0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.16 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.FjyRSbPb29 true 0.16/0.37 % Computer : n016.cluster.edu 0.16/0.37 % Model : x86_64 x86_64 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.37 % Memory : 8042.1875MB 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.37 % CPULimit : 1200 0.16/0.37 % WCLimit : 120 0.16/0.37 % DateTime : Tue Jul 13 11:37:38 EDT 2021 0.16/0.37 % CPUTime : 0.16/0.37 % Running portfolio for 120 s 0.16/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.16/0.37 % Number of cores: 8 0.16/0.38 % Python version: Python 3.6.8 0.16/0.38 % Running in HO mode 0.56/0.68 % Total configuration time : 828 0.56/0.68 % Estimated wc time : 983 0.56/0.68 % Estimated cpu time (8 cpus) : 122.875 0.56/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.57/0.77 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.57/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.58/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.58/0.80 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.58/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 137.73/18.19 % Solved by lams/40_c_ic.sh. 137.73/18.19 % running E: timeout 27 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.FjyRSbPb29/e_input5155e7 --cpu-limit=25 --auto-schedule -s -p 137.73/18.19 % done 3182 iterations in 17.364s 137.73/18.19 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 137.73/18.19 % SZS output start Refutation 137.73/18.19 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 137.73/18.19 thf(binintersectER_type, type, binintersectER: $o). 137.73/18.19 thf(setadjoinSub_type, type, setadjoinSub: $o). 137.73/18.19 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 137.73/18.19 thf(vacuousDall_type, type, vacuousDall: $o). 137.73/18.19 thf(setadjoinIR_type, type, setadjoinIR: $o). 137.73/18.19 thf(funcGraphProp1_type, type, funcGraphProp1: $o). 137.73/18.19 thf(funcext_type, type, funcext: $o). 137.73/18.19 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o). 137.73/18.19 thf(omega0Ax_type, type, omega0Ax: $o). 137.73/18.19 thf(subsetE_type, type, subsetE: $o). 137.73/18.19 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 137.73/18.19 thf(setminusER_type, type, setminusER: $o). 137.73/18.19 thf(setukpairinjL1_type, type, setukpairinjL1: $o). 137.73/18.19 thf(iftrue_type, type, iftrue: $o). 137.73/18.19 thf(lamProp_type, type, lamProp: $o). 137.73/18.19 thf(eqbreln_type, type, eqbreln: $o). 137.73/18.19 thf(binunionE_type, type, binunionE: $o). 137.73/18.19 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 137.73/18.19 thf(powersetE_type, type, powersetE: $o). 137.73/18.19 thf(upairequniteq_type, type, upairequniteq: $o). 137.73/18.19 thf(binunionRsub_type, type, binunionRsub: $o). 137.73/18.19 thf(binintersectT_lem_type, type, binintersectT_lem: $o). 137.73/18.19 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o). 137.73/18.19 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o). 137.73/18.19 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 137.73/18.19 thf(powerset__Cong_type, type, powerset__Cong: $o). 137.73/18.19 thf(singletonprop_type, type, singletonprop: $o). 137.73/18.19 thf(beta1_type, type, beta1: $o). 137.73/18.19 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o). 137.73/18.19 thf(omegaIndAx_type, type, omegaIndAx: $o). 137.73/18.19 thf(uniqinunit_type, type, uniqinunit: $o). 137.73/18.19 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 137.73/18.19 thf(exu__Cong_type, type, exu__Cong: $o). 137.73/18.19 thf(subset2powerset_type, type, subset2powerset: $o). 137.73/18.19 thf(setoftrueEq_type, type, setoftrueEq: $o). 137.73/18.19 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o). 137.73/18.19 thf(lam2p_type, type, lam2p: $o). 137.73/18.19 thf(iftrueProp1_type, type, iftrueProp1: $o). 137.73/18.19 thf(upairsetIL_type, type, upairsetIL: $o). 137.73/18.19 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 137.73/18.19 thf(ksndpairEq_type, type, ksndpairEq: $o). 137.73/18.19 thf(emptyI_type, type, emptyI: $o). 137.73/18.19 thf(setukpairIL_type, type, setukpairIL: $o). 137.73/18.19 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o). 137.73/18.19 thf(iftrueProp2_type, type, iftrueProp2: $o). 137.73/18.19 thf(funcImageSingleton_type, type, funcImageSingleton: $o). 137.73/18.19 thf(exuI3_type, type, exuI3: $o). 137.73/18.19 thf(emptysetAx_type, type, emptysetAx: $o). 137.73/18.19 thf(setukpairIR_type, type, setukpairIR: $o). 137.73/18.19 thf(funcinfuncset_type, type, funcinfuncset: $o). 137.73/18.19 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 137.73/18.19 thf(cartprodfstin_type, type, cartprodfstin: $o). 137.73/18.19 thf(setadjoinIL_type, type, setadjoinIL: $o). 137.73/18.19 thf(upairsubunion_type, type, upairsubunion: $o). 137.73/18.19 thf(theeq_type, type, theeq: $o). 137.73/18.19 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 137.73/18.19 thf(upairsetIR_type, type, upairsetIR: $o). 137.73/18.19 thf(funcextLem_type, type, funcextLem: $o). 137.73/18.19 thf(infuncsetfunc_type, type, infuncsetfunc: $o). 137.73/18.19 thf(setukpairinjR11_type, type, setukpairinjR11: $o). 137.73/18.19 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o). 137.73/18.19 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 137.73/18.19 thf(ksndsingleton_type, type, ksndsingleton: $o). 137.73/18.19 thf(setminusI_type, type, setminusI: $o). 137.73/18.19 thf(ap2p_type, type, ap2p: $o). 137.73/18.19 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o). 137.73/18.19 thf(setukpairinjR2_type, type, setukpairinjR2: $o). 137.73/18.19 thf(descrp_type, type, descrp: $o). 137.73/18.19 thf(binintersectI_type, type, binintersectI: $o). 137.73/18.19 thf(nonemptyI1_type, type, nonemptyI1: $o). 137.73/18.19 thf(emptysetsubset_type, type, emptysetsubset: $o). 137.73/18.19 thf(setunionAx_type, type, setunionAx: $o). 137.73/18.19 thf(notsubsetI_type, type, notsubsetI: $o). 137.73/18.19 thf(singletonsuniq_type, type, singletonsuniq: $o). 137.73/18.19 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o). 137.73/18.19 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 137.73/18.19 thf(upairset2IR_type, type, upairset2IR: $o). 137.73/18.19 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o). 137.73/18.19 thf(binunionLsub_type, type, binunionLsub: $o). 137.73/18.19 thf(subsetRefl_type, type, subsetRefl: $o). 137.73/18.19 thf(kfstpairEq_type, type, kfstpairEq: $o). 137.73/18.19 thf(powerset_type, type, powerset: $i > $i). 137.73/18.19 thf(setukpairinjR1_type, type, setukpairinjR1: $o). 137.73/18.19 thf(beta2_type, type, beta2: $o). 137.73/18.19 thf(nonemptyI_type, type, nonemptyI: $o). 137.73/18.19 thf(emptysetE_type, type, emptysetE: $o). 137.73/18.19 thf(sepInPowerset_type, type, sepInPowerset: $o). 137.73/18.19 thf(sk__71_type, type, sk__71: $i). 137.73/18.19 thf(iftrueorfalse_type, type, iftrueorfalse: $o). 137.73/18.19 thf(cartprodsndin_type, type, cartprodsndin: $o). 137.73/18.19 thf(cartprodmempair1_type, type, cartprodmempair1: $o). 137.73/18.19 thf(ap2apEq2_type, type, ap2apEq2: $o). 137.73/18.19 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 137.73/18.19 thf(powersetI_type, type, powersetI: $o). 137.73/18.19 thf(exuE2_type, type, exuE2: $o). 137.73/18.19 thf(exuE3e_type, type, exuE3e: $o). 137.73/18.19 thf(setminusSubset1_type, type, setminusSubset1: $o). 137.73/18.19 thf(notequalI2_type, type, notequalI2: $o). 137.73/18.19 thf(descr__Cong_type, type, descr__Cong: $o). 137.73/18.19 thf(iffalseProp1_type, type, iffalseProp1: $o). 137.73/18.19 thf(setextAx_type, type, setextAx: $o). 137.73/18.19 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 137.73/18.19 thf(eqinunit_type, type, eqinunit: $o). 137.73/18.19 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o). 137.73/18.19 thf(symdiffE_type, type, symdiffE: $o). 137.73/18.19 thf(upairinpowunion_type, type, upairinpowunion: $o). 137.73/18.19 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 137.73/18.19 thf(powersetAx_type, type, powersetAx: $o). 137.73/18.19 thf(upairset2E_type, type, upairset2E: $o). 137.73/18.19 thf(theprop_type, type, theprop: $o). 137.73/18.19 thf(subsetI2_type, type, subsetI2: $o). 137.73/18.19 thf(symdiffI1_type, type, symdiffI1: $o). 137.73/18.19 thf(kpair_type, type, kpair: $i > $i > $i). 137.73/18.19 thf(eta2_type, type, eta2: $o). 137.73/18.19 thf(binunion_type, type, binunion: $i > $i > $i). 137.73/18.19 thf(subsetI1_type, type, subsetI1: $o). 137.73/18.19 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 137.73/18.19 thf(replAx_type, type, replAx: $o). 137.73/18.19 thf(sk__72_type, type, sk__72: $i). 137.73/18.19 thf(subPowSU_type, type, subPowSU: $o). 137.73/18.19 thf(setunionE_type, type, setunionE: $o). 137.73/18.19 thf(brelnall2_type, type, brelnall2: $o). 137.73/18.19 thf(setunionsingleton_type, type, setunionsingleton: $o). 137.73/18.19 thf(setunion__Cong_type, type, setunion__Cong: $o). 137.73/18.19 thf(lamp_type, type, lamp: $o). 137.73/18.19 thf(iffalse_type, type, iffalse: $o). 137.73/18.19 thf(bs114d_type, type, bs114d: $o). 137.73/18.19 thf(setminusSubset2_type, type, setminusSubset2: $o). 137.73/18.19 thf(powersetE1_type, type, powersetE1: $o). 137.73/18.19 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o). 137.73/18.19 thf(omegaSAx_type, type, omegaSAx: $o). 137.73/18.19 thf(funcGraphProp4_type, type, funcGraphProp4: $o). 137.73/18.19 thf(setext_type, type, setext: $o). 137.73/18.19 thf(notequalI1_type, type, notequalI1: $o). 137.73/18.19 thf(setextsub_type, type, setextsub: $o). 137.73/18.19 thf(setukpairinjL2_type, type, setukpairinjL2: $o). 137.73/18.19 thf(kpairp_type, type, kpairp: $o). 137.73/18.19 thf(setukpairinjR_type, type, setukpairinjR: $o). 137.73/18.19 thf(omega__Cong_type, type, omega__Cong: $o). 137.73/18.19 thf(symdiffI2_type, type, symdiffI2: $o). 137.73/18.19 thf(apProp_type, type, apProp: $o). 137.73/18.19 thf(setbeta_type, type, setbeta: $o). 137.73/18.19 thf(dsetconstrER_type, type, dsetconstrER: $o). 137.73/18.19 thf(app_type, type, app: $o). 137.73/18.19 thf(nonemptyE1_type, type, nonemptyE1: $o). 137.73/18.19 thf(binunionIL_type, type, binunionIL: $o). 137.73/18.19 thf(prop2setE_type, type, prop2setE: $o). 137.73/18.19 thf(prop2set2propI_type, type, prop2set2propI: $o). 137.73/18.19 thf(notdallE_type, type, notdallE: $o). 137.73/18.19 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 137.73/18.19 thf(exuEu_type, type, exuEu: $o). 137.73/18.19 thf(singletoninpowerset_type, type, singletoninpowerset: $o). 137.73/18.19 thf(notinsingleton_type, type, notinsingleton: $o). 137.73/18.19 thf(upairsetE_type, type, upairsetE: $o). 137.73/18.19 thf(sk__73_type, type, sk__73: $i). 137.73/18.19 thf(emptyE1_type, type, emptyE1: $o). 137.73/18.19 thf(funcGraphProp3_type, type, funcGraphProp3: $o). 137.73/18.19 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 137.73/18.19 thf(cartprodmempair_type, type, cartprodmempair: $o). 137.73/18.19 thf(binunionEcases_type, type, binunionEcases: $o). 137.73/18.19 thf(symdiffIneg1_type, type, symdiffIneg1: $o). 137.73/18.19 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 137.73/18.19 thf(ex1I_type, type, ex1I: $o). 137.73/18.19 thf(ex1E1_type, type, ex1E1: $o). 137.73/18.19 thf(wellorderingAx_type, type, wellorderingAx: $o). 137.73/18.19 thf(singletoninpowunion_type, type, singletoninpowunion: $o). 137.73/18.19 thf(binintersectLsub_type, type, binintersectLsub: $o). 137.73/18.19 thf(binintersectRsub_type, type, binintersectRsub: $o). 137.73/18.19 thf(powersetsubset_type, type, powersetsubset: $o). 137.73/18.19 thf(emptyset_type, type, emptyset: $i). 137.73/18.19 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o). 137.73/18.19 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 137.73/18.19 thf(exuE1_type, type, exuE1: $o). 137.73/18.19 thf(inPowerset_type, type, inPowerset: $o). 137.73/18.19 thf(ifSingleton_type, type, ifSingleton: $o). 137.73/18.19 thf(in_type, type, in: $i > $i > $o). 137.73/18.19 thf(brelnall1_type, type, brelnall1: $o). 137.73/18.19 thf(cartprodpairin_type, type, cartprodpairin: $o). 137.73/18.19 thf(setunionI_type, type, setunionI: $o). 137.73/18.19 thf(in__Cong_type, type, in__Cong: $o). 137.73/18.19 thf(binintersect_type, type, binintersect: $i > $i > $i). 137.73/18.19 thf(setadjoinE_type, type, setadjoinE: $o). 137.73/18.19 thf(subsetTrans_type, type, subsetTrans: $o). 137.73/18.19 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 137.73/18.19 thf(symdiffIneg2_type, type, symdiffIneg2: $o). 137.73/18.19 thf(setminusIRneg_type, type, setminusIRneg: $o). 137.73/18.19 thf(setminusELneg_type, type, setminusELneg: $o). 137.73/18.19 thf(foundationAx_type, type, foundationAx: $o). 137.73/18.19 thf(sk__74_type, type, sk__74: $i > $i > $i). 137.73/18.19 thf(sepSubset_type, type, sepSubset: $o). 137.73/18.19 thf(exuE3u_type, type, exuE3u: $o). 137.73/18.19 thf(kpairiskpair_type, type, kpairiskpair: $o). 137.73/18.19 thf(funcGraphProp2_type, type, funcGraphProp2: $o). 137.73/18.19 thf(dpsetconstrI_type, type, dpsetconstrI: $o). 137.73/18.19 thf(setadjoinOr_type, type, setadjoinOr: $o). 137.73/18.19 thf(exuI1_type, type, exuI1: $o). 137.73/18.19 thf(setukpairinjR12_type, type, setukpairinjR12: $o). 137.73/18.19 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 137.73/18.19 thf(binunionIR_type, type, binunionIR: $o). 137.73/18.19 thf(inCongP_type, type, inCongP: $o). 137.73/18.19 thf(setminusLsub_type, type, setminusLsub: $o). 137.73/18.19 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 137.73/18.19 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 137.73/18.19 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 137.73/18.19 thf(setukpairinjL_type, type, setukpairinjL: $o). 137.73/18.19 thf(subbreln_type, type, subbreln: $o). 137.73/18.19 thf(setminusERneg_type, type, setminusERneg: $o). 137.73/18.19 thf(ifp_type, type, ifp: $o). 137.73/18.19 thf(eta1_type, type, eta1: $o). 137.73/18.19 thf(exuI2_type, type, exuI2: $o). 137.73/18.19 thf(powersetI1_type, type, powersetI1: $o). 137.73/18.19 thf(kpairsurjEq_type, type, kpairsurjEq: $o). 137.73/18.19 thf(iffalseProp2_type, type, iffalseProp2: $o). 137.73/18.19 thf(setunionsingleton1_type, type, setunionsingleton1: $o). 137.73/18.19 thf(dpsetconstrER_type, type, dpsetconstrER: $o). 137.73/18.19 thf(setminusILneg_type, type, setminusILneg: $o). 137.73/18.19 thf(dsetconstrI_type, type, dsetconstrI: $o). 137.73/18.19 thf(ex1I2_type, type, ex1I2: $o). 137.73/18.19 thf(funcext2_type, type, funcext2: $o). 137.73/18.19 thf(setminusEL_type, type, setminusEL: $o). 137.73/18.19 thf(singletonsubset_type, type, singletonsubset: $o). 137.73/18.19 thf(kfstsingleton_type, type, kfstsingleton: $o). 137.73/18.19 thf(secondinupair_type, type, secondinupair: $o). 137.73/18.19 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i). 137.73/18.19 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o). 137.73/18.19 thf(lam2lamEq_type, type, lam2lamEq: $o). 137.73/18.19 thf(ex1E2_type, type, ex1E2: $o). 137.73/18.19 thf(subsetE2_type, type, subsetE2: $o). 137.73/18.19 thf(singletonsswitch_type, type, singletonsswitch: $o). 137.73/18.19 thf(binintersectEL_type, type, binintersectEL: $o). 137.73/18.19 thf(setadjoinAx_type, type, setadjoinAx: $o). 137.73/18.19 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 137.73/18.19 thf(notinemptyset_type, type, notinemptyset: $o). 137.73/18.19 thf(prop2setI_type, type, prop2setI: $o). 137.73/18.19 thf(ap2apEq1_type, type, ap2apEq1: $o). 137.73/18.19 thf(setunionsingleton2_type, type, setunionsingleton2: $o). 137.73/18.19 thf(setunionE2_type, type, setunionE2: $o). 137.73/18.19 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o). 137.73/18.19 thf(subset_type, type, subset: $i > $i > $o). 137.73/18.19 thf(notdexE_type, type, notdexE: $o). 137.73/18.19 thf(ubforcartprodlem3, axiom, ubforcartprodlem3 = 137.73/18.19 (![A:$i,B:$i,Xx:$i]: 137.73/18.19 ( ( in @ Xx @ A ) => 137.73/18.19 ( ![Xy:$i]: 137.73/18.19 ( ( in @ Xy @ B ) => 137.73/18.19 ( in @ 137.73/18.19 ( kpair @ Xx @ Xy ) @ 137.73/18.19 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))). 137.73/18.19 thf('0', plain, 137.73/18.19 (( ubforcartprodlem3 ) = 137.73/18.19 ( ![X4:$i,X6:$i,X8:$i]: 137.73/18.19 ( ( in @ X8 @ X4 ) => 137.73/18.19 ( ![X10:$i]: 137.73/18.19 ( ( in @ X10 @ X6 ) => 137.73/18.19 ( in @ 137.73/18.19 ( kpair @ X8 @ X10 ) @ 137.73/18.19 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(ubforcartprodlem2, axiom, ubforcartprodlem2 = 137.73/18.19 (![A:$i,B:$i,Xx:$i]: 137.73/18.19 ( ( in @ Xx @ A ) => 137.73/18.19 ( ![Xy:$i]: 137.73/18.19 ( ( in @ Xy @ B ) => 137.73/18.19 ( in @ 137.73/18.19 ( setadjoin @ 137.73/18.19 ( setadjoin @ Xx @ emptyset ) @ 137.73/18.19 ( setadjoin @ 137.73/18.19 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ 137.73/18.19 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))). 137.73/18.19 thf('1', plain, 137.73/18.19 (( ubforcartprodlem2 ) = 137.73/18.19 ( ![X4:$i,X6:$i,X8:$i]: 137.73/18.19 ( ( in @ X8 @ X4 ) => 137.73/18.19 ( ![X10:$i]: 137.73/18.19 ( ( in @ X10 @ X6 ) => 137.73/18.19 ( in @ 137.73/18.19 ( setadjoin @ 137.73/18.19 ( setadjoin @ X8 @ emptyset ) @ 137.73/18.19 ( setadjoin @ 137.73/18.19 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ 137.73/18.19 emptyset ) ) @ 137.73/18.19 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(ubforcartprodlem1, axiom, ubforcartprodlem1 = 137.73/18.19 (![A:$i,B:$i,Xx:$i]: 137.73/18.19 ( ( in @ Xx @ A ) => 137.73/18.19 ( ![Xy:$i]: 137.73/18.19 ( ( in @ Xy @ B ) => 137.73/18.19 ( subset @ 137.73/18.19 ( setadjoin @ 137.73/18.19 ( setadjoin @ Xx @ emptyset ) @ 137.73/18.19 ( setadjoin @ 137.73/18.19 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ 137.73/18.19 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))). 137.73/18.19 thf('2', plain, 137.73/18.19 (( ubforcartprodlem1 ) = 137.73/18.19 ( ![X4:$i,X6:$i,X8:$i]: 137.73/18.19 ( ( in @ X8 @ X4 ) => 137.73/18.19 ( ![X10:$i]: 137.73/18.19 ( ( in @ X10 @ X6 ) => 137.73/18.19 ( subset @ 137.73/18.19 ( setadjoin @ 137.73/18.19 ( setadjoin @ X8 @ emptyset ) @ 137.73/18.19 ( setadjoin @ 137.73/18.19 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ 137.73/18.19 emptyset ) ) @ 137.73/18.19 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(upairinpowunion, axiom, upairinpowunion = 137.73/18.19 (![A:$i,B:$i,Xx:$i]: 137.73/18.19 ( ( in @ Xx @ A ) => 137.73/18.19 ( ![Xy:$i]: 137.73/18.19 ( ( in @ Xy @ B ) => 137.73/18.19 ( in @ 137.73/18.19 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ 137.73/18.19 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))). 137.73/18.19 thf('3', plain, 137.73/18.19 (( upairinpowunion ) = 137.73/18.19 ( ![X4:$i,X6:$i,X8:$i]: 137.73/18.19 ( ( in @ X8 @ X4 ) => 137.73/18.19 ( ![X10:$i]: 137.73/18.19 ( ( in @ X10 @ X6 ) => 137.73/18.19 ( in @ 137.73/18.19 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ 137.73/18.19 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(upairsubunion, axiom, upairsubunion = 137.73/18.19 (![A:$i,B:$i,Xx:$i]: 137.73/18.19 ( ( in @ Xx @ A ) => 137.73/18.19 ( ![Xy:$i]: 137.73/18.19 ( ( in @ Xy @ B ) => 137.73/18.19 ( subset @ 137.73/18.19 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ 137.73/18.19 ( binunion @ A @ B ) ) ) ) ))). 137.73/18.19 thf('4', plain, 137.73/18.19 (( upairsubunion ) = 137.73/18.19 ( ![X4:$i,X6:$i,X8:$i]: 137.73/18.19 ( ( in @ X8 @ X4 ) => 137.73/18.19 ( ![X10:$i]: 137.73/18.19 ( ( in @ X10 @ X6 ) => 137.73/18.19 ( subset @ 137.73/18.19 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ 137.73/18.19 ( binunion @ X4 @ X6 ) ) ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(singletoninpowunion, axiom, singletoninpowunion = 137.73/18.19 (![A:$i,B:$i,Xx:$i]: 137.73/18.19 ( ( in @ Xx @ A ) => 137.73/18.19 ( in @ 137.73/18.19 ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ))). 137.73/18.19 thf('5', plain, 137.73/18.19 (( singletoninpowunion ) = 137.73/18.19 ( ![X4:$i,X6:$i,X8:$i]: 137.73/18.19 ( ( in @ X8 @ X4 ) => 137.73/18.19 ( in @ 137.73/18.19 ( setadjoin @ X8 @ emptyset ) @ 137.73/18.19 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(singletoninpowerset, axiom, singletoninpowerset = 137.73/18.19 (![A:$i,Xx:$i]: 137.73/18.19 ( ( in @ Xx @ A ) => 137.73/18.19 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))). 137.73/18.19 thf('6', plain, 137.73/18.19 (( singletoninpowerset ) = 137.73/18.19 ( ![X4:$i,X6:$i]: 137.73/18.19 ( ( in @ X6 @ X4 ) => 137.73/18.19 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(bs114d, axiom, bs114d = 137.73/18.19 (![A:$i,B:$i,C:$i]: 137.73/18.19 ( ( binintersect @ A @ ( binunion @ B @ C ) ) = 137.73/18.19 ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ))). 137.73/18.19 thf('7', plain, 137.73/18.19 (( bs114d ) = 137.73/18.19 ( ![X4:$i,X6:$i,X8:$i]: 137.73/18.19 ( ( binintersect @ X4 @ ( binunion @ X6 @ X8 ) ) = 137.73/18.19 ( binunion @ ( binintersect @ X4 @ X6 ) @ ( binintersect @ X4 @ X8 ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(binunionRsub, axiom, binunionRsub = 137.73/18.19 (![A:$i,B:$i]: ( subset @ B @ ( binunion @ A @ B ) ))). 137.73/18.19 thf('8', plain, 137.73/18.19 (( binunionRsub ) = 137.73/18.19 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( binunion @ X4 @ X6 ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(binunionLsub, axiom, binunionLsub = 137.73/18.19 (![A:$i,B:$i]: ( subset @ A @ ( binunion @ A @ B ) ))). 137.73/18.19 thf('9', plain, 137.73/18.19 (( binunionLsub ) = 137.73/18.19 ( ![X4:$i,X6:$i]: ( subset @ X4 @ ( binunion @ X4 @ X6 ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(binunionE, axiom, binunionE = 137.73/18.19 (![A:$i,B:$i,Xx:$i]: 137.73/18.19 ( ( in @ Xx @ ( binunion @ A @ B ) ) => 137.73/18.19 ( ( in @ Xx @ A ) | ( in @ Xx @ B ) ) ))). 137.73/18.19 thf('10', plain, 137.73/18.19 (( binunionE ) = 137.73/18.19 ( ![X4:$i,X6:$i,X8:$i]: 137.73/18.19 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) => 137.73/18.19 ( ( in @ X8 @ X4 ) | ( in @ X8 @ X6 ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(binunionEcases, axiom, binunionEcases = 137.73/18.19 (![A:$i,B:$i,Xx:$i,Xphi:$o]: 137.73/18.19 ( ( in @ Xx @ ( binunion @ A @ B ) ) => 137.73/18.19 ( ( ( in @ Xx @ A ) => ( Xphi ) ) => 137.73/18.19 ( ( ( in @ Xx @ B ) => ( Xphi ) ) => ( Xphi ) ) ) ))). 137.73/18.19 thf('11', plain, 137.73/18.19 (( binunionEcases ) = 137.73/18.19 ( ![X4:$i,X6:$i,X8:$i,X10:$o]: 137.73/18.19 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) => 137.73/18.19 ( ( ( in @ X8 @ X4 ) => ( X10 ) ) => 137.73/18.19 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(binunionIR, axiom, binunionIR = 137.73/18.19 (![A:$i,B:$i,Xx:$i]: 137.73/18.19 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))). 137.73/18.19 thf('12', plain, 137.73/18.19 (( binunionIR ) = 137.73/18.19 ( ![X4:$i,X6:$i,X8:$i]: 137.73/18.19 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(binunionIL, axiom, binunionIL = 137.73/18.19 (![A:$i,B:$i,Xx:$i]: 137.73/18.19 ( ( in @ Xx @ A ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))). 137.73/18.19 thf('13', plain, 137.73/18.19 (( binunionIL ) = 137.73/18.19 ( ![X4:$i,X6:$i,X8:$i]: 137.73/18.19 ( ( in @ X8 @ X4 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(sepInPowerset, axiom, sepInPowerset = 137.73/18.19 (![A:$i,Xphi:( $i > $o )]: 137.73/18.19 ( in @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) @ ( powerset @ A ) ))). 137.73/18.19 thf('14', plain, 137.73/18.19 (( sepInPowerset ) = 137.73/18.19 ( ![X4:$i,X6:( $i > $o )]: 137.73/18.19 ( in @ 137.73/18.19 ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) @ 137.73/18.19 ( powerset @ X4 ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(powersetsubset, axiom, powersetsubset = 137.73/18.19 (![A:$i,B:$i]: 137.73/18.19 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))). 137.73/18.19 thf('15', plain, 137.73/18.19 (( powersetsubset ) = 137.73/18.19 ( ![X4:$i,X6:$i]: 137.73/18.19 ( ( subset @ X4 @ X6 ) => 137.73/18.19 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))). 137.73/18.19 thf('16', plain, 137.73/18.19 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(powersetE1, axiom, powersetE1 = 137.73/18.19 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))). 137.73/18.19 thf('17', plain, 137.73/18.19 (( powersetE1 ) = 137.73/18.19 ( ![X4:$i,X6:$i]: 137.73/18.19 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(powersetI1, axiom, powersetI1 = 137.73/18.19 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))). 137.73/18.19 thf('18', plain, 137.73/18.19 (( powersetI1 ) = 137.73/18.19 ( ![X4:$i,X6:$i]: 137.73/18.19 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(subset2powerset, axiom, subset2powerset = 137.73/18.19 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))). 137.73/18.19 thf('19', plain, 137.73/18.19 (( subset2powerset ) = 137.73/18.19 ( ![X4:$i,X6:$i]: 137.73/18.19 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(powerset__Cong, axiom, powerset__Cong = 137.73/18.19 (![A:$i,B:$i]: 137.73/18.19 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))). 137.73/18.19 thf('20', plain, 137.73/18.19 (( powerset__Cong ) = 137.73/18.19 ( ![X4:$i,X6:$i]: 137.73/18.19 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(powersetE, axiom, powersetE = 137.73/18.19 (![A:$i,B:$i,Xx:$i]: 137.73/18.19 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))). 137.73/18.19 thf('21', plain, 137.73/18.19 (( powersetE ) = 137.73/18.19 ( ![X4:$i,X6:$i,X8:$i]: 137.73/18.19 ( ( in @ X6 @ ( powerset @ X4 ) ) => 137.73/18.19 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(emptyInPowerset, axiom, emptyInPowerset = 137.73/18.19 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))). 137.73/18.19 thf('22', plain, 137.73/18.19 (( emptyInPowerset ) = 137.73/18.19 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(emptyinPowerset, axiom, emptyinPowerset = 137.73/18.19 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))). 137.73/18.19 thf('23', plain, 137.73/18.19 (( emptyinPowerset ) = 137.73/18.19 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(powersetI, axiom, powersetI = 137.73/18.19 (![A:$i,B:$i]: 137.73/18.19 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) => 137.73/18.19 ( in @ B @ ( powerset @ A ) ) ))). 137.73/18.19 thf('24', plain, 137.73/18.19 (( powersetI ) = 137.73/18.19 ( ![X4:$i,X6:$i]: 137.73/18.19 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) => 137.73/18.19 ( in @ X6 @ ( powerset @ X4 ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(powersetAx, axiom, powersetAx = 137.73/18.19 (![A:$i,B:$i]: 137.73/18.19 ( ( in @ B @ ( powerset @ A ) ) <=> 137.73/18.19 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))). 137.73/18.19 thf('25', plain, 137.73/18.19 (( powersetAx ) = 137.73/18.19 ( ![X4:$i,X6:$i]: 137.73/18.19 ( ( in @ X6 @ ( powerset @ X4 ) ) <=> 137.73/18.19 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )), 137.73/18.19 define([status(thm)])). 137.73/18.19 thf(binunionT_lem, conjecture, 137.73/18.19 (( setextAx ) => 137.73/18.19 ( ( emptysetAx ) => 137.73/18.19 ( ( setadjoinAx ) => 137.73/18.19 ( ( powersetAx ) => 137.73/18.19 ( ( setunionAx ) => 137.73/18.19 ( ( omega0Ax ) => 137.73/18.19 ( ( omegaSAx ) => 137.73/18.19 ( ( omegaIndAx ) => 137.73/18.19 ( ( replAx ) => 137.73/18.19 ( ( foundationAx ) => 137.73/18.19 ( ( wellorderingAx ) => 137.73/18.19 ( ( descrp ) => 137.73/18.19 ( ( dsetconstrI ) => 137.73/18.19 ( ( dsetconstrEL ) => 137.73/18.19 ( ( dsetconstrER ) => 137.73/18.19 ( ( exuE1 ) => 137.73/18.19 ( ( prop2setE ) => 137.73/18.19 ( ( emptysetE ) => 137.73/18.19 ( ( emptysetimpfalse ) => 137.73/18.19 ( ( notinemptyset ) => 137.73/18.19 ( ( exuE3e ) => 137.73/18.19 ( ( setext ) => 137.73/18.19 ( ( emptyI ) => 137.73/18.19 ( ( noeltsimpempty ) => 137.73/18.19 ( ( setbeta ) => 137.73/18.19 ( ( nonemptyE1 ) => 137.73/18.19 ( ( nonemptyI ) => 137.73/18.19 ( ( nonemptyI1 ) => 137.73/18.19 ( ( setadjoinIL ) => 137.73/18.19 ( ( emptyinunitempty ) => 137.73/18.19 ( ( setadjoinIR ) => 137.73/18.19 ( ( setadjoinE ) => 137.73/18.19 ( ( 137.73/18.19 setadjoinOr ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setoftrueEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 powersetI ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 emptyinPowerset ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 emptyInPowerset ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 powersetE ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setunionI ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setunionE ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subPowSU ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 exuE2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 nonemptyImpWitness ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 uniqinunit ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 notinsingleton ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 eqinunit ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 singletonsswitch ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 upairsetE ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 upairsetIL ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 upairsetIR ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 emptyE1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 vacuousDall ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 quantDeMorgan1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 quantDeMorgan2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 quantDeMorgan3 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 quantDeMorgan4 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 prop2setI ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 prop2set2propI ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 notdexE ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 notdallE ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 exuI1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 exuI3 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 exuI2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 inCongP ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 exuE3u ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 exu__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 emptyset__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setadjoin__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 powerset__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setunion__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 omega__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 exuEu ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 descr__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 dsetconstr__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subsetI1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 eqimpsubset2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 eqimpsubset1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subsetI2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 emptysetsubset ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subsetE ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subsetE2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 notsubsetI ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 notequalI1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 notequalI2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subsetRefl ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subsetTrans ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setadjoinSub ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setadjoinSub2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subset2powerset ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setextsub ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subsetemptysetimpeq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 powersetI1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 powersetE1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 inPowerset ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 powersetsubset ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 sepInPowerset ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 sepSubset ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binunionIL ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 upairset2IR ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binunionIR ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binunionEcases ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binunionE ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binunionLsub ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binunionRsub ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectI ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectSubset5 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectEL ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectLsub ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectSubset2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectSubset3 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectER ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 disjointsetsI1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectRsub ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectSubset4 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectSubset1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 bs114d ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusI ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusEL ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusER ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusSubset2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusERneg ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusELneg ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusILneg ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusIRneg ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusLsub ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusSubset1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 symdiffE ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 symdiffI1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 symdiffI2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 symdiffIneg1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 symdiffIneg2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 secondinupair ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairIL ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairIR ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 kpairiskpair ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 kpairp ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 singletonsubset ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 singletoninpowerset ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 singletoninpowunion ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 upairset2E ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 upairsubunion ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 upairinpowunion ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ubforcartprodlem1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ubforcartprodlem2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ubforcartprodlem3 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodpairin ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodmempair1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodmempair ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setunionE2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setunionsingleton1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setunionsingleton2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setunionsingleton ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 singletonprop ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ex1E1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ex1I ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ex1I2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 singletonsuniq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairinjL1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 kfstsingleton ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 theprop ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 kfstpairEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodfstin ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairinjL2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairinjL ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairinjR11 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairinjR12 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairinjR1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 upairequniteq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairinjR2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairinjR ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ksndsingleton ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ksndpairEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 kpairsurjEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodsndin ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodpairmemEL ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodpairmemER ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodmempaircEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodfstpairEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodsndpairEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodpairsurjEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 dpsetconstrI ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 dpsetconstrSub ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setOfPairsIsBReln ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 dpsetconstrERa ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 dpsetconstrEL1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 dpsetconstrEL2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 dpsetconstrER ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcImageSingleton ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 apProp ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 app ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 infuncsetfunc ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ap2p ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcinfuncset ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 lamProp ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 lamp ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 lam2p ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 brelnall1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 brelnall2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ex1E2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcGraphProp1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcGraphProp3 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcGraphProp2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcextLem ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcGraphProp4 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subbreln ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 eqbreln ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcext ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcext2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ap2apEq1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ap2apEq2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 beta1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 eta1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 lam2lamEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 beta2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 eta2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 iffalseProp1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 iffalseProp2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 iftrueProp1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 iftrueProp2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ifSingleton ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ifp ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 theeq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 iftrue ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 iffalse ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 iftrueorfalse ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectT_lem ) => 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 A:$i,X:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 A ) ) => 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 Y:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 Y @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 A ) ) => 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 ( 137.73/18.19 binunion @ 137.73/18.19 X @ Y ) @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 137.73/18.19 thf(zf_stmt_0, conjecture, 137.73/18.19 (( setextAx ) => 137.73/18.19 ( ( emptysetAx ) => 137.73/18.19 ( ( setadjoinAx ) => 137.73/18.19 ( ( ![X4:$i,X6:$i]: 137.73/18.19 ( ( in @ X6 @ ( powerset @ X4 ) ) <=> 137.73/18.19 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) => 137.73/18.19 ( ( setunionAx ) => 137.73/18.19 ( ( omega0Ax ) => 137.73/18.19 ( ( omegaSAx ) => 137.73/18.19 ( ( omegaIndAx ) => 137.73/18.19 ( ( replAx ) => 137.73/18.19 ( ( foundationAx ) => 137.73/18.19 ( ( wellorderingAx ) => 137.73/18.19 ( ( descrp ) => 137.73/18.19 ( ( dsetconstrI ) => 137.73/18.19 ( ( dsetconstrEL ) => 137.73/18.19 ( ( dsetconstrER ) => 137.73/18.19 ( ( exuE1 ) => 137.73/18.19 ( ( prop2setE ) => 137.73/18.19 ( ( emptysetE ) => 137.73/18.19 ( ( emptysetimpfalse ) => 137.73/18.19 ( ( notinemptyset ) => 137.73/18.19 ( ( exuE3e ) => 137.73/18.19 ( ( setext ) => 137.73/18.19 ( ( emptyI ) => 137.73/18.19 ( ( noeltsimpempty ) => 137.73/18.19 ( ( setbeta ) => 137.73/18.19 ( ( nonemptyE1 ) => 137.73/18.19 ( ( nonemptyI ) => 137.73/18.19 ( ( nonemptyI1 ) => 137.73/18.19 ( ( setadjoinIL ) => 137.73/18.19 ( ( emptyinunitempty ) => 137.73/18.19 ( ( setadjoinIR ) => 137.73/18.19 ( ( setadjoinE ) => 137.73/18.19 ( ( 137.73/18.19 setadjoinOr ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setoftrueEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X10:$i, 137.73/18.19 X12:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X14:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X14 @ X12 ) => 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X14 @ X10 ) ) ) => 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X12 @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 X10 ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X16:$i]: 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 emptyset @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 X16 ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X18:$i]: 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 emptyset @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 X18 ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X20:$i, 137.73/18.19 X22:$i, 137.73/18.19 X24:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X22 @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 X20 ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X24 @ X22 ) => 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X24 @ X20 ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setunionI ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setunionE ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subPowSU ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 exuE2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 nonemptyImpWitness ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 uniqinunit ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 notinsingleton ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 eqinunit ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 singletonsswitch ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 upairsetE ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 upairsetIL ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 upairsetIR ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 emptyE1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 vacuousDall ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 quantDeMorgan1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 quantDeMorgan2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 quantDeMorgan3 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 quantDeMorgan4 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 prop2setI ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 prop2set2propI ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 notdexE ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 notdallE ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 exuI1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 exuI3 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 exuI2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 inCongP ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 exuE3u ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 exu__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 emptyset__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setadjoin__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X26:$i, 137.73/18.19 X28:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 X26 ) = 137.73/18.19 ( 137.73/18.19 X28 ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 X26 ) = 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 X28 ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setunion__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 omega__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 exuEu ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 descr__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 dsetconstr__Cong ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subsetI1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 eqimpsubset2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 eqimpsubset1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subsetI2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 emptysetsubset ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subsetE ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subsetE2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 notsubsetI ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 notequalI1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 notequalI2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subsetRefl ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subsetTrans ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setadjoinSub ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setadjoinSub2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X30:$i, 137.73/18.19 X32:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subset @ 137.73/18.19 X30 @ X32 ) => 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X30 @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 X32 ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setextsub ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subsetemptysetimpeq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X34:$i, 137.73/18.19 X36:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subset @ 137.73/18.19 X36 @ X34 ) => 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X36 @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 X34 ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X38:$i, 137.73/18.19 X40:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X40 @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 X38 ) ) => 137.73/18.19 ( 137.73/18.19 subset @ 137.73/18.19 X40 @ X38 ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X42:$i]: 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X42 @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 X42 ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X44:$i, 137.73/18.19 X46:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subset @ 137.73/18.19 X44 @ X46 ) => 137.73/18.19 ( 137.73/18.19 subset @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 X44 ) @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 X46 ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X48:$i, 137.73/18.19 X50:( 137.73/18.19 $i > $o )]: 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 ( 137.73/18.19 dsetconstr 137.73/18.19 @ 137.73/18.19 X48 @ 137.73/18.19 ( 137.73/18.19 ^[ 137.73/18.19 V_1:$i]: 137.73/18.19 ( 137.73/18.19 X50 @ V_1 ) ) ) @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 X48 ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 sepSubset ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X52:$i, 137.73/18.19 X54:$i, 137.73/18.19 X56:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X56 @ X52 ) => 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X56 @ 137.73/18.19 ( 137.73/18.19 binunion @ 137.73/18.19 X52 @ X54 ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 upairset2IR ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X58:$i, 137.73/18.19 X60:$i, 137.73/18.19 X62:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X62 @ X60 ) => 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X62 @ 137.73/18.19 ( 137.73/18.19 binunion @ 137.73/18.19 X58 @ X60 ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X64:$i, 137.73/18.19 X66:$i, 137.73/18.19 X68:$i, 137.73/18.19 X70:$o]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X68 @ 137.73/18.19 ( 137.73/18.19 binunion @ 137.73/18.19 X64 @ X66 ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X68 @ X64 ) => 137.73/18.19 ( 137.73/18.19 X70 ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X68 @ X66 ) => 137.73/18.19 ( 137.73/18.19 X70 ) ) => 137.73/18.19 ( 137.73/18.19 X70 ) ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X72:$i, 137.73/18.19 X74:$i, 137.73/18.19 X76:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X76 @ 137.73/18.19 ( 137.73/18.19 binunion @ 137.73/18.19 X72 @ X74 ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X76 @ X74 ) | 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X76 @ X72 ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X78:$i, 137.73/18.19 X80:$i]: 137.73/18.19 ( 137.73/18.19 subset @ 137.73/18.19 X78 @ 137.73/18.19 ( 137.73/18.19 binunion @ 137.73/18.19 X78 @ X80 ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X82:$i, 137.73/18.19 X84:$i]: 137.73/18.19 ( 137.73/18.19 subset @ 137.73/18.19 X84 @ 137.73/18.19 ( 137.73/18.19 binunion @ 137.73/18.19 X82 @ X84 ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectI ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectSubset5 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectEL ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectLsub ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectSubset2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectSubset3 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectER ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 disjointsetsI1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectRsub ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectSubset4 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersectSubset1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X86:$i, 137.73/18.19 X88:$i, 137.73/18.19 X90:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 binintersect 137.73/18.19 @ 137.73/18.19 X86 @ 137.73/18.19 ( 137.73/18.19 binunion @ 137.73/18.19 X88 @ X90 ) ) = 137.73/18.19 ( 137.73/18.19 binunion @ 137.73/18.19 ( 137.73/18.19 binintersect 137.73/18.19 @ 137.73/18.19 X86 @ X88 ) @ 137.73/18.19 ( 137.73/18.19 binintersect 137.73/18.19 @ 137.73/18.19 X86 @ X90 ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusI ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusEL ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusER ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusSubset2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusERneg ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusELneg ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusILneg ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusIRneg ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusLsub ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setminusSubset1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 symdiffE ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 symdiffI1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 symdiffI2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 symdiffIneg1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 symdiffIneg2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 secondinupair ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairIL ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairIR ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 kpairiskpair ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 kpairp ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 singletonsubset ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X92:$i, 137.73/18.19 X94:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X94 @ X92 ) => 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 ( 137.73/18.19 setadjoin 137.73/18.19 @ 137.73/18.19 X94 @ 137.73/18.19 emptyset ) @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 X92 ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X96:$i, 137.73/18.19 X98:$i, 137.73/18.19 X100:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X100 @ X96 ) => 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 ( 137.73/18.19 setadjoin 137.73/18.19 @ 137.73/18.19 X100 @ 137.73/18.19 emptyset ) @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 ( 137.73/18.19 binunion @ 137.73/18.19 X96 @ X98 ) ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 upairset2E ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X102:$i, 137.73/18.19 X104:$i, 137.73/18.19 X106:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X106 @ 137.73/18.19 X102 ) => 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X108:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X108 @ 137.73/18.19 X104 ) => 137.73/18.19 ( 137.73/18.19 subset @ 137.73/18.19 ( 137.73/18.19 setadjoin 137.73/18.19 @ 137.73/18.19 X106 @ 137.73/18.19 ( 137.73/18.19 setadjoin 137.73/18.19 @ 137.73/18.19 X108 @ 137.73/18.19 emptyset ) ) @ 137.73/18.19 ( 137.73/18.19 binunion @ 137.73/18.19 X102 @ 137.73/18.19 X104 ) ) ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X110:$i, 137.73/18.19 X112:$i, 137.73/18.19 X114:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X114 @ 137.73/18.19 X110 ) => 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X116:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X116 @ 137.73/18.19 X112 ) => 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 ( 137.73/18.19 setadjoin 137.73/18.19 @ 137.73/18.19 X114 @ 137.73/18.19 ( 137.73/18.19 setadjoin 137.73/18.19 @ 137.73/18.19 X116 @ 137.73/18.19 emptyset ) ) @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 ( 137.73/18.19 binunion @ 137.73/18.19 X110 @ 137.73/18.19 X112 ) ) ) ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X118:$i, 137.73/18.19 X120:$i, 137.73/18.19 X122:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X122 @ 137.73/18.19 X118 ) => 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X124:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X124 @ 137.73/18.19 X120 ) => 137.73/18.19 ( 137.73/18.19 subset @ 137.73/18.19 ( 137.73/18.19 setadjoin 137.73/18.19 @ 137.73/18.19 ( 137.73/18.19 setadjoin 137.73/18.19 @ 137.73/18.19 X122 @ 137.73/18.19 emptyset ) @ 137.73/18.19 ( 137.73/18.19 setadjoin 137.73/18.19 @ 137.73/18.19 ( 137.73/18.19 setadjoin 137.73/18.19 @ 137.73/18.19 X122 @ 137.73/18.19 ( 137.73/18.19 setadjoin 137.73/18.19 @ 137.73/18.19 X124 @ 137.73/18.19 emptyset ) ) @ 137.73/18.19 emptyset ) ) @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 ( 137.73/18.19 binunion @ 137.73/18.19 X118 @ 137.73/18.19 X120 ) ) ) ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X126:$i, 137.73/18.19 X128:$i, 137.73/18.19 X130:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X130 @ 137.73/18.19 X126 ) => 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X132:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X132 @ 137.73/18.19 X128 ) => 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 ( 137.73/18.19 setadjoin 137.73/18.19 @ 137.73/18.19 ( 137.73/18.19 setadjoin 137.73/18.19 @ 137.73/18.19 X130 @ 137.73/18.19 emptyset ) @ 137.73/18.19 ( 137.73/18.19 setadjoin 137.73/18.19 @ 137.73/18.19 ( 137.73/18.19 setadjoin 137.73/18.19 @ 137.73/18.19 X130 @ 137.73/18.19 ( 137.73/18.19 setadjoin 137.73/18.19 @ 137.73/18.19 X132 @ 137.73/18.19 emptyset ) ) @ 137.73/18.19 emptyset ) ) @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 ( 137.73/18.19 binunion @ 137.73/18.19 X126 @ 137.73/18.19 X128 ) ) ) ) ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X134:$i, 137.73/18.19 X136:$i, 137.73/18.19 X138:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X138 @ 137.73/18.19 X134 ) => 137.73/18.19 ( 137.73/18.19 ![ 137.73/18.19 X140:$i]: 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 X140 @ 137.73/18.19 X136 ) => 137.73/18.19 ( 137.73/18.19 in @ 137.73/18.19 ( 137.73/18.19 kpair @ 137.73/18.19 X138 @ 137.73/18.19 X140 ) @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 ( 137.73/18.19 powerset @ 137.73/18.19 ( 137.73/18.19 binunion @ 137.73/18.19 X134 @ 137.73/18.19 X136 ) ) ) ) ) ) ) ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodpairin ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodmempair1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodmempair ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setunionE2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setunionsingleton1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setunionsingleton2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setunionsingleton ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 singletonprop ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ex1E1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ex1I ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ex1I2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 singletonsuniq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairinjL1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 kfstsingleton ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 theprop ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 kfstpairEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodfstin ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairinjL2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairinjL ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairinjR11 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairinjR12 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairinjR1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 upairequniteq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairinjR2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setukpairinjR ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ksndsingleton ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ksndpairEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 kpairsurjEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodsndin ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodpairmemEL ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodpairmemER ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodmempaircEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodfstpairEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodsndpairEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 cartprodpairsurjEq ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 dpsetconstrI ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 dpsetconstrSub ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 setOfPairsIsBReln ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 dpsetconstrERa ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 dpsetconstrEL1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 dpsetconstrEL2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 dpsetconstrER ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcImageSingleton ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 apProp ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 app ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 infuncsetfunc ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ap2p ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcinfuncset ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 lamProp ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 lamp ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 lam2p ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 brelnall1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 brelnall2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 ex1E2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcGraphProp1 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcGraphProp3 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcGraphProp2 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcextLem ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcGraphProp4 ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 subbreln ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 eqbreln ) => 137.73/18.19 ( 137.73/18.19 ( 137.73/18.19 funcext ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcext2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ap2apEq1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ap2apEq2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 beta1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 eta1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 lam2lamEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 beta2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 eta2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iffalseProp1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iffalseProp2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iftrueProp1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iftrueProp2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ifSingleton ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ifp ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 theeq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iftrue ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iffalse ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iftrueorfalse ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectT_lem ) => 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X142:$i, 137.73/18.20 X144:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X144 @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X142 ) ) => 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X146:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X146 @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X142 ) ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 ( 137.73/18.20 binunion @ 137.73/18.20 X144 @ 137.73/18.20 X146 ) @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X142 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 137.73/18.20 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o). 137.73/18.20 thf(zf_stmt_2, axiom, 137.73/18.20 (![X8:$i,X6:$i,X4:$i]: 137.73/18.20 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=> 137.73/18.20 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))). 137.73/18.20 thf(zf_stmt_3, conjecture, 137.73/18.20 (( setextAx ) => 137.73/18.20 ( ( emptysetAx ) => 137.73/18.20 ( ( setadjoinAx ) => 137.73/18.20 ( ( ![X4:$i,X6:$i]: 137.73/18.20 ( ( in @ X6 @ ( powerset @ X4 ) ) <=> 137.73/18.20 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) => 137.73/18.20 ( ( setunionAx ) => 137.73/18.20 ( ( omega0Ax ) => 137.73/18.20 ( ( omegaSAx ) => 137.73/18.20 ( ( omegaIndAx ) => 137.73/18.20 ( ( replAx ) => 137.73/18.20 ( ( foundationAx ) => 137.73/18.20 ( ( wellorderingAx ) => 137.73/18.20 ( ( descrp ) => 137.73/18.20 ( ( dsetconstrI ) => 137.73/18.20 ( ( dsetconstrEL ) => 137.73/18.20 ( ( dsetconstrER ) => 137.73/18.20 ( ( exuE1 ) => 137.73/18.20 ( ( prop2setE ) => 137.73/18.20 ( ( emptysetE ) => 137.73/18.20 ( ( emptysetimpfalse ) => 137.73/18.20 ( ( notinemptyset ) => 137.73/18.20 ( ( exuE3e ) => 137.73/18.20 ( ( setext ) => 137.73/18.20 ( ( emptyI ) => 137.73/18.20 ( ( noeltsimpempty ) => 137.73/18.20 ( ( setbeta ) => 137.73/18.20 ( ( nonemptyE1 ) => 137.73/18.20 ( ( nonemptyI ) => 137.73/18.20 ( ( nonemptyI1 ) => 137.73/18.20 ( ( setadjoinIL ) => 137.73/18.20 ( ( emptyinunitempty ) => 137.73/18.20 ( ( setadjoinIR ) => 137.73/18.20 ( ( setadjoinE ) => 137.73/18.20 ( ( 137.73/18.20 setadjoinOr ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setoftrueEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X10:$i, 137.73/18.20 X12:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X14:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X14 @ X12 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X14 @ X10 ) ) ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X12 @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X10 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X16:$i]: 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 emptyset @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X16 ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X18:$i]: 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 emptyset @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X18 ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X20:$i, 137.73/18.20 X22:$i, 137.73/18.20 X24:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X22 @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X20 ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X24 @ X22 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X24 @ X20 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setunionI ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setunionE ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subPowSU ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 exuE2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 nonemptyImpWitness ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 uniqinunit ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 notinsingleton ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 eqinunit ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 singletonsswitch ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 upairsetE ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 upairsetIL ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 upairsetIR ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 emptyE1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 vacuousDall ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 quantDeMorgan1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 quantDeMorgan2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 quantDeMorgan3 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 quantDeMorgan4 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 prop2setI ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 prop2set2propI ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 notdexE ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 notdallE ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 exuI1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 exuI3 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 exuI2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 inCongP ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in__Cong ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 exuE3u ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 exu__Cong ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 emptyset__Cong ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setadjoin__Cong ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X26:$i, 137.73/18.20 X28:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 X26 ) = 137.73/18.20 ( 137.73/18.20 X28 ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X26 ) = 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X28 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setunion__Cong ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 omega__Cong ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 exuEu ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 descr__Cong ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 dsetconstr__Cong ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subsetI1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 eqimpsubset2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 eqimpsubset1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subsetI2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 emptysetsubset ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subsetE ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subsetE2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 notsubsetI ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 notequalI1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 notequalI2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subsetRefl ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subsetTrans ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setadjoinSub ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setadjoinSub2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X30:$i, 137.73/18.20 X32:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 X30 @ X32 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X30 @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X32 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setextsub ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subsetemptysetimpeq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X34:$i, 137.73/18.20 X36:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 X36 @ X34 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X36 @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X34 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X38:$i, 137.73/18.20 X40:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X40 @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X38 ) ) => 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 X40 @ X38 ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X42:$i]: 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X42 @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X42 ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X44:$i, 137.73/18.20 X46:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 X44 @ X46 ) => 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X44 ) @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X46 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X48:$i, 137.73/18.20 X50:( 137.73/18.20 $i > $o )]: 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 ( 137.73/18.20 dsetconstr 137.73/18.20 @ 137.73/18.20 X48 @ 137.73/18.20 ( 137.73/18.20 ^[ 137.73/18.20 V_1:$i]: 137.73/18.20 ( 137.73/18.20 X50 @ V_1 ) ) ) @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X48 ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 sepSubset ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X52:$i, 137.73/18.20 X54:$i, 137.73/18.20 X56:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X56 @ X52 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X56 @ 137.73/18.20 ( 137.73/18.20 binunion @ 137.73/18.20 X52 @ X54 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 upairset2IR ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X58:$i, 137.73/18.20 X60:$i, 137.73/18.20 X62:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X62 @ X60 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X62 @ 137.73/18.20 ( 137.73/18.20 binunion @ 137.73/18.20 X58 @ X60 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X64:$i, 137.73/18.20 X66:$i, 137.73/18.20 X68:$i, 137.73/18.20 X70:$o]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X68 @ 137.73/18.20 ( 137.73/18.20 binunion @ 137.73/18.20 X64 @ X66 ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X68 @ X64 ) => 137.73/18.20 ( 137.73/18.20 X70 ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X68 @ X66 ) => 137.73/18.20 ( 137.73/18.20 X70 ) ) => 137.73/18.20 ( 137.73/18.20 X70 ) ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X72:$i, 137.73/18.20 X74:$i, 137.73/18.20 X76:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X76 @ 137.73/18.20 ( 137.73/18.20 binunion @ 137.73/18.20 X72 @ X74 ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X76 @ X72 ) | 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X76 @ X74 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X78:$i, 137.73/18.20 X80:$i]: 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 X78 @ 137.73/18.20 ( 137.73/18.20 binunion @ 137.73/18.20 X78 @ X80 ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X82:$i, 137.73/18.20 X84:$i]: 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 X84 @ 137.73/18.20 ( 137.73/18.20 binunion @ 137.73/18.20 X82 @ X84 ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectI ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectSubset5 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectEL ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectLsub ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectSubset2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectSubset3 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectER ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 disjointsetsI1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectRsub ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectSubset4 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectSubset1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X86:$i, 137.73/18.20 X88:$i, 137.73/18.20 X90:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersect 137.73/18.20 @ 137.73/18.20 X86 @ 137.73/18.20 ( 137.73/18.20 binunion @ 137.73/18.20 X88 @ X90 ) ) = 137.73/18.20 ( 137.73/18.20 binunion @ 137.73/18.20 ( 137.73/18.20 binintersect 137.73/18.20 @ 137.73/18.20 X86 @ X88 ) @ 137.73/18.20 ( 137.73/18.20 binintersect 137.73/18.20 @ 137.73/18.20 X86 @ X90 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusI ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusEL ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusER ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusSubset2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusERneg ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusELneg ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusILneg ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusIRneg ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusLsub ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusSubset1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 symdiffE ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 symdiffI1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 symdiffI2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 symdiffIneg1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 symdiffIneg2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 secondinupair ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairIL ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairIR ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 kpairiskpair ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 kpairp ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 singletonsubset ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X92:$i, 137.73/18.20 X94:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X94 @ X92 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X94 @ 137.73/18.20 emptyset ) @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X92 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X96:$i, 137.73/18.20 X98:$i, 137.73/18.20 X100:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X100 @ X96 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X100 @ 137.73/18.20 emptyset ) @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 ( 137.73/18.20 binunion @ 137.73/18.20 X96 @ X98 ) ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 upairset2E ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X102:$i, 137.73/18.20 X104:$i, 137.73/18.20 X106:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X106 @ 137.73/18.20 X102 ) => 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X108:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X108 @ 137.73/18.20 X104 ) => 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X106 @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X108 @ 137.73/18.20 emptyset ) ) @ 137.73/18.20 ( 137.73/18.20 binunion @ 137.73/18.20 X102 @ 137.73/18.20 X104 ) ) ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X110:$i, 137.73/18.20 X112:$i, 137.73/18.20 X114:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X114 @ 137.73/18.20 X110 ) => 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X116:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X116 @ 137.73/18.20 X112 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X114 @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X116 @ 137.73/18.20 emptyset ) ) @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 ( 137.73/18.20 binunion @ 137.73/18.20 X110 @ 137.73/18.20 X112 ) ) ) ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X118:$i, 137.73/18.20 X120:$i, 137.73/18.20 X122:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X122 @ 137.73/18.20 X118 ) => 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X124:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X124 @ 137.73/18.20 X120 ) => 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X122 @ 137.73/18.20 emptyset ) @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X122 @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X124 @ 137.73/18.20 emptyset ) ) @ 137.73/18.20 emptyset ) ) @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 ( 137.73/18.20 binunion @ 137.73/18.20 X118 @ 137.73/18.20 X120 ) ) ) ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X126:$i, 137.73/18.20 X128:$i, 137.73/18.20 X130:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X130 @ 137.73/18.20 X126 ) => 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X132:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X132 @ 137.73/18.20 X128 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X130 @ 137.73/18.20 emptyset ) @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X130 @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X132 @ 137.73/18.20 emptyset ) ) @ 137.73/18.20 emptyset ) ) @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 ( 137.73/18.20 binunion @ 137.73/18.20 X126 @ 137.73/18.20 X128 ) ) ) ) ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X134:$i, 137.73/18.20 X136:$i, 137.73/18.20 X138:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X138 @ 137.73/18.20 X134 ) => 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X140:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X140 @ 137.73/18.20 X136 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 ( 137.73/18.20 kpair @ 137.73/18.20 X138 @ 137.73/18.20 X140 ) @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 ( 137.73/18.20 binunion @ 137.73/18.20 X134 @ 137.73/18.20 X136 ) ) ) ) ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodpairin ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodmempair1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodmempair ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setunionE2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setunionsingleton1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setunionsingleton2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setunionsingleton ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 singletonprop ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ex1E1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ex1I ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ex1I2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 singletonsuniq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairinjL1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 kfstsingleton ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 theprop ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 kfstpairEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodfstin ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairinjL2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairinjL ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairinjR11 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairinjR12 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairinjR1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 upairequniteq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairinjR2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairinjR ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ksndsingleton ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ksndpairEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 kpairsurjEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodsndin ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodpairmemEL ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodpairmemER ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodmempaircEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodfstpairEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodsndpairEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodpairsurjEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 dpsetconstrI ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 dpsetconstrSub ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setOfPairsIsBReln ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 dpsetconstrERa ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 dpsetconstrEL1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 dpsetconstrEL2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 dpsetconstrER ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcImageSingleton ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 apProp ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 app ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 infuncsetfunc ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ap2p ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcinfuncset ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 lamProp ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 lamp ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 lam2p ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 brelnall1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 brelnall2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ex1E2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcGraphProp1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcGraphProp3 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcGraphProp2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcextLem ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcGraphProp4 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subbreln ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 eqbreln ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcext ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcext2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ap2apEq1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ap2apEq2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 beta1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 eta1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 lam2lamEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 beta2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 eta2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iffalseProp1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iffalseProp2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iftrueProp1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iftrueProp2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ifSingleton ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ifp ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 theeq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iftrue ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iffalse ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iftrueorfalse ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectT_lem ) => 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X142:$i, 137.73/18.20 X144:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X144 @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X142 ) ) => 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X146:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X146 @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X142 ) ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 ( 137.73/18.20 binunion @ 137.73/18.20 X144 @ 137.73/18.20 X146 ) @ 137.73/18.20 ( 137.73/18.20 powerset @ 137.73/18.20 X142 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 137.73/18.20 thf(zf_stmt_4, negated_conjecture, 137.73/18.20 (~( ( setextAx ) => 137.73/18.20 ( ( emptysetAx ) => 137.73/18.20 ( ( setadjoinAx ) => 137.73/18.20 ( ( ![X4:$i,X6:$i]: 137.73/18.20 ( ( in @ X6 @ ( powerset @ X4 ) ) <=> 137.73/18.20 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) => 137.73/18.20 ( ( setunionAx ) => 137.73/18.20 ( ( omega0Ax ) => 137.73/18.20 ( ( omegaSAx ) => 137.73/18.20 ( ( omegaIndAx ) => 137.73/18.20 ( ( replAx ) => 137.73/18.20 ( ( foundationAx ) => 137.73/18.20 ( ( wellorderingAx ) => 137.73/18.20 ( ( descrp ) => 137.73/18.20 ( ( dsetconstrI ) => 137.73/18.20 ( ( dsetconstrEL ) => 137.73/18.20 ( ( dsetconstrER ) => 137.73/18.20 ( ( exuE1 ) => 137.73/18.20 ( ( prop2setE ) => 137.73/18.20 ( ( emptysetE ) => 137.73/18.20 ( ( emptysetimpfalse ) => 137.73/18.20 ( ( notinemptyset ) => 137.73/18.20 ( ( exuE3e ) => 137.73/18.20 ( ( setext ) => 137.73/18.20 ( ( emptyI ) => 137.73/18.20 ( ( noeltsimpempty ) => 137.73/18.20 ( ( setbeta ) => 137.73/18.20 ( ( nonemptyE1 ) => 137.73/18.20 ( ( nonemptyI ) => 137.73/18.20 ( ( nonemptyI1 ) => 137.73/18.20 ( ( setadjoinIL ) => 137.73/18.20 ( ( emptyinunitempty ) => 137.73/18.20 ( ( setadjoinIR ) => 137.73/18.20 ( ( 137.73/18.20 setadjoinE ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setadjoinOr ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setoftrueEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X10:$i, 137.73/18.20 X12:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X14:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X14 @ X12 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X14 @ X10 ) ) ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X12 @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X10 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X16:$i]: 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 emptyset @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X16 ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X18:$i]: 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 emptyset @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X18 ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X20:$i, 137.73/18.20 X22:$i, 137.73/18.20 X24:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X22 @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X20 ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X24 @ X22 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X24 @ X20 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setunionI ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setunionE ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subPowSU ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 exuE2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 nonemptyImpWitness ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 uniqinunit ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 notinsingleton ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 eqinunit ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 singletonsswitch ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 upairsetE ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 upairsetIL ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 upairsetIR ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 emptyE1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 vacuousDall ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 quantDeMorgan1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 quantDeMorgan2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 quantDeMorgan3 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 quantDeMorgan4 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 prop2setI ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 prop2set2propI ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 notdexE ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 notdallE ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 exuI1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 exuI3 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 exuI2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 inCongP ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in__Cong ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 exuE3u ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 exu__Cong ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 emptyset__Cong ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setadjoin__Cong ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X26:$i, 137.73/18.20 X28:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 X26 ) = 137.73/18.20 ( 137.73/18.20 X28 ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X26 ) = 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X28 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setunion__Cong ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 omega__Cong ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 exuEu ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 descr__Cong ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 dsetconstr__Cong ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subsetI1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 eqimpsubset2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 eqimpsubset1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subsetI2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 emptysetsubset ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subsetE ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subsetE2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 notsubsetI ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 notequalI1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 notequalI2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subsetRefl ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subsetTrans ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setadjoinSub ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setadjoinSub2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X30:$i, 137.73/18.20 X32:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 X30 @ X32 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X30 @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X32 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setextsub ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subsetemptysetimpeq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X34:$i, 137.73/18.20 X36:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 X36 @ X34 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X36 @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X34 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X38:$i, 137.73/18.20 X40:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X40 @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X38 ) ) => 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 X40 @ X38 ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X42:$i]: 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X42 @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X42 ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X44:$i, 137.73/18.20 X46:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 X44 @ X46 ) => 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X44 ) @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X46 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X48:$i, 137.73/18.20 X50:( 137.73/18.20 $i > $o )]: 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 ( 137.73/18.20 dsetconstr 137.73/18.20 @ 137.73/18.20 X48 @ 137.73/18.20 ( 137.73/18.20 ^[ 137.73/18.20 V_1:$i]: 137.73/18.20 ( 137.73/18.20 X50 @ V_1 ) ) ) @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X48 ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 sepSubset ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X52:$i, 137.73/18.20 X54:$i, 137.73/18.20 X56:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X56 @ X52 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X56 @ 137.73/18.20 ( 137.73/18.20 binunion 137.73/18.20 @ 137.73/18.20 X52 @ X54 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 upairset2IR ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X58:$i, 137.73/18.20 X60:$i, 137.73/18.20 X62:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X62 @ X60 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X62 @ 137.73/18.20 ( 137.73/18.20 binunion 137.73/18.20 @ 137.73/18.20 X58 @ X60 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X64:$i, 137.73/18.20 X66:$i, 137.73/18.20 X68:$i, 137.73/18.20 X70:$o]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X68 @ 137.73/18.20 ( 137.73/18.20 binunion 137.73/18.20 @ 137.73/18.20 X64 @ X66 ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X68 @ X64 ) => 137.73/18.20 ( 137.73/18.20 X70 ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X68 @ X66 ) => 137.73/18.20 ( 137.73/18.20 X70 ) ) => 137.73/18.20 ( 137.73/18.20 X70 ) ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X72:$i, 137.73/18.20 X74:$i, 137.73/18.20 X76:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X76 @ 137.73/18.20 ( 137.73/18.20 binunion 137.73/18.20 @ 137.73/18.20 X72 @ X74 ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X76 @ X72 ) | 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X76 @ X74 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X78:$i, 137.73/18.20 X80:$i]: 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 X78 @ 137.73/18.20 ( 137.73/18.20 binunion 137.73/18.20 @ 137.73/18.20 X78 @ X80 ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X82:$i, 137.73/18.20 X84:$i]: 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 X84 @ 137.73/18.20 ( 137.73/18.20 binunion 137.73/18.20 @ 137.73/18.20 X82 @ X84 ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectI ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectSubset5 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectEL ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectLsub ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectSubset2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectSubset3 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectER ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 disjointsetsI1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectRsub ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectSubset4 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectSubset1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X86:$i, 137.73/18.20 X88:$i, 137.73/18.20 X90:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersect 137.73/18.20 @ 137.73/18.20 X86 @ 137.73/18.20 ( 137.73/18.20 binunion 137.73/18.20 @ 137.73/18.20 X88 @ X90 ) ) = 137.73/18.20 ( 137.73/18.20 binunion 137.73/18.20 @ 137.73/18.20 ( 137.73/18.20 binintersect 137.73/18.20 @ 137.73/18.20 X86 @ X88 ) @ 137.73/18.20 ( 137.73/18.20 binintersect 137.73/18.20 @ 137.73/18.20 X86 @ X90 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusI ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusEL ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusER ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusSubset2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusERneg ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusELneg ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusILneg ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusIRneg ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusLsub ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setminusSubset1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 symdiffE ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 symdiffI1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 symdiffI2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 symdiffIneg1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 symdiffIneg2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 secondinupair ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairIL ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairIR ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 kpairiskpair ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 kpairp ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 singletonsubset ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X92:$i, 137.73/18.20 X94:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X94 @ X92 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X94 @ 137.73/18.20 emptyset ) @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X92 ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X96:$i, 137.73/18.20 X98:$i, 137.73/18.20 X100:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X100 @ 137.73/18.20 X96 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X100 @ 137.73/18.20 emptyset ) @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 ( 137.73/18.20 binunion 137.73/18.20 @ 137.73/18.20 X96 @ X98 ) ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 upairset2E ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X102:$i, 137.73/18.20 X104:$i, 137.73/18.20 X106:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X106 @ 137.73/18.20 X102 ) => 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X108:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X108 @ 137.73/18.20 X104 ) => 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X106 @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X108 @ 137.73/18.20 emptyset ) ) @ 137.73/18.20 ( 137.73/18.20 binunion 137.73/18.20 @ 137.73/18.20 X102 @ 137.73/18.20 X104 ) ) ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X110:$i, 137.73/18.20 X112:$i, 137.73/18.20 X114:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X114 @ 137.73/18.20 X110 ) => 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X116:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X116 @ 137.73/18.20 X112 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X114 @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X116 @ 137.73/18.20 emptyset ) ) @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 ( 137.73/18.20 binunion 137.73/18.20 @ 137.73/18.20 X110 @ 137.73/18.20 X112 ) ) ) ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X118:$i, 137.73/18.20 X120:$i, 137.73/18.20 X122:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X122 @ 137.73/18.20 X118 ) => 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X124:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X124 @ 137.73/18.20 X120 ) => 137.73/18.20 ( 137.73/18.20 subset @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X122 @ 137.73/18.20 emptyset ) @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X122 @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X124 @ 137.73/18.20 emptyset ) ) @ 137.73/18.20 emptyset ) ) @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 ( 137.73/18.20 binunion 137.73/18.20 @ 137.73/18.20 X118 @ 137.73/18.20 X120 ) ) ) ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X126:$i, 137.73/18.20 X128:$i, 137.73/18.20 X130:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X130 @ 137.73/18.20 X126 ) => 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X132:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X132 @ 137.73/18.20 X128 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X130 @ 137.73/18.20 emptyset ) @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X130 @ 137.73/18.20 ( 137.73/18.20 setadjoin 137.73/18.20 @ 137.73/18.20 X132 @ 137.73/18.20 emptyset ) ) @ 137.73/18.20 emptyset ) ) @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 ( 137.73/18.20 binunion 137.73/18.20 @ 137.73/18.20 X126 @ 137.73/18.20 X128 ) ) ) ) ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X134:$i, 137.73/18.20 X136:$i, 137.73/18.20 X138:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X138 @ 137.73/18.20 X134 ) => 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X140:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X140 @ 137.73/18.20 X136 ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 ( 137.73/18.20 kpair @ 137.73/18.20 X138 @ 137.73/18.20 X140 ) @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 ( 137.73/18.20 binunion 137.73/18.20 @ 137.73/18.20 X134 @ 137.73/18.20 X136 ) ) ) ) ) ) ) ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodpairin ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodmempair1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodmempair ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setunionE2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setunionsingleton1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setunionsingleton2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setunionsingleton ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 singletonprop ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ex1E1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ex1I ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ex1I2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 singletonsuniq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairinjL1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 kfstsingleton ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 theprop ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 kfstpairEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodfstin ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairinjL2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairinjL ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairinjR11 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairinjR12 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairinjR1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 upairequniteq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairinjR2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setukpairinjR ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ksndsingleton ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ksndpairEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 kpairsurjEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodsndin ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodpairmemEL ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodpairmemER ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodmempaircEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodfstpairEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodsndpairEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 cartprodpairsurjEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 dpsetconstrI ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 dpsetconstrSub ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 setOfPairsIsBReln ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 dpsetconstrERa ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 dpsetconstrEL1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 dpsetconstrEL2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 dpsetconstrER ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcImageSingleton ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 apProp ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 app ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 infuncsetfunc ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ap2p ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcinfuncset ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 lamProp ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 lamp ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 lam2p ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 brelnall1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 brelnall2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ex1E2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcGraphProp1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcGraphProp3 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcGraphProp2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcextLem ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcGraphProp4 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 subbreln ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 eqbreln ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcext ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 funcext2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ap2apEq1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ap2apEq2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 beta1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 eta1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 lam2lamEq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 beta2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 eta2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iffalseProp1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iffalseProp2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iftrueProp1 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iftrueProp2 ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ifSingleton ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 ifp ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 theeq ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iftrue ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iffalse ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 iftrueorfalse ) => 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 binintersectT_lem ) => 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X142:$i, 137.73/18.20 X144:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X144 @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X142 ) ) => 137.73/18.20 ( 137.73/18.20 ![ 137.73/18.20 X146:$i]: 137.73/18.20 ( 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 X146 @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X142 ) ) => 137.73/18.20 ( 137.73/18.20 in @ 137.73/18.20 ( 137.73/18.20 binunion 137.73/18.20 @ 137.73/18.20 X144 @ 137.73/18.20 X146 ) @ 137.73/18.20 ( 137.73/18.20 powerset 137.73/18.20 @ 137.73/18.20 X142 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 137.73/18.20 inference('cnf.neg', [status(esa)], [zf_stmt_3])). 137.73/18.20 thf(zip_derived_cl119, plain, 137.73/18.20 (~ (in @ (binunion @ sk__72 @ sk__73) @ (powerset @ sk__71))), 137.73/18.20 inference('cnf', [status(esa)], [zf_stmt_4])). 137.73/18.20 thf(zip_derived_cl20, plain, 137.73/18.20 (![X0 : $i, X1 : $i]: 137.73/18.20 ( (in @ X0 @ (powerset @ X1)) | ~ (in @ (sk__74 @ X0 @ X1) @ X1))), 137.73/18.20 inference('cnf', [status(esa)], [zf_stmt_4])). 137.73/18.20 thf(zip_derived_cl21, plain, 137.73/18.20 (![X0 : $i, X1 : $i]: 137.73/18.20 ( (in @ X0 @ (powerset @ X1)) | (in @ (sk__74 @ X0 @ X1) @ X0))), 137.73/18.20 inference('cnf', [status(esa)], [zf_stmt_4])). 137.73/18.20 thf(zip_derived_cl55, plain, 137.73/18.20 (![X14 : $i, X15 : $i, X16 : $i]: 137.73/18.20 ( (in @ X14 @ X15) 137.73/18.20 | (in @ X14 @ X16) 137.73/18.20 | ~ (in @ X14 @ (binunion @ X16 @ X15)))), 137.73/18.20 inference('cnf', [status(esa)], [zf_stmt_4])). 137.73/18.20 thf(zip_derived_cl259, plain, 137.73/18.20 (![X0 : $i, X1 : $i, X2 : $i]: 137.73/18.20 ( (in @ (binunion @ X1 @ X0) @ (powerset @ X2)) 137.73/18.20 | (in @ (sk__74 @ (binunion @ X1 @ X0) @ X2) @ X1) 137.73/18.20 | (in @ (sk__74 @ (binunion @ X1 @ X0) @ X2) @ X0))), 137.73/18.20 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl55])). 137.73/18.20 thf(zip_derived_cl120, plain, ( (in @ sk__72 @ (powerset @ sk__71))), 137.73/18.20 inference('cnf', [status(esa)], [zf_stmt_4])). 137.73/18.20 thf(zip_derived_cl218, plain, 137.73/18.20 (![X61 : $i, X62 : $i, X63 : $i]: 137.73/18.20 (~ (in @ X61 @ (powerset @ X62)) 137.73/18.20 | (in @ X63 @ X62) 137.73/18.20 | ~ (in @ X63 @ X61))), 137.73/18.20 inference('cnf', [status(esa)], [zf_stmt_4])). 137.73/18.20 thf(zip_derived_cl293, plain, 137.73/18.20 (![X0 : $i]: (~ (in @ X0 @ sk__72) | (in @ X0 @ sk__71))), 137.73/18.20 inference('sup-', [status(thm)], [zip_derived_cl120, zip_derived_cl218])). 137.73/18.20 thf(zip_derived_cl118, plain, ( (in @ sk__73 @ (powerset @ sk__71))), 137.73/18.20 inference('cnf', [status(esa)], [zf_stmt_4])). 137.73/18.20 thf(zip_derived_cl218, plain, 137.73/18.20 (![X61 : $i, X62 : $i, X63 : $i]: 137.73/18.20 (~ (in @ X61 @ (powerset @ X62)) 137.73/18.20 | (in @ X63 @ X62) 137.73/18.20 | ~ (in @ X63 @ X61))), 137.73/18.20 inference('cnf', [status(esa)], [zf_stmt_4])). 137.73/18.20 thf(zip_derived_cl292, plain, 137.73/18.20 (![X0 : $i]: (~ (in @ X0 @ sk__73) | (in @ X0 @ sk__71))), 137.73/18.20 inference('sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl218])). 137.73/18.20 thf(zip_derived_cl13102, plain, ($false), 137.73/18.20 inference('eprover', [status(thm)], 137.73/18.20 [zip_derived_cl119, zip_derived_cl20, zip_derived_cl259, 137.73/18.20 zip_derived_cl293, zip_derived_cl292])). 137.73/18.20 137.73/18.20 % SZS output end Refutation 137.73/18.20 137.73/18.20 137.73/18.20 % Terminating... 137.73/18.23 % Runner terminated. 137.73/18.23 % Zipperpin 1.5 exiting 137.73/18.24 EOF