%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU711^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.pQAWGB0kXH true
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:55:53 PM UTC 2025
% Result : Theorem 67.20s 9.11s
% Output : Refutation 67.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU711^1 : TPTP v9.2.0. Released v3.7.0.
% 0.13/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.pQAWGB0kXH true
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Oct 1 16:04:23 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.33 % Running portfolio for 300 s
% 0.13/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.34 % Running in HO mode
% 0.53/0.65 % Total configuration time : 828
% 0.53/0.65 % Estimated wc time : 1656
% 0.53/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.54/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.54/0.75 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.54/0.76 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 67.20/9.11 % Solved by lams/40_c_ic.sh.
% 67.20/9.11 % done 2566 iterations in 8.277s
% 67.20/9.11 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 67.20/9.11 % SZS output start Refutation
% 67.20/9.11 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 67.20/9.11 thf(notdexE_type, type, notdexE: $o).
% 67.20/9.11 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 67.20/9.11 thf(setunionAx_type, type, setunionAx: $o).
% 67.20/9.11 thf(setminusELneg_type, type, setminusELneg: $o).
% 67.20/9.11 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 67.20/9.11 thf(ex1E1_type, type, ex1E1: $o).
% 67.20/9.11 thf(powersetE_type, type, powersetE: $o).
% 67.20/9.11 thf(omegaSAx_type, type, omegaSAx: $o).
% 67.20/9.11 thf(exuI1_type, type, exuI1: $o).
% 67.20/9.11 thf(exuI2_type, type, exuI2: $o).
% 67.20/9.11 thf(notequalI2_type, type, notequalI2: $o).
% 67.20/9.11 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 67.20/9.11 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 67.20/9.11 thf(upairsubunion_type, type, upairsubunion: $o).
% 67.20/9.11 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 67.20/9.11 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 67.20/9.11 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 67.20/9.11 thf(setminusILneg_type, type, setminusILneg: $o).
% 67.20/9.11 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 67.20/9.11 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 67.20/9.11 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 67.20/9.11 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 67.20/9.11 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 67.20/9.11 thf(iftrue_type, type, iftrue: $o).
% 67.20/9.11 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 67.20/9.11 thf(ifSingleton_type, type, ifSingleton: $o).
% 67.20/9.11 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 67.20/9.11 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 67.20/9.11 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 67.20/9.11 thf(lamProp_type, type, lamProp: $o).
% 67.20/9.11 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 67.20/9.11 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 67.20/9.11 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 67.20/9.11 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 67.20/9.11 thf(setukpairIR_type, type, setukpairIR: $o).
% 67.20/9.11 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 67.20/9.11 thf(lam2p_type, type, lam2p: $o).
% 67.20/9.11 thf(kpair_type, type, kpair: $i > $i > $i).
% 67.20/9.11 thf(binunionE_type, type, binunionE: $o).
% 67.20/9.11 thf(setext_type, type, setext: $o).
% 67.20/9.11 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 67.20/9.11 thf(sk__71_type, type, sk__71: $i).
% 67.20/9.11 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 67.20/9.11 thf(descr__Cong_type, type, descr__Cong: $o).
% 67.20/9.11 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 67.20/9.11 thf(eqbreln_type, type, eqbreln: $o).
% 67.20/9.11 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 67.20/9.11 thf(in_type, type, in: $i > $i > $o).
% 67.20/9.11 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 67.20/9.11 thf(binunion_type, type, binunion: $i > $i > $i).
% 67.20/9.11 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 67.20/9.11 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 67.20/9.11 thf(beta1_type, type, beta1: $o).
% 67.20/9.11 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 67.20/9.11 thf(symdiffI2_type, type, symdiffI2: $o).
% 67.20/9.11 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 67.20/9.11 thf(upairset2IR_type, type, upairset2IR: $o).
% 67.20/9.11 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 67.20/9.11 thf(subsetE_type, type, subsetE: $o).
% 67.20/9.11 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 67.20/9.11 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 67.20/9.11 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 67.20/9.11 thf(setbeta_type, type, setbeta: $o).
% 67.20/9.11 thf(eqinunit_type, type, eqinunit: $o).
% 67.20/9.11 thf(upairsetIL_type, type, upairsetIL: $o).
% 67.20/9.11 thf(powersetI1_type, type, powersetI1: $o).
% 67.20/9.11 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 67.20/9.11 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 67.20/9.11 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 67.20/9.11 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 67.20/9.11 thf(powersetAx_type, type, powersetAx: $o).
% 67.20/9.11 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 67.20/9.11 thf(sk__72_type, type, sk__72: $i).
% 67.20/9.11 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 67.20/9.11 thf(powersetI_type, type, powersetI: $o).
% 67.20/9.11 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 67.20/9.11 thf(upairsetIR_type, type, upairsetIR: $o).
% 67.20/9.11 thf(lamp_type, type, lamp: $o).
% 67.20/9.11 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 67.20/9.11 thf(inCongP_type, type, inCongP: $o).
% 67.20/9.11 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 67.20/9.11 thf(exuE3e_type, type, exuE3e: $o).
% 67.20/9.11 thf(emptysetE_type, type, emptysetE: $o).
% 67.20/9.11 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 67.20/9.11 thf(setunionI_type, type, setunionI: $o).
% 67.20/9.11 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 67.20/9.11 thf(prop2setI_type, type, prop2setI: $o).
% 67.20/9.11 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 67.20/9.11 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 67.20/9.11 thf(setminusER_type, type, setminusER: $o).
% 67.20/9.11 thf(exuE2_type, type, exuE2: $o).
% 67.20/9.11 thf(emptyset_type, type, emptyset: $i).
% 67.20/9.11 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 67.20/9.11 thf(ex1I_type, type, ex1I: $o).
% 67.20/9.11 thf(ex1E2_type, type, ex1E2: $o).
% 67.20/9.11 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 67.20/9.11 thf(powersetsubset_type, type, powersetsubset: $o).
% 67.20/9.11 thf(subPowSU_type, type, subPowSU: $o).
% 67.20/9.11 thf(notequalI1_type, type, notequalI1: $o).
% 67.20/9.11 thf(notinemptyset_type, type, notinemptyset: $o).
% 67.20/9.11 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 67.20/9.11 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 67.20/9.11 thf(subsetTrans_type, type, subsetTrans: $o).
% 67.20/9.11 thf(kpairp_type, type, kpairp: $o).
% 67.20/9.11 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 67.20/9.11 thf(setminusI_type, type, setminusI: $o).
% 67.20/9.11 thf(binunionIL_type, type, binunionIL: $o).
% 67.20/9.11 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 67.20/9.11 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 67.20/9.11 thf(sk__73_type, type, sk__73: $i).
% 67.20/9.11 thf(subsetE2_type, type, subsetE2: $o).
% 67.20/9.11 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 67.20/9.11 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 67.20/9.11 thf(beta2_type, type, beta2: $o).
% 67.20/9.11 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 67.20/9.11 thf(setextsub_type, type, setextsub: $o).
% 67.20/9.11 thf(binunionLsub_type, type, binunionLsub: $o).
% 67.20/9.11 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 67.20/9.11 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 67.20/9.11 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 67.20/9.11 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 67.20/9.11 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 67.20/9.11 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 67.20/9.11 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 67.20/9.11 thf(setunionE_type, type, setunionE: $o).
% 67.20/9.11 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 67.20/9.11 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 67.20/9.11 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 67.20/9.11 thf(binunionIR_type, type, binunionIR: $o).
% 67.20/9.11 thf(theeq_type, type, theeq: $o).
% 67.20/9.11 thf(setadjoinE_type, type, setadjoinE: $o).
% 67.20/9.11 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 67.20/9.11 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 67.20/9.11 thf(ap2p_type, type, ap2p: $o).
% 67.20/9.11 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 67.20/9.11 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 67.20/9.11 thf(exuE1_type, type, exuE1: $o).
% 67.20/9.11 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 67.20/9.11 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 67.20/9.11 thf(setminusLsub_type, type, setminusLsub: $o).
% 67.20/9.11 thf(funcextLem_type, type, funcextLem: $o).
% 67.20/9.11 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 67.20/9.11 thf(notinsingleton_type, type, notinsingleton: $o).
% 67.20/9.11 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 67.20/9.11 thf(exuEu_type, type, exuEu: $o).
% 67.20/9.11 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 67.20/9.11 thf(upairsetE_type, type, upairsetE: $o).
% 67.20/9.11 thf(omega0Ax_type, type, omega0Ax: $o).
% 67.20/9.11 thf(notsubsetI_type, type, notsubsetI: $o).
% 67.20/9.11 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 67.20/9.11 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 67.20/9.11 thf(setextAx_type, type, setextAx: $o).
% 67.20/9.11 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 67.20/9.11 thf(powersetE1_type, type, powersetE1: $o).
% 67.20/9.11 thf(bs114d_type, type, bs114d: $o).
% 67.20/9.11 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 67.20/9.11 thf(ifp_type, type, ifp: $o).
% 67.20/9.11 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 67.20/9.11 thf(subsetI1_type, type, subsetI1: $o).
% 67.20/9.11 thf(symdiffE_type, type, symdiffE: $o).
% 67.20/9.11 thf(descrp_type, type, descrp: $o).
% 67.20/9.11 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 67.20/9.11 thf(foundationAx_type, type, foundationAx: $o).
% 67.20/9.11 thf(emptysetAx_type, type, emptysetAx: $o).
% 67.20/9.11 thf(emptyI_type, type, emptyI: $o).
% 67.20/9.11 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 67.20/9.11 thf(eta2_type, type, eta2: $o).
% 67.20/9.11 thf(binintersectEL_type, type, binintersectEL: $o).
% 67.20/9.11 thf(emptyE1_type, type, emptyE1: $o).
% 67.20/9.11 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 67.20/9.11 thf(vacuousDall_type, type, vacuousDall: $o).
% 67.20/9.11 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 67.20/9.11 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 67.20/9.11 thf(binintersectI_type, type, binintersectI: $o).
% 67.20/9.11 thf(funcext_type, type, funcext: $o).
% 67.20/9.11 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 67.20/9.11 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 67.20/9.11 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 67.20/9.11 thf(brelnall2_type, type, brelnall2: $o).
% 67.20/9.11 thf(ex1I2_type, type, ex1I2: $o).
% 67.20/9.11 thf(symdiffI1_type, type, symdiffI1: $o).
% 67.20/9.11 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 67.20/9.11 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 67.20/9.11 thf(theprop_type, type, theprop: $o).
% 67.20/9.11 thf(subsetI2_type, type, subsetI2: $o).
% 67.20/9.11 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 67.20/9.11 thf(setminusERneg_type, type, setminusERneg: $o).
% 67.20/9.11 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 67.20/9.11 thf(omega__Cong_type, type, omega__Cong: $o).
% 67.20/9.11 thf(subsetRefl_type, type, subsetRefl: $o).
% 67.20/9.11 thf(uniqinunit_type, type, uniqinunit: $o).
% 67.20/9.11 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 67.20/9.11 thf(prop2setE_type, type, prop2setE: $o).
% 67.20/9.11 thf(binunionEcases_type, type, binunionEcases: $o).
% 67.20/9.11 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 67.20/9.11 thf(nonemptyI_type, type, nonemptyI: $o).
% 67.20/9.11 thf(app_type, type, app: $o).
% 67.20/9.11 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 67.20/9.11 thf(exuE3u_type, type, exuE3u: $o).
% 67.20/9.11 thf(eta1_type, type, eta1: $o).
% 67.20/9.11 thf(setminusEL_type, type, setminusEL: $o).
% 67.20/9.11 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 67.20/9.11 thf(sk__74_type, type, sk__74: $i > $i > $i).
% 67.20/9.11 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 67.20/9.11 thf(sepSubset_type, type, sepSubset: $o).
% 67.20/9.11 thf(upairset2E_type, type, upairset2E: $o).
% 67.20/9.11 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 67.20/9.11 thf(exuI3_type, type, exuI3: $o).
% 67.20/9.11 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 67.20/9.11 thf(apProp_type, type, apProp: $o).
% 67.20/9.11 thf(notdallE_type, type, notdallE: $o).
% 67.20/9.11 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 67.20/9.11 thf(binintersectER_type, type, binintersectER: $o).
% 67.20/9.11 thf(brelnall1_type, type, brelnall1: $o).
% 67.20/9.11 thf(powerset_type, type, powerset: $i > $i).
% 67.20/9.11 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 67.20/9.11 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 67.20/9.11 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 67.20/9.11 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 67.20/9.11 thf(exu__Cong_type, type, exu__Cong: $o).
% 67.20/9.11 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 67.20/9.11 thf(secondinupair_type, type, secondinupair: $o).
% 67.20/9.11 thf(singletonprop_type, type, singletonprop: $o).
% 67.20/9.11 thf(singletonsubset_type, type, singletonsubset: $o).
% 67.20/9.11 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 67.20/9.11 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 67.20/9.11 thf(replAx_type, type, replAx: $o).
% 67.20/9.11 thf(upairequniteq_type, type, upairequniteq: $o).
% 67.20/9.11 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 67.20/9.11 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 67.20/9.11 thf(setukpairIL_type, type, setukpairIL: $o).
% 67.20/9.11 thf(setunionE2_type, type, setunionE2: $o).
% 67.20/9.11 thf(inPowerset_type, type, inPowerset: $o).
% 67.20/9.11 thf(iffalse_type, type, iffalse: $o).
% 67.20/9.11 thf(funcext2_type, type, funcext2: $o).
% 67.20/9.11 thf(subset_type, type, subset: $i > $i > $o).
% 67.20/9.11 thf(subbreln_type, type, subbreln: $o).
% 67.20/9.11 thf(in__Cong_type, type, in__Cong: $o).
% 67.20/9.11 thf(binunionRsub_type, type, binunionRsub: $o).
% 67.20/9.11 thf(subset2powerset_type, type, subset2powerset: $o).
% 67.20/9.11 thf(ubforcartprodlem3, axiom, ubforcartprodlem3 =
% 67.20/9.11 (![A:$i,B:$i,Xx:$i]:
% 67.20/9.11 ( ( in @ Xx @ A ) =>
% 67.20/9.11 ( ![Xy:$i]:
% 67.20/9.11 ( ( in @ Xy @ B ) =>
% 67.20/9.11 ( in @
% 67.20/9.11 ( kpair @ Xx @ Xy ) @
% 67.20/9.11 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 67.20/9.11 thf('0', plain,
% 67.20/9.11 (( ubforcartprodlem3 ) =
% 67.20/9.11 ( ![X4:$i,X6:$i,X8:$i]:
% 67.20/9.11 ( ( in @ X8 @ X4 ) =>
% 67.20/9.11 ( ![X10:$i]:
% 67.20/9.11 ( ( in @ X10 @ X6 ) =>
% 67.20/9.11 ( in @
% 67.20/9.11 ( kpair @ X8 @ X10 ) @
% 67.20/9.11 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(ubforcartprodlem2, axiom, ubforcartprodlem2 =
% 67.20/9.11 (![A:$i,B:$i,Xx:$i]:
% 67.20/9.11 ( ( in @ Xx @ A ) =>
% 67.20/9.11 ( ![Xy:$i]:
% 67.20/9.11 ( ( in @ Xy @ B ) =>
% 67.20/9.11 ( in @
% 67.20/9.11 ( setadjoin @
% 67.20/9.11 ( setadjoin @ Xx @ emptyset ) @
% 67.20/9.11 ( setadjoin @
% 67.20/9.11 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 67.20/9.11 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 67.20/9.11 thf('1', plain,
% 67.20/9.11 (( ubforcartprodlem2 ) =
% 67.20/9.11 ( ![X4:$i,X6:$i,X8:$i]:
% 67.20/9.11 ( ( in @ X8 @ X4 ) =>
% 67.20/9.11 ( ![X10:$i]:
% 67.20/9.11 ( ( in @ X10 @ X6 ) =>
% 67.20/9.11 ( in @
% 67.20/9.11 ( setadjoin @
% 67.20/9.11 ( setadjoin @ X8 @ emptyset ) @
% 67.20/9.11 ( setadjoin @
% 67.20/9.11 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 67.20/9.11 emptyset ) ) @
% 67.20/9.11 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(ubforcartprodlem1, axiom, ubforcartprodlem1 =
% 67.20/9.11 (![A:$i,B:$i,Xx:$i]:
% 67.20/9.11 ( ( in @ Xx @ A ) =>
% 67.20/9.11 ( ![Xy:$i]:
% 67.20/9.11 ( ( in @ Xy @ B ) =>
% 67.20/9.11 ( subset @
% 67.20/9.11 ( setadjoin @
% 67.20/9.11 ( setadjoin @ Xx @ emptyset ) @
% 67.20/9.11 ( setadjoin @
% 67.20/9.11 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 67.20/9.11 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 67.20/9.11 thf('2', plain,
% 67.20/9.11 (( ubforcartprodlem1 ) =
% 67.20/9.11 ( ![X4:$i,X6:$i,X8:$i]:
% 67.20/9.11 ( ( in @ X8 @ X4 ) =>
% 67.20/9.11 ( ![X10:$i]:
% 67.20/9.11 ( ( in @ X10 @ X6 ) =>
% 67.20/9.11 ( subset @
% 67.20/9.11 ( setadjoin @
% 67.20/9.11 ( setadjoin @ X8 @ emptyset ) @
% 67.20/9.11 ( setadjoin @
% 67.20/9.11 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 67.20/9.11 emptyset ) ) @
% 67.20/9.11 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(upairinpowunion, axiom, upairinpowunion =
% 67.20/9.11 (![A:$i,B:$i,Xx:$i]:
% 67.20/9.11 ( ( in @ Xx @ A ) =>
% 67.20/9.11 ( ![Xy:$i]:
% 67.20/9.11 ( ( in @ Xy @ B ) =>
% 67.20/9.11 ( in @
% 67.20/9.11 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 67.20/9.11 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 67.20/9.11 thf('3', plain,
% 67.20/9.11 (( upairinpowunion ) =
% 67.20/9.11 ( ![X4:$i,X6:$i,X8:$i]:
% 67.20/9.11 ( ( in @ X8 @ X4 ) =>
% 67.20/9.11 ( ![X10:$i]:
% 67.20/9.11 ( ( in @ X10 @ X6 ) =>
% 67.20/9.11 ( in @
% 67.20/9.11 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 67.20/9.11 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(upairsubunion, axiom, upairsubunion =
% 67.20/9.11 (![A:$i,B:$i,Xx:$i]:
% 67.20/9.11 ( ( in @ Xx @ A ) =>
% 67.20/9.11 ( ![Xy:$i]:
% 67.20/9.11 ( ( in @ Xy @ B ) =>
% 67.20/9.11 ( subset @
% 67.20/9.11 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 67.20/9.11 ( binunion @ A @ B ) ) ) ) ))).
% 67.20/9.11 thf('4', plain,
% 67.20/9.11 (( upairsubunion ) =
% 67.20/9.11 ( ![X4:$i,X6:$i,X8:$i]:
% 67.20/9.11 ( ( in @ X8 @ X4 ) =>
% 67.20/9.11 ( ![X10:$i]:
% 67.20/9.11 ( ( in @ X10 @ X6 ) =>
% 67.20/9.11 ( subset @
% 67.20/9.11 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 67.20/9.11 ( binunion @ X4 @ X6 ) ) ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(singletoninpowunion, axiom, singletoninpowunion =
% 67.20/9.11 (![A:$i,B:$i,Xx:$i]:
% 67.20/9.11 ( ( in @ Xx @ A ) =>
% 67.20/9.11 ( in @
% 67.20/9.11 ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ))).
% 67.20/9.11 thf('5', plain,
% 67.20/9.11 (( singletoninpowunion ) =
% 67.20/9.11 ( ![X4:$i,X6:$i,X8:$i]:
% 67.20/9.11 ( ( in @ X8 @ X4 ) =>
% 67.20/9.11 ( in @
% 67.20/9.11 ( setadjoin @ X8 @ emptyset ) @
% 67.20/9.11 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(singletoninpowerset, axiom, singletoninpowerset =
% 67.20/9.11 (![A:$i,Xx:$i]:
% 67.20/9.11 ( ( in @ Xx @ A ) =>
% 67.20/9.11 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 67.20/9.11 thf('6', plain,
% 67.20/9.11 (( singletoninpowerset ) =
% 67.20/9.11 ( ![X4:$i,X6:$i]:
% 67.20/9.11 ( ( in @ X6 @ X4 ) =>
% 67.20/9.11 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(bs114d, axiom, bs114d =
% 67.20/9.11 (![A:$i,B:$i,C:$i]:
% 67.20/9.11 ( ( binintersect @ A @ ( binunion @ B @ C ) ) =
% 67.20/9.11 ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ))).
% 67.20/9.11 thf('7', plain,
% 67.20/9.11 (( bs114d ) =
% 67.20/9.11 ( ![X4:$i,X6:$i,X8:$i]:
% 67.20/9.11 ( ( binintersect @ X4 @ ( binunion @ X6 @ X8 ) ) =
% 67.20/9.11 ( binunion @ ( binintersect @ X4 @ X6 ) @ ( binintersect @ X4 @ X8 ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(binunionRsub, axiom, binunionRsub =
% 67.20/9.11 (![A:$i,B:$i]: ( subset @ B @ ( binunion @ A @ B ) ))).
% 67.20/9.11 thf('8', plain,
% 67.20/9.11 (( binunionRsub ) =
% 67.20/9.11 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( binunion @ X4 @ X6 ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(binunionLsub, axiom, binunionLsub =
% 67.20/9.11 (![A:$i,B:$i]: ( subset @ A @ ( binunion @ A @ B ) ))).
% 67.20/9.11 thf('9', plain,
% 67.20/9.11 (( binunionLsub ) =
% 67.20/9.11 ( ![X4:$i,X6:$i]: ( subset @ X4 @ ( binunion @ X4 @ X6 ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(binunionE, axiom, binunionE =
% 67.20/9.11 (![A:$i,B:$i,Xx:$i]:
% 67.20/9.11 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 67.20/9.11 ( ( in @ Xx @ A ) | ( in @ Xx @ B ) ) ))).
% 67.20/9.11 thf('10', plain,
% 67.20/9.11 (( binunionE ) =
% 67.20/9.11 ( ![X4:$i,X6:$i,X8:$i]:
% 67.20/9.11 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 67.20/9.11 ( ( in @ X8 @ X4 ) | ( in @ X8 @ X6 ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(binunionEcases, axiom, binunionEcases =
% 67.20/9.11 (![A:$i,B:$i,Xx:$i,Xphi:$o]:
% 67.20/9.11 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 67.20/9.11 ( ( ( in @ Xx @ A ) => ( Xphi ) ) =>
% 67.20/9.11 ( ( ( in @ Xx @ B ) => ( Xphi ) ) => ( Xphi ) ) ) ))).
% 67.20/9.11 thf('11', plain,
% 67.20/9.11 (( binunionEcases ) =
% 67.20/9.11 ( ![X4:$i,X6:$i,X8:$i,X10:$o]:
% 67.20/9.11 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 67.20/9.11 ( ( ( in @ X8 @ X4 ) => ( X10 ) ) =>
% 67.20/9.11 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(binunionIR, axiom, binunionIR =
% 67.20/9.11 (![A:$i,B:$i,Xx:$i]:
% 67.20/9.11 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 67.20/9.11 thf('12', plain,
% 67.20/9.11 (( binunionIR ) =
% 67.20/9.11 ( ![X4:$i,X6:$i,X8:$i]:
% 67.20/9.11 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(binunionIL, axiom, binunionIL =
% 67.20/9.11 (![A:$i,B:$i,Xx:$i]:
% 67.20/9.11 ( ( in @ Xx @ A ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 67.20/9.11 thf('13', plain,
% 67.20/9.11 (( binunionIL ) =
% 67.20/9.11 ( ![X4:$i,X6:$i,X8:$i]:
% 67.20/9.11 ( ( in @ X8 @ X4 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(sepInPowerset, axiom, sepInPowerset =
% 67.20/9.11 (![A:$i,Xphi:( $i > $o )]:
% 67.20/9.11 ( in @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) @ ( powerset @ A ) ))).
% 67.20/9.11 thf('14', plain,
% 67.20/9.11 (( sepInPowerset ) =
% 67.20/9.11 ( ![X4:$i,X6:( $i > $o )]:
% 67.20/9.11 ( in @
% 67.20/9.11 ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) @
% 67.20/9.11 ( powerset @ X4 ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(powersetsubset, axiom, powersetsubset =
% 67.20/9.11 (![A:$i,B:$i]:
% 67.20/9.11 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 67.20/9.11 thf('15', plain,
% 67.20/9.11 (( powersetsubset ) =
% 67.20/9.11 ( ![X4:$i,X6:$i]:
% 67.20/9.11 ( ( subset @ X4 @ X6 ) =>
% 67.20/9.11 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 67.20/9.11 thf('16', plain,
% 67.20/9.11 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(powersetE1, axiom, powersetE1 =
% 67.20/9.11 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 67.20/9.11 thf('17', plain,
% 67.20/9.11 (( powersetE1 ) =
% 67.20/9.11 ( ![X4:$i,X6:$i]:
% 67.20/9.11 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(powersetI1, axiom, powersetI1 =
% 67.20/9.11 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 67.20/9.11 thf('18', plain,
% 67.20/9.11 (( powersetI1 ) =
% 67.20/9.11 ( ![X4:$i,X6:$i]:
% 67.20/9.11 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(subset2powerset, axiom, subset2powerset =
% 67.20/9.11 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 67.20/9.11 thf('19', plain,
% 67.20/9.11 (( subset2powerset ) =
% 67.20/9.11 ( ![X4:$i,X6:$i]:
% 67.20/9.11 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(powerset__Cong, axiom, powerset__Cong =
% 67.20/9.11 (![A:$i,B:$i]:
% 67.20/9.11 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 67.20/9.11 thf('20', plain,
% 67.20/9.11 (( powerset__Cong ) =
% 67.20/9.11 ( ![X4:$i,X6:$i]:
% 67.20/9.11 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(powersetE, axiom, powersetE =
% 67.20/9.11 (![A:$i,B:$i,Xx:$i]:
% 67.20/9.11 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 67.20/9.11 thf('21', plain,
% 67.20/9.11 (( powersetE ) =
% 67.20/9.11 ( ![X4:$i,X6:$i,X8:$i]:
% 67.20/9.11 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 67.20/9.11 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(emptyInPowerset, axiom, emptyInPowerset =
% 67.20/9.11 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 67.20/9.11 thf('22', plain,
% 67.20/9.11 (( emptyInPowerset ) =
% 67.20/9.11 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(emptyinPowerset, axiom, emptyinPowerset =
% 67.20/9.11 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 67.20/9.11 thf('23', plain,
% 67.20/9.11 (( emptyinPowerset ) =
% 67.20/9.11 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(powersetI, axiom, powersetI =
% 67.20/9.11 (![A:$i,B:$i]:
% 67.20/9.11 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 67.20/9.11 ( in @ B @ ( powerset @ A ) ) ))).
% 67.20/9.11 thf('24', plain,
% 67.20/9.11 (( powersetI ) =
% 67.20/9.11 ( ![X4:$i,X6:$i]:
% 67.20/9.11 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 67.20/9.11 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(powersetAx, axiom, powersetAx =
% 67.20/9.11 (![A:$i,B:$i]:
% 67.20/9.11 ( ( in @ B @ ( powerset @ A ) ) <=>
% 67.20/9.11 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 67.20/9.11 thf('25', plain,
% 67.20/9.11 (( powersetAx ) =
% 67.20/9.11 ( ![X4:$i,X6:$i]:
% 67.20/9.11 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 67.20/9.11 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 67.20/9.11 define([status(thm)])).
% 67.20/9.11 thf(binunionT_lem, conjecture,
% 67.20/9.11 (( setextAx ) =>
% 67.20/9.11 ( ( emptysetAx ) =>
% 67.20/9.11 ( ( setadjoinAx ) =>
% 67.20/9.11 ( ( powersetAx ) =>
% 67.20/9.11 ( ( setunionAx ) =>
% 67.20/9.11 ( ( omega0Ax ) =>
% 67.20/9.11 ( ( omegaSAx ) =>
% 67.20/9.11 ( ( omegaIndAx ) =>
% 67.20/9.11 ( ( replAx ) =>
% 67.20/9.11 ( ( foundationAx ) =>
% 67.20/9.11 ( ( wellorderingAx ) =>
% 67.20/9.11 ( ( descrp ) =>
% 67.20/9.11 ( ( dsetconstrI ) =>
% 67.20/9.11 ( ( dsetconstrEL ) =>
% 67.20/9.11 ( ( dsetconstrER ) =>
% 67.20/9.11 ( ( exuE1 ) =>
% 67.20/9.11 ( ( prop2setE ) =>
% 67.20/9.11 ( ( emptysetE ) =>
% 67.20/9.11 ( ( emptysetimpfalse ) =>
% 67.20/9.11 ( ( notinemptyset ) =>
% 67.20/9.11 ( ( exuE3e ) =>
% 67.20/9.11 ( ( setext ) =>
% 67.20/9.11 ( ( emptyI ) =>
% 67.20/9.11 ( ( noeltsimpempty ) =>
% 67.20/9.11 ( ( setbeta ) =>
% 67.20/9.11 ( ( nonemptyE1 ) =>
% 67.20/9.11 ( ( nonemptyI ) =>
% 67.20/9.11 ( ( nonemptyI1 ) =>
% 67.20/9.11 ( ( setadjoinIL ) =>
% 67.20/9.11 ( ( emptyinunitempty ) =>
% 67.20/9.11 ( ( setadjoinIR ) =>
% 67.20/9.11 ( ( setadjoinE ) =>
% 67.20/9.11 ( (
% 67.20/9.11 setadjoinOr ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setoftrueEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 powersetI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 emptyinPowerset ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 emptyInPowerset ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 powersetE ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionE ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subPowSU ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 exuE2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 nonemptyImpWitness ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 uniqinunit ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 notinsingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 eqinunit ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 singletonsswitch ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairsetE ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairsetIL ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairsetIR ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 emptyE1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 vacuousDall ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 quantDeMorgan1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 quantDeMorgan2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 quantDeMorgan3 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 quantDeMorgan4 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 prop2setI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 prop2set2propI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 notdexE ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 notdallE ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 exuI1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 exuI3 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 exuI2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 inCongP ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 exuE3u ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 exu__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 emptyset__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setadjoin__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 powerset__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunion__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 omega__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 exuEu ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 descr__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dsetconstr__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subsetI1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 eqimpsubset2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 eqimpsubset1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subsetI2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 emptysetsubset ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subsetE ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subsetE2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 notsubsetI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 notequalI1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 notequalI2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subsetRefl ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subsetTrans ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setadjoinSub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setadjoinSub2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subset2powerset ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setextsub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subsetemptysetimpeq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 powersetI1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 powersetE1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 inPowerset ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 powersetsubset ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 sepInPowerset ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 sepSubset ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binunionIL ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairset2IR ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binunionIR ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binunionEcases ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binunionE ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binunionLsub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binunionRsub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectSubset5 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectEL ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectLsub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectSubset2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectSubset3 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectER ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 disjointsetsI1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectRsub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectSubset4 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectSubset1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 bs114d ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusEL ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusER ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusSubset2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusERneg ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusELneg ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusILneg ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusIRneg ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusLsub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusSubset1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 symdiffE ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 symdiffI1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 symdiffI2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 symdiffIneg1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 symdiffIneg2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 secondinupair ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairIL ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairIR ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 kpairiskpair ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 kpairp ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 singletonsubset ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 singletoninpowerset ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 singletoninpowunion ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairset2E ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairsubunion ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairinpowunion ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ubforcartprodlem1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ubforcartprodlem2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ubforcartprodlem3 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodpairin ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodmempair1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodmempair ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionE2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionsingleton1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionsingleton2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionsingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 singletonprop ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ex1E1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ex1I ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ex1I2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 singletonsuniq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjL1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 kfstsingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 theprop ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 kfstpairEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodfstin ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjL2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjL ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjR11 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjR12 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjR1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairequniteq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjR2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjR ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ksndsingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ksndpairEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 kpairsurjEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodsndin ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodpairmemEL ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodpairmemER ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodmempaircEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodfstpairEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodsndpairEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodpairsurjEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrSub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setOfPairsIsBReln ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrERa ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrEL1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrEL2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrER ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcImageSingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 apProp ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 app ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 infuncsetfunc ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ap2p ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcinfuncset ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 lamProp ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 lamp ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 lam2p ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 brelnall1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 brelnall2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ex1E2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcGraphProp1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcGraphProp3 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcGraphProp2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcextLem ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcGraphProp4 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subbreln ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 eqbreln ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcext ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcext2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ap2apEq1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ap2apEq2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 beta1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 eta1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 lam2lamEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 beta2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 eta2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 iffalseProp1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 iffalseProp2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 iftrueProp1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 iftrueProp2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ifSingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ifp ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 theeq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 iftrue ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 iffalse ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 iftrueorfalse ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectT_lem ) =>
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 A:$i,X:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 A ) ) =>
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 Y:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 Y @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 A ) ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X @ Y ) @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 67.20/9.11 thf(zf_stmt_0, conjecture,
% 67.20/9.11 (( setextAx ) =>
% 67.20/9.11 ( ( emptysetAx ) =>
% 67.20/9.11 ( ( setadjoinAx ) =>
% 67.20/9.11 ( ( ![X4:$i,X6:$i]:
% 67.20/9.11 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 67.20/9.11 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 67.20/9.11 ( ( setunionAx ) =>
% 67.20/9.11 ( ( omega0Ax ) =>
% 67.20/9.11 ( ( omegaSAx ) =>
% 67.20/9.11 ( ( omegaIndAx ) =>
% 67.20/9.11 ( ( replAx ) =>
% 67.20/9.11 ( ( foundationAx ) =>
% 67.20/9.11 ( ( wellorderingAx ) =>
% 67.20/9.11 ( ( descrp ) =>
% 67.20/9.11 ( ( dsetconstrI ) =>
% 67.20/9.11 ( ( dsetconstrEL ) =>
% 67.20/9.11 ( ( dsetconstrER ) =>
% 67.20/9.11 ( ( exuE1 ) =>
% 67.20/9.11 ( ( prop2setE ) =>
% 67.20/9.11 ( ( emptysetE ) =>
% 67.20/9.11 ( ( emptysetimpfalse ) =>
% 67.20/9.11 ( ( notinemptyset ) =>
% 67.20/9.11 ( ( exuE3e ) =>
% 67.20/9.11 ( ( setext ) =>
% 67.20/9.11 ( ( emptyI ) =>
% 67.20/9.11 ( ( noeltsimpempty ) =>
% 67.20/9.11 ( ( setbeta ) =>
% 67.20/9.11 ( ( nonemptyE1 ) =>
% 67.20/9.11 ( ( nonemptyI ) =>
% 67.20/9.11 ( ( nonemptyI1 ) =>
% 67.20/9.11 ( ( setadjoinIL ) =>
% 67.20/9.11 ( ( emptyinunitempty ) =>
% 67.20/9.11 ( ( setadjoinIR ) =>
% 67.20/9.11 ( ( setadjoinE ) =>
% 67.20/9.11 ( (
% 67.20/9.11 setadjoinOr ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setoftrueEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X10:$i,
% 67.20/9.11 X12:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X14:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X14 @ X12 ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X14 @ X10 ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X12 @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X10 ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X16:$i]:
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 emptyset @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X16 ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X18:$i]:
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 emptyset @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X18 ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X20:$i,
% 67.20/9.11 X22:$i,
% 67.20/9.11 X24:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X22 @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X20 ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X24 @ X22 ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X24 @ X20 ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionE ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subPowSU ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 exuE2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 nonemptyImpWitness ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 uniqinunit ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 notinsingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 eqinunit ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 singletonsswitch ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairsetE ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairsetIL ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairsetIR ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 emptyE1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 vacuousDall ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 quantDeMorgan1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 quantDeMorgan2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 quantDeMorgan3 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 quantDeMorgan4 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 prop2setI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 prop2set2propI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 notdexE ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 notdallE ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 exuI1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 exuI3 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 exuI2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 inCongP ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 exuE3u ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 exu__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 emptyset__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setadjoin__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X26:$i,
% 67.20/9.11 X28:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 X26 ) =
% 67.20/9.11 (
% 67.20/9.11 X28 ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X26 ) =
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X28 ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunion__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 omega__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 exuEu ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 descr__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dsetconstr__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subsetI1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 eqimpsubset2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 eqimpsubset1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subsetI2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 emptysetsubset ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subsetE ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subsetE2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 notsubsetI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 notequalI1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 notequalI2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subsetRefl ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subsetTrans ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setadjoinSub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setadjoinSub2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X30:$i,
% 67.20/9.11 X32:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subset @
% 67.20/9.11 X30 @ X32 ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X30 @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X32 ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setextsub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subsetemptysetimpeq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X34:$i,
% 67.20/9.11 X36:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subset @
% 67.20/9.11 X36 @ X34 ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X36 @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X34 ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X38:$i,
% 67.20/9.11 X40:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X40 @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X38 ) ) =>
% 67.20/9.11 (
% 67.20/9.11 subset @
% 67.20/9.11 X40 @ X38 ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X42:$i]:
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X42 @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X42 ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X44:$i,
% 67.20/9.11 X46:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subset @
% 67.20/9.11 X44 @ X46 ) =>
% 67.20/9.11 (
% 67.20/9.11 subset @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X44 ) @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X46 ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X48:$i,
% 67.20/9.11 X50:(
% 67.20/9.11 $i > $o )]:
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 (
% 67.20/9.11 dsetconstr
% 67.20/9.11 @
% 67.20/9.11 X48 @
% 67.20/9.11 (
% 67.20/9.11 ^[
% 67.20/9.11 V_1:$i]:
% 67.20/9.11 (
% 67.20/9.11 X50 @ V_1 ) ) ) @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X48 ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 sepSubset ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X52:$i,
% 67.20/9.11 X54:$i,
% 67.20/9.11 X56:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X56 @ X52 ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X56 @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X52 @ X54 ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairset2IR ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X58:$i,
% 67.20/9.11 X60:$i,
% 67.20/9.11 X62:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X62 @ X60 ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X62 @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X58 @ X60 ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X64:$i,
% 67.20/9.11 X66:$i,
% 67.20/9.11 X68:$i,
% 67.20/9.11 X70:$o]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X68 @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X64 @ X66 ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X68 @ X64 ) =>
% 67.20/9.11 (
% 67.20/9.11 X70 ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X68 @ X66 ) =>
% 67.20/9.11 (
% 67.20/9.11 X70 ) ) =>
% 67.20/9.11 (
% 67.20/9.11 X70 ) ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X72:$i,
% 67.20/9.11 X74:$i,
% 67.20/9.11 X76:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X76 @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X72 @ X74 ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X76 @ X74 ) |
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X76 @ X72 ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X78:$i,
% 67.20/9.11 X80:$i]:
% 67.20/9.11 (
% 67.20/9.11 subset @
% 67.20/9.11 X78 @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X78 @ X80 ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X82:$i,
% 67.20/9.11 X84:$i]:
% 67.20/9.11 (
% 67.20/9.11 subset @
% 67.20/9.11 X84 @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X82 @ X84 ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectSubset5 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectEL ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectLsub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectSubset2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectSubset3 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectER ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 disjointsetsI1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectRsub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectSubset4 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectSubset1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X86:$i,
% 67.20/9.11 X88:$i,
% 67.20/9.11 X90:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersect
% 67.20/9.11 @
% 67.20/9.11 X86 @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X88 @ X90 ) ) =
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 (
% 67.20/9.11 binintersect
% 67.20/9.11 @
% 67.20/9.11 X86 @ X88 ) @
% 67.20/9.11 (
% 67.20/9.11 binintersect
% 67.20/9.11 @
% 67.20/9.11 X86 @ X90 ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusEL ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusER ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusSubset2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusERneg ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusELneg ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusILneg ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusIRneg ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusLsub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusSubset1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 symdiffE ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 symdiffI1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 symdiffI2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 symdiffIneg1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 symdiffIneg2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 secondinupair ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairIL ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairIR ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 kpairiskpair ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 kpairp ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 singletonsubset ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X92:$i,
% 67.20/9.11 X94:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X94 @ X92 ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 (
% 67.20/9.11 setadjoin
% 67.20/9.11 @
% 67.20/9.11 X94 @
% 67.20/9.11 emptyset ) @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X92 ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X96:$i,
% 67.20/9.11 X98:$i,
% 67.20/9.11 X100:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X100 @ X96 ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 (
% 67.20/9.11 setadjoin
% 67.20/9.11 @
% 67.20/9.11 X100 @
% 67.20/9.11 emptyset ) @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X96 @ X98 ) ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairset2E ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X102:$i,
% 67.20/9.11 X104:$i,
% 67.20/9.11 X106:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X106 @
% 67.20/9.11 X102 ) =>
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X108:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X108 @
% 67.20/9.11 X104 ) =>
% 67.20/9.11 (
% 67.20/9.11 subset @
% 67.20/9.11 (
% 67.20/9.11 setadjoin
% 67.20/9.11 @
% 67.20/9.11 X106 @
% 67.20/9.11 (
% 67.20/9.11 setadjoin
% 67.20/9.11 @
% 67.20/9.11 X108 @
% 67.20/9.11 emptyset ) ) @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X102 @
% 67.20/9.11 X104 ) ) ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X110:$i,
% 67.20/9.11 X112:$i,
% 67.20/9.11 X114:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X114 @
% 67.20/9.11 X110 ) =>
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X116:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X116 @
% 67.20/9.11 X112 ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 (
% 67.20/9.11 setadjoin
% 67.20/9.11 @
% 67.20/9.11 X114 @
% 67.20/9.11 (
% 67.20/9.11 setadjoin
% 67.20/9.11 @
% 67.20/9.11 X116 @
% 67.20/9.11 emptyset ) ) @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X110 @
% 67.20/9.11 X112 ) ) ) ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X118:$i,
% 67.20/9.11 X120:$i,
% 67.20/9.11 X122:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X122 @
% 67.20/9.11 X118 ) =>
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X124:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X124 @
% 67.20/9.11 X120 ) =>
% 67.20/9.11 (
% 67.20/9.11 subset @
% 67.20/9.11 (
% 67.20/9.11 setadjoin
% 67.20/9.11 @
% 67.20/9.11 (
% 67.20/9.11 setadjoin
% 67.20/9.11 @
% 67.20/9.11 X122 @
% 67.20/9.11 emptyset ) @
% 67.20/9.11 (
% 67.20/9.11 setadjoin
% 67.20/9.11 @
% 67.20/9.11 (
% 67.20/9.11 setadjoin
% 67.20/9.11 @
% 67.20/9.11 X122 @
% 67.20/9.11 (
% 67.20/9.11 setadjoin
% 67.20/9.11 @
% 67.20/9.11 X124 @
% 67.20/9.11 emptyset ) ) @
% 67.20/9.11 emptyset ) ) @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X118 @
% 67.20/9.11 X120 ) ) ) ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X126:$i,
% 67.20/9.11 X128:$i,
% 67.20/9.11 X130:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X130 @
% 67.20/9.11 X126 ) =>
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X132:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X132 @
% 67.20/9.11 X128 ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 (
% 67.20/9.11 setadjoin
% 67.20/9.11 @
% 67.20/9.11 (
% 67.20/9.11 setadjoin
% 67.20/9.11 @
% 67.20/9.11 X130 @
% 67.20/9.11 emptyset ) @
% 67.20/9.11 (
% 67.20/9.11 setadjoin
% 67.20/9.11 @
% 67.20/9.11 (
% 67.20/9.11 setadjoin
% 67.20/9.11 @
% 67.20/9.11 X130 @
% 67.20/9.11 (
% 67.20/9.11 setadjoin
% 67.20/9.11 @
% 67.20/9.11 X132 @
% 67.20/9.11 emptyset ) ) @
% 67.20/9.11 emptyset ) ) @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X126 @
% 67.20/9.11 X128 ) ) ) ) ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X134:$i,
% 67.20/9.11 X136:$i,
% 67.20/9.11 X138:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X138 @
% 67.20/9.11 X134 ) =>
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X140:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X140 @
% 67.20/9.11 X136 ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 (
% 67.20/9.11 kpair @
% 67.20/9.11 X138 @
% 67.20/9.11 X140 ) @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X134 @
% 67.20/9.11 X136 ) ) ) ) ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodpairin ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodmempair1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodmempair ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionE2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionsingleton1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionsingleton2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionsingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 singletonprop ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ex1E1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ex1I ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ex1I2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 singletonsuniq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjL1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 kfstsingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 theprop ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 kfstpairEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodfstin ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjL2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjL ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjR11 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjR12 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjR1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairequniteq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjR2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjR ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ksndsingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ksndpairEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 kpairsurjEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodsndin ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodpairmemEL ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodpairmemER ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodmempaircEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodfstpairEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodsndpairEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodpairsurjEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrSub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setOfPairsIsBReln ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrERa ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrEL1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrEL2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrER ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcImageSingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 apProp ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 app ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 infuncsetfunc ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ap2p ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcinfuncset ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 lamProp ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 lamp ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 lam2p ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 brelnall1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 brelnall2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ex1E2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcGraphProp1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcGraphProp3 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcGraphProp2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcextLem ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcGraphProp4 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subbreln ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 eqbreln ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcext ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcext2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ap2apEq1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ap2apEq2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 beta1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 eta1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 lam2lamEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 beta2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 eta2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 iffalseProp1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 iffalseProp2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 iftrueProp1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 iftrueProp2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ifSingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ifp ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 theeq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 iftrue ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 iffalse ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 iftrueorfalse ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectT_lem ) =>
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X142:$i,
% 67.20/9.11 X144:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X144 @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X142 ) ) =>
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X146:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X146 @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X142 ) ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X144 @
% 67.20/9.11 X146 ) @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X142 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 67.20/9.11 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 67.20/9.11 thf(zf_stmt_2, axiom,
% 67.20/9.11 (![X8:$i,X6:$i,X4:$i]:
% 67.20/9.11 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 67.20/9.11 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 67.20/9.11 thf(zf_stmt_3, conjecture,
% 67.20/9.11 (( setextAx ) =>
% 67.20/9.11 ( ( emptysetAx ) =>
% 67.20/9.11 ( ( setadjoinAx ) =>
% 67.20/9.11 ( ( ![X4:$i,X6:$i]:
% 67.20/9.11 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 67.20/9.11 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 67.20/9.11 ( ( setunionAx ) =>
% 67.20/9.11 ( ( omega0Ax ) =>
% 67.20/9.11 ( ( omegaSAx ) =>
% 67.20/9.11 ( ( omegaIndAx ) =>
% 67.20/9.11 ( ( replAx ) =>
% 67.20/9.11 ( ( foundationAx ) =>
% 67.20/9.11 ( ( wellorderingAx ) =>
% 67.20/9.11 ( ( descrp ) =>
% 67.20/9.11 ( ( dsetconstrI ) =>
% 67.20/9.11 ( ( dsetconstrEL ) =>
% 67.20/9.11 ( ( dsetconstrER ) =>
% 67.20/9.11 ( ( exuE1 ) =>
% 67.20/9.11 ( ( prop2setE ) =>
% 67.20/9.11 ( ( emptysetE ) =>
% 67.20/9.11 ( ( emptysetimpfalse ) =>
% 67.20/9.11 ( ( notinemptyset ) =>
% 67.20/9.11 ( ( exuE3e ) =>
% 67.20/9.11 ( ( setext ) =>
% 67.20/9.11 ( ( emptyI ) =>
% 67.20/9.11 ( ( noeltsimpempty ) =>
% 67.20/9.11 ( ( setbeta ) =>
% 67.20/9.11 ( ( nonemptyE1 ) =>
% 67.20/9.11 ( ( nonemptyI ) =>
% 67.20/9.11 ( ( nonemptyI1 ) =>
% 67.20/9.11 ( ( setadjoinIL ) =>
% 67.20/9.11 ( ( emptyinunitempty ) =>
% 67.20/9.11 ( ( setadjoinIR ) =>
% 67.20/9.11 ( ( setadjoinE ) =>
% 67.20/9.11 ( (
% 67.20/9.11 setadjoinOr ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setoftrueEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X10:$i,
% 67.20/9.11 X12:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X14:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X14 @ X12 ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X14 @ X10 ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X12 @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X10 ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X16:$i]:
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 emptyset @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X16 ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X18:$i]:
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 emptyset @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X18 ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X20:$i,
% 67.20/9.11 X22:$i,
% 67.20/9.11 X24:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X22 @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X20 ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X24 @ X22 ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X24 @ X20 ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionE ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subPowSU ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 exuE2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 nonemptyImpWitness ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 uniqinunit ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 notinsingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 eqinunit ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 singletonsswitch ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairsetE ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairsetIL ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairsetIR ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 emptyE1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 vacuousDall ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 quantDeMorgan1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 quantDeMorgan2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 quantDeMorgan3 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 quantDeMorgan4 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 prop2setI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
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% 67.20/9.11 (
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% 67.20/9.11 X26:$i,
% 67.20/9.11 X28:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
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% 67.20/9.11 X26 ) =
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% 67.20/9.11 X28 ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 powerset @
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% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X28 ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunion__Cong ) =>
% 67.20/9.11 (
% 67.20/9.11 (
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% 67.20/9.11 in @
% 67.20/9.11 X30 @
% 67.20/9.11 (
% 67.20/9.11 powerset @
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% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setextsub ) =>
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% 67.20/9.11 X36:$i]:
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% 67.20/9.11 (
% 67.20/9.11 in @
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% 67.20/9.11 (
% 67.20/9.11 powerset @
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% 67.20/9.11 X40 @
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% 67.20/9.11 (
% 67.20/9.11 subset @
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% 67.20/9.11 (
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% 67.20/9.11 X46:$i]:
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% 67.20/9.11 (
% 67.20/9.11 powerset @
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% 67.20/9.11 (
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% 67.20/9.11 (
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% 67.20/9.11 X48:$i,
% 67.20/9.11 X50:(
% 67.20/9.11 $i > $o )]:
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 (
% 67.20/9.11 dsetconstr
% 67.20/9.11 @
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% 67.20/9.11 (
% 67.20/9.11 ^[
% 67.20/9.11 V_1:$i]:
% 67.20/9.11 (
% 67.20/9.11 X50 @ V_1 ) ) ) @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 X48 ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 sepSubset ) =>
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% 67.20/9.11 X54:$i,
% 67.20/9.11 X56:$i]:
% 67.20/9.11 (
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% 67.20/9.11 X56 @ X52 ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X56 @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X52 @ X54 ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
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% 67.20/9.11 X66:$i,
% 67.20/9.11 X68:$i,
% 67.20/9.11 X70:$o]:
% 67.20/9.11 (
% 67.20/9.11 (
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% 67.20/9.11 (
% 67.20/9.11 (
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% 67.20/9.11 in @
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% 67.20/9.11 (
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% 67.20/9.11 (
% 67.20/9.11 (
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% 67.20/9.11 (
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% 67.20/9.11 ![
% 67.20/9.11 X72:$i,
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% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X76 @
% 67.20/9.11 (
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% 67.20/9.11 (
% 67.20/9.11 (
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% 67.20/9.11 in @
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% 67.20/9.11 (
% 67.20/9.11 (
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% 67.20/9.11 X78:$i,
% 67.20/9.11 X80:$i]:
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% 67.20/9.11 subset @
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% 67.20/9.11 X78 @ X80 ) ) ) =>
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% 67.20/9.11 X84:$i]:
% 67.20/9.11 (
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% 67.20/9.11 (
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% 67.20/9.11 (
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% 67.20/9.11 (
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% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectLsub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectSubset2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectSubset3 ) =>
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% 67.20/9.11 (
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% 67.20/9.11 (
% 67.20/9.11 disjointsetsI1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersectRsub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
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% 67.20/9.11 (
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% 67.20/9.11 (
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% 67.20/9.11 X86:$i,
% 67.20/9.11 X88:$i,
% 67.20/9.11 X90:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 binintersect
% 67.20/9.11 @
% 67.20/9.11 X86 @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X88 @ X90 ) ) =
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 (
% 67.20/9.11 binintersect
% 67.20/9.11 @
% 67.20/9.11 X86 @ X88 ) @
% 67.20/9.11 (
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% 67.20/9.11 @
% 67.20/9.11 X86 @ X90 ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setminusEL ) =>
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% 67.20/9.11 (
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% 67.20/9.11 (
% 67.20/9.11 setminusERneg ) =>
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% 67.20/9.11 (
% 67.20/9.11 setminusELneg ) =>
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% 67.20/9.11 (
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% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 symdiffIneg1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
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% 67.20/9.11 (
% 67.20/9.11 (
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% 67.20/9.11 (
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% 67.20/9.11 (
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% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 kpairiskpair ) =>
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% 67.20/9.11 (
% 67.20/9.11 kpairp ) =>
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% 67.20/9.11 (
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% 67.20/9.11 X94 @ X92 ) =>
% 67.20/9.11 (
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% 67.20/9.11 (
% 67.20/9.11 setadjoin
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% 67.20/9.11 emptyset ) @
% 67.20/9.11 (
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% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X96:$i,
% 67.20/9.11 X98:$i,
% 67.20/9.11 X100:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
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% 67.20/9.11 X100 @ X96 ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
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% 67.20/9.11 @
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% 67.20/9.11 emptyset ) @
% 67.20/9.11 (
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% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairset2E ) =>
% 67.20/9.11 (
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% 67.20/9.11 ![
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% 67.20/9.11 X104:$i,
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% 67.20/9.11 (
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% 67.20/9.11 (
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% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X110:$i,
% 67.20/9.11 X112:$i,
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% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X114 @
% 67.20/9.11 X110 ) =>
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X116:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X116 @
% 67.20/9.11 X112 ) =>
% 67.20/9.11 (
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% 67.20/9.11 (
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% 67.20/9.11 X118:$i,
% 67.20/9.11 X120:$i,
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% 67.20/9.11 in @
% 67.20/9.11 X122 @
% 67.20/9.11 X118 ) =>
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% 67.20/9.11 ![
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% 67.20/9.11 (
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% 67.20/9.11 X128:$i,
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% 67.20/9.11 emptyset ) ) @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X126 @
% 67.20/9.11 X128 ) ) ) ) ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X134:$i,
% 67.20/9.11 X136:$i,
% 67.20/9.11 X138:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X138 @
% 67.20/9.11 X134 ) =>
% 67.20/9.11 (
% 67.20/9.11 ![
% 67.20/9.11 X140:$i]:
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 X140 @
% 67.20/9.11 X136 ) =>
% 67.20/9.11 (
% 67.20/9.11 in @
% 67.20/9.11 (
% 67.20/9.11 kpair @
% 67.20/9.11 X138 @
% 67.20/9.11 X140 ) @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 (
% 67.20/9.11 powerset @
% 67.20/9.11 (
% 67.20/9.11 binunion @
% 67.20/9.11 X134 @
% 67.20/9.11 X136 ) ) ) ) ) ) ) ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodpairin ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodmempair1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodmempair ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionE2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionsingleton1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionsingleton2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setunionsingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 singletonprop ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ex1E1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ex1I ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ex1I2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 singletonsuniq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjL1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 kfstsingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 theprop ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 kfstpairEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodfstin ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjL2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjL ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjR11 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjR12 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjR1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 upairequniteq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjR2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setukpairinjR ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ksndsingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ksndpairEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 kpairsurjEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodsndin ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodpairmemEL ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodpairmemER ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodmempaircEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodfstpairEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodsndpairEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 cartprodpairsurjEq ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrI ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrSub ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 setOfPairsIsBReln ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrERa ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrEL1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrEL2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 dpsetconstrER ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcImageSingleton ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 apProp ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 app ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 infuncsetfunc ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ap2p ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcinfuncset ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 lamProp ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 lamp ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 lam2p ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 brelnall1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 brelnall2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ex1E2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcGraphProp1 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcGraphProp3 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcGraphProp2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcextLem ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcGraphProp4 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 subbreln ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 eqbreln ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcext ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 funcext2 ) =>
% 67.20/9.11 (
% 67.20/9.11 (
% 67.20/9.11 ap2apEq1 ) =>
% 67.20/9.11 (
% 67.20/9.12 (
% 67.20/9.12 ap2apEq2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 beta1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 eta1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 lam2lamEq ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 beta2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 eta2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 iffalseProp1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 iffalseProp2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 iftrueProp1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 iftrueProp2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ifSingleton ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ifp ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 theeq ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 iftrue ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 iffalse ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 iftrueorfalse ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 binintersectT_lem ) =>
% 67.20/9.12 (
% 67.20/9.12 ![
% 67.20/9.12 X142:$i,
% 67.20/9.12 X144:$i]:
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X144 @
% 67.20/9.12 (
% 67.20/9.12 powerset @
% 67.20/9.12 X142 ) ) =>
% 67.20/9.12 (
% 67.20/9.12 ![
% 67.20/9.12 X146:$i]:
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X146 @
% 67.20/9.12 (
% 67.20/9.12 powerset @
% 67.20/9.12 X142 ) ) =>
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 (
% 67.20/9.12 binunion @
% 67.20/9.12 X144 @
% 67.20/9.12 X146 ) @
% 67.20/9.12 (
% 67.20/9.12 powerset @
% 67.20/9.12 X142 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 67.20/9.12 thf(zf_stmt_4, negated_conjecture,
% 67.20/9.12 (~( ( setextAx ) =>
% 67.20/9.12 ( ( emptysetAx ) =>
% 67.20/9.12 ( ( setadjoinAx ) =>
% 67.20/9.12 ( ( ![X4:$i,X6:$i]:
% 67.20/9.12 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 67.20/9.12 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 67.20/9.12 ( ( setunionAx ) =>
% 67.20/9.12 ( ( omega0Ax ) =>
% 67.20/9.12 ( ( omegaSAx ) =>
% 67.20/9.12 ( ( omegaIndAx ) =>
% 67.20/9.12 ( ( replAx ) =>
% 67.20/9.12 ( ( foundationAx ) =>
% 67.20/9.12 ( ( wellorderingAx ) =>
% 67.20/9.12 ( ( descrp ) =>
% 67.20/9.12 ( ( dsetconstrI ) =>
% 67.20/9.12 ( ( dsetconstrEL ) =>
% 67.20/9.12 ( ( dsetconstrER ) =>
% 67.20/9.12 ( ( exuE1 ) =>
% 67.20/9.12 ( ( prop2setE ) =>
% 67.20/9.12 ( ( emptysetE ) =>
% 67.20/9.12 ( ( emptysetimpfalse ) =>
% 67.20/9.12 ( ( notinemptyset ) =>
% 67.20/9.12 ( ( exuE3e ) =>
% 67.20/9.12 ( ( setext ) =>
% 67.20/9.12 ( ( emptyI ) =>
% 67.20/9.12 ( ( noeltsimpempty ) =>
% 67.20/9.12 ( ( setbeta ) =>
% 67.20/9.12 ( ( nonemptyE1 ) =>
% 67.20/9.12 ( ( nonemptyI ) =>
% 67.20/9.12 ( ( nonemptyI1 ) =>
% 67.20/9.12 ( ( setadjoinIL ) =>
% 67.20/9.12 ( ( emptyinunitempty ) =>
% 67.20/9.12 ( ( setadjoinIR ) =>
% 67.20/9.12 ( (
% 67.20/9.12 setadjoinE ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setadjoinOr ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setoftrueEq ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ![
% 67.20/9.12 X10:$i,
% 67.20/9.12 X12:$i]:
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ![
% 67.20/9.12 X14:$i]:
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X14 @ X12 ) =>
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X14 @ X10 ) ) ) =>
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X12 @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 X10 ) ) ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ![
% 67.20/9.12 X16:$i]:
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 emptyset @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 X16 ) ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ![
% 67.20/9.12 X18:$i]:
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 emptyset @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 X18 ) ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ![
% 67.20/9.12 X20:$i,
% 67.20/9.12 X22:$i,
% 67.20/9.12 X24:$i]:
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X22 @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 X20 ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X24 @ X22 ) =>
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X24 @ X20 ) ) ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setunionI ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setunionE ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 subPowSU ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 exuE2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 nonemptyImpWitness ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 uniqinunit ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 notinsingleton ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 eqinunit ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 singletonsswitch ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 upairsetE ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 upairsetIL ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 upairsetIR ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 emptyE1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 vacuousDall ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 quantDeMorgan1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 quantDeMorgan2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 quantDeMorgan3 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 quantDeMorgan4 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 prop2setI ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 prop2set2propI ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 notdexE ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 notdallE ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 exuI1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 exuI3 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 exuI2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 inCongP ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 in__Cong ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 exuE3u ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 exu__Cong ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 emptyset__Cong ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setadjoin__Cong ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ![
% 67.20/9.12 X26:$i,
% 67.20/9.12 X28:$i]:
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 X26 ) =
% 67.20/9.12 (
% 67.20/9.12 X28 ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 X26 ) =
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 X28 ) ) ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setunion__Cong ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 omega__Cong ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 exuEu ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 descr__Cong ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 dsetconstr__Cong ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 subsetI1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 eqimpsubset2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 eqimpsubset1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 subsetI2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 emptysetsubset ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 subsetE ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 subsetE2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 notsubsetI ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 notequalI1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 notequalI2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 subsetRefl ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 subsetTrans ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setadjoinSub ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setadjoinSub2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ![
% 67.20/9.12 X30:$i,
% 67.20/9.12 X32:$i]:
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 subset @
% 67.20/9.12 X30 @ X32 ) =>
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X30 @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 X32 ) ) ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
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% 67.20/9.12 X34:$i,
% 67.20/9.12 X36:$i]:
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% 67.20/9.12 X36 @ X34 ) =>
% 67.20/9.12 (
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% 67.20/9.12 X36 @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 X34 ) ) ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ![
% 67.20/9.12 X38:$i,
% 67.20/9.12 X40:$i]:
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% 67.20/9.12 X40 @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 X38 ) ) =>
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% 67.20/9.12 X40 @ X38 ) ) ) =>
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% 67.20/9.12 @
% 67.20/9.12 X42 ) ) ) =>
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% 67.20/9.12 X46:$i]:
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% 67.20/9.12 X44 @ X46 ) =>
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% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 X44 ) @
% 67.20/9.12 (
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% 67.20/9.12 @
% 67.20/9.12 X46 ) ) ) ) =>
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% 67.20/9.12 X50:(
% 67.20/9.12 $i > $o )]:
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% 67.20/9.12 (
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% 67.20/9.12 X48 @
% 67.20/9.12 (
% 67.20/9.12 ^[
% 67.20/9.12 V_1:$i]:
% 67.20/9.12 (
% 67.20/9.12 X50 @ V_1 ) ) ) @
% 67.20/9.12 (
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% 67.20/9.12 @
% 67.20/9.12 X48 ) ) ) =>
% 67.20/9.12 (
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% 67.20/9.12 in @
% 67.20/9.12 X56 @
% 67.20/9.12 (
% 67.20/9.12 binunion
% 67.20/9.12 @
% 67.20/9.12 X52 @ X54 ) ) ) ) =>
% 67.20/9.12 (
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% 67.20/9.12 in @
% 67.20/9.12 X62 @
% 67.20/9.12 (
% 67.20/9.12 binunion
% 67.20/9.12 @
% 67.20/9.12 X58 @ X60 ) ) ) ) =>
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% 67.20/9.12 (
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% 67.20/9.12 X66:$i,
% 67.20/9.12 X68:$i,
% 67.20/9.12 X70:$o]:
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% 67.20/9.12 X68 @
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% 67.20/9.12 @
% 67.20/9.12 X64 @ X66 ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 in @
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% 67.20/9.12 X70 ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X68 @ X66 ) =>
% 67.20/9.12 (
% 67.20/9.12 X70 ) ) =>
% 67.20/9.12 (
% 67.20/9.12 X70 ) ) ) ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ![
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% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X76 @
% 67.20/9.12 (
% 67.20/9.12 binunion
% 67.20/9.12 @
% 67.20/9.12 X72 @ X74 ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X76 @ X72 ) |
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X76 @ X74 ) ) ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ![
% 67.20/9.12 X78:$i,
% 67.20/9.12 X80:$i]:
% 67.20/9.12 (
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% 67.20/9.12 X78 @
% 67.20/9.12 (
% 67.20/9.12 binunion
% 67.20/9.12 @
% 67.20/9.12 X78 @ X80 ) ) ) =>
% 67.20/9.12 (
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% 67.20/9.12 X82:$i,
% 67.20/9.12 X84:$i]:
% 67.20/9.12 (
% 67.20/9.12 subset @
% 67.20/9.12 X84 @
% 67.20/9.12 (
% 67.20/9.12 binunion
% 67.20/9.12 @
% 67.20/9.12 X82 @ X84 ) ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 binintersectI ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 binintersectSubset5 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 binintersectEL ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 binintersectLsub ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 binintersectSubset2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 binintersectSubset3 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 binintersectER ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 disjointsetsI1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 binintersectRsub ) =>
% 67.20/9.12 (
% 67.20/9.12 (
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% 67.20/9.12 (
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% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ![
% 67.20/9.12 X86:$i,
% 67.20/9.12 X88:$i,
% 67.20/9.12 X90:$i]:
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 binintersect
% 67.20/9.12 @
% 67.20/9.12 X86 @
% 67.20/9.12 (
% 67.20/9.12 binunion
% 67.20/9.12 @
% 67.20/9.12 X88 @ X90 ) ) =
% 67.20/9.12 (
% 67.20/9.12 binunion
% 67.20/9.12 @
% 67.20/9.12 (
% 67.20/9.12 binintersect
% 67.20/9.12 @
% 67.20/9.12 X86 @ X88 ) @
% 67.20/9.12 (
% 67.20/9.12 binintersect
% 67.20/9.12 @
% 67.20/9.12 X86 @ X90 ) ) ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setminusI ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setminusEL ) =>
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% 67.20/9.12 (
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% 67.20/9.12 (
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% 67.20/9.12 (
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% 67.20/9.12 (
% 67.20/9.12 (
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% 67.20/9.12 (
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% 67.20/9.12 (
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% 67.20/9.12 in @
% 67.20/9.12 (
% 67.20/9.12 setadjoin
% 67.20/9.12 @
% 67.20/9.12 X94 @
% 67.20/9.12 emptyset ) @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 X92 ) ) ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ![
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% 67.20/9.12 (
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% 67.20/9.12 X100 @
% 67.20/9.12 X96 ) =>
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 (
% 67.20/9.12 setadjoin
% 67.20/9.12 @
% 67.20/9.12 X100 @
% 67.20/9.12 emptyset ) @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 (
% 67.20/9.12 binunion
% 67.20/9.12 @
% 67.20/9.12 X96 @ X98 ) ) ) ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 upairset2E ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ![
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% 67.20/9.12 X104:$i,
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% 67.20/9.12 (
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% 67.20/9.12 X104 ) =>
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% 67.20/9.12 (
% 67.20/9.12 setadjoin
% 67.20/9.12 @
% 67.20/9.12 X106 @
% 67.20/9.12 (
% 67.20/9.12 setadjoin
% 67.20/9.12 @
% 67.20/9.12 X108 @
% 67.20/9.12 emptyset ) ) @
% 67.20/9.12 (
% 67.20/9.12 binunion
% 67.20/9.12 @
% 67.20/9.12 X102 @
% 67.20/9.12 X104 ) ) ) ) ) ) =>
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% 67.20/9.12 (
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% 67.20/9.12 (
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% 67.20/9.12 setadjoin
% 67.20/9.12 @
% 67.20/9.12 X114 @
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% 67.20/9.12 setadjoin
% 67.20/9.12 @
% 67.20/9.12 X116 @
% 67.20/9.12 emptyset ) ) @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 (
% 67.20/9.12 binunion
% 67.20/9.12 @
% 67.20/9.12 X110 @
% 67.20/9.12 X112 ) ) ) ) ) ) ) =>
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% 67.20/9.12 X118:$i,
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% 67.20/9.12 X118 ) =>
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% 67.20/9.12 @
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% 67.20/9.12 setadjoin
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% 67.20/9.12 setadjoin
% 67.20/9.12 @
% 67.20/9.12 X124 @
% 67.20/9.12 emptyset ) ) @
% 67.20/9.12 emptyset ) ) @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 (
% 67.20/9.12 binunion
% 67.20/9.12 @
% 67.20/9.12 X118 @
% 67.20/9.12 X120 ) ) ) ) ) ) ) =>
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% 67.20/9.12 (
% 67.20/9.12 ![
% 67.20/9.12 X126:$i,
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% 67.20/9.12 (
% 67.20/9.12 setadjoin
% 67.20/9.12 @
% 67.20/9.12 (
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% 67.20/9.12 @
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% 67.20/9.12 setadjoin
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% 67.20/9.12 setadjoin
% 67.20/9.12 @
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% 67.20/9.12 setadjoin
% 67.20/9.12 @
% 67.20/9.12 X132 @
% 67.20/9.12 emptyset ) ) @
% 67.20/9.12 emptyset ) ) @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 (
% 67.20/9.12 binunion
% 67.20/9.12 @
% 67.20/9.12 X126 @
% 67.20/9.12 X128 ) ) ) ) ) ) ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ![
% 67.20/9.12 X134:$i,
% 67.20/9.12 X136:$i,
% 67.20/9.12 X138:$i]:
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X138 @
% 67.20/9.12 X134 ) =>
% 67.20/9.12 (
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% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X140 @
% 67.20/9.12 X136 ) =>
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 (
% 67.20/9.12 kpair @
% 67.20/9.12 X138 @
% 67.20/9.12 X140 ) @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 (
% 67.20/9.12 binunion
% 67.20/9.12 @
% 67.20/9.12 X134 @
% 67.20/9.12 X136 ) ) ) ) ) ) ) ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 cartprodpairin ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 cartprodmempair1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 cartprodmempair ) =>
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% 67.20/9.12 (
% 67.20/9.12 setunionE2 ) =>
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% 67.20/9.12 (
% 67.20/9.12 setunionsingleton1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
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% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setunionsingleton ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 singletonprop ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ex1E1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ex1I ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ex1I2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 singletonsuniq ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setukpairinjL1 ) =>
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% 67.20/9.12 (
% 67.20/9.12 kfstsingleton ) =>
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% 67.20/9.12 (
% 67.20/9.12 theprop ) =>
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% 67.20/9.12 (
% 67.20/9.12 kfstpairEq ) =>
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% 67.20/9.12 (
% 67.20/9.12 cartprodfstin ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setukpairinjL2 ) =>
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% 67.20/9.12 (
% 67.20/9.12 setukpairinjL ) =>
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% 67.20/9.12 (
% 67.20/9.12 setukpairinjR11 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setukpairinjR12 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setukpairinjR1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 upairequniteq ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setukpairinjR2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setukpairinjR ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ksndsingleton ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ksndpairEq ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 kpairsurjEq ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 cartprodsndin ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 cartprodpairmemEL ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 cartprodpairmemER ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 cartprodmempaircEq ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 cartprodfstpairEq ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 cartprodsndpairEq ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 cartprodpairsurjEq ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 dpsetconstrI ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 dpsetconstrSub ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 setOfPairsIsBReln ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 dpsetconstrERa ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 dpsetconstrEL1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 dpsetconstrEL2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 dpsetconstrER ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 funcImageSingleton ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 apProp ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 app ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 infuncsetfunc ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ap2p ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 funcinfuncset ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 lamProp ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 lamp ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 lam2p ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 brelnall1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 brelnall2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ex1E2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 funcGraphProp1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 funcGraphProp3 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 funcGraphProp2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 funcextLem ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 funcGraphProp4 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 subbreln ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 eqbreln ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 funcext ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 funcext2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ap2apEq1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ap2apEq2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 beta1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 eta1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 lam2lamEq ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 beta2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 eta2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 iffalseProp1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 iffalseProp2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 iftrueProp1 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 iftrueProp2 ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ifSingleton ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 ifp ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 theeq ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 iftrue ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 iffalse ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 iftrueorfalse ) =>
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 binintersectT_lem ) =>
% 67.20/9.12 (
% 67.20/9.12 ![
% 67.20/9.12 X142:$i,
% 67.20/9.12 X144:$i]:
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X144 @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 X142 ) ) =>
% 67.20/9.12 (
% 67.20/9.12 ![
% 67.20/9.12 X146:$i]:
% 67.20/9.12 (
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 X146 @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 X142 ) ) =>
% 67.20/9.12 (
% 67.20/9.12 in @
% 67.20/9.12 (
% 67.20/9.12 binunion
% 67.20/9.12 @
% 67.20/9.12 X144 @
% 67.20/9.12 X146 ) @
% 67.20/9.12 (
% 67.20/9.12 powerset
% 67.20/9.12 @
% 67.20/9.12 X142 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 67.20/9.12 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 67.20/9.12 thf(zip_derived_cl119, plain,
% 67.20/9.12 (~ (in @ (binunion @ sk__72 @ sk__73) @ (powerset @ sk__71))),
% 67.20/9.12 inference('cnf', [status(esa)], [zf_stmt_4])).
% 67.20/9.12 thf(zip_derived_cl20, plain,
% 67.20/9.12 (![X0 : $i, X1 : $i]:
% 67.20/9.12 ( (in @ X0 @ (powerset @ X1)) | ~ (in @ (sk__74 @ X0 @ X1) @ X1))),
% 67.20/9.12 inference('cnf', [status(esa)], [zf_stmt_4])).
% 67.20/9.12 thf(zip_derived_cl21, plain,
% 67.20/9.12 (![X0 : $i, X1 : $i]:
% 67.20/9.12 ( (in @ X0 @ (powerset @ X1)) | (in @ (sk__74 @ X0 @ X1) @ X0))),
% 67.20/9.12 inference('cnf', [status(esa)], [zf_stmt_4])).
% 67.20/9.12 thf(zip_derived_cl55, plain,
% 67.20/9.12 (![X14 : $i, X15 : $i, X16 : $i]:
% 67.20/9.12 ( (in @ X14 @ X15)
% 67.20/9.12 | (in @ X14 @ X16)
% 67.20/9.12 | ~ (in @ X14 @ (binunion @ X16 @ X15)))),
% 67.20/9.12 inference('cnf', [status(esa)], [zf_stmt_4])).
% 67.20/9.12 thf(zip_derived_cl259, plain,
% 67.20/9.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 67.20/9.12 ( (in @ (binunion @ X1 @ X0) @ (powerset @ X2))
% 67.20/9.12 | (in @ (sk__74 @ (binunion @ X1 @ X0) @ X2) @ X1)
% 67.20/9.12 | (in @ (sk__74 @ (binunion @ X1 @ X0) @ X2) @ X0))),
% 67.20/9.12 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl55])).
% 67.20/9.12 thf(zip_derived_cl118, plain, ( (in @ sk__73 @ (powerset @ sk__71))),
% 67.20/9.12 inference('cnf', [status(esa)], [zf_stmt_4])).
% 67.20/9.12 thf(zip_derived_cl218, plain,
% 67.20/9.12 (![X61 : $i, X62 : $i, X63 : $i]:
% 67.20/9.12 (~ (in @ X61 @ (powerset @ X62))
% 67.20/9.12 | (in @ X63 @ X62)
% 67.20/9.12 | ~ (in @ X63 @ X61))),
% 67.20/9.12 inference('cnf', [status(esa)], [zf_stmt_4])).
% 67.20/9.12 thf(zip_derived_cl292, plain,
% 67.20/9.12 (![X0 : $i]: (~ (in @ X0 @ sk__73) | (in @ X0 @ sk__71))),
% 67.20/9.12 inference('sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl218])).
% 67.20/9.12 thf(zip_derived_cl120, plain, ( (in @ sk__72 @ (powerset @ sk__71))),
% 67.20/9.12 inference('cnf', [status(esa)], [zf_stmt_4])).
% 67.20/9.12 thf(zip_derived_cl218, plain,
% 67.20/9.12 (![X61 : $i, X62 : $i, X63 : $i]:
% 67.20/9.12 (~ (in @ X61 @ (powerset @ X62))
% 67.20/9.12 | (in @ X63 @ X62)
% 67.20/9.12 | ~ (in @ X63 @ X61))),
% 67.20/9.12 inference('cnf', [status(esa)], [zf_stmt_4])).
% 67.20/9.12 thf(zip_derived_cl293, plain,
% 67.20/9.12 (![X0 : $i]: (~ (in @ X0 @ sk__72) | (in @ X0 @ sk__71))),
% 67.20/9.12 inference('sup-', [status(thm)], [zip_derived_cl120, zip_derived_cl218])).
% 67.20/9.12 thf(zip_derived_cl11057, plain, ($false),
% 67.20/9.12 inference('eprover', [status(thm)],
% 67.20/9.12 [zip_derived_cl119, zip_derived_cl20, zip_derived_cl259,
% 67.20/9.12 zip_derived_cl292, zip_derived_cl293])).
% 67.20/9.12
% 67.20/9.12 % SZS output end Refutation
% 67.20/9.12
% 67.20/9.12
% 67.20/9.12 % Terminating...
% 67.34/9.25 % Runner terminated.
% 67.34/9.27 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------