 119.84/17.06 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o). 119.84/17.06 thf(descr__Cong_type, type, descr__Cong: $o). 119.84/17.06 thf(kfstsingleton_type, type, kfstsingleton: $o). 119.84/17.06 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o). 119.84/17.06 thf(doubleComplementEq_type, type, doubleComplementEq: $o). 119.84/17.06 thf(eqbreln_type, type, eqbreln: $o). 119.84/17.06 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 119.84/17.06 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect: 119.84/17.06 $o). 119.84/17.06 thf(in_type, type, in: $i > $i > $o). 119.84/17.06 thf(binunionT_lem_type, type, binunionT_lem: $o). 119.84/17.06 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 119.84/17.06 thf(complementT_lem_type, type, complementT_lem: $o). 119.84/17.06 thf(binunion_type, type, binunion: $i > $i > $i). 119.84/17.06 thf(kpairsurjEq_type, type, kpairsurjEq: $o). 119.84/17.06 thf(setadjoinIR_type, type, setadjoinIR: $o). 119.84/17.06 thf(doubleComplementE1_type, type, doubleComplementE1: $o). 119.84/17.06 thf(beta1_type, type, beta1: $o). 119.84/17.06 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 119.84/17.06 thf(powersetTE1_type, type, powersetTE1: $o). 119.84/17.06 thf(symdiffI2_type, type, symdiffI2: $o). 119.84/17.06 thf(iftrueProp2_type, type, iftrueProp2: $o). 119.84/17.06 thf(upairset2IR_type, type, upairset2IR: $o). 119.84/17.06 thf(iffalseProp2_type, type, iffalseProp2: $o). 119.84/17.06 thf(subsetE_type, type, subsetE: $o). 119.84/17.06 thf(prop2set2propI_type, type, prop2set2propI: $o). 119.84/17.06 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 119.84/17.06 thf(setbeta_type, type, setbeta: $o). 119.84/17.06 thf(eqinunit_type, type, eqinunit: $o). 119.84/17.06 thf(upairsetIL_type, type, upairsetIL: $o). 119.84/17.06 thf(powersetI1_type, type, powersetI1: $o). 119.84/17.06 thf(kfstpairEq_type, type, kfstpairEq: $o). 119.84/17.06 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 119.84/17.06 thf(setminusIRneg_type, type, setminusIRneg: $o). 119.84/17.06 thf(ap2apEq1_type, type, ap2apEq1: $o). 119.84/17.06 thf(powersetAx_type, type, powersetAx: $o). 119.84/17.06 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 119.84/17.06 thf(singletoninpowunion_type, type, singletoninpowunion: $o). 119.84/17.06 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o). 119.84/17.06 thf(powersetI_type, type, powersetI: $o). 119.84/17.06 thf(cartprodmempair_type, type, cartprodmempair: $o). 119.84/17.06 thf(upairsetIR_type, type, upairsetIR: $o). 119.84/17.06 thf(lamp_type, type, lamp: $o). 119.84/17.06 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o). 119.84/17.06 thf(inCongP_type, type, inCongP: $o). 119.84/17.06 thf(setadjoinSub_type, type, setadjoinSub: $o). 119.84/17.06 thf(exuE3e_type, type, exuE3e: $o). 119.84/17.06 thf(emptysetE_type, type, emptysetE: $o). 119.84/17.06 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 119.84/17.06 thf(setunionI_type, type, setunionI: $o). 119.84/17.06 thf(sk__158_type, type, sk__158: $i). 119.84/17.06 thf(setunion__Cong_type, type, setunion__Cong: $o). 119.84/17.06 thf(prop2setI_type, type, prop2setI: $o). 119.84/17.06 thf(singletonsuniq_type, type, singletonsuniq: $o). 119.84/17.06 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 119.84/17.06 thf(setminusER_type, type, setminusER: $o). 119.84/17.06 thf(exuE2_type, type, exuE2: $o). 119.84/17.06 thf(emptyset_type, type, emptyset: $i). 119.84/17.06 thf(setukpairinjR11_type, type, setukpairinjR11: $o). 119.84/17.06 thf(ex1I_type, type, ex1I: $o). 119.84/17.06 thf(ex1E2_type, type, ex1E2: $o). 119.84/17.06 thf(setminus_type, type, setminus: $i > $i > $i). 119.84/17.06 thf(setukpairinjL1_type, type, setukpairinjL1: $o). 119.84/17.06 thf(powersetsubset_type, type, powersetsubset: $o). 119.84/17.06 thf(binunionTILcontra_type, type, binunionTILcontra: $o). 119.84/17.06 thf(subPowSU_type, type, subPowSU: $o). 119.84/17.06 thf(notequalI1_type, type, notequalI1: $o). 119.84/17.06 thf(contrasubsetT_type, type, contrasubsetT: $o). 119.84/17.06 thf(notinemptyset_type, type, notinemptyset: $o). 119.84/17.06 thf(lam2lamEq_type, type, lam2lamEq: $o). 119.84/17.06 thf(nonemptyI1_type, type, nonemptyI1: $o). 119.84/17.06 thf(subsetTrans_type, type, subsetTrans: $o). 119.84/17.06 thf(kpairp_type, type, kpairp: $o). 119.84/17.06 thf(setukpairinjR12_type, type, setukpairinjR12: $o). 119.84/17.06 thf(setminusI_type, type, setminusI: $o). 119.84/17.06 thf(binunionIL_type, type, binunionIL: $o). 119.84/17.06 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o). 119.84/17.06 thf(setunionsingleton_type, type, setunionsingleton: $o). 119.84/17.06 thf(subsetE2_type, type, subsetE2: $o). 119.84/17.06 thf(singletonsswitch_type, type, singletonsswitch: $o). 119.84/17.06 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o). 119.84/17.06 thf(beta2_type, type, beta2: $o). 119.84/17.06 thf(dpsetconstrI_type, type, dpsetconstrI: $o). 119.84/17.06 thf(setextsub_type, type, setextsub: $o). 119.84/17.06 thf(binunionLsub_type, type, binunionLsub: $o). 119.84/17.06 thf(setunionsingleton1_type, type, setunionsingleton1: $o). 119.84/17.06 thf(binintersect_type, type, binintersect: $i > $i > $i). 119.84/17.06 thf(iftrueorfalse_type, type, iftrueorfalse: $o). 119.84/17.06 thf(emptysetsubset_type, type, emptysetsubset: $o). 119.84/17.06 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 119.84/17.06 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o). 119.84/17.06 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o). 119.84/17.06 thf(setunionE_type, type, setunionE: $o). 119.84/17.06 thf(ksndsingleton_type, type, ksndsingleton: $o). 119.84/17.06 thf(setminusSubset1_type, type, setminusSubset1: $o). 119.84/17.06 thf(powersetT_lem_type, type, powersetT_lem: $o). 119.84/17.06 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 119.84/17.06 thf(binunionIR_type, type, binunionIR: $o). 119.84/17.06 thf(theeq_type, type, theeq: $o). 119.84/17.06 thf(setadjoinE_type, type, setadjoinE: $o). 119.84/17.06 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o). 119.84/17.06 thf(infuncsetfunc_type, type, infuncsetfunc: $o). 119.84/17.06 thf(ap2apEq2_type, type, ap2apEq2: $o). 119.84/17.06 thf(ap2p_type, type, ap2p: $o). 119.84/17.06 thf(setadjoinIL_type, type, setadjoinIL: $o). 119.84/17.06 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o). 119.84/17.06 thf(exuE1_type, type, exuE1: $o). 119.84/17.06 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o). 119.84/17.06 thf(binintersectRsub_type, type, binintersectRsub: $o). 119.84/17.06 thf(setminusLsub_type, type, setminusLsub: $o). 119.84/17.06 thf(funcextLem_type, type, funcextLem: $o). 119.84/17.06 thf(setukpairinjR_type, type, setukpairinjR: $o). 119.84/17.06 thf(notinsingleton_type, type, notinsingleton: $o). 119.84/17.06 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions: 119.84/17.06 $o). 119.84/17.06 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 119.84/17.06 thf(exuEu_type, type, exuEu: $o). 119.84/17.06 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 119.84/17.06 thf(upairsetE_type, type, upairsetE: $o). 119.84/17.06 thf(omega0Ax_type, type, omega0Ax: $o). 119.84/17.06 thf(subsetTI_type, type, subsetTI: $o). 119.84/17.06 thf(notsubsetI_type, type, notsubsetI: $o). 119.84/17.06 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o). 119.84/17.06 thf(iffalseProp1_type, type, iffalseProp1: $o). 119.84/17.06 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 119.84/17.06 thf(setextAx_type, type, setextAx: $o). 119.84/17.06 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o). 119.84/17.06 thf(powersetE1_type, type, powersetE1: $o). 119.84/17.06 thf(bs114d_type, type, bs114d: $o). 119.84/17.06 thf(contrasubsetT3_type, type, contrasubsetT3: $o). 119.84/17.06 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 119.84/17.06 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o). 119.84/17.06 thf(ifp_type, type, ifp: $o). 119.84/17.06 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o). 119.84/17.06 thf(powersetTI1_type, type, powersetTI1: $o). 119.84/17.06 thf(binintersectLsub_type, type, binintersectLsub: $o). 119.84/17.06 thf(subsetI1_type, type, subsetI1: $o). 119.84/17.06 thf(symdiffE_type, type, symdiffE: $o). 119.84/17.06 thf(descrp_type, type, descrp: $o). 119.84/17.06 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 119.84/17.06 thf(foundationAx_type, type, foundationAx: $o). 119.84/17.06 thf(emptysetAx_type, type, emptysetAx: $o). 119.84/17.06 thf(emptyI_type, type, emptyI: $o). 119.84/17.06 thf(setadjoinOr_type, type, setadjoinOr: $o). 119.84/17.06 thf(eta2_type, type, eta2: $o). 119.84/17.06 thf(binintersectEL_type, type, binintersectEL: $o). 119.84/17.06 thf(emptyE1_type, type, emptyE1: $o). 119.84/17.06 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 119.84/17.06 thf(complementTI1_type, type, complementTI1: $o). 119.84/17.06 thf(vacuousDall_type, type, vacuousDall: $o). 119.84/17.06 thf(dsetconstrER_type, type, dsetconstrER: $o). 119.84/17.06 thf(binintersectI_type, type, binintersectI: $o). 119.84/17.06 thf(funcext_type, type, funcext: $o). 119.84/17.06 thf(funcGraphProp4_type, type, funcGraphProp4: $o). 119.84/17.06 thf(cartprodpairin_type, type, cartprodpairin: $o). 119.84/17.06 thf(cartprodmempair1_type, type, cartprodmempair1: $o). 119.84/17.06 thf(brelnall2_type, type, brelnall2: $o). 119.84/17.06 thf(setextT_type, type, setextT: $o). 119.84/17.06 thf(ex1I2_type, type, ex1I2: $o). 119.84/17.06 thf(symdiffI1_type, type, symdiffI1: $o). 119.84/17.06 thf(sk__160_type, type, sk__160: $i > $i > $i). 119.84/17.06 thf(setukpairinjR2_type, type, setukpairinjR2: $o). 119.84/17.06 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o). 119.84/17.06 thf(theprop_type, type, theprop: $o). 119.84/17.06 thf(subsetI2_type, type, subsetI2: $o). 119.84/17.06 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect: 119.84/17.06 $o). 119.84/17.06 thf(setminusT_lem_type, type, setminusT_lem: $o). 119.84/17.06 thf(symdiffIneg1_type, type, symdiffIneg1: $o). 119.84/17.06 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o). 119.84/17.06 thf(setminusERneg_type, type, setminusERneg: $o). 119.84/17.06 thf(symdiffIneg2_type, type, symdiffIneg2: $o). 119.84/17.06 thf(omega__Cong_type, type, omega__Cong: $o). 119.84/17.06 thf(subsetRefl_type, type, subsetRefl: $o). 119.84/17.06 thf(uniqinunit_type, type, uniqinunit: $o). 119.84/17.06 thf(sk__157_type, type, sk__157: $i). 119.84/17.06 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect: 119.84/17.06 $o). 119.84/17.06 thf(setminusSubset2_type, type, setminusSubset2: $o). 119.84/17.06 thf(prop2setE_type, type, prop2setE: $o). 119.84/17.06 thf(binunionEcases_type, type, binunionEcases: $o). 119.84/17.06 thf(funcinfuncset_type, type, funcinfuncset: $o). 119.84/17.06 thf(complementTE1_type, type, complementTE1: $o). 119.84/17.06 thf(nonemptyI_type, type, nonemptyI: $o). 119.84/17.06 thf(app_type, type, app: $o). 119.84/17.06 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 119.84/17.06 thf(exuE3u_type, type, exuE3u: $o). 119.84/17.06 thf(eta1_type, type, eta1: $o). 119.84/17.06 thf(setminusEL_type, type, setminusEL: $o). 119.84/17.06 thf(cartprodfstin_type, type, cartprodfstin: $o). 119.84/17.06 thf(setunionsingleton2_type, type, setunionsingleton2: $o). 119.84/17.06 thf(sepSubset_type, type, sepSubset: $o). 119.84/17.06 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o). 119.84/17.06 thf(upairset2E_type, type, upairset2E: $o). 119.84/17.06 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 119.84/17.06 thf(exuI3_type, type, exuI3: $o). 119.84/17.06 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o). 119.84/17.06 thf(apProp_type, type, apProp: $o). 119.84/17.06 thf(notdallE_type, type, notdallE: $o). 119.84/17.06 thf(iftrueProp1_type, type, iftrueProp1: $o). 119.84/17.06 thf(binintersectER_type, type, binintersectER: $o). 119.84/17.06 thf(brelnall1_type, type, brelnall1: $o). 119.84/17.06 thf(powerset_type, type, powerset: $i > $i). 119.84/17.06 thf(dsetconstrI_type, type, dsetconstrI: $o). 119.84/17.06 thf(funcGraphProp1_type, type, funcGraphProp1: $o). 119.84/17.06 thf(binintersectT_lem_type, type, binintersectT_lem: $o). 119.84/17.06 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 119.84/17.06 thf(exu__Cong_type, type, exu__Cong: $o). 119.84/17.06 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 119.84/17.06 thf(contrasubsetT2_type, type, contrasubsetT2: $o). 119.84/17.06 thf(secondinupair_type, type, secondinupair: $o). 119.84/17.06 thf(singletonprop_type, type, singletonprop: $o). 119.84/17.06 thf(singletonsubset_type, type, singletonsubset: $o). 119.84/17.06 thf(contrasubsetT1_type, type, contrasubsetT1: $o). 119.84/17.06 thf(singletoninpowerset_type, type, singletoninpowerset: $o). 119.84/17.06 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 119.84/17.06 thf(replAx_type, type, replAx: $o). 119.84/17.06 thf(upairequniteq_type, type, upairequniteq: $o). 119.84/17.06 thf(nonemptyE1_type, type, nonemptyE1: $o). 119.84/17.06 thf(omegaIndAx_type, type, omegaIndAx: $o). 119.84/17.06 thf(setukpairIL_type, type, setukpairIL: $o). 119.84/17.06 thf(setunionE2_type, type, setunionE2: $o). 119.84/17.06 thf(inPowerset_type, type, inPowerset: $o). 119.84/17.06 thf(iffalse_type, type, iffalse: $o). 119.84/17.06 thf(funcext2_type, type, funcext2: $o). 119.84/17.06 thf(subset_type, type, subset: $i > $i > $o). 119.84/17.06 thf(subbreln_type, type, subbreln: $o). 119.84/17.06 thf(in__Cong_type, type, in__Cong: $o). 119.84/17.06 thf(binunionRsub_type, type, binunionRsub: $o). 119.84/17.06 thf(subset2powerset_type, type, subset2powerset: $o). 119.84/17.06 thf(inIntersectImpInIntersectUnions, axiom, inIntersectImpInIntersectUnions = 119.84/17.06 (![A:$i,X:$i]: 119.84/17.06 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.06 ( ![Y:$i]: 119.84/17.06 ( ( in @ Y @ ( powerset @ A ) ) => 119.84/17.06 ( ![Z:$i]: 119.84/17.06 ( ( in @ Z @ ( powerset @ A ) ) => 119.84/17.06 ( ![Xx:$i]: 119.84/17.06 ( ( in @ Xx @ A ) => 119.84/17.06 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) => 119.84/17.06 ( in @ 119.84/17.06 Xx @ 119.84/17.06 ( binintersect @ 119.84/17.06 ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ))). 119.84/17.06 thf('0', plain, 119.84/17.06 (( inIntersectImpInIntersectUnions ) = 119.84/17.06 ( ![X4:$i,X6:$i]: 119.84/17.06 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X8:$i]: 119.84/17.06 ( ( in @ X8 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X10:$i]: 119.84/17.06 ( ( in @ X10 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X12:$i]: 119.84/17.06 ( ( in @ X12 @ X4 ) => 119.84/17.06 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) => 119.84/17.06 ( in @ 119.84/17.06 X12 @ 119.84/17.06 ( binintersect @ 119.84/17.06 ( binunion @ X6 @ X10 ) @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) ) ) )), 119.84/17.06 define([status(thm)])). 119.84/17.06 thf(inIntersectImpInUnion2, axiom, inIntersectImpInUnion2 = 119.84/17.06 (![A:$i,X:$i]: 119.84/17.06 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.06 ( ![Y:$i]: 119.84/17.06 ( ( in @ Y @ ( powerset @ A ) ) => 119.84/17.06 ( ![Z:$i]: 119.84/17.06 ( ( in @ Z @ ( powerset @ A ) ) => 119.84/17.06 ( ![Xx:$i]: 119.84/17.06 ( ( in @ Xx @ A ) => 119.84/17.06 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) => 119.84/17.06 ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ))). 119.84/17.06 thf('1', plain, 119.84/17.06 (( inIntersectImpInUnion2 ) = 119.84/17.06 ( ![X4:$i,X6:$i]: 119.84/17.06 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X8:$i]: 119.84/17.06 ( ( in @ X8 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X10:$i]: 119.84/17.06 ( ( in @ X10 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X12:$i]: 119.84/17.06 ( ( in @ X12 @ X4 ) => 119.84/17.06 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) => 119.84/17.06 ( in @ X12 @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) ) )), 119.84/17.06 define([status(thm)])). 119.84/17.06 thf(inIntersectImpInUnion, axiom, inIntersectImpInUnion = 119.84/17.06 (![A:$i,X:$i]: 119.84/17.06 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.06 ( ![Y:$i]: 119.84/17.06 ( ( in @ Y @ ( powerset @ A ) ) => 119.84/17.06 ( ![Z:$i]: 119.84/17.06 ( ( in @ Z @ ( powerset @ A ) ) => 119.84/17.06 ( ![Xx:$i]: 119.84/17.06 ( ( in @ Xx @ A ) => 119.84/17.06 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) => 119.84/17.06 ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ))). 119.84/17.06 thf('2', plain, 119.84/17.06 (( inIntersectImpInUnion ) = 119.84/17.06 ( ![X4:$i,X6:$i]: 119.84/17.06 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X8:$i]: 119.84/17.06 ( ( in @ X8 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X10:$i]: 119.84/17.06 ( ( in @ X10 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X12:$i]: 119.84/17.06 ( ( in @ X12 @ X4 ) => 119.84/17.06 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) => 119.84/17.06 ( in @ X12 @ ( binunion @ X6 @ X10 ) ) ) ) ) ) ) ) ) ) )), 119.84/17.06 define([status(thm)])). 119.84/17.06 thf(binunionTIRcontra, axiom, binunionTIRcontra = 119.84/17.06 (![A:$i,X:$i]: 119.84/17.06 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.06 ( ![Y:$i]: 119.84/17.06 ( ( in @ Y @ ( powerset @ A ) ) => 119.84/17.06 ( ![Xx:$i]: 119.84/17.06 ( ( in @ Xx @ A ) => 119.84/17.06 ( ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) => 119.84/17.06 ( ~( in @ Xx @ Y ) ) ) ) ) ) ) ))). 119.84/17.06 thf('3', plain, 119.84/17.06 (( binunionTIRcontra ) = 119.84/17.06 ( ![X4:$i,X6:$i]: 119.84/17.06 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X8:$i]: 119.84/17.06 ( ( in @ X8 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X10:$i]: 119.84/17.06 ( ( in @ X10 @ X4 ) => 119.84/17.06 ( ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) => 119.84/17.06 ( ~( in @ X10 @ X8 ) ) ) ) ) ) ) ) )), 119.84/17.06 define([status(thm)])). 119.84/17.06 thf(binunionTILcontra, axiom, binunionTILcontra = 119.84/17.06 (![A:$i,X:$i]: 119.84/17.06 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.06 ( ![Y:$i]: 119.84/17.06 ( ( in @ Y @ ( powerset @ A ) ) => 119.84/17.06 ( ![Xx:$i]: 119.84/17.06 ( ( in @ Xx @ A ) => 119.84/17.06 ( ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) => 119.84/17.06 ( ~( in @ Xx @ X ) ) ) ) ) ) ) ))). 119.84/17.06 thf('4', plain, 119.84/17.06 (( binunionTILcontra ) = 119.84/17.06 ( ![X4:$i,X6:$i]: 119.84/17.06 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X8:$i]: 119.84/17.06 ( ( in @ X8 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X10:$i]: 119.84/17.06 ( ( in @ X10 @ X4 ) => 119.84/17.06 ( ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) => 119.84/17.06 ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) )), 119.84/17.06 define([status(thm)])). 119.84/17.06 thf(complementInPowersetComplementIntersect, axiom, 119.84/17.06 complementInPowersetComplementIntersect = 119.84/17.06 (![A:$i,X:$i]: 119.84/17.06 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.06 ( ![Y:$i]: 119.84/17.06 ( ( in @ Y @ ( powerset @ A ) ) => 119.84/17.06 ( in @ 119.84/17.06 ( setminus @ A @ X ) @ 119.84/17.06 ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ))). 119.84/17.06 thf('5', plain, 119.84/17.06 (( complementInPowersetComplementIntersect ) = 119.84/17.06 ( ![X4:$i,X6:$i]: 119.84/17.06 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X8:$i]: 119.84/17.06 ( ( in @ X8 @ ( powerset @ X4 ) ) => 119.84/17.06 ( in @ 119.84/17.06 ( setminus @ X4 @ X6 ) @ 119.84/17.06 ( powerset @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) )), 119.84/17.06 define([status(thm)])). 119.84/17.06 thf(complementSubsetComplementIntersect, axiom, 119.84/17.06 complementSubsetComplementIntersect = 119.84/17.06 (![A:$i,X:$i]: 119.84/17.06 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.06 ( ![Y:$i]: 119.84/17.06 ( ( in @ Y @ ( powerset @ A ) ) => 119.84/17.06 ( subset @ 119.84/17.06 ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ))). 119.84/17.06 thf('6', plain, 119.84/17.06 (( complementSubsetComplementIntersect ) = 119.84/17.06 ( ![X4:$i,X6:$i]: 119.84/17.06 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X8:$i]: 119.84/17.06 ( ( in @ X8 @ ( powerset @ X4 ) ) => 119.84/17.06 ( subset @ 119.84/17.06 ( setminus @ X4 @ X6 ) @ 119.84/17.06 ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) )), 119.84/17.06 define([status(thm)])). 119.84/17.06 thf(complementImpComplementIntersect, axiom, 119.84/17.06 complementImpComplementIntersect = 119.84/17.06 (![A:$i,X:$i]: 119.84/17.06 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.06 ( ![Y:$i]: 119.84/17.06 ( ( in @ Y @ ( powerset @ A ) ) => 119.84/17.06 ( ![Xx:$i]: 119.84/17.06 ( ( in @ Xx @ A ) => 119.84/17.06 ( ( in @ Xx @ ( setminus @ A @ X ) ) => 119.84/17.06 ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))). 119.84/17.06 thf('7', plain, 119.84/17.06 (( complementImpComplementIntersect ) = 119.84/17.06 ( ![X4:$i,X6:$i]: 119.84/17.06 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X8:$i]: 119.84/17.06 ( ( in @ X8 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X10:$i]: 119.84/17.06 ( ( in @ X10 @ X4 ) => 119.84/17.06 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) => 119.84/17.06 ( in @ 119.84/17.06 X10 @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )), 119.84/17.06 define([status(thm)])). 119.84/17.06 thf(complementTnotintersectT, axiom, complementTnotintersectT = 119.84/17.06 (![A:$i,X:$i]: 119.84/17.06 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.06 ( ![Y:$i]: 119.84/17.06 ( ( in @ Y @ ( powerset @ A ) ) => 119.84/17.06 ( ![Xx:$i]: 119.84/17.06 ( ( in @ Xx @ A ) => 119.84/17.06 ( ( in @ Xx @ ( setminus @ A @ X ) ) => 119.84/17.06 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))). 119.84/17.06 thf('8', plain, 119.84/17.06 (( complementTnotintersectT ) = 119.84/17.06 ( ![X4:$i,X6:$i]: 119.84/17.06 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X8:$i]: 119.84/17.06 ( ( in @ X8 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X10:$i]: 119.84/17.06 ( ( in @ X10 @ X4 ) => 119.84/17.06 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) => 119.84/17.06 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )), 119.84/17.06 define([status(thm)])). 119.84/17.06 thf(binintersectTERcontra, axiom, binintersectTERcontra = 119.84/17.06 (![A:$i,X:$i]: 119.84/17.06 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.06 ( ![Y:$i]: 119.84/17.06 ( ( in @ Y @ ( powerset @ A ) ) => 119.84/17.06 ( ![Xx:$i]: 119.84/17.06 ( ( in @ Xx @ A ) => 119.84/17.06 ( ( ~( in @ Xx @ Y ) ) => 119.84/17.06 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))). 119.84/17.06 thf('9', plain, 119.84/17.06 (( binintersectTERcontra ) = 119.84/17.06 ( ![X4:$i,X6:$i]: 119.84/17.06 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X8:$i]: 119.84/17.06 ( ( in @ X8 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X10:$i]: 119.84/17.06 ( ( in @ X10 @ X4 ) => 119.84/17.06 ( ( ~( in @ X10 @ X8 ) ) => 119.84/17.06 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )), 119.84/17.06 define([status(thm)])). 119.84/17.06 thf(binintersectTELcontra, axiom, binintersectTELcontra = 119.84/17.06 (![A:$i,X:$i]: 119.84/17.06 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.06 ( ![Y:$i]: 119.84/17.06 ( ( in @ Y @ ( powerset @ A ) ) => 119.84/17.06 ( ![Xx:$i]: 119.84/17.06 ( ( in @ Xx @ A ) => 119.84/17.06 ( ( ~( in @ Xx @ X ) ) => 119.84/17.06 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))). 119.84/17.06 thf('10', plain, 119.84/17.06 (( binintersectTELcontra ) = 119.84/17.06 ( ![X4:$i,X6:$i]: 119.84/17.06 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X8:$i]: 119.84/17.06 ( ( in @ X8 @ ( powerset @ X4 ) ) => 119.84/17.06 ( ![X10:$i]: 119.84/17.06 ( ( in @ X10 @ X4 ) => 119.84/17.06 ( ( ~( in @ X10 @ X6 ) ) => 119.84/17.06 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )), 119.84/17.06 define([status(thm)])). 119.84/17.06 thf(powersetTE1, axiom, powersetTE1 = 119.84/17.06 (![A:$i,X:$i]: 119.84/17.06 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.06 ( ![Y:$i]: 119.84/17.07 ( ( in @ Y @ ( powerset @ A ) ) => 119.84/17.07 ( ![Xx:$i]: 119.84/17.07 ( ( in @ Xx @ A ) => 119.84/17.07 ( ( in @ X @ ( powerset @ Y ) ) => 119.84/17.07 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))). 119.84/17.07 thf('11', plain, 119.84/17.07 (( powersetTE1 ) = 119.84/17.07 ( ![X4:$i,X6:$i]: 119.84/17.07 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.07 ( ![X8:$i]: 119.84/17.07 ( ( in @ X8 @ ( powerset @ X4 ) ) => 119.84/17.07 ( ![X10:$i]: 119.84/17.07 ( ( in @ X10 @ X4 ) => 119.84/17.07 ( ( in @ X6 @ ( powerset @ X8 ) ) => 119.84/17.07 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(powersetTI1, axiom, powersetTI1 = 119.84/17.07 (![A:$i,X:$i]: 119.84/17.07 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.07 ( ![Y:$i]: 119.84/17.07 ( ( in @ Y @ ( powerset @ A ) ) => 119.84/17.07 ( ( ![Xx:$i]: 119.84/17.07 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) => 119.84/17.07 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))). 119.84/17.07 thf('12', plain, 119.84/17.07 (( powersetTI1 ) = 119.84/17.07 ( ![X4:$i,X6:$i]: 119.84/17.07 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.07 ( ![X8:$i]: 119.84/17.07 ( ( in @ X8 @ ( powerset @ X4 ) ) => 119.84/17.07 ( ( ![X10:$i]: 119.84/17.07 ( ( in @ X10 @ X4 ) => 119.84/17.07 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) => 119.84/17.07 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(setextT, axiom, setextT = 119.84/17.07 (![A:$i,X:$i]: 119.84/17.07 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.07 ( ![Y:$i]: 119.84/17.07 ( ( in @ Y @ ( powerset @ A ) ) => 119.84/17.07 ( ( ![Xx:$i]: 119.84/17.07 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) => 119.84/17.07 ( ( ![Xx:$i]: 119.84/17.07 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) => 119.84/17.07 ( ( X ) = ( Y ) ) ) ) ) ) ))). 119.84/17.07 thf('13', plain, 119.84/17.07 (( setextT ) = 119.84/17.07 ( ![X4:$i,X6:$i]: 119.84/17.07 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.07 ( ![X8:$i]: 119.84/17.07 ( ( in @ X8 @ ( powerset @ X4 ) ) => 119.84/17.07 ( ( ![X10:$i]: 119.84/17.07 ( ( in @ X10 @ X4 ) => 119.84/17.07 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) => 119.84/17.07 ( ( ![X12:$i]: 119.84/17.07 ( ( in @ X12 @ X4 ) => 119.84/17.07 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) => 119.84/17.07 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(powersetT_lem, axiom, powersetT_lem = 119.84/17.07 (![A:$i,X:$i]: 119.84/17.07 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.07 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))). 119.84/17.07 thf('14', plain, 119.84/17.07 (( powersetT_lem ) = 119.84/17.07 ( ![X4:$i,X6:$i]: 119.84/17.07 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.07 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binunionT_lem, axiom, binunionT_lem = 119.84/17.07 (![A:$i,X:$i]: 119.84/17.07 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.07 ( ![Y:$i]: 119.84/17.07 ( ( in @ Y @ ( powerset @ A ) ) => 119.84/17.07 ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ))). 119.84/17.07 thf('15', plain, 119.84/17.07 (( binunionT_lem ) = 119.84/17.07 ( ![X4:$i,X6:$i]: 119.84/17.07 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.07 ( ![X8:$i]: 119.84/17.07 ( ( in @ X8 @ ( powerset @ X4 ) ) => 119.84/17.07 ( in @ ( binunion @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binintersectT_lem, axiom, binintersectT_lem = 119.84/17.07 (![A:$i,X:$i]: 119.84/17.07 ( ( in @ X @ ( powerset @ A ) ) => 119.84/17.07 ( ![Y:$i]: 119.84/17.07 ( ( in @ Y @ ( powerset @ A ) ) => 119.84/17.07 ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ))). 119.84/17.07 thf('16', plain, 119.84/17.07 (( binintersectT_lem ) = 119.84/17.07 ( ![X4:$i,X6:$i]: 119.84/17.07 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.07 ( ![X8:$i]: 119.84/17.07 ( ( in @ X8 @ ( powerset @ X4 ) ) => 119.84/17.07 ( in @ ( binintersect @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(ubforcartprodlem3, axiom, ubforcartprodlem3 = 119.84/17.07 (![A:$i,B:$i,Xx:$i]: 119.84/17.07 ( ( in @ Xx @ A ) => 119.84/17.07 ( ![Xy:$i]: 119.84/17.07 ( ( in @ Xy @ B ) => 119.84/17.07 ( in @ 119.84/17.07 ( kpair @ Xx @ Xy ) @ 119.84/17.07 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))). 119.84/17.07 thf('17', plain, 119.84/17.07 (( ubforcartprodlem3 ) = 119.84/17.07 ( ![X4:$i,X6:$i,X8:$i]: 119.84/17.07 ( ( in @ X8 @ X4 ) => 119.84/17.07 ( ![X10:$i]: 119.84/17.07 ( ( in @ X10 @ X6 ) => 119.84/17.07 ( in @ 119.84/17.07 ( kpair @ X8 @ X10 ) @ 119.84/17.07 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(ubforcartprodlem2, axiom, ubforcartprodlem2 = 119.84/17.07 (![A:$i,B:$i,Xx:$i]: 119.84/17.07 ( ( in @ Xx @ A ) => 119.84/17.07 ( ![Xy:$i]: 119.84/17.07 ( ( in @ Xy @ B ) => 119.84/17.07 ( in @ 119.84/17.07 ( setadjoin @ 119.84/17.07 ( setadjoin @ Xx @ emptyset ) @ 119.84/17.07 ( setadjoin @ 119.84/17.07 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ 119.84/17.07 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))). 119.84/17.07 thf('18', plain, 119.84/17.07 (( ubforcartprodlem2 ) = 119.84/17.07 ( ![X4:$i,X6:$i,X8:$i]: 119.84/17.07 ( ( in @ X8 @ X4 ) => 119.84/17.07 ( ![X10:$i]: 119.84/17.07 ( ( in @ X10 @ X6 ) => 119.84/17.07 ( in @ 119.84/17.07 ( setadjoin @ 119.84/17.07 ( setadjoin @ X8 @ emptyset ) @ 119.84/17.07 ( setadjoin @ 119.84/17.07 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ 119.84/17.07 emptyset ) ) @ 119.84/17.07 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(ubforcartprodlem1, axiom, ubforcartprodlem1 = 119.84/17.07 (![A:$i,B:$i,Xx:$i]: 119.84/17.07 ( ( in @ Xx @ A ) => 119.84/17.07 ( ![Xy:$i]: 119.84/17.07 ( ( in @ Xy @ B ) => 119.84/17.07 ( subset @ 119.84/17.07 ( setadjoin @ 119.84/17.07 ( setadjoin @ Xx @ emptyset ) @ 119.84/17.07 ( setadjoin @ 119.84/17.07 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ 119.84/17.07 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))). 119.84/17.07 thf('19', plain, 119.84/17.07 (( ubforcartprodlem1 ) = 119.84/17.07 ( ![X4:$i,X6:$i,X8:$i]: 119.84/17.07 ( ( in @ X8 @ X4 ) => 119.84/17.07 ( ![X10:$i]: 119.84/17.07 ( ( in @ X10 @ X6 ) => 119.84/17.07 ( subset @ 119.84/17.07 ( setadjoin @ 119.84/17.07 ( setadjoin @ X8 @ emptyset ) @ 119.84/17.07 ( setadjoin @ 119.84/17.07 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ 119.84/17.07 emptyset ) ) @ 119.84/17.07 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(upairinpowunion, axiom, upairinpowunion = 119.84/17.07 (![A:$i,B:$i,Xx:$i]: 119.84/17.07 ( ( in @ Xx @ A ) => 119.84/17.07 ( ![Xy:$i]: 119.84/17.07 ( ( in @ Xy @ B ) => 119.84/17.07 ( in @ 119.84/17.07 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ 119.84/17.07 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))). 119.84/17.07 thf('20', plain, 119.84/17.07 (( upairinpowunion ) = 119.84/17.07 ( ![X4:$i,X6:$i,X8:$i]: 119.84/17.07 ( ( in @ X8 @ X4 ) => 119.84/17.07 ( ![X10:$i]: 119.84/17.07 ( ( in @ X10 @ X6 ) => 119.84/17.07 ( in @ 119.84/17.07 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ 119.84/17.07 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(upairsubunion, axiom, upairsubunion = 119.84/17.07 (![A:$i,B:$i,Xx:$i]: 119.84/17.07 ( ( in @ Xx @ A ) => 119.84/17.07 ( ![Xy:$i]: 119.84/17.07 ( ( in @ Xy @ B ) => 119.84/17.07 ( subset @ 119.84/17.07 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ 119.84/17.07 ( binunion @ A @ B ) ) ) ) ))). 119.84/17.07 thf('21', plain, 119.84/17.07 (( upairsubunion ) = 119.84/17.07 ( ![X4:$i,X6:$i,X8:$i]: 119.84/17.07 ( ( in @ X8 @ X4 ) => 119.84/17.07 ( ![X10:$i]: 119.84/17.07 ( ( in @ X10 @ X6 ) => 119.84/17.07 ( subset @ 119.84/17.07 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ 119.84/17.07 ( binunion @ X4 @ X6 ) ) ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(singletoninpowunion, axiom, singletoninpowunion = 119.84/17.07 (![A:$i,B:$i,Xx:$i]: 119.84/17.07 ( ( in @ Xx @ A ) => 119.84/17.07 ( in @ 119.84/17.07 ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ))). 119.84/17.07 thf('22', plain, 119.84/17.07 (( singletoninpowunion ) = 119.84/17.07 ( ![X4:$i,X6:$i,X8:$i]: 119.84/17.07 ( ( in @ X8 @ X4 ) => 119.84/17.07 ( in @ 119.84/17.07 ( setadjoin @ X8 @ emptyset ) @ 119.84/17.07 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(bs114d, axiom, bs114d = 119.84/17.07 (![A:$i,B:$i,C:$i]: 119.84/17.07 ( ( binintersect @ A @ ( binunion @ B @ C ) ) = 119.84/17.07 ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ))). 119.84/17.07 thf('23', plain, 119.84/17.07 (( bs114d ) = 119.84/17.07 ( ![X4:$i,X6:$i,X8:$i]: 119.84/17.07 ( ( binintersect @ X4 @ ( binunion @ X6 @ X8 ) ) = 119.84/17.07 ( binunion @ ( binintersect @ X4 @ X6 ) @ ( binintersect @ X4 @ X8 ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binintersectSubset1, axiom, binintersectSubset1 = 119.84/17.07 (![A:$i,B:$i]: 119.84/17.07 ( ( ( binintersect @ A @ B ) = ( A ) ) => ( subset @ A @ B ) ))). 119.84/17.07 thf('24', plain, 119.84/17.07 (( binintersectSubset1 ) = 119.84/17.07 ( ![X4:$i,X6:$i]: 119.84/17.07 ( ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) => ( subset @ X4 @ X6 ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binintersectSubset4, axiom, binintersectSubset4 = 119.84/17.07 (![A:$i,B:$i]: 119.84/17.07 ( ( subset @ B @ A ) => ( ( binintersect @ A @ B ) = ( B ) ) ))). 119.84/17.07 thf('25', plain, 119.84/17.07 (( binintersectSubset4 ) = 119.84/17.07 ( ![X4:$i,X6:$i]: 119.84/17.07 ( ( subset @ X6 @ X4 ) => ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binintersectRsub, axiom, binintersectRsub = 119.84/17.07 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ B ))). 119.84/17.07 thf('26', plain, 119.84/17.07 (( binintersectRsub ) = 119.84/17.07 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X6 ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(disjointsetsI1, axiom, disjointsetsI1 = 119.84/17.07 (![A:$i,B:$i]: 119.84/17.07 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ B ) & ( in @ Xx @ A ) ) ) ) => 119.84/17.07 ( ( binintersect @ A @ B ) = ( emptyset ) ) ))). 119.84/17.07 thf('27', plain, 119.84/17.07 (( disjointsetsI1 ) = 119.84/17.07 ( ![X4:$i,X6:$i]: 119.84/17.07 ( ( ~( ?[X8:$i]: ( ( in @ X8 @ X6 ) & ( in @ X8 @ X4 ) ) ) ) => 119.84/17.07 ( ( binintersect @ X4 @ X6 ) = ( emptyset ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binintersectER, axiom, binintersectER = 119.84/17.07 (![A:$i,B:$i,Xx:$i]: 119.84/17.07 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ B ) ))). 119.84/17.07 thf('28', plain, 119.84/17.07 (( binintersectER ) = 119.84/17.07 ( ![X4:$i,X6:$i,X8:$i]: 119.84/17.07 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X6 ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binintersectSubset3, axiom, binintersectSubset3 = 119.84/17.07 (![A:$i,B:$i]: 119.84/17.07 ( ( ( binintersect @ A @ B ) = ( B ) ) => ( subset @ B @ A ) ))). 119.84/17.07 thf('29', plain, 119.84/17.07 (( binintersectSubset3 ) = 119.84/17.07 ( ![X4:$i,X6:$i]: 119.84/17.07 ( ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binintersectSubset2, axiom, binintersectSubset2 = 119.84/17.07 (![A:$i,B:$i]: 119.84/17.07 ( ( subset @ A @ B ) => ( ( binintersect @ A @ B ) = ( A ) ) ))). 119.84/17.07 thf('30', plain, 119.84/17.07 (( binintersectSubset2 ) = 119.84/17.07 ( ![X4:$i,X6:$i]: 119.84/17.07 ( ( subset @ X4 @ X6 ) => ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binintersectLsub, axiom, binintersectLsub = 119.84/17.07 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ A ))). 119.84/17.07 thf('31', plain, 119.84/17.07 (( binintersectLsub ) = 119.84/17.07 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X4 ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binintersectEL, axiom, binintersectEL = 119.84/17.07 (![A:$i,B:$i,Xx:$i]: 119.84/17.07 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ A ) ))). 119.84/17.07 thf('32', plain, 119.84/17.07 (( binintersectEL ) = 119.84/17.07 ( ![X4:$i,X6:$i,X8:$i]: 119.84/17.07 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binintersectSubset5, axiom, binintersectSubset5 = 119.84/17.07 (![A:$i,B:$i,C:$i]: 119.84/17.07 ( ( subset @ C @ A ) => 119.84/17.07 ( ( subset @ C @ B ) => ( subset @ C @ ( binintersect @ A @ B ) ) ) ))). 119.84/17.07 thf('33', plain, 119.84/17.07 (( binintersectSubset5 ) = 119.84/17.07 ( ![X4:$i,X6:$i,X8:$i]: 119.84/17.07 ( ( subset @ X8 @ X4 ) => 119.84/17.07 ( ( subset @ X8 @ X6 ) => 119.84/17.07 ( subset @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binintersectI, axiom, binintersectI = 119.84/17.07 (![A:$i,B:$i,Xx:$i]: 119.84/17.07 ( ( in @ Xx @ A ) => 119.84/17.07 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ))). 119.84/17.07 thf('34', plain, 119.84/17.07 (( binintersectI ) = 119.84/17.07 ( ![X4:$i,X6:$i,X8:$i]: 119.84/17.07 ( ( in @ X8 @ X4 ) => 119.84/17.07 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binunionRsub, axiom, binunionRsub = 119.84/17.07 (![A:$i,B:$i]: ( subset @ B @ ( binunion @ A @ B ) ))). 119.84/17.07 thf('35', plain, 119.84/17.07 (( binunionRsub ) = 119.84/17.07 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( binunion @ X4 @ X6 ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binunionLsub, axiom, binunionLsub = 119.84/17.07 (![A:$i,B:$i]: ( subset @ A @ ( binunion @ A @ B ) ))). 119.84/17.07 thf('36', plain, 119.84/17.07 (( binunionLsub ) = 119.84/17.07 ( ![X4:$i,X6:$i]: ( subset @ X4 @ ( binunion @ X4 @ X6 ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binunionE, axiom, binunionE = 119.84/17.07 (![A:$i,B:$i,Xx:$i]: 119.84/17.07 ( ( in @ Xx @ ( binunion @ A @ B ) ) => 119.84/17.07 ( ( in @ Xx @ A ) | ( in @ Xx @ B ) ) ))). 119.84/17.07 thf('37', plain, 119.84/17.07 (( binunionE ) = 119.84/17.07 ( ![X4:$i,X6:$i,X8:$i]: 119.84/17.07 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) => 119.84/17.07 ( ( in @ X8 @ X4 ) | ( in @ X8 @ X6 ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binunionEcases, axiom, binunionEcases = 119.84/17.07 (![A:$i,B:$i,Xx:$i,Xphi:$o]: 119.84/17.07 ( ( in @ Xx @ ( binunion @ A @ B ) ) => 119.84/17.07 ( ( ( in @ Xx @ A ) => ( Xphi ) ) => 119.84/17.07 ( ( ( in @ Xx @ B ) => ( Xphi ) ) => ( Xphi ) ) ) ))). 119.84/17.07 thf('38', plain, 119.84/17.07 (( binunionEcases ) = 119.84/17.07 ( ![X4:$i,X6:$i,X8:$i,X10:$o]: 119.84/17.07 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) => 119.84/17.07 ( ( ( in @ X8 @ X4 ) => ( X10 ) ) => 119.84/17.07 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binunionIR, axiom, binunionIR = 119.84/17.07 (![A:$i,B:$i,Xx:$i]: 119.84/17.07 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))). 119.84/17.07 thf('39', plain, 119.84/17.07 (( binunionIR ) = 119.84/17.07 ( ![X4:$i,X6:$i,X8:$i]: 119.84/17.07 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(binunionIL, axiom, binunionIL = 119.84/17.07 (![A:$i,B:$i,Xx:$i]: 119.84/17.07 ( ( in @ Xx @ A ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))). 119.84/17.07 thf('40', plain, 119.84/17.07 (( binunionIL ) = 119.84/17.07 ( ![X4:$i,X6:$i,X8:$i]: 119.84/17.07 ( ( in @ X8 @ X4 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))). 119.84/17.07 thf('41', plain, 119.84/17.07 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(powerset__Cong, axiom, powerset__Cong = 119.84/17.07 (![A:$i,B:$i]: 119.84/17.07 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))). 119.84/17.07 thf('42', plain, 119.84/17.07 (( powerset__Cong ) = 119.84/17.07 ( ![X4:$i,X6:$i]: 119.84/17.07 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(powersetE, axiom, powersetE = 119.84/17.07 (![A:$i,B:$i,Xx:$i]: 119.84/17.07 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))). 119.84/17.07 thf('43', plain, 119.84/17.07 (( powersetE ) = 119.84/17.07 ( ![X4:$i,X6:$i,X8:$i]: 119.84/17.07 ( ( in @ X6 @ ( powerset @ X4 ) ) => 119.84/17.07 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(emptyInPowerset, axiom, emptyInPowerset = 119.84/17.07 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))). 119.84/17.07 thf('44', plain, 119.84/17.07 (( emptyInPowerset ) = 119.84/17.07 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(emptyinPowerset, axiom, emptyinPowerset = 119.84/17.07 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))). 119.84/17.07 thf('45', plain, 119.84/17.07 (( emptyinPowerset ) = 119.84/17.07 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(powersetI, axiom, powersetI = 119.84/17.07 (![A:$i,B:$i]: 119.84/17.07 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) => 119.84/17.07 ( in @ B @ ( powerset @ A ) ) ))). 119.84/17.07 thf('46', plain, 119.84/17.07 (( powersetI ) = 119.84/17.07 ( ![X4:$i,X6:$i]: 119.84/17.07 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) => 119.84/17.07 ( in @ X6 @ ( powerset @ X4 ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(powersetAx, axiom, powersetAx = 119.84/17.07 (![A:$i,B:$i]: 119.84/17.07 ( ( in @ B @ ( powerset @ A ) ) <=> 119.84/17.07 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))). 119.84/17.07 thf('47', plain, 119.84/17.07 (( powersetAx ) = 119.84/17.07 ( ![X4:$i,X6:$i]: 119.84/17.07 ( ( in @ X6 @ ( powerset @ X4 ) ) <=> 119.84/17.07 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )), 119.84/17.07 define([status(thm)])). 119.84/17.07 thf(intersectInPowersetIntersectUnions, conjecture, 119.84/17.07 (( setextAx ) => 119.84/17.07 ( ( emptysetAx ) => 119.84/17.07 ( ( setadjoinAx ) => 119.84/17.07 ( ( powersetAx ) => 119.84/17.07 ( ( setunionAx ) => 119.84/17.07 ( ( omega0Ax ) => 119.84/17.07 ( ( omegaSAx ) => 119.84/17.07 ( ( omegaIndAx ) => 119.84/17.07 ( ( replAx ) => 119.84/17.07 ( ( foundationAx ) => 119.84/17.07 ( ( wellorderingAx ) => 119.84/17.07 ( ( descrp ) => 119.84/17.07 ( ( dsetconstrI ) => 119.84/17.07 ( ( dsetconstrEL ) => 119.84/17.07 ( ( dsetconstrER ) => 119.84/17.07 ( ( exuE1 ) => 119.84/17.07 ( ( prop2setE ) => 119.84/17.07 ( ( emptysetE ) => 119.84/17.07 ( ( emptysetimpfalse ) => 119.84/17.07 ( ( notinemptyset ) => 119.84/17.07 ( ( exuE3e ) => 119.84/17.07 ( ( setext ) => 119.84/17.07 ( ( emptyI ) => 119.84/17.07 ( ( noeltsimpempty ) => 119.84/17.07 ( ( setbeta ) => 119.84/17.07 ( ( nonemptyE1 ) => 119.84/17.07 ( ( nonemptyI ) => 119.84/17.07 ( ( nonemptyI1 ) => 119.84/17.07 ( ( setadjoinIL ) => 119.84/17.07 ( ( emptyinunitempty ) => 119.84/17.07 ( ( setadjoinIR ) => 119.84/17.07 ( ( setadjoinE ) => 119.84/17.07 ( ( 119.84/17.07 setadjoinOr ) => 119.84/17.07 ( 119.84/17.07 ( 119.84/17.07 setoftrueEq ) => 119.84/17.07 ( 119.84/17.07 ( 119.84/17.07 powersetI ) => 119.84/17.07 ( 119.84/17.07 ( 119.84/17.07 emptyinPowerset ) => 119.84/17.07 ( 119.84/17.07 ( 119.84/17.07 emptyInPowerset ) => 119.84/17.07 ( 119.84/17.07 ( 119.84/17.07 powersetE ) => 119.84/17.07 ( 119.84/17.07 ( 119.84/17.07 setunionI ) => 119.84/17.07 ( 119.84/17.07 ( 119.84/17.07 setunionE ) => 119.84/17.07 ( 119.84/17.07 ( 119.84/17.07 subPowSU ) => 119.84/17.07 ( 119.84/17.07 ( 119.84/17.07 exuE2 ) => 119.84/17.07 ( 119.84/17.07 ( 119.84/17.07 nonemptyImpWitness ) => 119.84/17.07 ( 119.84/17.07 ( 119.84/17.07 uniqinunit ) => 119.84/17.07 ( 119.84/17.07 ( 119.84/17.07 notinsingleton ) => 119.84/17.07 ( 119.84/17.07 ( 119.84/17.07 eqinunit ) => 119.84/17.07 ( 119.84/17.08 ( 119.84/17.08 singletonsswitch ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 upairsetE ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 upairsetIL ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 upairsetIR ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 emptyE1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 vacuousDall ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 quantDeMorgan1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 quantDeMorgan2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 quantDeMorgan3 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 quantDeMorgan4 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 prop2setI ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 prop2set2propI ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 notdexE ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 notdallE ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 exuI1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 exuI3 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 exuI2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 inCongP ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 in__Cong ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 exuE3u ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 exu__Cong ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 emptyset__Cong ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setadjoin__Cong ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 powerset__Cong ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setunion__Cong ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 omega__Cong ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 exuEu ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 descr__Cong ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 dsetconstr__Cong ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 subsetI1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 eqimpsubset2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 eqimpsubset1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 subsetI2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 emptysetsubset ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 subsetE ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 subsetE2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 notsubsetI ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 notequalI1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 notequalI2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 subsetRefl ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 subsetTrans ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setadjoinSub ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setadjoinSub2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 subset2powerset ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setextsub ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 subsetemptysetimpeq ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 powersetI1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 powersetE1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 inPowerset ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 powersetsubset ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 sepInPowerset ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 sepSubset ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binunionIL ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 upairset2IR ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binunionIR ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binunionEcases ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binunionE ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binunionLsub ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binunionRsub ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binintersectI ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binintersectSubset5 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binintersectEL ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binintersectLsub ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binintersectSubset2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binintersectSubset3 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binintersectER ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 disjointsetsI1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binintersectRsub ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binintersectSubset4 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binintersectSubset1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 bs114d ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setminusI ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setminusEL ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setminusER ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setminusSubset2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setminusERneg ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setminusELneg ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setminusILneg ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setminusIRneg ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setminusLsub ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setminusSubset1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 symdiffE ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 symdiffI1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 symdiffI2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 symdiffIneg1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 symdiffIneg2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 secondinupair ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setukpairIL ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setukpairIR ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 kpairiskpair ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 kpairp ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 singletonsubset ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 singletoninpowerset ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 singletoninpowunion ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 upairset2E ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 upairsubunion ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 upairinpowunion ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 ubforcartprodlem1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 ubforcartprodlem2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 ubforcartprodlem3 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 cartprodpairin ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 cartprodmempair1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 cartprodmempair ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setunionE2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setunionsingleton1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setunionsingleton2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setunionsingleton ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 singletonprop ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 ex1E1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 ex1I ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 ex1I2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 singletonsuniq ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setukpairinjL1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 kfstsingleton ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 theprop ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 kfstpairEq ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 cartprodfstin ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setukpairinjL2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setukpairinjL ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setukpairinjR11 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setukpairinjR12 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setukpairinjR1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 upairequniteq ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setukpairinjR2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setukpairinjR ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 ksndsingleton ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 ksndpairEq ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 kpairsurjEq ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 cartprodsndin ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 cartprodpairmemEL ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 cartprodpairmemER ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 cartprodmempaircEq ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 cartprodfstpairEq ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 cartprodsndpairEq ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 cartprodpairsurjEq ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 dpsetconstrI ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 dpsetconstrSub ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setOfPairsIsBReln ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 dpsetconstrERa ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 dpsetconstrEL1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 dpsetconstrEL2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 dpsetconstrER ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 funcImageSingleton ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 apProp ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 app ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 infuncsetfunc ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 ap2p ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 funcinfuncset ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 lamProp ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 lamp ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 lam2p ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 brelnall1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 brelnall2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 ex1E2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 funcGraphProp1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 funcGraphProp3 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 funcGraphProp2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 funcextLem ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 funcGraphProp4 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 subbreln ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 eqbreln ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 funcext ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 funcext2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 ap2apEq1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 ap2apEq2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 beta1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 eta1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 lam2lamEq ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 beta2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 eta2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 iffalseProp1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 iffalseProp2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 iftrueProp1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 iftrueProp2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 ifSingleton ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 ifp ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 theeq ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 iftrue ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 iffalse ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 iftrueorfalse ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binintersectT_lem ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binunionT_lem ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 powersetT_lem ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setminusT_lem ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 complementT_lem ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 setextT ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 subsetTI ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 powersetTI1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 powersetTE1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 complementTI1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 complementTE1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binintersectTELcontra ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binintersectTERcontra ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 contrasubsetT ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 contrasubsetT1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 contrasubsetT2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 contrasubsetT3 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 doubleComplementI1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 doubleComplementE1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 doubleComplementSub1 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 doubleComplementSub2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 doubleComplementEq ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 complementTnotintersectT ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 complementImpComplementIntersect ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 complementSubsetComplementIntersect ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 complementInPowersetComplementIntersect ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 contraSubsetComplement ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 complementTcontraSubset ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binunionTILcontra ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 binunionTIRcontra ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 inIntersectImpInUnion ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 inIntersectImpInUnion2 ) => 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 inIntersectImpInIntersectUnions ) => 119.84/17.08 ( 119.84/17.08 ![ 119.84/17.08 A:$i,X:$i]: 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 in @ 119.84/17.08 X @ 119.84/17.08 ( 119.84/17.08 powerset @ 119.84/17.08 A ) ) => 119.84/17.08 ( 119.84/17.08 ![ 119.84/17.08 Y:$i]: 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 in @ 119.84/17.08 Y @ 119.84/17.08 ( 119.84/17.08 powerset @ 119.84/17.08 A ) ) => 119.84/17.08 ( 119.84/17.08 ![ 119.84/17.08 Z:$i]: 119.84/17.08 ( 119.84/17.08 ( 119.84/17.08 in @ 119.84/17.08 Z @ 119.84/17.08 ( 119.84/17.08 powerset @ 119.84/17.08 A ) ) => 119.84/17.08 ( 119.84/17.08 in @ 119.84/17.08 ( 119.84/17.08 binintersect 119.84/17.08 @ 119.84/17.08 X @ Y ) @ 119.84/17.08 ( 119.84/17.08 powerset @ 119.84/17.08 ( 119.84/17.08 binintersect 119.84/17.08 @ 119.84/17.08 ( 119.84/17.08 binunion @ 119.84/17.08 X @ Z ) @ 119.84/17.08 ( 119.84/17.09 binunion @ 119.84/17.09 Y @ Z ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 119.84/17.09 thf(zf_stmt_0, conjecture, 119.84/17.09 (( setextAx ) => 119.84/17.09 ( ( emptysetAx ) => 119.84/17.09 ( ( setadjoinAx ) => 119.84/17.09 ( ( ![X4:$i,X6:$i]: 119.84/17.09 ( ( in @ X6 @ ( powerset @ X4 ) ) <=> 119.84/17.09 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) => 119.84/17.09 ( ( setunionAx ) => 119.84/17.09 ( ( omega0Ax ) => 119.84/17.09 ( ( omegaSAx ) => 119.84/17.09 ( ( omegaIndAx ) => 119.84/17.09 ( ( replAx ) => 119.84/17.09 ( ( foundationAx ) => 119.84/17.09 ( ( wellorderingAx ) => 119.84/17.09 ( ( descrp ) => 119.84/17.09 ( ( dsetconstrI ) => 119.84/17.09 ( ( dsetconstrEL ) => 119.84/17.09 ( ( dsetconstrER ) => 119.84/17.09 ( ( exuE1 ) => 119.84/17.09 ( ( prop2setE ) => 119.84/17.09 ( ( emptysetE ) => 119.84/17.09 ( ( emptysetimpfalse ) => 119.84/17.09 ( ( notinemptyset ) => 119.84/17.09 ( ( exuE3e ) => 119.84/17.09 ( ( setext ) => 119.84/17.09 ( ( emptyI ) => 119.84/17.09 ( ( noeltsimpempty ) => 119.84/17.09 ( ( setbeta ) => 119.84/17.09 ( ( nonemptyE1 ) => 119.84/17.09 ( ( nonemptyI ) => 119.84/17.09 ( ( nonemptyI1 ) => 119.84/17.09 ( ( setadjoinIL ) => 119.84/17.09 ( ( emptyinunitempty ) => 119.84/17.09 ( ( setadjoinIR ) => 119.84/17.09 ( ( setadjoinE ) => 119.84/17.09 ( ( 119.84/17.09 setadjoinOr ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setoftrueEq ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X10:$i, 119.84/17.09 X12:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X14:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X14 @ X12 ) => 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X14 @ X10 ) ) ) => 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X12 @ 119.84/17.09 ( 119.84/17.09 powerset @ 119.84/17.09 X10 ) ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X16:$i]: 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 emptyset @ 119.84/17.09 ( 119.84/17.09 powerset @ 119.84/17.09 X16 ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X18:$i]: 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 emptyset @ 119.84/17.09 ( 119.84/17.09 powerset @ 119.84/17.09 X18 ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X20:$i, 119.84/17.09 X22:$i, 119.84/17.09 X24:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X22 @ 119.84/17.09 ( 119.84/17.09 powerset @ 119.84/17.09 X20 ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X24 @ X22 ) => 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X24 @ X20 ) ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setunionI ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setunionE ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 subPowSU ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 exuE2 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 nonemptyImpWitness ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 uniqinunit ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 notinsingleton ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 eqinunit ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 singletonsswitch ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 upairsetE ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 upairsetIL ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 upairsetIR ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 emptyE1 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 vacuousDall ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 quantDeMorgan1 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 quantDeMorgan2 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 quantDeMorgan3 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 quantDeMorgan4 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 prop2setI ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 prop2set2propI ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 notdexE ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 notdallE ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 exuI1 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 exuI3 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 exuI2 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 inCongP ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in__Cong ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 exuE3u ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 exu__Cong ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 emptyset__Cong ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setadjoin__Cong ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X26:$i, 119.84/17.09 X28:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 X26 ) = 119.84/17.09 ( 119.84/17.09 X28 ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 powerset @ 119.84/17.09 X26 ) = 119.84/17.09 ( 119.84/17.09 powerset @ 119.84/17.09 X28 ) ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setunion__Cong ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 omega__Cong ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 exuEu ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 descr__Cong ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 dsetconstr__Cong ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 subsetI1 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 eqimpsubset2 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 eqimpsubset1 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 subsetI2 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 emptysetsubset ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 subsetE ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 subsetE2 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 notsubsetI ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 notequalI1 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 notequalI2 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 subsetRefl ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 subsetTrans ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setadjoinSub ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setadjoinSub2 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 subset2powerset ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setextsub ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 subsetemptysetimpeq ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 powersetI1 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 powersetE1 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X30:$i]: 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X30 @ 119.84/17.09 ( 119.84/17.09 powerset @ 119.84/17.09 X30 ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 powersetsubset ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 sepInPowerset ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 sepSubset ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X32:$i, 119.84/17.09 X34:$i, 119.84/17.09 X36:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X36 @ X32 ) => 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X36 @ 119.84/17.09 ( 119.84/17.09 binunion @ 119.84/17.09 X32 @ X34 ) ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 upairset2IR ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X38:$i, 119.84/17.09 X40:$i, 119.84/17.09 X42:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X42 @ X40 ) => 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X42 @ 119.84/17.09 ( 119.84/17.09 binunion @ 119.84/17.09 X38 @ X40 ) ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X44:$i, 119.84/17.09 X46:$i, 119.84/17.09 X48:$i, 119.84/17.09 X50:$o]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X48 @ 119.84/17.09 ( 119.84/17.09 binunion @ 119.84/17.09 X44 @ X46 ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X48 @ X44 ) => 119.84/17.09 ( 119.84/17.09 X50 ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X48 @ X46 ) => 119.84/17.09 ( 119.84/17.09 X50 ) ) => 119.84/17.09 ( 119.84/17.09 X50 ) ) ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X52:$i, 119.84/17.09 X54:$i, 119.84/17.09 X56:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X56 @ 119.84/17.09 ( 119.84/17.09 binunion @ 119.84/17.09 X52 @ X54 ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X56 @ X54 ) | 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X56 @ X52 ) ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X58:$i, 119.84/17.09 X60:$i]: 119.84/17.09 ( 119.84/17.09 subset @ 119.84/17.09 X58 @ 119.84/17.09 ( 119.84/17.09 binunion @ 119.84/17.09 X58 @ X60 ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X62:$i, 119.84/17.09 X64:$i]: 119.84/17.09 ( 119.84/17.09 subset @ 119.84/17.09 X64 @ 119.84/17.09 ( 119.84/17.09 binunion @ 119.84/17.09 X62 @ X64 ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X66:$i, 119.84/17.09 X68:$i, 119.84/17.09 X70:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X70 @ X66 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X70 @ X68 ) => 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X70 @ 119.84/17.09 ( 119.84/17.09 binintersect 119.84/17.09 @ 119.84/17.09 X66 @ X68 ) ) ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X72:$i, 119.84/17.09 X74:$i, 119.84/17.09 X76:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 subset @ 119.84/17.09 X76 @ X72 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 subset @ 119.84/17.09 X76 @ X74 ) => 119.84/17.09 ( 119.84/17.09 subset @ 119.84/17.09 X76 @ 119.84/17.09 ( 119.84/17.09 binintersect 119.84/17.09 @ 119.84/17.09 X72 @ X74 ) ) ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X78:$i, 119.84/17.09 X80:$i, 119.84/17.09 X82:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X82 @ 119.84/17.09 ( 119.84/17.09 binintersect 119.84/17.09 @ 119.84/17.09 X78 @ X80 ) ) => 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X82 @ X78 ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X84:$i, 119.84/17.09 X86:$i]: 119.84/17.09 ( 119.84/17.09 subset @ 119.84/17.09 ( 119.84/17.09 binintersect 119.84/17.09 @ 119.84/17.09 X84 @ X86 ) @ 119.84/17.09 X84 ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X88:$i, 119.84/17.09 X90:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 subset @ 119.84/17.09 X88 @ X90 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 binintersect 119.84/17.09 @ 119.84/17.09 X88 @ X90 ) = 119.84/17.09 ( 119.84/17.09 X88 ) ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X92:$i, 119.84/17.09 X94:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 binintersect 119.84/17.09 @ 119.84/17.09 X92 @ X94 ) = 119.84/17.09 ( 119.84/17.09 X94 ) ) => 119.84/17.09 ( 119.84/17.09 subset @ 119.84/17.09 X94 @ X92 ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X96:$i, 119.84/17.09 X98:$i, 119.84/17.09 X100:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X100 @ 119.84/17.09 ( 119.84/17.09 binintersect 119.84/17.09 @ 119.84/17.09 X96 @ X98 ) ) => 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X100 @ X98 ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X102:$i, 119.84/17.09 X104:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ~( 119.84/17.09 ?[ 119.84/17.09 X106:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X106 @ 119.84/17.09 X102 ) & 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X106 @ 119.84/17.09 X104 ) ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 binintersect 119.84/17.09 @ 119.84/17.09 X102 @ 119.84/17.09 X104 ) = 119.84/17.09 ( 119.84/17.09 emptyset ) ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X108:$i, 119.84/17.09 X110:$i]: 119.84/17.09 ( 119.84/17.09 subset @ 119.84/17.09 ( 119.84/17.09 binintersect 119.84/17.09 @ 119.84/17.09 X108 @ 119.84/17.09 X110 ) @ 119.84/17.09 X110 ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X112:$i, 119.84/17.09 X114:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 subset @ 119.84/17.09 X114 @ 119.84/17.09 X112 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 binintersect 119.84/17.09 @ 119.84/17.09 X112 @ 119.84/17.09 X114 ) = 119.84/17.09 ( 119.84/17.09 X114 ) ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X116:$i, 119.84/17.09 X118:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 binintersect 119.84/17.09 @ 119.84/17.09 X116 @ 119.84/17.09 X118 ) = 119.84/17.09 ( 119.84/17.09 X116 ) ) => 119.84/17.09 ( 119.84/17.09 subset @ 119.84/17.09 X116 @ 119.84/17.09 X118 ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X120:$i, 119.84/17.09 X122:$i, 119.84/17.09 X124:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 binintersect 119.84/17.09 @ 119.84/17.09 X120 @ 119.84/17.09 ( 119.84/17.09 binunion @ 119.84/17.09 X122 @ 119.84/17.09 X124 ) ) = 119.84/17.09 ( 119.84/17.09 binunion @ 119.84/17.09 ( 119.84/17.09 binintersect 119.84/17.09 @ 119.84/17.09 X120 @ 119.84/17.09 X122 ) @ 119.84/17.09 ( 119.84/17.09 binintersect 119.84/17.09 @ 119.84/17.09 X120 @ 119.84/17.09 X124 ) ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setminusI ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setminusEL ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setminusER ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setminusSubset2 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setminusERneg ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setminusELneg ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setminusILneg ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setminusIRneg ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setminusLsub ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setminusSubset1 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 symdiffE ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 symdiffI1 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 symdiffI2 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 symdiffIneg1 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 symdiffIneg2 ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 secondinupair ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setukpairIL ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 setukpairIR ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 kpairiskpair ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 kpairp ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 singletonsubset ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 singletoninpowerset ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X126:$i, 119.84/17.09 X128:$i, 119.84/17.09 X130:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X130 @ 119.84/17.09 X126 ) => 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 ( 119.84/17.09 setadjoin 119.84/17.09 @ 119.84/17.09 X130 @ 119.84/17.09 emptyset ) @ 119.84/17.09 ( 119.84/17.09 powerset @ 119.84/17.09 ( 119.84/17.09 binunion @ 119.84/17.09 X126 @ 119.84/17.09 X128 ) ) ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 upairset2E ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X132:$i, 119.84/17.09 X134:$i, 119.84/17.09 X136:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X136 @ 119.84/17.09 X132 ) => 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X138:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X138 @ 119.84/17.09 X134 ) => 119.84/17.09 ( 119.84/17.09 subset @ 119.84/17.09 ( 119.84/17.09 setadjoin 119.84/17.09 @ 119.84/17.09 X136 @ 119.84/17.09 ( 119.84/17.09 setadjoin 119.84/17.09 @ 119.84/17.09 X138 @ 119.84/17.09 emptyset ) ) @ 119.84/17.09 ( 119.84/17.09 binunion @ 119.84/17.09 X132 @ 119.84/17.09 X134 ) ) ) ) ) ) => 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X140:$i, 119.84/17.09 X142:$i, 119.84/17.09 X144:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X144 @ 119.84/17.09 X140 ) => 119.84/17.09 ( 119.84/17.09 ![ 119.84/17.09 X146:$i]: 119.84/17.09 ( 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 X146 @ 119.84/17.09 X142 ) => 119.84/17.09 ( 119.84/17.09 in @ 119.84/17.09 ( 119.84/17.09 setadjoin 119.84/17.09 @ 119.84/17.09 X144 @ 119.84/17.09 ( 119.84/17.09 setadjoin 119.84/17.09 @ 119.84/17.09 X146 @ 119.84/17.10 emptyset ) ) @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 ( 119.84/17.10 binunion @ 119.84/17.10 X140 @ 119.84/17.10 X142 ) ) ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X148:$i, 119.84/17.10 X150:$i, 119.84/17.10 X152:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X152 @ 119.84/17.10 X148 ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X154:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X154 @ 119.84/17.10 X150 ) => 119.84/17.10 ( 119.84/17.10 subset @ 119.84/17.10 ( 119.84/17.10 setadjoin 119.84/17.10 @ 119.84/17.10 ( 119.84/17.10 setadjoin 119.84/17.10 @ 119.84/17.10 X152 @ 119.84/17.10 emptyset ) @ 119.84/17.10 ( 119.84/17.10 setadjoin 119.84/17.10 @ 119.84/17.10 ( 119.84/17.10 setadjoin 119.84/17.10 @ 119.84/17.10 X152 @ 119.84/17.10 ( 119.84/17.10 setadjoin 119.84/17.10 @ 119.84/17.10 X154 @ 119.84/17.10 emptyset ) ) @ 119.84/17.10 emptyset ) ) @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 ( 119.84/17.10 binunion @ 119.84/17.10 X148 @ 119.84/17.10 X150 ) ) ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X156:$i, 119.84/17.10 X158:$i, 119.84/17.10 X160:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X160 @ 119.84/17.10 X156 ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X162:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X162 @ 119.84/17.10 X158 ) => 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 ( 119.84/17.10 setadjoin 119.84/17.10 @ 119.84/17.10 ( 119.84/17.10 setadjoin 119.84/17.10 @ 119.84/17.10 X160 @ 119.84/17.10 emptyset ) @ 119.84/17.10 ( 119.84/17.10 setadjoin 119.84/17.10 @ 119.84/17.10 ( 119.84/17.10 setadjoin 119.84/17.10 @ 119.84/17.10 X160 @ 119.84/17.10 ( 119.84/17.10 setadjoin 119.84/17.10 @ 119.84/17.10 X162 @ 119.84/17.10 emptyset ) ) @ 119.84/17.10 emptyset ) ) @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 ( 119.84/17.10 binunion @ 119.84/17.10 X156 @ 119.84/17.10 X158 ) ) ) ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X164:$i, 119.84/17.10 X166:$i, 119.84/17.10 X168:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X168 @ 119.84/17.10 X164 ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X170:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X170 @ 119.84/17.10 X166 ) => 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 ( 119.84/17.10 kpair @ 119.84/17.10 X168 @ 119.84/17.10 X170 ) @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 ( 119.84/17.10 binunion @ 119.84/17.10 X164 @ 119.84/17.10 X166 ) ) ) ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 cartprodpairin ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 cartprodmempair1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 cartprodmempair ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 setunionE2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 setunionsingleton1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 setunionsingleton2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 setunionsingleton ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 singletonprop ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ex1E1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ex1I ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ex1I2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 singletonsuniq ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 setukpairinjL1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 kfstsingleton ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 theprop ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 kfstpairEq ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 cartprodfstin ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 setukpairinjL2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 setukpairinjL ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 setukpairinjR11 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 setukpairinjR12 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 setukpairinjR1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 upairequniteq ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 setukpairinjR2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 setukpairinjR ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ksndsingleton ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ksndpairEq ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 kpairsurjEq ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 cartprodsndin ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 cartprodpairmemEL ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 cartprodpairmemER ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 cartprodmempaircEq ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 cartprodfstpairEq ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 cartprodsndpairEq ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 cartprodpairsurjEq ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 dpsetconstrI ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 dpsetconstrSub ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 setOfPairsIsBReln ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 dpsetconstrERa ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 dpsetconstrEL1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 dpsetconstrEL2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 dpsetconstrER ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 funcImageSingleton ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 apProp ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 app ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 infuncsetfunc ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ap2p ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 funcinfuncset ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 lamProp ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 lamp ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 lam2p ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 brelnall1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 brelnall2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ex1E2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 funcGraphProp1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 funcGraphProp3 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 funcGraphProp2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 funcextLem ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 funcGraphProp4 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 subbreln ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 eqbreln ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 funcext ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 funcext2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ap2apEq1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ap2apEq2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 beta1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 eta1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 lam2lamEq ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 beta2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 eta2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 iffalseProp1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 iffalseProp2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 iftrueProp1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 iftrueProp2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ifSingleton ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ifp ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 theeq ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 iftrue ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 iffalse ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 iftrueorfalse ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X172:$i, 119.84/17.10 X174:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X174 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X172 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X176:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X176 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X172 ) ) => 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 ( 119.84/17.10 binintersect 119.84/17.10 @ 119.84/17.10 X174 @ 119.84/17.10 X176 ) @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X172 ) ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X178:$i, 119.84/17.10 X180:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X180 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X178 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X182:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X182 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X178 ) ) => 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 ( 119.84/17.10 binunion @ 119.84/17.10 X180 @ 119.84/17.10 X182 ) @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X178 ) ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X184:$i, 119.84/17.10 X186:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X186 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X184 ) ) => 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X186 ) @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X184 ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 setminusT_lem ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 complementT_lem ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X188:$i, 119.84/17.10 X190:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X190 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X188 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X192:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X192 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X188 ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X194:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X194 @ 119.84/17.10 X188 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X194 @ 119.84/17.10 X190 ) => 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X194 @ 119.84/17.10 X192 ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X196:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X196 @ 119.84/17.10 X188 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X196 @ 119.84/17.10 X192 ) => 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X196 @ 119.84/17.10 X190 ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 X190 ) = 119.84/17.10 ( 119.84/17.10 X192 ) ) ) ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 subsetTI ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X198:$i, 119.84/17.10 X200:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X200 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X198 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X202:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X202 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X198 ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X204:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X204 @ 119.84/17.10 X198 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X204 @ 119.84/17.10 X200 ) => 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X204 @ 119.84/17.10 X202 ) ) ) ) => 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X200 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X202 ) ) ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X206:$i, 119.84/17.10 X208:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X208 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X206 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X210:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X210 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X206 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X212:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X212 @ 119.84/17.10 X206 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X208 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X210 ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X212 @ 119.84/17.10 X208 ) => 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X212 @ 119.84/17.10 X210 ) ) ) ) ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 complementTI1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 complementTE1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X214:$i, 119.84/17.10 X216:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X216 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X214 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X218:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X218 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X214 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X220:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X220 @ 119.84/17.10 X214 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ~( 119.84/17.10 in @ 119.84/17.10 X220 @ 119.84/17.10 X216 ) ) => 119.84/17.10 ( 119.84/17.10 ~( 119.84/17.10 in @ 119.84/17.10 X220 @ 119.84/17.10 ( 119.84/17.10 binintersect 119.84/17.10 @ 119.84/17.10 X216 @ 119.84/17.10 X218 ) ) ) ) ) ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X222:$i, 119.84/17.10 X224:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X224 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X222 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X226:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X226 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X222 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X228:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X228 @ 119.84/17.10 X222 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ~( 119.84/17.10 in @ 119.84/17.10 X228 @ 119.84/17.10 X226 ) ) => 119.84/17.10 ( 119.84/17.10 ~( 119.84/17.10 in @ 119.84/17.10 X228 @ 119.84/17.10 ( 119.84/17.10 binintersect 119.84/17.10 @ 119.84/17.10 X224 @ 119.84/17.10 X226 ) ) ) ) ) ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 contrasubsetT ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 contrasubsetT1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 contrasubsetT2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 contrasubsetT3 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 doubleComplementI1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 doubleComplementE1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 doubleComplementSub1 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 doubleComplementSub2 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 doubleComplementEq ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X230:$i, 119.84/17.10 X232:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X232 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X230 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X234:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X234 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X230 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X236:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X236 @ 119.84/17.10 X230 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X236 @ 119.84/17.10 ( 119.84/17.10 setminus @ 119.84/17.10 X230 @ 119.84/17.10 X232 ) ) => 119.84/17.10 ( 119.84/17.10 ~( 119.84/17.10 in @ 119.84/17.10 X236 @ 119.84/17.10 ( 119.84/17.10 binintersect 119.84/17.10 @ 119.84/17.10 X232 @ 119.84/17.10 X234 ) ) ) ) ) ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X238:$i, 119.84/17.10 X240:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X240 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X238 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X242:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X242 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X238 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X244:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X244 @ 119.84/17.10 X238 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X244 @ 119.84/17.10 ( 119.84/17.10 setminus @ 119.84/17.10 X238 @ 119.84/17.10 X240 ) ) => 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X244 @ 119.84/17.10 ( 119.84/17.10 setminus @ 119.84/17.10 X238 @ 119.84/17.10 ( 119.84/17.10 binintersect 119.84/17.10 @ 119.84/17.10 X240 @ 119.84/17.10 X242 ) ) ) ) ) ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X246:$i, 119.84/17.10 X248:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X248 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X246 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X250:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X250 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X246 ) ) => 119.84/17.10 ( 119.84/17.10 subset @ 119.84/17.10 ( 119.84/17.10 setminus @ 119.84/17.10 X246 @ 119.84/17.10 X248 ) @ 119.84/17.10 ( 119.84/17.10 setminus @ 119.84/17.10 X246 @ 119.84/17.10 ( 119.84/17.10 binintersect 119.84/17.10 @ 119.84/17.10 X248 @ 119.84/17.10 X250 ) ) ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X252:$i, 119.84/17.10 X254:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X254 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X252 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X256:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X256 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X252 ) ) => 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 ( 119.84/17.10 setminus @ 119.84/17.10 X252 @ 119.84/17.10 X254 ) @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 ( 119.84/17.10 setminus @ 119.84/17.10 X252 @ 119.84/17.10 ( 119.84/17.10 binintersect 119.84/17.10 @ 119.84/17.10 X254 @ 119.84/17.10 X256 ) ) ) ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 contraSubsetComplement ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 complementTcontraSubset ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X258:$i, 119.84/17.10 X260:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X260 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X258 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X262:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X262 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X258 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X264:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X264 @ 119.84/17.10 X258 ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ~( 119.84/17.10 in @ 119.84/17.10 X264 @ 119.84/17.10 ( 119.84/17.10 binunion 119.84/17.10 @ 119.84/17.10 X260 @ 119.84/17.10 X262 ) ) ) => 119.84/17.10 ( 119.84/17.10 ~( 119.84/17.10 in @ 119.84/17.10 X264 @ 119.84/17.10 X260 ) ) ) ) ) ) ) ) ) => 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X266:$i, 119.84/17.10 X268:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X268 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X266 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X270:$i]: 119.84/17.10 ( 119.84/17.10 ( 119.84/17.10 in @ 119.84/17.10 X270 @ 119.84/17.10 ( 119.84/17.10 powerset @ 119.84/17.10 X266 ) ) => 119.84/17.10 ( 119.84/17.10 ![ 119.84/17.10 X272:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X272 @ 119.84/17.11 X266 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ~( 119.84/17.11 in @ 119.84/17.11 X272 @ 119.84/17.11 ( 119.84/17.11 binunion 119.84/17.11 @ 119.84/17.11 X268 @ 119.84/17.11 X270 ) ) ) => 119.84/17.11 ( 119.84/17.11 ~( 119.84/17.11 in @ 119.84/17.11 X272 @ 119.84/17.11 X270 ) ) ) ) ) ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X274:$i, 119.84/17.11 X276:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X276 @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X274 ) ) => 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X278:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X278 @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X274 ) ) => 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X280:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X280 @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X274 ) ) => 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X282:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X282 @ 119.84/17.11 X274 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X282 @ 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X276 @ 119.84/17.11 X278 ) ) => 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X282 @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X276 @ 119.84/17.11 X280 ) ) ) ) ) ) ) ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X284:$i, 119.84/17.11 X286:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X286 @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X284 ) ) => 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X288:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X288 @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X284 ) ) => 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X290:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X290 @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X284 ) ) => 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X292:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X292 @ 119.84/17.11 X284 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X292 @ 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X286 @ 119.84/17.11 X288 ) ) => 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X292 @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X288 @ 119.84/17.11 X290 ) ) ) ) ) ) ) ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X294:$i, 119.84/17.11 X296:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X296 @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X294 ) ) => 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X298:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X298 @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X294 ) ) => 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X300:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X300 @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X294 ) ) => 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X302:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X302 @ 119.84/17.11 X294 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X302 @ 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X296 @ 119.84/17.11 X298 ) ) => 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X302 @ 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X296 @ 119.84/17.11 X300 ) @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X298 @ 119.84/17.11 X300 ) ) ) ) ) ) ) ) ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X304:$i, 119.84/17.11 X306:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X306 @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X304 ) ) => 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X308:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X308 @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X304 ) ) => 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X310:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X310 @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X304 ) ) => 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X306 @ 119.84/17.11 X308 ) @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X306 @ 119.84/17.11 X310 ) @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X308 @ 119.84/17.11 X310 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 119.84/17.11 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o). 119.84/17.11 thf(zf_stmt_2, axiom, 119.84/17.11 (![X8:$i,X6:$i,X4:$i]: 119.84/17.11 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=> 119.84/17.11 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))). 119.84/17.11 thf(zf_stmt_3, conjecture, 119.84/17.11 (( setextAx ) => 119.84/17.11 ( ( emptysetAx ) => 119.84/17.11 ( ( setadjoinAx ) => 119.84/17.11 ( ( ![X4:$i,X6:$i]: 119.84/17.11 ( ( in @ X6 @ ( powerset @ X4 ) ) <=> 119.84/17.11 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) => 119.84/17.11 ( ( setunionAx ) => 119.84/17.11 ( ( omega0Ax ) => 119.84/17.11 ( ( omegaSAx ) => 119.84/17.11 ( ( omegaIndAx ) => 119.84/17.11 ( ( replAx ) => 119.84/17.11 ( ( foundationAx ) => 119.84/17.11 ( ( wellorderingAx ) => 119.84/17.11 ( ( descrp ) => 119.84/17.11 ( ( dsetconstrI ) => 119.84/17.11 ( ( dsetconstrEL ) => 119.84/17.11 ( ( dsetconstrER ) => 119.84/17.11 ( ( exuE1 ) => 119.84/17.11 ( ( prop2setE ) => 119.84/17.11 ( ( emptysetE ) => 119.84/17.11 ( ( emptysetimpfalse ) => 119.84/17.11 ( ( notinemptyset ) => 119.84/17.11 ( ( exuE3e ) => 119.84/17.11 ( ( setext ) => 119.84/17.11 ( ( emptyI ) => 119.84/17.11 ( ( noeltsimpempty ) => 119.84/17.11 ( ( setbeta ) => 119.84/17.11 ( ( nonemptyE1 ) => 119.84/17.11 ( ( nonemptyI ) => 119.84/17.11 ( ( nonemptyI1 ) => 119.84/17.11 ( ( setadjoinIL ) => 119.84/17.11 ( ( emptyinunitempty ) => 119.84/17.11 ( ( setadjoinIR ) => 119.84/17.11 ( ( setadjoinE ) => 119.84/17.11 ( ( 119.84/17.11 setadjoinOr ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setoftrueEq ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X10:$i, 119.84/17.11 X12:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X14:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X14 @ X12 ) => 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X14 @ X10 ) ) ) => 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X12 @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X10 ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X16:$i]: 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 emptyset @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X16 ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X18:$i]: 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 emptyset @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X18 ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X20:$i, 119.84/17.11 X22:$i, 119.84/17.11 X24:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X22 @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X20 ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X24 @ X22 ) => 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X24 @ X20 ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setunionI ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setunionE ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 subPowSU ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 exuE2 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 nonemptyImpWitness ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 uniqinunit ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 notinsingleton ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 eqinunit ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 singletonsswitch ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 upairsetE ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 upairsetIL ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 upairsetIR ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 emptyE1 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 vacuousDall ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 quantDeMorgan1 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 quantDeMorgan2 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 quantDeMorgan3 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 quantDeMorgan4 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 prop2setI ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 prop2set2propI ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 notdexE ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 notdallE ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 exuI1 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 exuI3 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 exuI2 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 inCongP ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in__Cong ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 exuE3u ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 exu__Cong ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 emptyset__Cong ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setadjoin__Cong ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X26:$i, 119.84/17.11 X28:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 X26 ) = 119.84/17.11 ( 119.84/17.11 X28 ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X26 ) = 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X28 ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setunion__Cong ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 omega__Cong ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 exuEu ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 descr__Cong ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 dsetconstr__Cong ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 subsetI1 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 eqimpsubset2 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 eqimpsubset1 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 subsetI2 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 emptysetsubset ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 subsetE ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 subsetE2 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 notsubsetI ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 notequalI1 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 notequalI2 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 subsetRefl ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 subsetTrans ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setadjoinSub ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setadjoinSub2 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 subset2powerset ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setextsub ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 subsetemptysetimpeq ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 powersetI1 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 powersetE1 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X30:$i]: 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X30 @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 X30 ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 powersetsubset ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 sepInPowerset ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 sepSubset ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X32:$i, 119.84/17.11 X34:$i, 119.84/17.11 X36:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X36 @ X32 ) => 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X36 @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X32 @ X34 ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 upairset2IR ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X38:$i, 119.84/17.11 X40:$i, 119.84/17.11 X42:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X42 @ X40 ) => 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X42 @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X38 @ X40 ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X44:$i, 119.84/17.11 X46:$i, 119.84/17.11 X48:$i, 119.84/17.11 X50:$o]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X48 @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X44 @ X46 ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X48 @ X44 ) => 119.84/17.11 ( 119.84/17.11 X50 ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X48 @ X46 ) => 119.84/17.11 ( 119.84/17.11 X50 ) ) => 119.84/17.11 ( 119.84/17.11 X50 ) ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X52:$i, 119.84/17.11 X54:$i, 119.84/17.11 X56:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X56 @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X52 @ X54 ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X56 @ X52 ) | 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X56 @ X54 ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X58:$i, 119.84/17.11 X60:$i]: 119.84/17.11 ( 119.84/17.11 subset @ 119.84/17.11 X58 @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X58 @ X60 ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X62:$i, 119.84/17.11 X64:$i]: 119.84/17.11 ( 119.84/17.11 subset @ 119.84/17.11 X64 @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X62 @ X64 ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X66:$i, 119.84/17.11 X68:$i, 119.84/17.11 X70:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X70 @ X66 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X70 @ X68 ) => 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X70 @ 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X66 @ X68 ) ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X72:$i, 119.84/17.11 X74:$i, 119.84/17.11 X76:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 subset @ 119.84/17.11 X76 @ X72 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 subset @ 119.84/17.11 X76 @ X74 ) => 119.84/17.11 ( 119.84/17.11 subset @ 119.84/17.11 X76 @ 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X72 @ X74 ) ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X78:$i, 119.84/17.11 X80:$i, 119.84/17.11 X82:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X82 @ 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X78 @ X80 ) ) => 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X82 @ X78 ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X84:$i, 119.84/17.11 X86:$i]: 119.84/17.11 ( 119.84/17.11 subset @ 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X84 @ X86 ) @ 119.84/17.11 X84 ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X88:$i, 119.84/17.11 X90:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 subset @ 119.84/17.11 X88 @ X90 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X88 @ X90 ) = 119.84/17.11 ( 119.84/17.11 X88 ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X92:$i, 119.84/17.11 X94:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X92 @ X94 ) = 119.84/17.11 ( 119.84/17.11 X94 ) ) => 119.84/17.11 ( 119.84/17.11 subset @ 119.84/17.11 X94 @ X92 ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X96:$i, 119.84/17.11 X98:$i, 119.84/17.11 X100:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X100 @ 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X96 @ X98 ) ) => 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X100 @ X98 ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X102:$i, 119.84/17.11 X104:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ~( 119.84/17.11 ?[ 119.84/17.11 X106:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X106 @ 119.84/17.11 X104 ) & 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X106 @ 119.84/17.11 X102 ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X102 @ 119.84/17.11 X104 ) = 119.84/17.11 ( 119.84/17.11 emptyset ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X108:$i, 119.84/17.11 X110:$i]: 119.84/17.11 ( 119.84/17.11 subset @ 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X108 @ 119.84/17.11 X110 ) @ 119.84/17.11 X110 ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X112:$i, 119.84/17.11 X114:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 subset @ 119.84/17.11 X114 @ 119.84/17.11 X112 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X112 @ 119.84/17.11 X114 ) = 119.84/17.11 ( 119.84/17.11 X114 ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X116:$i, 119.84/17.11 X118:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X116 @ 119.84/17.11 X118 ) = 119.84/17.11 ( 119.84/17.11 X116 ) ) => 119.84/17.11 ( 119.84/17.11 subset @ 119.84/17.11 X116 @ 119.84/17.11 X118 ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X120:$i, 119.84/17.11 X122:$i, 119.84/17.11 X124:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X120 @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X122 @ 119.84/17.11 X124 ) ) = 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X120 @ 119.84/17.11 X122 ) @ 119.84/17.11 ( 119.84/17.11 binintersect 119.84/17.11 @ 119.84/17.11 X120 @ 119.84/17.11 X124 ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setminusI ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setminusEL ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setminusER ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setminusSubset2 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setminusERneg ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setminusELneg ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setminusILneg ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setminusIRneg ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setminusLsub ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setminusSubset1 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 symdiffE ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 symdiffI1 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 symdiffI2 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 symdiffIneg1 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 symdiffIneg2 ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 secondinupair ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setukpairIL ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 setukpairIR ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 kpairiskpair ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 kpairp ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 singletonsubset ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 singletoninpowerset ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X126:$i, 119.84/17.11 X128:$i, 119.84/17.11 X130:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X130 @ 119.84/17.11 X126 ) => 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 ( 119.84/17.11 setadjoin 119.84/17.11 @ 119.84/17.11 X130 @ 119.84/17.11 emptyset ) @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X126 @ 119.84/17.11 X128 ) ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 upairset2E ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X132:$i, 119.84/17.11 X134:$i, 119.84/17.11 X136:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X136 @ 119.84/17.11 X132 ) => 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X138:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X138 @ 119.84/17.11 X134 ) => 119.84/17.11 ( 119.84/17.11 subset @ 119.84/17.11 ( 119.84/17.11 setadjoin 119.84/17.11 @ 119.84/17.11 X136 @ 119.84/17.11 ( 119.84/17.11 setadjoin 119.84/17.11 @ 119.84/17.11 X138 @ 119.84/17.11 emptyset ) ) @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X132 @ 119.84/17.11 X134 ) ) ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X140:$i, 119.84/17.11 X142:$i, 119.84/17.11 X144:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X144 @ 119.84/17.11 X140 ) => 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X146:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X146 @ 119.84/17.11 X142 ) => 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 ( 119.84/17.11 setadjoin 119.84/17.11 @ 119.84/17.11 X144 @ 119.84/17.11 ( 119.84/17.11 setadjoin 119.84/17.11 @ 119.84/17.11 X146 @ 119.84/17.11 emptyset ) ) @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X140 @ 119.84/17.11 X142 ) ) ) ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X148:$i, 119.84/17.11 X150:$i, 119.84/17.11 X152:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X152 @ 119.84/17.11 X148 ) => 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X154:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X154 @ 119.84/17.11 X150 ) => 119.84/17.11 ( 119.84/17.11 subset @ 119.84/17.11 ( 119.84/17.11 setadjoin 119.84/17.11 @ 119.84/17.11 ( 119.84/17.11 setadjoin 119.84/17.11 @ 119.84/17.11 X152 @ 119.84/17.11 emptyset ) @ 119.84/17.11 ( 119.84/17.11 setadjoin 119.84/17.11 @ 119.84/17.11 ( 119.84/17.11 setadjoin 119.84/17.11 @ 119.84/17.11 X152 @ 119.84/17.11 ( 119.84/17.11 setadjoin 119.84/17.11 @ 119.84/17.11 X154 @ 119.84/17.11 emptyset ) ) @ 119.84/17.11 emptyset ) ) @ 119.84/17.11 ( 119.84/17.11 powerset @ 119.84/17.11 ( 119.84/17.11 binunion @ 119.84/17.11 X148 @ 119.84/17.11 X150 ) ) ) ) ) ) ) => 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X156:$i, 119.84/17.11 X158:$i, 119.84/17.11 X160:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X160 @ 119.84/17.11 X156 ) => 119.84/17.11 ( 119.84/17.11 ![ 119.84/17.11 X162:$i]: 119.84/17.11 ( 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 X162 @ 119.84/17.11 X158 ) => 119.84/17.11 ( 119.84/17.11 in @ 119.84/17.11 ( 119.84/17.11 setadjoin 119.84/17.11 @ 119.84/17.11 ( 119.84/17.11 setadjoin 119.84/17.11 @ 119.84/17.11 X160 @ 119.84/17.11 emptyset ) @ 119.84/17.11 ( 119.84/17.11 setadjoin 119.84/17.11 @ 119.84/17.12 ( 119.84/17.12 setadjoin 119.84/17.12 @ 119.84/17.12 X160 @ 119.84/17.12 ( 119.84/17.12 setadjoin 119.84/17.12 @ 119.84/17.12 X162 @ 119.84/17.12 emptyset ) ) @ 119.84/17.12 emptyset ) ) @ 119.84/17.12 ( 119.84/17.12 powerset @ 119.84/17.12 ( 119.84/17.12 powerset @ 119.84/17.12 ( 119.84/17.12 binunion @ 119.84/17.12 X156 @ 119.84/17.12 X158 ) ) ) ) ) ) ) ) => 119.84/17.12 ( 119.84/17.12 ( 119.84/17.12 ![ 119.84/17.12 X164:$i, 119.84/17.12 X166:$i, 119.84/17.12 X168:$i]: 119.84/17.12 ( 119.84/17.12 ( 119.84/17.12 in @ 119.84/17.12 X168 @ 119.84/17.12 X164 ) => 119.84/17.12 ( 119.84/17.12 ![ 119.84/17.12 X170:$i]: 119.84/17.12 ( 119.84/17.12 ( 119.84/17.12 in @ 119.84/17.12 X170 @ 119.84/17.12 X166 ) => 119.84/17.12 ( 119.84/17.12 in @ 119.84/17.12 ( 119.84/17.12 kpair @ 119.84/17.12 X168 @ 119.84/17.12 X170 ) @ 119.84/17.12 ( 119.84/17.12 powerset @ 119.84/17.12 ( 119.84/17.12 powerset @ 119.84/17.12 ( 119.84/17.12 binunion @ 119.84/17.12 X164 @ 119.84/17.12 X166 ) ) ) ) ) ) ) ) => 119.84/17.12 ( 119.84/17.12 ( 119.84/17.12 cartprodpairin ) => 119.84/17.12 ( 119.84/17.12 ( 119.84/17.12 cartprodmempair1 ) => 119.84/17.12 ( 119.84/17.12 ( 119.84/17.12 cartprodmempair ) => 119.84/17.12 ( 119.84/17.12 ( 119.84/17.12 setunionE2 ) => 119.84/17.12 ( 119.84/17.12 ( 119.84/17.12 setunionsingleton1 ) => 119.84/17.12 ( 119.84/17.12 ( 128.05/17.12 setunionsingleton2 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 setunionsingleton ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 singletonprop ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ex1E1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ex1I ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ex1I2 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 singletonsuniq ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 setukpairinjL1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 kfstsingleton ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 theprop ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 kfstpairEq ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 cartprodfstin ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 setukpairinjL2 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 setukpairinjL ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 setukpairinjR11 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 setukpairinjR12 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 setukpairinjR1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 upairequniteq ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 setukpairinjR2 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 setukpairinjR ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ksndsingleton ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ksndpairEq ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 kpairsurjEq ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 cartprodsndin ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 cartprodpairmemEL ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 cartprodpairmemER ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 cartprodmempaircEq ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 cartprodfstpairEq ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 cartprodsndpairEq ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 cartprodpairsurjEq ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 dpsetconstrI ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 dpsetconstrSub ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 setOfPairsIsBReln ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 dpsetconstrERa ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 dpsetconstrEL1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 dpsetconstrEL2 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 dpsetconstrER ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 funcImageSingleton ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 apProp ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 app ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 infuncsetfunc ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ap2p ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 funcinfuncset ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 lamProp ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 lamp ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 lam2p ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 brelnall1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 brelnall2 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ex1E2 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 funcGraphProp1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 funcGraphProp3 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 funcGraphProp2 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 funcextLem ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 funcGraphProp4 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 subbreln ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 eqbreln ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 funcext ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 funcext2 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ap2apEq1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ap2apEq2 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 beta1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 eta1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 lam2lamEq ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 beta2 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 eta2 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 iffalseProp1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 iffalseProp2 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 iftrueProp1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 iftrueProp2 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ifSingleton ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ifp ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 theeq ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 iftrue ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 iffalse ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 iftrueorfalse ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X172:$i, 128.05/17.12 X174:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X174 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X172 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X176:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X176 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X172 ) ) => 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 ( 128.05/17.12 binintersect 128.05/17.12 @ 128.05/17.12 X174 @ 128.05/17.12 X176 ) @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X172 ) ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X178:$i, 128.05/17.12 X180:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X180 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X178 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X182:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X182 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X178 ) ) => 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 ( 128.05/17.12 binunion @ 128.05/17.12 X180 @ 128.05/17.12 X182 ) @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X178 ) ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X184:$i, 128.05/17.12 X186:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X186 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X184 ) ) => 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X186 ) @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X184 ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 setminusT_lem ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 complementT_lem ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X188:$i, 128.05/17.12 X190:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X190 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X188 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X192:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X192 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X188 ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X194:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X194 @ 128.05/17.12 X188 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X194 @ 128.05/17.12 X190 ) => 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X194 @ 128.05/17.12 X192 ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X196:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X196 @ 128.05/17.12 X188 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X196 @ 128.05/17.12 X192 ) => 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X196 @ 128.05/17.12 X190 ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 X190 ) = 128.05/17.12 ( 128.05/17.12 X192 ) ) ) ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 subsetTI ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X198:$i, 128.05/17.12 X200:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X200 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X198 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X202:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X202 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X198 ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X204:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X204 @ 128.05/17.12 X198 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X204 @ 128.05/17.12 X200 ) => 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X204 @ 128.05/17.12 X202 ) ) ) ) => 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X200 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X202 ) ) ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X206:$i, 128.05/17.12 X208:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X208 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X206 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X210:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X210 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X206 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X212:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X212 @ 128.05/17.12 X206 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X208 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X210 ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X212 @ 128.05/17.12 X208 ) => 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X212 @ 128.05/17.12 X210 ) ) ) ) ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 complementTI1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 complementTE1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X214:$i, 128.05/17.12 X216:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X216 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X214 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X218:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X218 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X214 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X220:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X220 @ 128.05/17.12 X214 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ~( 128.05/17.12 in @ 128.05/17.12 X220 @ 128.05/17.12 X216 ) ) => 128.05/17.12 ( 128.05/17.12 ~( 128.05/17.12 in @ 128.05/17.12 X220 @ 128.05/17.12 ( 128.05/17.12 binintersect 128.05/17.12 @ 128.05/17.12 X216 @ 128.05/17.12 X218 ) ) ) ) ) ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X222:$i, 128.05/17.12 X224:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X224 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X222 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X226:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X226 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X222 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X228:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X228 @ 128.05/17.12 X222 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ~( 128.05/17.12 in @ 128.05/17.12 X228 @ 128.05/17.12 X226 ) ) => 128.05/17.12 ( 128.05/17.12 ~( 128.05/17.12 in @ 128.05/17.12 X228 @ 128.05/17.12 ( 128.05/17.12 binintersect 128.05/17.12 @ 128.05/17.12 X224 @ 128.05/17.12 X226 ) ) ) ) ) ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 contrasubsetT ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 contrasubsetT1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 contrasubsetT2 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 contrasubsetT3 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 doubleComplementI1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 doubleComplementE1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 doubleComplementSub1 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 doubleComplementSub2 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 doubleComplementEq ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X230:$i, 128.05/17.12 X232:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X232 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X230 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X234:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X234 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X230 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X236:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X236 @ 128.05/17.12 X230 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X236 @ 128.05/17.12 ( 128.05/17.12 setminus @ 128.05/17.12 X230 @ 128.05/17.12 X232 ) ) => 128.05/17.12 ( 128.05/17.12 ~( 128.05/17.12 in @ 128.05/17.12 X236 @ 128.05/17.12 ( 128.05/17.12 binintersect 128.05/17.12 @ 128.05/17.12 X232 @ 128.05/17.12 X234 ) ) ) ) ) ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X238:$i, 128.05/17.12 X240:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X240 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X238 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X242:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X242 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X238 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X244:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X244 @ 128.05/17.12 X238 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X244 @ 128.05/17.12 ( 128.05/17.12 setminus @ 128.05/17.12 X238 @ 128.05/17.12 X240 ) ) => 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X244 @ 128.05/17.12 ( 128.05/17.12 setminus @ 128.05/17.12 X238 @ 128.05/17.12 ( 128.05/17.12 binintersect 128.05/17.12 @ 128.05/17.12 X240 @ 128.05/17.12 X242 ) ) ) ) ) ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X246:$i, 128.05/17.12 X248:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X248 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X246 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X250:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X250 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X246 ) ) => 128.05/17.12 ( 128.05/17.12 subset @ 128.05/17.12 ( 128.05/17.12 setminus @ 128.05/17.12 X246 @ 128.05/17.12 X248 ) @ 128.05/17.12 ( 128.05/17.12 setminus @ 128.05/17.12 X246 @ 128.05/17.12 ( 128.05/17.12 binintersect 128.05/17.12 @ 128.05/17.12 X248 @ 128.05/17.12 X250 ) ) ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X252:$i, 128.05/17.12 X254:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X254 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X252 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X256:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X256 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X252 ) ) => 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 ( 128.05/17.12 setminus @ 128.05/17.12 X252 @ 128.05/17.12 X254 ) @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 ( 128.05/17.12 setminus @ 128.05/17.12 X252 @ 128.05/17.12 ( 128.05/17.12 binintersect 128.05/17.12 @ 128.05/17.12 X254 @ 128.05/17.12 X256 ) ) ) ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 contraSubsetComplement ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 complementTcontraSubset ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X258:$i, 128.05/17.12 X260:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X260 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X258 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X262:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X262 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X258 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X264:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X264 @ 128.05/17.12 X258 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ~( 128.05/17.12 in @ 128.05/17.12 X264 @ 128.05/17.12 ( 128.05/17.12 binunion 128.05/17.12 @ 128.05/17.12 X260 @ 128.05/17.12 X262 ) ) ) => 128.05/17.12 ( 128.05/17.12 ~( 128.05/17.12 in @ 128.05/17.12 X264 @ 128.05/17.12 X260 ) ) ) ) ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X266:$i, 128.05/17.12 X268:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X268 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X266 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X270:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X270 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X266 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X272:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X272 @ 128.05/17.12 X266 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ~( 128.05/17.12 in @ 128.05/17.12 X272 @ 128.05/17.12 ( 128.05/17.12 binunion 128.05/17.12 @ 128.05/17.12 X268 @ 128.05/17.12 X270 ) ) ) => 128.05/17.12 ( 128.05/17.12 ~( 128.05/17.12 in @ 128.05/17.12 X272 @ 128.05/17.12 X270 ) ) ) ) ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X274:$i, 128.05/17.12 X276:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X276 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X274 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X278:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X278 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X274 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X280:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X280 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X274 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X282:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X282 @ 128.05/17.12 X274 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X282 @ 128.05/17.12 ( 128.05/17.12 binintersect 128.05/17.12 @ 128.05/17.12 X276 @ 128.05/17.12 X278 ) ) => 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X282 @ 128.05/17.12 ( 128.05/17.12 binunion @ 128.05/17.12 X276 @ 128.05/17.12 X280 ) ) ) ) ) ) ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X284:$i, 128.05/17.12 X286:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X286 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X284 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X288:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X288 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X284 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X290:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X290 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X284 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X292:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X292 @ 128.05/17.12 X284 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X292 @ 128.05/17.12 ( 128.05/17.12 binintersect 128.05/17.12 @ 128.05/17.12 X286 @ 128.05/17.12 X288 ) ) => 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X292 @ 128.05/17.12 ( 128.05/17.12 binunion @ 128.05/17.12 X288 @ 128.05/17.12 X290 ) ) ) ) ) ) ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X294:$i, 128.05/17.12 X296:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X296 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X294 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X298:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X298 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X294 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X300:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X300 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X294 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X302:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X302 @ 128.05/17.12 X294 ) => 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X302 @ 128.05/17.12 ( 128.05/17.12 binintersect 128.05/17.12 @ 128.05/17.12 X296 @ 128.05/17.12 X298 ) ) => 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X302 @ 128.05/17.12 ( 128.05/17.12 binintersect 128.05/17.12 @ 128.05/17.12 ( 128.05/17.12 binunion @ 128.05/17.12 X296 @ 128.05/17.12 X300 ) @ 128.05/17.12 ( 128.05/17.12 binunion @ 128.05/17.12 X298 @ 128.05/17.12 X300 ) ) ) ) ) ) ) ) ) ) ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X304:$i, 128.05/17.12 X306:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X306 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X304 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X308:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X308 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X304 ) ) => 128.05/17.12 ( 128.05/17.12 ![ 128.05/17.12 X310:$i]: 128.05/17.12 ( 128.05/17.12 ( 128.05/17.12 in @ 128.05/17.12 X310 @ 128.05/17.12 ( 128.05/17.12 powerset @ 128.05/17.12 X304 ) ) => 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 ( 128.05/17.13 binintersect 128.05/17.13 @ 128.05/17.13 X306 @ 128.05/17.13 X308 ) @ 128.05/17.13 ( 128.05/17.13 powerset @ 128.05/17.13 ( 128.05/17.13 binintersect 128.05/17.13 @ 128.05/17.13 ( 128.05/17.13 binunion @ 128.05/17.13 X306 @ 128.05/17.13 X310 ) @ 128.05/17.13 ( 128.05/17.13 binunion @ 128.05/17.13 X308 @ 128.05/17.13 X310 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 128.05/17.13 thf(zf_stmt_4, negated_conjecture, 128.05/17.13 (~( ( setextAx ) => 128.05/17.13 ( ( emptysetAx ) => 128.05/17.13 ( ( setadjoinAx ) => 128.05/17.13 ( ( ![X4:$i,X6:$i]: 128.05/17.13 ( ( in @ X6 @ ( powerset @ X4 ) ) <=> 128.05/17.13 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) => 128.05/17.13 ( ( setunionAx ) => 128.05/17.13 ( ( omega0Ax ) => 128.05/17.13 ( ( omegaSAx ) => 128.05/17.13 ( ( omegaIndAx ) => 128.05/17.13 ( ( replAx ) => 128.05/17.13 ( ( foundationAx ) => 128.05/17.13 ( ( wellorderingAx ) => 128.05/17.13 ( ( descrp ) => 128.05/17.13 ( ( dsetconstrI ) => 128.05/17.13 ( ( dsetconstrEL ) => 128.05/17.13 ( ( dsetconstrER ) => 128.05/17.13 ( ( exuE1 ) => 128.05/17.13 ( ( prop2setE ) => 128.05/17.13 ( ( emptysetE ) => 128.05/17.13 ( ( emptysetimpfalse ) => 128.05/17.13 ( ( notinemptyset ) => 128.05/17.13 ( ( exuE3e ) => 128.05/17.13 ( ( setext ) => 128.05/17.13 ( ( emptyI ) => 128.05/17.13 ( ( noeltsimpempty ) => 128.05/17.13 ( ( setbeta ) => 128.05/17.13 ( ( nonemptyE1 ) => 128.05/17.13 ( ( nonemptyI ) => 128.05/17.13 ( ( nonemptyI1 ) => 128.05/17.13 ( ( setadjoinIL ) => 128.05/17.13 ( ( emptyinunitempty ) => 128.05/17.13 ( ( setadjoinIR ) => 128.05/17.13 ( ( 128.05/17.13 setadjoinE ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setadjoinOr ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setoftrueEq ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X10:$i, 128.05/17.13 X12:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X14:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X14 @ X12 ) => 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X14 @ X10 ) ) ) => 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X12 @ 128.05/17.13 ( 128.05/17.13 powerset 128.05/17.13 @ 128.05/17.13 X10 ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X16:$i]: 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 emptyset @ 128.05/17.13 ( 128.05/17.13 powerset 128.05/17.13 @ 128.05/17.13 X16 ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X18:$i]: 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 emptyset @ 128.05/17.13 ( 128.05/17.13 powerset 128.05/17.13 @ 128.05/17.13 X18 ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X20:$i, 128.05/17.13 X22:$i, 128.05/17.13 X24:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X22 @ 128.05/17.13 ( 128.05/17.13 powerset 128.05/17.13 @ 128.05/17.13 X20 ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X24 @ X22 ) => 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X24 @ X20 ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setunionI ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setunionE ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 subPowSU ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 exuE2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 nonemptyImpWitness ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 uniqinunit ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 notinsingleton ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 eqinunit ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 singletonsswitch ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 upairsetE ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 upairsetIL ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 upairsetIR ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 emptyE1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 vacuousDall ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 quantDeMorgan1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 quantDeMorgan2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 quantDeMorgan3 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 quantDeMorgan4 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 prop2setI ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 prop2set2propI ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 notdexE ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 notdallE ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 exuI1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 exuI3 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 exuI2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 inCongP ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in__Cong ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 exuE3u ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 exu__Cong ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 emptyset__Cong ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setadjoin__Cong ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X26:$i, 128.05/17.13 X28:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 X26 ) = 128.05/17.13 ( 128.05/17.13 X28 ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 powerset 128.05/17.13 @ 128.05/17.13 X26 ) = 128.05/17.13 ( 128.05/17.13 powerset 128.05/17.13 @ 128.05/17.13 X28 ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setunion__Cong ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 omega__Cong ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 exuEu ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 descr__Cong ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 dsetconstr__Cong ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 subsetI1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 eqimpsubset2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 eqimpsubset1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 subsetI2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 emptysetsubset ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 subsetE ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 subsetE2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 notsubsetI ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 notequalI1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 notequalI2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 subsetRefl ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 subsetTrans ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setadjoinSub ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setadjoinSub2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 subset2powerset ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setextsub ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 subsetemptysetimpeq ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 powersetI1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 powersetE1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X30:$i]: 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X30 @ 128.05/17.13 ( 128.05/17.13 powerset 128.05/17.13 @ 128.05/17.13 X30 ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 powersetsubset ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 sepInPowerset ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 sepSubset ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X32:$i, 128.05/17.13 X34:$i, 128.05/17.13 X36:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X36 @ X32 ) => 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X36 @ 128.05/17.13 ( 128.05/17.13 binunion 128.05/17.13 @ 128.05/17.13 X32 @ X34 ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 upairset2IR ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X38:$i, 128.05/17.13 X40:$i, 128.05/17.13 X42:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X42 @ X40 ) => 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X42 @ 128.05/17.13 ( 128.05/17.13 binunion 128.05/17.13 @ 128.05/17.13 X38 @ X40 ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X44:$i, 128.05/17.13 X46:$i, 128.05/17.13 X48:$i, 128.05/17.13 X50:$o]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X48 @ 128.05/17.13 ( 128.05/17.13 binunion 128.05/17.13 @ 128.05/17.13 X44 @ X46 ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X48 @ X44 ) => 128.05/17.13 ( 128.05/17.13 X50 ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X48 @ X46 ) => 128.05/17.13 ( 128.05/17.13 X50 ) ) => 128.05/17.13 ( 128.05/17.13 X50 ) ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X52:$i, 128.05/17.13 X54:$i, 128.05/17.13 X56:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X56 @ 128.05/17.13 ( 128.05/17.13 binunion 128.05/17.13 @ 128.05/17.13 X52 @ X54 ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X56 @ X52 ) | 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X56 @ X54 ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X58:$i, 128.05/17.13 X60:$i]: 128.05/17.13 ( 128.05/17.13 subset @ 128.05/17.13 X58 @ 128.05/17.13 ( 128.05/17.13 binunion 128.05/17.13 @ 128.05/17.13 X58 @ X60 ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X62:$i, 128.05/17.13 X64:$i]: 128.05/17.13 ( 128.05/17.13 subset @ 128.05/17.13 X64 @ 128.05/17.13 ( 128.05/17.13 binunion 128.05/17.13 @ 128.05/17.13 X62 @ X64 ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X66:$i, 128.05/17.13 X68:$i, 128.05/17.13 X70:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X70 @ X66 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X70 @ X68 ) => 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X70 @ 128.05/17.13 ( 128.05/17.13 binintersect 128.05/17.13 @ 128.05/17.13 X66 @ X68 ) ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X72:$i, 128.05/17.13 X74:$i, 128.05/17.13 X76:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 subset @ 128.05/17.13 X76 @ X72 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 subset @ 128.05/17.13 X76 @ X74 ) => 128.05/17.13 ( 128.05/17.13 subset @ 128.05/17.13 X76 @ 128.05/17.13 ( 128.05/17.13 binintersect 128.05/17.13 @ 128.05/17.13 X72 @ X74 ) ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X78:$i, 128.05/17.13 X80:$i, 128.05/17.13 X82:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X82 @ 128.05/17.13 ( 128.05/17.13 binintersect 128.05/17.13 @ 128.05/17.13 X78 @ X80 ) ) => 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X82 @ X78 ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X84:$i, 128.05/17.13 X86:$i]: 128.05/17.13 ( 128.05/17.13 subset @ 128.05/17.13 ( 128.05/17.13 binintersect 128.05/17.13 @ 128.05/17.13 X84 @ X86 ) @ 128.05/17.13 X84 ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X88:$i, 128.05/17.13 X90:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 subset @ 128.05/17.13 X88 @ X90 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 binintersect 128.05/17.13 @ 128.05/17.13 X88 @ X90 ) = 128.05/17.13 ( 128.05/17.13 X88 ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X92:$i, 128.05/17.13 X94:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 binintersect 128.05/17.13 @ 128.05/17.13 X92 @ X94 ) = 128.05/17.13 ( 128.05/17.13 X94 ) ) => 128.05/17.13 ( 128.05/17.13 subset @ 128.05/17.13 X94 @ X92 ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X96:$i, 128.05/17.13 X98:$i, 128.05/17.13 X100:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X100 @ 128.05/17.13 ( 128.05/17.13 binintersect 128.05/17.13 @ 128.05/17.13 X96 @ X98 ) ) => 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X100 @ 128.05/17.13 X98 ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X102:$i, 128.05/17.13 X104:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ~ 128.05/17.13 ( 128.05/17.13 ?[ 128.05/17.13 X106:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X106 @ 128.05/17.13 X104 ) & 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X106 @ 128.05/17.13 X102 ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 binintersect 128.05/17.13 @ 128.05/17.13 X102 @ 128.05/17.13 X104 ) = 128.05/17.13 ( 128.05/17.13 emptyset ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X108:$i, 128.05/17.13 X110:$i]: 128.05/17.13 ( 128.05/17.13 subset @ 128.05/17.13 ( 128.05/17.13 binintersect 128.05/17.13 @ 128.05/17.13 X108 @ 128.05/17.13 X110 ) @ 128.05/17.13 X110 ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X112:$i, 128.05/17.13 X114:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 subset @ 128.05/17.13 X114 @ 128.05/17.13 X112 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 binintersect 128.05/17.13 @ 128.05/17.13 X112 @ 128.05/17.13 X114 ) = 128.05/17.13 ( 128.05/17.13 X114 ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X116:$i, 128.05/17.13 X118:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 binintersect 128.05/17.13 @ 128.05/17.13 X116 @ 128.05/17.13 X118 ) = 128.05/17.13 ( 128.05/17.13 X116 ) ) => 128.05/17.13 ( 128.05/17.13 subset @ 128.05/17.13 X116 @ 128.05/17.13 X118 ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X120:$i, 128.05/17.13 X122:$i, 128.05/17.13 X124:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 binintersect 128.05/17.13 @ 128.05/17.13 X120 @ 128.05/17.13 ( 128.05/17.13 binunion 128.05/17.13 @ 128.05/17.13 X122 @ 128.05/17.13 X124 ) ) = 128.05/17.13 ( 128.05/17.13 binunion 128.05/17.13 @ 128.05/17.13 ( 128.05/17.13 binintersect 128.05/17.13 @ 128.05/17.13 X120 @ 128.05/17.13 X122 ) @ 128.05/17.13 ( 128.05/17.13 binintersect 128.05/17.13 @ 128.05/17.13 X120 @ 128.05/17.13 X124 ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setminusI ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setminusEL ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setminusER ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setminusSubset2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setminusERneg ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setminusELneg ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setminusILneg ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setminusIRneg ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setminusLsub ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setminusSubset1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 symdiffE ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 symdiffI1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 symdiffI2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 symdiffIneg1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 symdiffIneg2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 secondinupair ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setukpairIL ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setukpairIR ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 kpairiskpair ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 kpairp ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 singletonsubset ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 singletoninpowerset ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X126:$i, 128.05/17.13 X128:$i, 128.05/17.13 X130:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X130 @ 128.05/17.13 X126 ) => 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 ( 128.05/17.13 setadjoin 128.05/17.13 @ 128.05/17.13 X130 @ 128.05/17.13 emptyset ) @ 128.05/17.13 ( 128.05/17.13 powerset 128.05/17.13 @ 128.05/17.13 ( 128.05/17.13 binunion 128.05/17.13 @ 128.05/17.13 X126 @ 128.05/17.13 X128 ) ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 upairset2E ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X132:$i, 128.05/17.13 X134:$i, 128.05/17.13 X136:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X136 @ 128.05/17.13 X132 ) => 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X138:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X138 @ 128.05/17.13 X134 ) => 128.05/17.13 ( 128.05/17.13 subset @ 128.05/17.13 ( 128.05/17.13 setadjoin 128.05/17.13 @ 128.05/17.13 X136 @ 128.05/17.13 ( 128.05/17.13 setadjoin 128.05/17.13 @ 128.05/17.13 X138 @ 128.05/17.13 emptyset ) ) @ 128.05/17.13 ( 128.05/17.13 binunion 128.05/17.13 @ 128.05/17.13 X132 @ 128.05/17.13 X134 ) ) ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X140:$i, 128.05/17.13 X142:$i, 128.05/17.13 X144:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X144 @ 128.05/17.13 X140 ) => 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X146:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X146 @ 128.05/17.13 X142 ) => 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 ( 128.05/17.13 setadjoin 128.05/17.13 @ 128.05/17.13 X144 @ 128.05/17.13 ( 128.05/17.13 setadjoin 128.05/17.13 @ 128.05/17.13 X146 @ 128.05/17.13 emptyset ) ) @ 128.05/17.13 ( 128.05/17.13 powerset 128.05/17.13 @ 128.05/17.13 ( 128.05/17.13 binunion 128.05/17.13 @ 128.05/17.13 X140 @ 128.05/17.13 X142 ) ) ) ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X148:$i, 128.05/17.13 X150:$i, 128.05/17.13 X152:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X152 @ 128.05/17.13 X148 ) => 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X154:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X154 @ 128.05/17.13 X150 ) => 128.05/17.13 ( 128.05/17.13 subset @ 128.05/17.13 ( 128.05/17.13 setadjoin 128.05/17.13 @ 128.05/17.13 ( 128.05/17.13 setadjoin 128.05/17.13 @ 128.05/17.13 X152 @ 128.05/17.13 emptyset ) @ 128.05/17.13 ( 128.05/17.13 setadjoin 128.05/17.13 @ 128.05/17.13 ( 128.05/17.13 setadjoin 128.05/17.13 @ 128.05/17.13 X152 @ 128.05/17.13 ( 128.05/17.13 setadjoin 128.05/17.13 @ 128.05/17.13 X154 @ 128.05/17.13 emptyset ) ) @ 128.05/17.13 emptyset ) ) @ 128.05/17.13 ( 128.05/17.13 powerset 128.05/17.13 @ 128.05/17.13 ( 128.05/17.13 binunion 128.05/17.13 @ 128.05/17.13 X148 @ 128.05/17.13 X150 ) ) ) ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X156:$i, 128.05/17.13 X158:$i, 128.05/17.13 X160:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X160 @ 128.05/17.13 X156 ) => 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X162:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X162 @ 128.05/17.13 X158 ) => 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 ( 128.05/17.13 setadjoin 128.05/17.13 @ 128.05/17.13 ( 128.05/17.13 setadjoin 128.05/17.13 @ 128.05/17.13 X160 @ 128.05/17.13 emptyset ) @ 128.05/17.13 ( 128.05/17.13 setadjoin 128.05/17.13 @ 128.05/17.13 ( 128.05/17.13 setadjoin 128.05/17.13 @ 128.05/17.13 X160 @ 128.05/17.13 ( 128.05/17.13 setadjoin 128.05/17.13 @ 128.05/17.13 X162 @ 128.05/17.13 emptyset ) ) @ 128.05/17.13 emptyset ) ) @ 128.05/17.13 ( 128.05/17.13 powerset 128.05/17.13 @ 128.05/17.13 ( 128.05/17.13 powerset 128.05/17.13 @ 128.05/17.13 ( 128.05/17.13 binunion 128.05/17.13 @ 128.05/17.13 X156 @ 128.05/17.13 X158 ) ) ) ) ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X164:$i, 128.05/17.13 X166:$i, 128.05/17.13 X168:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X168 @ 128.05/17.13 X164 ) => 128.05/17.13 ( 128.05/17.13 ![ 128.05/17.13 X170:$i]: 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 X170 @ 128.05/17.13 X166 ) => 128.05/17.13 ( 128.05/17.13 in @ 128.05/17.13 ( 128.05/17.13 kpair @ 128.05/17.13 X168 @ 128.05/17.13 X170 ) @ 128.05/17.13 ( 128.05/17.13 powerset 128.05/17.13 @ 128.05/17.13 ( 128.05/17.13 powerset 128.05/17.13 @ 128.05/17.13 ( 128.05/17.13 binunion 128.05/17.13 @ 128.05/17.13 X164 @ 128.05/17.13 X166 ) ) ) ) ) ) ) ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 cartprodpairin ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 cartprodmempair1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 cartprodmempair ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setunionE2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setunionsingleton1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setunionsingleton2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setunionsingleton ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 singletonprop ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ex1E1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ex1I ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ex1I2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 singletonsuniq ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setukpairinjL1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 kfstsingleton ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 theprop ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 kfstpairEq ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 cartprodfstin ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setukpairinjL2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setukpairinjL ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setukpairinjR11 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setukpairinjR12 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setukpairinjR1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 upairequniteq ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setukpairinjR2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setukpairinjR ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ksndsingleton ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ksndpairEq ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 kpairsurjEq ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 cartprodsndin ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 cartprodpairmemEL ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 cartprodpairmemER ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 cartprodmempaircEq ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 cartprodfstpairEq ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 cartprodsndpairEq ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 cartprodpairsurjEq ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 dpsetconstrI ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 dpsetconstrSub ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 setOfPairsIsBReln ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 dpsetconstrERa ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 dpsetconstrEL1 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 dpsetconstrEL2 ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 dpsetconstrER ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 funcImageSingleton ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 apProp ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 app ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 infuncsetfunc ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 ap2p ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 funcinfuncset ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 lamProp ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 lamp ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 lam2p ) => 128.05/17.13 ( 128.05/17.13 ( 128.05/17.13 brelnall1 ) => 128.05/17.13 ( 128.05/17.14 ( 128.05/17.14 brelnall2 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ex1E2 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 funcGraphProp1 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 funcGraphProp3 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 funcGraphProp2 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 funcextLem ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 funcGraphProp4 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 subbreln ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 eqbreln ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 funcext ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 funcext2 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ap2apEq1 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ap2apEq2 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 beta1 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 eta1 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 lam2lamEq ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 beta2 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 eta2 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 iffalseProp1 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 iffalseProp2 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 iftrueProp1 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 iftrueProp2 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ifSingleton ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ifp ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 theeq ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 iftrue ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 iffalse ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 iftrueorfalse ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X172:$i, 128.05/17.14 X174:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X174 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X172 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X176:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X176 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X172 ) ) => 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 ( 128.05/17.14 binintersect 128.05/17.14 @ 128.05/17.14 X174 @ 128.05/17.14 X176 ) @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X172 ) ) ) ) ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X178:$i, 128.05/17.14 X180:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X180 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X178 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X182:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X182 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X178 ) ) => 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 ( 128.05/17.14 binunion 128.05/17.14 @ 128.05/17.14 X180 @ 128.05/17.14 X182 ) @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X178 ) ) ) ) ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X184:$i, 128.05/17.14 X186:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X186 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X184 ) ) => 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X186 ) @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X184 ) ) ) ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 setminusT_lem ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 complementT_lem ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X188:$i, 128.05/17.14 X190:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X190 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X188 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X192:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X192 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X188 ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X194:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X194 @ 128.05/17.14 X188 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X194 @ 128.05/17.14 X190 ) => 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X194 @ 128.05/17.14 X192 ) ) ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X196:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X196 @ 128.05/17.14 X188 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X196 @ 128.05/17.14 X192 ) => 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X196 @ 128.05/17.14 X190 ) ) ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 X190 ) = 128.05/17.14 ( 128.05/17.14 X192 ) ) ) ) ) ) ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 subsetTI ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X198:$i, 128.05/17.14 X200:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X200 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X198 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X202:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X202 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X198 ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X204:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X204 @ 128.05/17.14 X198 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X204 @ 128.05/17.14 X200 ) => 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X204 @ 128.05/17.14 X202 ) ) ) ) => 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X200 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X202 ) ) ) ) ) ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X206:$i, 128.05/17.14 X208:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X208 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X206 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X210:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X210 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X206 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X212:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X212 @ 128.05/17.14 X206 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X208 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X210 ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X212 @ 128.05/17.14 X208 ) => 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X212 @ 128.05/17.14 X210 ) ) ) ) ) ) ) ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 complementTI1 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 complementTE1 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X214:$i, 128.05/17.14 X216:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X216 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X214 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X218:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X218 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X214 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X220:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X220 @ 128.05/17.14 X214 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ~ 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X220 @ 128.05/17.14 X216 ) ) => 128.05/17.14 ( 128.05/17.14 ~ 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X220 @ 128.05/17.14 ( 128.05/17.14 binintersect 128.05/17.14 @ 128.05/17.14 X216 @ 128.05/17.14 X218 ) ) ) ) ) ) ) ) ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X222:$i, 128.05/17.14 X224:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X224 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X222 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X226:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X226 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X222 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X228:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X228 @ 128.05/17.14 X222 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ~ 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X228 @ 128.05/17.14 X226 ) ) => 128.05/17.14 ( 128.05/17.14 ~ 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X228 @ 128.05/17.14 ( 128.05/17.14 binintersect 128.05/17.14 @ 128.05/17.14 X224 @ 128.05/17.14 X226 ) ) ) ) ) ) ) ) ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 contrasubsetT ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 contrasubsetT1 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 contrasubsetT2 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 contrasubsetT3 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 doubleComplementI1 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 doubleComplementE1 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 doubleComplementSub1 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 doubleComplementSub2 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 doubleComplementEq ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X230:$i, 128.05/17.14 X232:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X232 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X230 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X234:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X234 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X230 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X236:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X236 @ 128.05/17.14 X230 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X236 @ 128.05/17.14 ( 128.05/17.14 setminus 128.05/17.14 @ 128.05/17.14 X230 @ 128.05/17.14 X232 ) ) => 128.05/17.14 ( 128.05/17.14 ~ 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X236 @ 128.05/17.14 ( 128.05/17.14 binintersect 128.05/17.14 @ 128.05/17.14 X232 @ 128.05/17.14 X234 ) ) ) ) ) ) ) ) ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X238:$i, 128.05/17.14 X240:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X240 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X238 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X242:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X242 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X238 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X244:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X244 @ 128.05/17.14 X238 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X244 @ 128.05/17.14 ( 128.05/17.14 setminus 128.05/17.14 @ 128.05/17.14 X238 @ 128.05/17.14 X240 ) ) => 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X244 @ 128.05/17.14 ( 128.05/17.14 setminus 128.05/17.14 @ 128.05/17.14 X238 @ 128.05/17.14 ( 128.05/17.14 binintersect 128.05/17.14 @ 128.05/17.14 X240 @ 128.05/17.14 X242 ) ) ) ) ) ) ) ) ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X246:$i, 128.05/17.14 X248:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X248 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X246 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X250:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X250 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X246 ) ) => 128.05/17.14 ( 128.05/17.14 subset @ 128.05/17.14 ( 128.05/17.14 setminus 128.05/17.14 @ 128.05/17.14 X246 @ 128.05/17.14 X248 ) @ 128.05/17.14 ( 128.05/17.14 setminus 128.05/17.14 @ 128.05/17.14 X246 @ 128.05/17.14 ( 128.05/17.14 binintersect 128.05/17.14 @ 128.05/17.14 X248 @ 128.05/17.14 X250 ) ) ) ) ) ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X252:$i, 128.05/17.14 X254:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X254 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X252 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X256:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X256 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X252 ) ) => 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 ( 128.05/17.14 setminus 128.05/17.14 @ 128.05/17.14 X252 @ 128.05/17.14 X254 ) @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 ( 128.05/17.14 setminus 128.05/17.14 @ 128.05/17.14 X252 @ 128.05/17.14 ( 128.05/17.14 binintersect 128.05/17.14 @ 128.05/17.14 X254 @ 128.05/17.14 X256 ) ) ) ) ) ) ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 contraSubsetComplement ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 complementTcontraSubset ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X258:$i, 128.05/17.14 X260:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X260 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X258 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X262:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X262 @ 128.05/17.14 ( 128.05/17.14 powerset 128.05/17.14 @ 128.05/17.14 X258 ) ) => 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X264:$i]: 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X264 @ 128.05/17.14 X258 ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ~ 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X264 @ 128.05/17.14 ( 128.05/17.14 binunion 128.05/17.14 @ 128.05/17.14 X260 @ 128.05/17.14 X262 ) ) ) => 128.05/17.14 ( 128.05/17.14 ~ 128.05/17.14 ( 128.05/17.14 in @ 128.05/17.14 X264 @ 128.05/17.14 X260 ) ) ) ) ) ) ) ) ) => 128.05/17.14 ( 128.05/17.14 ( 128.05/17.14 ![ 128.05/17.14 X266:$i, 128.05/17.14 X268:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X268 @ 128.05/17.15 ( 128.05/17.15 powerset 128.05/17.15 @ 128.05/17.15 X266 ) ) => 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X270:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X270 @ 128.05/17.15 ( 128.05/17.15 powerset 128.05/17.15 @ 128.05/17.15 X266 ) ) => 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X272:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X272 @ 128.05/17.15 X266 ) => 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 ~ 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X272 @ 128.05/17.15 ( 128.05/17.15 binunion 128.05/17.15 @ 128.05/17.15 X268 @ 128.05/17.15 X270 ) ) ) => 128.05/17.15 ( 128.05/17.15 ~ 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X272 @ 128.05/17.15 X270 ) ) ) ) ) ) ) ) ) => 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X274:$i, 128.05/17.15 X276:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X276 @ 128.05/17.15 ( 128.05/17.15 powerset 128.05/17.15 @ 128.05/17.15 X274 ) ) => 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X278:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X278 @ 128.05/17.15 ( 128.05/17.15 powerset 128.05/17.15 @ 128.05/17.15 X274 ) ) => 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X280:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X280 @ 128.05/17.15 ( 128.05/17.15 powerset 128.05/17.15 @ 128.05/17.15 X274 ) ) => 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X282:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X282 @ 128.05/17.15 X274 ) => 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X282 @ 128.05/17.15 ( 128.05/17.15 binintersect 128.05/17.15 @ 128.05/17.15 X276 @ 128.05/17.15 X278 ) ) => 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X282 @ 128.05/17.15 ( 128.05/17.15 binunion 128.05/17.15 @ 128.05/17.15 X276 @ 128.05/17.15 X280 ) ) ) ) ) ) ) ) ) ) ) => 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X284:$i, 128.05/17.15 X286:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X286 @ 128.05/17.15 ( 128.05/17.15 powerset 128.05/17.15 @ 128.05/17.15 X284 ) ) => 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X288:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X288 @ 128.05/17.15 ( 128.05/17.15 powerset 128.05/17.15 @ 128.05/17.15 X284 ) ) => 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X290:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X290 @ 128.05/17.15 ( 128.05/17.15 powerset 128.05/17.15 @ 128.05/17.15 X284 ) ) => 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X292:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X292 @ 128.05/17.15 X284 ) => 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X292 @ 128.05/17.15 ( 128.05/17.15 binintersect 128.05/17.15 @ 128.05/17.15 X286 @ 128.05/17.15 X288 ) ) => 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X292 @ 128.05/17.15 ( 128.05/17.15 binunion 128.05/17.15 @ 128.05/17.15 X288 @ 128.05/17.15 X290 ) ) ) ) ) ) ) ) ) ) ) => 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X294:$i, 128.05/17.15 X296:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X296 @ 128.05/17.15 ( 128.05/17.15 powerset 128.05/17.15 @ 128.05/17.15 X294 ) ) => 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X298:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X298 @ 128.05/17.15 ( 128.05/17.15 powerset 128.05/17.15 @ 128.05/17.15 X294 ) ) => 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X300:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X300 @ 128.05/17.15 ( 128.05/17.15 powerset 128.05/17.15 @ 128.05/17.15 X294 ) ) => 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X302:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X302 @ 128.05/17.15 X294 ) => 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X302 @ 128.05/17.15 ( 128.05/17.15 binintersect 128.05/17.15 @ 128.05/17.15 X296 @ 128.05/17.15 X298 ) ) => 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X302 @ 128.05/17.15 ( 128.05/17.15 binintersect 128.05/17.15 @ 128.05/17.15 ( 128.05/17.15 binunion 128.05/17.15 @ 128.05/17.15 X296 @ 128.05/17.15 X300 ) @ 128.05/17.15 ( 128.05/17.15 binunion 128.05/17.15 @ 128.05/17.15 X298 @ 128.05/17.15 X300 ) ) ) ) ) ) ) ) ) ) ) ) => 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X304:$i, 128.05/17.15 X306:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X306 @ 128.05/17.15 ( 128.05/17.15 powerset 128.05/17.15 @ 128.05/17.15 X304 ) ) => 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X308:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X308 @ 128.05/17.15 ( 128.05/17.15 powerset 128.05/17.15 @ 128.05/17.15 X304 ) ) => 128.05/17.15 ( 128.05/17.15 ![ 128.05/17.15 X310:$i]: 128.05/17.15 ( 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 X310 @ 128.05/17.15 ( 128.05/17.15 powerset 128.05/17.15 @ 128.05/17.15 X304 ) ) => 128.05/17.15 ( 128.05/17.15 in @ 128.05/17.15 ( 128.05/17.15 binintersect 128.05/17.15 @ 128.05/17.15 X306 @ 128.05/17.15 X308 ) @ 128.05/17.15 ( 128.05/17.15 powerset 128.05/17.15 @ 128.05/17.15 ( 128.05/17.15 binintersect 128.05/17.15 @ 128.05/17.15 ( 128.05/17.15 binunion 128.05/17.15 @ 128.05/17.15 X306 @ 128.05/17.15 X310 ) @ 128.05/17.15 ( 128.05/17.15 binunion 128.05/17.15 @ 128.05/17.15 X308 @ 128.05/17.15 X310 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 128.05/17.15 inference('cnf.neg', [status(esa)], [zf_stmt_3])). 128.05/17.15 thf(zip_derived_cl223, plain, 128.05/17.15 (![X122 : $i, X123 : $i]: 128.05/17.15 (((binintersect @ X122 @ X123) = (X122)) | ~ (subset @ X122 @ X123))), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl58, plain, 128.05/17.15 (![X18 : $i, X19 : $i]: (subset @ (binintersect @ X18 @ X19) @ X18)), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl358, plain, 128.05/17.15 (![X0 : $i, X1 : $i]: 128.05/17.15 ((binintersect @ (binintersect @ X0 @ X1) @ X0) 128.05/17.15 = (binintersect @ X0 @ X1))), 128.05/17.15 inference('sup+', [status(thm)], [zip_derived_cl223, zip_derived_cl58])). 128.05/17.15 thf(zip_derived_cl221, plain, 128.05/17.15 (![X117 : $i, X118 : $i]: (subset @ (binintersect @ X117 @ X118) @ X118)), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl223, plain, 128.05/17.15 (![X122 : $i, X123 : $i]: 128.05/17.15 (((binintersect @ X122 @ X123) = (X122)) | ~ (subset @ X122 @ X123))), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl221, plain, 128.05/17.15 (![X117 : $i, X118 : $i]: (subset @ (binintersect @ X117 @ X118) @ X118)), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl357, plain, 128.05/17.15 (![X0 : $i, X1 : $i]: 128.05/17.15 ((binintersect @ (binintersect @ X1 @ X0) @ X0) 128.05/17.15 = (binintersect @ X1 @ X0))), 128.05/17.15 inference('sup+', [status(thm)], [zip_derived_cl223, zip_derived_cl221])). 128.05/17.15 thf(zip_derived_cl57, plain, 128.05/17.15 (![X15 : $i, X16 : $i, X17 : $i]: 128.05/17.15 (~ (subset @ X15 @ X16) 128.05/17.15 | (subset @ X15 @ (binintersect @ X17 @ X16)) 128.05/17.15 | ~ (subset @ X15 @ X17))), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl136, plain, 128.05/17.15 (~ (in @ (binintersect @ sk__156 @ sk__157) @ 128.05/17.15 (powerset @ 128.05/17.15 (binintersect @ (binunion @ sk__156 @ sk__158) @ 128.05/17.15 (binunion @ sk__157 @ sk__158))))), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl223, plain, 128.05/17.15 (![X122 : $i, X123 : $i]: 128.05/17.15 (((binintersect @ X122 @ X123) = (X122)) | ~ (subset @ X122 @ X123))), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl226, plain, 128.05/17.15 (![X130 : $i, X131 : $i]: (subset @ X130 @ (binunion @ X130 @ X131))), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl360, plain, 128.05/17.15 (![X0 : $i, X1 : $i]: ((binintersect @ X1 @ (binunion @ X1 @ X0)) = (X1))), 128.05/17.15 inference('sup+', [status(thm)], [zip_derived_cl223, zip_derived_cl226])). 128.05/17.15 thf(zip_derived_cl63, plain, 128.05/17.15 (![X26 : $i, X27 : $i, X28 : $i]: 128.05/17.15 ((binintersect @ X26 @ (binunion @ X27 @ X28)) 128.05/17.15 = (binunion @ (binintersect @ X26 @ X27) @ 128.05/17.15 (binintersect @ X26 @ X28)))), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl62, plain, 128.05/17.15 (![X24 : $i, X25 : $i]: 128.05/17.15 (((binintersect @ X25 @ X24) = (X24)) | ~ (subset @ X24 @ X25))), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl226, plain, 128.05/17.15 (![X130 : $i, X131 : $i]: (subset @ X130 @ (binunion @ X130 @ X131))), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl332, plain, 128.05/17.15 (![X0 : $i, X1 : $i]: ((binintersect @ (binunion @ X1 @ X0) @ X1) = (X1))), 128.05/17.15 inference('sup+', [status(thm)], [zip_derived_cl62, zip_derived_cl226])). 128.05/17.15 thf(zip_derived_cl62, plain, 128.05/17.15 (![X24 : $i, X25 : $i]: 128.05/17.15 (((binintersect @ X25 @ X24) = (X24)) | ~ (subset @ X24 @ X25))), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl221, plain, 128.05/17.15 (![X117 : $i, X118 : $i]: (subset @ (binintersect @ X117 @ X118) @ X118)), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl329, plain, 128.05/17.15 (![X0 : $i, X1 : $i]: 128.05/17.15 ((binintersect @ X0 @ (binintersect @ X1 @ X0)) 128.05/17.15 = (binintersect @ X1 @ X0))), 128.05/17.15 inference('sup+', [status(thm)], [zip_derived_cl62, zip_derived_cl221])). 128.05/17.15 thf(zip_derived_cl223, plain, 128.05/17.15 (![X122 : $i, X123 : $i]: 128.05/17.15 (((binintersect @ X122 @ X123) = (X122)) | ~ (subset @ X122 @ X123))), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl21, plain, 128.05/17.15 (![X0 : $i, X1 : $i]: 128.05/17.15 ( (in @ X0 @ (powerset @ X1)) | (in @ (sk__160 @ X0 @ X1) @ X0))), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl222, plain, 128.05/17.15 (![X119 : $i, X120 : $i, X121 : $i]: 128.05/17.15 ( (in @ X119 @ X120) | ~ (in @ X119 @ (binintersect @ X121 @ X120)))), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl309, plain, 128.05/17.15 (![X0 : $i, X1 : $i, X2 : $i]: 128.05/17.15 ( (in @ (binintersect @ X1 @ X0) @ (powerset @ X2)) 128.05/17.15 | (in @ (sk__160 @ (binintersect @ X1 @ X0) @ X2) @ X0))), 128.05/17.15 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl222])). 128.05/17.15 thf(zip_derived_cl20, plain, 128.05/17.15 (![X0 : $i, X1 : $i]: 128.05/17.15 ( (in @ X0 @ (powerset @ X1)) | ~ (in @ (sk__160 @ X0 @ X1) @ X1))), 128.05/17.15 inference('cnf', [status(esa)], [zf_stmt_4])). 128.05/17.15 thf(zip_derived_cl9166, plain, ($false), 128.05/17.15 inference('eprover', [status(thm)], 128.05/17.15 [zip_derived_cl358, zip_derived_cl221, zip_derived_cl357, 128.05/17.15 zip_derived_cl57, zip_derived_cl136, zip_derived_cl360, 128.05/17.15 zip_derived_cl63, zip_derived_cl332, zip_derived_cl329, 128.05/17.15 zip_derived_cl223, zip_derived_cl309, zip_derived_cl20])). 128.05/17.15 128.05/17.15 % SZS output end Refutation 128.05/17.15 128.05/17.15 128.05/17.15 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 128.05/17.15 % Terminating... 18.40/17.26 % Runner terminated. 7.77/17.30 % Zipperpin 1.5 exiting 7.77/17.34 EOF