%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU710^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.YLPQdr5Hki true
% Computer : n020.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 46.16s 9.47s
% Output : Refutation 46.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.24 % Problem : SEU710^1 : TPTP v9.2.0. Released v3.7.0.
% 0.06/0.25 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.YLPQdr5Hki true
% 0.10/0.44 % Computer : n020.cluster.edu
% 0.10/0.44 % Model : x86_64 x86_64
% 0.10/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.44 % Memory : 8042.1875MB
% 0.10/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.44 % CPULimit : 300
% 0.10/0.44 % WCLimit : 300
% 0.10/0.44 % DateTime : Wed Oct 1 16:07:23 EDT 2025
% 0.10/0.46 % CPUTime :
% 0.10/0.46 % Running portfolio for 300 s
% 0.10/0.46 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.46 % Number of cores: 8
% 0.10/0.46 % Python version: Python 3.6.8
% 0.10/0.47 % Running in HO mode
% 0.25/0.76 % Total configuration time : 828
% 0.25/0.76 % Estimated wc time : 1656
% 0.25/0.76 % Estimated cpu time (8 cpus) : 207.0
% 0.27/0.90 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.27/0.97 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.27/0.97 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.27/0.97 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.27/1.01 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.27/1.01 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.27/1.02 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.27/1.04 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 46.16/9.47 % Solved by lams/40_c_ic.sh.
% 46.16/9.47 % done 3099 iterations in 8.246s
% 46.16/9.47 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 46.16/9.47 % SZS output start Refutation
% 46.16/9.47 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 46.16/9.47 thf(notdexE_type, type, notdexE: $o).
% 46.16/9.47 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 46.16/9.47 thf(setunionAx_type, type, setunionAx: $o).
% 46.16/9.47 thf(setminusELneg_type, type, setminusELneg: $o).
% 46.16/9.47 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 46.16/9.47 thf(ex1E1_type, type, ex1E1: $o).
% 46.16/9.47 thf(powersetE_type, type, powersetE: $o).
% 46.16/9.47 thf(omegaSAx_type, type, omegaSAx: $o).
% 46.16/9.47 thf(exuI1_type, type, exuI1: $o).
% 46.16/9.47 thf(exuI2_type, type, exuI2: $o).
% 46.16/9.47 thf(notequalI2_type, type, notequalI2: $o).
% 46.16/9.47 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 46.16/9.47 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 46.16/9.47 thf(upairsubunion_type, type, upairsubunion: $o).
% 46.16/9.47 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 46.16/9.47 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 46.16/9.47 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 46.16/9.47 thf(setminusILneg_type, type, setminusILneg: $o).
% 46.16/9.47 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 46.16/9.47 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 46.16/9.47 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 46.16/9.47 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 46.16/9.47 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 46.16/9.47 thf(iftrue_type, type, iftrue: $o).
% 46.16/9.47 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 46.16/9.47 thf(ifSingleton_type, type, ifSingleton: $o).
% 46.16/9.47 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 46.16/9.47 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 46.16/9.47 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 46.16/9.47 thf(lamProp_type, type, lamProp: $o).
% 46.16/9.47 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 46.16/9.47 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 46.16/9.47 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 46.16/9.47 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 46.16/9.47 thf(setukpairIR_type, type, setukpairIR: $o).
% 46.16/9.47 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 46.16/9.47 thf(lam2p_type, type, lam2p: $o).
% 46.16/9.47 thf(binunionE_type, type, binunionE: $o).
% 46.16/9.47 thf(setext_type, type, setext: $o).
% 46.16/9.47 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 46.16/9.47 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 46.16/9.47 thf(descr__Cong_type, type, descr__Cong: $o).
% 46.16/9.47 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 46.16/9.47 thf(eqbreln_type, type, eqbreln: $o).
% 46.16/9.47 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 46.16/9.47 thf(in_type, type, in: $i > $i > $o).
% 46.16/9.47 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 46.16/9.47 thf(binunion_type, type, binunion: $i > $i > $i).
% 46.16/9.47 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 46.16/9.47 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 46.16/9.47 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 46.16/9.47 thf(beta1_type, type, beta1: $o).
% 46.16/9.47 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 46.16/9.47 thf(symdiffI2_type, type, symdiffI2: $o).
% 46.16/9.47 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 46.16/9.47 thf(upairset2IR_type, type, upairset2IR: $o).
% 46.16/9.47 thf(sk__59_type, type, sk__59: $i).
% 46.16/9.47 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 46.16/9.47 thf(subsetE_type, type, subsetE: $o).
% 46.16/9.47 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 46.16/9.47 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 46.16/9.47 thf(setbeta_type, type, setbeta: $o).
% 46.16/9.47 thf(eqinunit_type, type, eqinunit: $o).
% 46.16/9.47 thf(upairsetIL_type, type, upairsetIL: $o).
% 46.16/9.47 thf(powersetI1_type, type, powersetI1: $o).
% 46.16/9.47 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 46.16/9.47 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 46.16/9.47 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 46.16/9.47 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 46.16/9.47 thf(powersetAx_type, type, powersetAx: $o).
% 46.16/9.47 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 46.16/9.47 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 46.16/9.47 thf(powersetI_type, type, powersetI: $o).
% 46.16/9.47 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 46.16/9.47 thf(upairsetIR_type, type, upairsetIR: $o).
% 46.16/9.47 thf(lamp_type, type, lamp: $o).
% 46.16/9.47 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 46.16/9.47 thf(inCongP_type, type, inCongP: $o).
% 46.16/9.47 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 46.16/9.47 thf(exuE3e_type, type, exuE3e: $o).
% 46.16/9.47 thf(emptysetE_type, type, emptysetE: $o).
% 46.16/9.47 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 46.16/9.47 thf(setunionI_type, type, setunionI: $o).
% 46.16/9.47 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 46.16/9.47 thf(prop2setI_type, type, prop2setI: $o).
% 46.16/9.47 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 46.16/9.47 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 46.16/9.47 thf(setminusER_type, type, setminusER: $o).
% 46.16/9.47 thf(exuE2_type, type, exuE2: $o).
% 46.16/9.47 thf(emptyset_type, type, emptyset: $i).
% 46.16/9.47 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 46.16/9.47 thf(ex1I_type, type, ex1I: $o).
% 46.16/9.47 thf(ex1E2_type, type, ex1E2: $o).
% 46.16/9.47 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 46.16/9.47 thf(powersetsubset_type, type, powersetsubset: $o).
% 46.16/9.47 thf(subPowSU_type, type, subPowSU: $o).
% 46.16/9.47 thf(notequalI1_type, type, notequalI1: $o).
% 46.16/9.47 thf(notinemptyset_type, type, notinemptyset: $o).
% 46.16/9.47 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 46.16/9.47 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 46.16/9.47 thf(subsetTrans_type, type, subsetTrans: $o).
% 46.16/9.47 thf(kpairp_type, type, kpairp: $o).
% 46.16/9.47 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 46.16/9.47 thf(setminusI_type, type, setminusI: $o).
% 46.16/9.47 thf(binunionIL_type, type, binunionIL: $o).
% 46.16/9.47 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 46.16/9.47 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 46.16/9.47 thf(subsetE2_type, type, subsetE2: $o).
% 46.16/9.47 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 46.16/9.47 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 46.16/9.47 thf(beta2_type, type, beta2: $o).
% 46.16/9.47 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 46.16/9.47 thf(setextsub_type, type, setextsub: $o).
% 46.16/9.47 thf(binunionLsub_type, type, binunionLsub: $o).
% 46.16/9.47 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 46.16/9.47 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 46.16/9.47 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 46.16/9.47 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 46.16/9.47 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 46.16/9.47 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 46.16/9.47 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 46.16/9.47 thf(setunionE_type, type, setunionE: $o).
% 46.16/9.47 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 46.16/9.47 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 46.16/9.47 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 46.16/9.47 thf(binunionIR_type, type, binunionIR: $o).
% 46.16/9.47 thf(theeq_type, type, theeq: $o).
% 46.16/9.47 thf(setadjoinE_type, type, setadjoinE: $o).
% 46.16/9.47 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 46.16/9.47 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 46.16/9.47 thf(ap2p_type, type, ap2p: $o).
% 46.16/9.47 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 46.16/9.47 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 46.16/9.47 thf(exuE1_type, type, exuE1: $o).
% 46.16/9.47 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 46.16/9.47 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 46.16/9.47 thf(setminusLsub_type, type, setminusLsub: $o).
% 46.16/9.47 thf(funcextLem_type, type, funcextLem: $o).
% 46.16/9.47 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 46.16/9.47 thf(notinsingleton_type, type, notinsingleton: $o).
% 46.16/9.47 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 46.16/9.47 thf(exuEu_type, type, exuEu: $o).
% 46.16/9.47 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 46.16/9.47 thf(upairsetE_type, type, upairsetE: $o).
% 46.16/9.47 thf(omega0Ax_type, type, omega0Ax: $o).
% 46.16/9.47 thf(notsubsetI_type, type, notsubsetI: $o).
% 46.16/9.47 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 46.16/9.47 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 46.16/9.47 thf(setextAx_type, type, setextAx: $o).
% 46.16/9.47 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 46.16/9.47 thf(powersetE1_type, type, powersetE1: $o).
% 46.16/9.47 thf(bs114d_type, type, bs114d: $o).
% 46.16/9.47 thf(sk__58_type, type, sk__58: $i).
% 46.16/9.47 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 46.16/9.47 thf(ifp_type, type, ifp: $o).
% 46.16/9.47 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 46.16/9.47 thf(subsetI1_type, type, subsetI1: $o).
% 46.16/9.47 thf(symdiffE_type, type, symdiffE: $o).
% 46.16/9.47 thf(sk__60_type, type, sk__60: $i).
% 46.16/9.47 thf(descrp_type, type, descrp: $o).
% 46.16/9.47 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 46.16/9.47 thf(foundationAx_type, type, foundationAx: $o).
% 46.16/9.47 thf(emptysetAx_type, type, emptysetAx: $o).
% 46.16/9.47 thf(emptyI_type, type, emptyI: $o).
% 46.16/9.47 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 46.16/9.47 thf(eta2_type, type, eta2: $o).
% 46.16/9.47 thf(binintersectEL_type, type, binintersectEL: $o).
% 46.16/9.47 thf(emptyE1_type, type, emptyE1: $o).
% 46.16/9.47 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 46.16/9.47 thf(vacuousDall_type, type, vacuousDall: $o).
% 46.16/9.47 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 46.16/9.47 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 46.16/9.47 thf(binintersectI_type, type, binintersectI: $o).
% 46.16/9.47 thf(funcext_type, type, funcext: $o).
% 46.16/9.47 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 46.16/9.47 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 46.16/9.47 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 46.16/9.47 thf(brelnall2_type, type, brelnall2: $o).
% 46.16/9.47 thf(ex1I2_type, type, ex1I2: $o).
% 46.16/9.47 thf(symdiffI1_type, type, symdiffI1: $o).
% 46.16/9.47 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 46.16/9.47 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 46.16/9.47 thf(theprop_type, type, theprop: $o).
% 46.16/9.47 thf(subsetI2_type, type, subsetI2: $o).
% 46.16/9.47 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 46.16/9.47 thf(setminusERneg_type, type, setminusERneg: $o).
% 46.16/9.47 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 46.16/9.47 thf(omega__Cong_type, type, omega__Cong: $o).
% 46.16/9.47 thf(subsetRefl_type, type, subsetRefl: $o).
% 46.16/9.47 thf(uniqinunit_type, type, uniqinunit: $o).
% 46.16/9.47 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 46.16/9.47 thf(prop2setE_type, type, prop2setE: $o).
% 46.16/9.47 thf(binunionEcases_type, type, binunionEcases: $o).
% 46.16/9.47 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 46.16/9.47 thf(nonemptyI_type, type, nonemptyI: $o).
% 46.16/9.47 thf(app_type, type, app: $o).
% 46.16/9.47 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 46.16/9.47 thf(exuE3u_type, type, exuE3u: $o).
% 46.16/9.47 thf(eta1_type, type, eta1: $o).
% 46.16/9.47 thf(setminusEL_type, type, setminusEL: $o).
% 46.16/9.47 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 46.16/9.47 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 46.16/9.47 thf(sepSubset_type, type, sepSubset: $o).
% 46.16/9.47 thf(upairset2E_type, type, upairset2E: $o).
% 46.16/9.47 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 46.16/9.47 thf(exuI3_type, type, exuI3: $o).
% 46.16/9.47 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 46.16/9.47 thf(apProp_type, type, apProp: $o).
% 46.16/9.47 thf(notdallE_type, type, notdallE: $o).
% 46.16/9.47 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 46.16/9.47 thf(binintersectER_type, type, binintersectER: $o).
% 46.16/9.47 thf(brelnall1_type, type, brelnall1: $o).
% 46.16/9.47 thf(powerset_type, type, powerset: $i > $i).
% 46.16/9.47 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 46.16/9.47 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 46.16/9.47 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 46.16/9.47 thf(exu__Cong_type, type, exu__Cong: $o).
% 46.16/9.47 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 46.16/9.47 thf(secondinupair_type, type, secondinupair: $o).
% 46.16/9.47 thf(singletonprop_type, type, singletonprop: $o).
% 46.16/9.47 thf(singletonsubset_type, type, singletonsubset: $o).
% 46.16/9.47 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 46.16/9.47 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 46.16/9.47 thf(replAx_type, type, replAx: $o).
% 46.16/9.47 thf(upairequniteq_type, type, upairequniteq: $o).
% 46.16/9.47 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 46.16/9.47 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 46.16/9.47 thf(setukpairIL_type, type, setukpairIL: $o).
% 46.16/9.47 thf(setunionE2_type, type, setunionE2: $o).
% 46.16/9.47 thf(inPowerset_type, type, inPowerset: $o).
% 46.16/9.47 thf(iffalse_type, type, iffalse: $o).
% 46.16/9.47 thf(funcext2_type, type, funcext2: $o).
% 46.16/9.47 thf(subset_type, type, subset: $i > $i > $o).
% 46.16/9.47 thf(subbreln_type, type, subbreln: $o).
% 46.16/9.47 thf(in__Cong_type, type, in__Cong: $o).
% 46.16/9.47 thf(binunionRsub_type, type, binunionRsub: $o).
% 46.16/9.47 thf(subset2powerset_type, type, subset2powerset: $o).
% 46.16/9.47 thf(singletoninpowerset, axiom, singletoninpowerset =
% 46.16/9.47 (![A:$i,Xx:$i]:
% 46.16/9.47 ( ( in @ Xx @ A ) =>
% 46.16/9.47 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 46.16/9.47 thf('0', plain,
% 46.16/9.47 (( singletoninpowerset ) =
% 46.16/9.47 ( ![X4:$i,X6:$i]:
% 46.16/9.47 ( ( in @ X6 @ X4 ) =>
% 46.16/9.47 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(bs114d, axiom, bs114d =
% 46.16/9.47 (![A:$i,B:$i,C:$i]:
% 46.16/9.47 ( ( binintersect @ A @ ( binunion @ B @ C ) ) =
% 46.16/9.47 ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ))).
% 46.16/9.47 thf('1', plain,
% 46.16/9.47 (( bs114d ) =
% 46.16/9.47 ( ![X4:$i,X6:$i,X8:$i]:
% 46.16/9.47 ( ( binintersect @ X4 @ ( binunion @ X6 @ X8 ) ) =
% 46.16/9.47 ( binunion @ ( binintersect @ X4 @ X6 ) @ ( binintersect @ X4 @ X8 ) ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(binintersectSubset1, axiom, binintersectSubset1 =
% 46.16/9.47 (![A:$i,B:$i]:
% 46.16/9.47 ( ( ( binintersect @ A @ B ) = ( A ) ) => ( subset @ A @ B ) ))).
% 46.16/9.47 thf('2', plain,
% 46.16/9.47 (( binintersectSubset1 ) =
% 46.16/9.47 ( ![X4:$i,X6:$i]:
% 46.16/9.47 ( ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) => ( subset @ X4 @ X6 ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(binintersectSubset4, axiom, binintersectSubset4 =
% 46.16/9.47 (![A:$i,B:$i]:
% 46.16/9.47 ( ( subset @ B @ A ) => ( ( binintersect @ A @ B ) = ( B ) ) ))).
% 46.16/9.47 thf('3', plain,
% 46.16/9.47 (( binintersectSubset4 ) =
% 46.16/9.47 ( ![X4:$i,X6:$i]:
% 46.16/9.47 ( ( subset @ X6 @ X4 ) => ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(binintersectRsub, axiom, binintersectRsub =
% 46.16/9.47 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ B ))).
% 46.16/9.47 thf('4', plain,
% 46.16/9.47 (( binintersectRsub ) =
% 46.16/9.47 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X6 ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(disjointsetsI1, axiom, disjointsetsI1 =
% 46.16/9.47 (![A:$i,B:$i]:
% 46.16/9.47 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ B ) & ( in @ Xx @ A ) ) ) ) =>
% 46.16/9.47 ( ( binintersect @ A @ B ) = ( emptyset ) ) ))).
% 46.16/9.47 thf('5', plain,
% 46.16/9.47 (( disjointsetsI1 ) =
% 46.16/9.47 ( ![X4:$i,X6:$i]:
% 46.16/9.47 ( ( ~( ?[X8:$i]: ( ( in @ X8 @ X6 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 46.16/9.47 ( ( binintersect @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(binintersectER, axiom, binintersectER =
% 46.16/9.47 (![A:$i,B:$i,Xx:$i]:
% 46.16/9.47 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ B ) ))).
% 46.16/9.47 thf('6', plain,
% 46.16/9.47 (( binintersectER ) =
% 46.16/9.47 ( ![X4:$i,X6:$i,X8:$i]:
% 46.16/9.47 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X6 ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(binintersectSubset3, axiom, binintersectSubset3 =
% 46.16/9.47 (![A:$i,B:$i]:
% 46.16/9.47 ( ( ( binintersect @ A @ B ) = ( B ) ) => ( subset @ B @ A ) ))).
% 46.16/9.47 thf('7', plain,
% 46.16/9.47 (( binintersectSubset3 ) =
% 46.16/9.47 ( ![X4:$i,X6:$i]:
% 46.16/9.47 ( ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(binintersectSubset2, axiom, binintersectSubset2 =
% 46.16/9.47 (![A:$i,B:$i]:
% 46.16/9.47 ( ( subset @ A @ B ) => ( ( binintersect @ A @ B ) = ( A ) ) ))).
% 46.16/9.47 thf('8', plain,
% 46.16/9.47 (( binintersectSubset2 ) =
% 46.16/9.47 ( ![X4:$i,X6:$i]:
% 46.16/9.47 ( ( subset @ X4 @ X6 ) => ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(binintersectLsub, axiom, binintersectLsub =
% 46.16/9.47 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ A ))).
% 46.16/9.47 thf('9', plain,
% 46.16/9.47 (( binintersectLsub ) =
% 46.16/9.47 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X4 ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(binintersectEL, axiom, binintersectEL =
% 46.16/9.47 (![A:$i,B:$i,Xx:$i]:
% 46.16/9.47 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 46.16/9.47 thf('10', plain,
% 46.16/9.47 (( binintersectEL ) =
% 46.16/9.47 ( ![X4:$i,X6:$i,X8:$i]:
% 46.16/9.47 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(binintersectSubset5, axiom, binintersectSubset5 =
% 46.16/9.47 (![A:$i,B:$i,C:$i]:
% 46.16/9.47 ( ( subset @ C @ A ) =>
% 46.16/9.47 ( ( subset @ C @ B ) => ( subset @ C @ ( binintersect @ A @ B ) ) ) ))).
% 46.16/9.47 thf('11', plain,
% 46.16/9.47 (( binintersectSubset5 ) =
% 46.16/9.47 ( ![X4:$i,X6:$i,X8:$i]:
% 46.16/9.47 ( ( subset @ X8 @ X4 ) =>
% 46.16/9.47 ( ( subset @ X8 @ X6 ) =>
% 46.16/9.47 ( subset @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(binintersectI, axiom, binintersectI =
% 46.16/9.47 (![A:$i,B:$i,Xx:$i]:
% 46.16/9.47 ( ( in @ Xx @ A ) =>
% 46.16/9.47 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ))).
% 46.16/9.47 thf('12', plain,
% 46.16/9.47 (( binintersectI ) =
% 46.16/9.47 ( ![X4:$i,X6:$i,X8:$i]:
% 46.16/9.47 ( ( in @ X8 @ X4 ) =>
% 46.16/9.47 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(sepInPowerset, axiom, sepInPowerset =
% 46.16/9.47 (![A:$i,Xphi:( $i > $o )]:
% 46.16/9.47 ( in @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) @ ( powerset @ A ) ))).
% 46.16/9.47 thf('13', plain,
% 46.16/9.47 (( sepInPowerset ) =
% 46.16/9.47 ( ![X4:$i,X6:( $i > $o )]:
% 46.16/9.47 ( in @
% 46.16/9.47 ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) @
% 46.16/9.47 ( powerset @ X4 ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(powersetsubset, axiom, powersetsubset =
% 46.16/9.47 (![A:$i,B:$i]:
% 46.16/9.47 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 46.16/9.47 thf('14', plain,
% 46.16/9.47 (( powersetsubset ) =
% 46.16/9.47 ( ![X4:$i,X6:$i]:
% 46.16/9.47 ( ( subset @ X4 @ X6 ) =>
% 46.16/9.47 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 46.16/9.47 thf('15', plain,
% 46.16/9.47 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(powersetE1, axiom, powersetE1 =
% 46.16/9.47 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 46.16/9.47 thf('16', plain,
% 46.16/9.47 (( powersetE1 ) =
% 46.16/9.47 ( ![X4:$i,X6:$i]:
% 46.16/9.47 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(powersetI1, axiom, powersetI1 =
% 46.16/9.47 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 46.16/9.47 thf('17', plain,
% 46.16/9.47 (( powersetI1 ) =
% 46.16/9.47 ( ![X4:$i,X6:$i]:
% 46.16/9.47 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(subset2powerset, axiom, subset2powerset =
% 46.16/9.47 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 46.16/9.47 thf('18', plain,
% 46.16/9.47 (( subset2powerset ) =
% 46.16/9.47 ( ![X4:$i,X6:$i]:
% 46.16/9.47 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(powerset__Cong, axiom, powerset__Cong =
% 46.16/9.47 (![A:$i,B:$i]:
% 46.16/9.47 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 46.16/9.47 thf('19', plain,
% 46.16/9.47 (( powerset__Cong ) =
% 46.16/9.47 ( ![X4:$i,X6:$i]:
% 46.16/9.47 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(powersetE, axiom, powersetE =
% 46.16/9.47 (![A:$i,B:$i,Xx:$i]:
% 46.16/9.47 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 46.16/9.47 thf('20', plain,
% 46.16/9.47 (( powersetE ) =
% 46.16/9.47 ( ![X4:$i,X6:$i,X8:$i]:
% 46.16/9.47 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 46.16/9.47 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(emptyInPowerset, axiom, emptyInPowerset =
% 46.16/9.47 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 46.16/9.47 thf('21', plain,
% 46.16/9.47 (( emptyInPowerset ) =
% 46.16/9.47 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(emptyinPowerset, axiom, emptyinPowerset =
% 46.16/9.47 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 46.16/9.47 thf('22', plain,
% 46.16/9.47 (( emptyinPowerset ) =
% 46.16/9.47 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(powersetI, axiom, powersetI =
% 46.16/9.47 (![A:$i,B:$i]:
% 46.16/9.47 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 46.16/9.47 ( in @ B @ ( powerset @ A ) ) ))).
% 46.16/9.47 thf('23', plain,
% 46.16/9.47 (( powersetI ) =
% 46.16/9.47 ( ![X4:$i,X6:$i]:
% 46.16/9.47 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 46.16/9.47 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(powersetAx, axiom, powersetAx =
% 46.16/9.47 (![A:$i,B:$i]:
% 46.16/9.47 ( ( in @ B @ ( powerset @ A ) ) <=>
% 46.16/9.47 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 46.16/9.47 thf('24', plain,
% 46.16/9.47 (( powersetAx ) =
% 46.16/9.47 ( ![X4:$i,X6:$i]:
% 46.16/9.47 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 46.16/9.47 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 46.16/9.47 define([status(thm)])).
% 46.16/9.47 thf(binintersectT_lem, conjecture,
% 46.16/9.47 (( setextAx ) =>
% 46.16/9.47 ( ( emptysetAx ) =>
% 46.16/9.47 ( ( setadjoinAx ) =>
% 46.16/9.47 ( ( powersetAx ) =>
% 46.16/9.47 ( ( setunionAx ) =>
% 46.16/9.47 ( ( omega0Ax ) =>
% 46.16/9.47 ( ( omegaSAx ) =>
% 46.16/9.47 ( ( omegaIndAx ) =>
% 46.16/9.47 ( ( replAx ) =>
% 46.16/9.47 ( ( foundationAx ) =>
% 46.16/9.47 ( ( wellorderingAx ) =>
% 46.16/9.47 ( ( descrp ) =>
% 46.16/9.47 ( ( dsetconstrI ) =>
% 46.16/9.47 ( ( dsetconstrEL ) =>
% 46.16/9.47 ( ( dsetconstrER ) =>
% 46.16/9.47 ( ( exuE1 ) =>
% 46.16/9.47 ( ( prop2setE ) =>
% 46.16/9.47 ( ( emptysetE ) =>
% 46.16/9.47 ( ( emptysetimpfalse ) =>
% 46.16/9.47 ( ( notinemptyset ) =>
% 46.16/9.47 ( ( exuE3e ) =>
% 46.16/9.47 ( ( setext ) =>
% 46.16/9.47 ( ( emptyI ) =>
% 46.16/9.47 ( ( noeltsimpempty ) =>
% 46.16/9.47 ( ( setbeta ) =>
% 46.16/9.47 ( ( nonemptyE1 ) =>
% 46.16/9.47 ( ( nonemptyI ) =>
% 46.16/9.47 ( ( nonemptyI1 ) =>
% 46.16/9.47 ( ( setadjoinIL ) =>
% 46.16/9.47 ( ( emptyinunitempty ) =>
% 46.16/9.47 ( ( setadjoinIR ) =>
% 46.16/9.47 ( ( setadjoinE ) =>
% 46.16/9.47 ( (
% 46.16/9.47 setadjoinOr ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setoftrueEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 powersetI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 emptyinPowerset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 emptyInPowerset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 powersetE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subPowSU ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 exuE2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 nonemptyImpWitness ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 uniqinunit ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 notinsingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eqinunit ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletonsswitch ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairsetE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairsetIL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairsetIR ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 emptyE1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 vacuousDall ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 quantDeMorgan1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 quantDeMorgan2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 quantDeMorgan3 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 quantDeMorgan4 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 prop2setI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 prop2set2propI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 notdexE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 notdallE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 exuI1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 exuI3 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 exuI2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 inCongP ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 exuE3u ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 exu__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 emptyset__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setadjoin__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 powerset__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunion__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 omega__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 exuEu ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 descr__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dsetconstr__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subsetI1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eqimpsubset2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eqimpsubset1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subsetI2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 emptysetsubset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subsetE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subsetE2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 notsubsetI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 notequalI1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 notequalI2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subsetRefl ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subsetTrans ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setadjoinSub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setadjoinSub2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subset2powerset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setextsub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subsetemptysetimpeq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 powersetI1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 powersetE1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 inPowerset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 powersetsubset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 sepInPowerset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 sepSubset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionIL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairset2IR ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionIR ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionEcases ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionLsub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionRsub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersectI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersectSubset5 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersectEL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersectLsub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersectSubset2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersectSubset3 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersectER ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 disjointsetsI1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersectRsub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersectSubset4 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersectSubset1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 bs114d ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusEL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusER ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusSubset2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusERneg ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusELneg ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusILneg ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusIRneg ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusLsub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusSubset1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 symdiffE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 symdiffI1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 symdiffI2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 symdiffIneg1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 symdiffIneg2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 secondinupair ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairIL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairIR ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kpairiskpair ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kpairp ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletonsubset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletoninpowerset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletoninpowunion ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairset2E ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairsubunion ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairinpowunion ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ubforcartprodlem1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ubforcartprodlem2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ubforcartprodlem3 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodpairin ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodmempair1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodmempair ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionE2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionsingleton1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionsingleton2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionsingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletonprop ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ex1E1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ex1I ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ex1I2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletonsuniq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjL1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kfstsingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 theprop ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kfstpairEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodfstin ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjL2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR11 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR12 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairequniteq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ksndsingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ksndpairEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kpairsurjEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodsndin ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodpairmemEL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodpairmemER ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodmempaircEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodfstpairEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodsndpairEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodpairsurjEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrSub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setOfPairsIsBReln ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrERa ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrEL1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrEL2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrER ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcImageSingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 apProp ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 app ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 infuncsetfunc ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ap2p ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcinfuncset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 lamProp ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 lamp ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 lam2p ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 brelnall1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 brelnall2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ex1E2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcGraphProp1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcGraphProp3 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcGraphProp2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcextLem ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcGraphProp4 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subbreln ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eqbreln ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcext ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcext2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ap2apEq1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ap2apEq2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 beta1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eta1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 lam2lamEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 beta2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eta2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iffalseProp1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iffalseProp2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iftrueProp1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iftrueProp2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ifSingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ifp ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 theeq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iftrue ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iffalse ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iftrueorfalse ) =>
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 A:$i,X:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 A ) ) =>
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 Y:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 Y @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 A ) ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X @ Y ) @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 46.16/9.47 thf(zf_stmt_0, conjecture,
% 46.16/9.47 (( setextAx ) =>
% 46.16/9.47 ( ( emptysetAx ) =>
% 46.16/9.47 ( ( setadjoinAx ) =>
% 46.16/9.47 ( ( ![X4:$i,X6:$i]:
% 46.16/9.47 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 46.16/9.47 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 46.16/9.47 ( ( setunionAx ) =>
% 46.16/9.47 ( ( omega0Ax ) =>
% 46.16/9.47 ( ( omegaSAx ) =>
% 46.16/9.47 ( ( omegaIndAx ) =>
% 46.16/9.47 ( ( replAx ) =>
% 46.16/9.47 ( ( foundationAx ) =>
% 46.16/9.47 ( ( wellorderingAx ) =>
% 46.16/9.47 ( ( descrp ) =>
% 46.16/9.47 ( ( dsetconstrI ) =>
% 46.16/9.47 ( ( dsetconstrEL ) =>
% 46.16/9.47 ( ( dsetconstrER ) =>
% 46.16/9.47 ( ( exuE1 ) =>
% 46.16/9.47 ( ( prop2setE ) =>
% 46.16/9.47 ( ( emptysetE ) =>
% 46.16/9.47 ( ( emptysetimpfalse ) =>
% 46.16/9.47 ( ( notinemptyset ) =>
% 46.16/9.47 ( ( exuE3e ) =>
% 46.16/9.47 ( ( setext ) =>
% 46.16/9.47 ( ( emptyI ) =>
% 46.16/9.47 ( ( noeltsimpempty ) =>
% 46.16/9.47 ( ( setbeta ) =>
% 46.16/9.47 ( ( nonemptyE1 ) =>
% 46.16/9.47 ( ( nonemptyI ) =>
% 46.16/9.47 ( ( nonemptyI1 ) =>
% 46.16/9.47 ( ( setadjoinIL ) =>
% 46.16/9.47 ( ( emptyinunitempty ) =>
% 46.16/9.47 ( ( setadjoinIR ) =>
% 46.16/9.47 ( ( setadjoinE ) =>
% 46.16/9.47 ( (
% 46.16/9.47 setadjoinOr ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setoftrueEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X10:$i,
% 46.16/9.47 X12:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X14:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X14 @ X12 ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X14 @ X10 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X12 @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X10 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X16:$i]:
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 emptyset @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X16 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X18:$i]:
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 emptyset @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X18 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X20:$i,
% 46.16/9.47 X22:$i,
% 46.16/9.47 X24:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X22 @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X20 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X24 @ X22 ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X24 @ X20 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subPowSU ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 exuE2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 nonemptyImpWitness ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 uniqinunit ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 notinsingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eqinunit ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletonsswitch ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairsetE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairsetIL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairsetIR ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 emptyE1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 vacuousDall ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 quantDeMorgan1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 quantDeMorgan2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 quantDeMorgan3 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 quantDeMorgan4 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 prop2setI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 prop2set2propI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 notdexE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 notdallE ) =>
% 46.16/9.47 (
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% 46.16/9.47 (
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% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 emptyset__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setadjoin__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X26:$i,
% 46.16/9.47 X28:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 X26 ) =
% 46.16/9.47 (
% 46.16/9.47 X28 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X26 ) =
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X28 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunion__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 omega__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 exuEu ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 descr__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
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% 46.16/9.47 (
% 46.16/9.47 subsetI1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eqimpsubset2 ) =>
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% 46.16/9.47 subsetTrans ) =>
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% 46.16/9.47 (
% 46.16/9.47 setadjoinSub ) =>
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% 46.16/9.47 setadjoinSub2 ) =>
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% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X30:$i,
% 46.16/9.47 X32:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X30 @ X32 ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X30 @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X32 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setextsub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subsetemptysetimpeq ) =>
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% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X34:$i,
% 46.16/9.47 X36:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X36 @ X34 ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X36 @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X34 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X38:$i,
% 46.16/9.47 X40:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X40 @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X38 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X40 @ X38 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X42:$i]:
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X42 @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X42 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X44:$i,
% 46.16/9.47 X46:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X44 @ X46 ) =>
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X44 ) @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X46 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X48:$i,
% 46.16/9.47 X50:(
% 46.16/9.47 $i > $o )]:
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 (
% 46.16/9.47 dsetconstr
% 46.16/9.47 @
% 46.16/9.47 X48 @
% 46.16/9.47 (
% 46.16/9.47 ^[
% 46.16/9.47 V_1:$i]:
% 46.16/9.47 (
% 46.16/9.47 X50 @ V_1 ) ) ) @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X48 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 sepSubset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionIL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairset2IR ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionIR ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionEcases ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionLsub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionRsub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X52:$i,
% 46.16/9.47 X54:$i,
% 46.16/9.47 X56:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X56 @ X52 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X56 @ X54 ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X56 @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X52 @ X54 ) ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X58:$i,
% 46.16/9.47 X60:$i,
% 46.16/9.47 X62:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X62 @ X58 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X62 @ X60 ) =>
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X62 @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X58 @ X60 ) ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X64:$i,
% 46.16/9.47 X66:$i,
% 46.16/9.47 X68:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X68 @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X64 @ X66 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X68 @ X64 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X70:$i,
% 46.16/9.47 X72:$i]:
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X70 @ X72 ) @
% 46.16/9.47 X70 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X74:$i,
% 46.16/9.47 X76:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X74 @ X76 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X74 @ X76 ) =
% 46.16/9.47 (
% 46.16/9.47 X74 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X78:$i,
% 46.16/9.47 X80:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X78 @ X80 ) =
% 46.16/9.47 (
% 46.16/9.47 X80 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X80 @ X78 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X82:$i,
% 46.16/9.47 X84:$i,
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% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X86 @
% 46.16/9.47 (
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% 46.16/9.47 @
% 46.16/9.47 X82 @ X84 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X86 @ X84 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
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% 46.16/9.47 X88:$i,
% 46.16/9.47 X90:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ~(
% 46.16/9.47 ?[
% 46.16/9.47 X92:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X92 @ X88 ) &
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X92 @ X90 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X88 @ X90 ) =
% 46.16/9.47 (
% 46.16/9.47 emptyset ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X94:$i,
% 46.16/9.47 X96:$i]:
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% 46.16/9.47 subset @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X94 @ X96 ) @
% 46.16/9.47 X96 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X98:$i,
% 46.16/9.47 X100:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X100 @ X98 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X98 @ X100 ) =
% 46.16/9.47 (
% 46.16/9.47 X100 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X102:$i,
% 46.16/9.47 X104:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X102 @
% 46.16/9.47 X104 ) =
% 46.16/9.47 (
% 46.16/9.47 X102 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X102 @
% 46.16/9.47 X104 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X106:$i,
% 46.16/9.47 X108:$i,
% 46.16/9.47 X110:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X106 @
% 46.16/9.47 (
% 46.16/9.47 binunion @
% 46.16/9.47 X108 @
% 46.16/9.47 X110 ) ) =
% 46.16/9.47 (
% 46.16/9.47 binunion @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X106 @
% 46.16/9.47 X108 ) @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X106 @
% 46.16/9.47 X110 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusEL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusER ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusSubset2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusERneg ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusELneg ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusILneg ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusIRneg ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusLsub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusSubset1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 symdiffE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 symdiffI1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 symdiffI2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 symdiffIneg1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 symdiffIneg2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 secondinupair ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairIL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairIR ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kpairiskpair ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kpairp ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletonsubset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X112:$i,
% 46.16/9.47 X114:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X114 @
% 46.16/9.47 X112 ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 (
% 46.16/9.47 setadjoin
% 46.16/9.47 @
% 46.16/9.47 X114 @
% 46.16/9.47 emptyset ) @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X112 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletoninpowunion ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairset2E ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairsubunion ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairinpowunion ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ubforcartprodlem1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ubforcartprodlem2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ubforcartprodlem3 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodpairin ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodmempair1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodmempair ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionE2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionsingleton1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionsingleton2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionsingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletonprop ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ex1E1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ex1I ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ex1I2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletonsuniq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjL1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kfstsingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 theprop ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kfstpairEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodfstin ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjL2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR11 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR12 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairequniteq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ksndsingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ksndpairEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kpairsurjEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodsndin ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodpairmemEL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodpairmemER ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodmempaircEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodfstpairEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodsndpairEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodpairsurjEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrSub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setOfPairsIsBReln ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrERa ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrEL1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrEL2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrER ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcImageSingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 apProp ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 app ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 infuncsetfunc ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ap2p ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcinfuncset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 lamProp ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 lamp ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 lam2p ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 brelnall1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 brelnall2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ex1E2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcGraphProp1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcGraphProp3 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcGraphProp2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcextLem ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcGraphProp4 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subbreln ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eqbreln ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcext ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcext2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ap2apEq1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ap2apEq2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 beta1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eta1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 lam2lamEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 beta2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eta2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iffalseProp1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iffalseProp2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iftrueProp1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iftrueProp2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ifSingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ifp ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 theeq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iftrue ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iffalse ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iftrueorfalse ) =>
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X116:$i,
% 46.16/9.47 X118:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X118 @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X116 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X120:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X120 @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X116 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X118 @
% 46.16/9.47 X120 ) @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X116 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 46.16/9.47 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 46.16/9.47 thf(zf_stmt_2, axiom,
% 46.16/9.47 (![X8:$i,X6:$i,X4:$i]:
% 46.16/9.47 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 46.16/9.47 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 46.16/9.47 thf(zf_stmt_3, conjecture,
% 46.16/9.47 (( setextAx ) =>
% 46.16/9.47 ( ( emptysetAx ) =>
% 46.16/9.47 ( ( setadjoinAx ) =>
% 46.16/9.47 ( ( ![X4:$i,X6:$i]:
% 46.16/9.47 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 46.16/9.47 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 46.16/9.47 ( ( setunionAx ) =>
% 46.16/9.47 ( ( omega0Ax ) =>
% 46.16/9.47 ( ( omegaSAx ) =>
% 46.16/9.47 ( ( omegaIndAx ) =>
% 46.16/9.47 ( ( replAx ) =>
% 46.16/9.47 ( ( foundationAx ) =>
% 46.16/9.47 ( ( wellorderingAx ) =>
% 46.16/9.47 ( ( descrp ) =>
% 46.16/9.47 ( ( dsetconstrI ) =>
% 46.16/9.47 ( ( dsetconstrEL ) =>
% 46.16/9.47 ( ( dsetconstrER ) =>
% 46.16/9.47 ( ( exuE1 ) =>
% 46.16/9.47 ( ( prop2setE ) =>
% 46.16/9.47 ( ( emptysetE ) =>
% 46.16/9.47 ( ( emptysetimpfalse ) =>
% 46.16/9.47 ( ( notinemptyset ) =>
% 46.16/9.47 ( ( exuE3e ) =>
% 46.16/9.47 ( ( setext ) =>
% 46.16/9.47 ( ( emptyI ) =>
% 46.16/9.47 ( ( noeltsimpempty ) =>
% 46.16/9.47 ( ( setbeta ) =>
% 46.16/9.47 ( ( nonemptyE1 ) =>
% 46.16/9.47 ( ( nonemptyI ) =>
% 46.16/9.47 ( ( nonemptyI1 ) =>
% 46.16/9.47 ( ( setadjoinIL ) =>
% 46.16/9.47 ( ( emptyinunitempty ) =>
% 46.16/9.47 ( ( setadjoinIR ) =>
% 46.16/9.47 ( ( setadjoinE ) =>
% 46.16/9.47 ( (
% 46.16/9.47 setadjoinOr ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setoftrueEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X10:$i,
% 46.16/9.47 X12:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X14:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X14 @ X12 ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X14 @ X10 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X12 @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X10 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X16:$i]:
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 emptyset @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X16 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X18:$i]:
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 emptyset @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X18 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X20:$i,
% 46.16/9.47 X22:$i,
% 46.16/9.47 X24:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X22 @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X20 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X24 @ X22 ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X24 @ X20 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subPowSU ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 exuE2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 nonemptyImpWitness ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 uniqinunit ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 notinsingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eqinunit ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletonsswitch ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairsetE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairsetIL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairsetIR ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 emptyE1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 vacuousDall ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 quantDeMorgan1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 quantDeMorgan2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 quantDeMorgan3 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 quantDeMorgan4 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 prop2setI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 prop2set2propI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 notdexE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 notdallE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 exuI1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 exuI3 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 exuI2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 inCongP ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 exuE3u ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 exu__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 emptyset__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setadjoin__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X26:$i,
% 46.16/9.47 X28:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 X26 ) =
% 46.16/9.47 (
% 46.16/9.47 X28 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X26 ) =
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X28 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunion__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 omega__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 exuEu ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 descr__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dsetconstr__Cong ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subsetI1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eqimpsubset2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eqimpsubset1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subsetI2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 emptysetsubset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subsetE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subsetE2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 notsubsetI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 notequalI1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 notequalI2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subsetRefl ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subsetTrans ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setadjoinSub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setadjoinSub2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X30:$i,
% 46.16/9.47 X32:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X30 @ X32 ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X30 @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X32 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setextsub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subsetemptysetimpeq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X34:$i,
% 46.16/9.47 X36:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X36 @ X34 ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X36 @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X34 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X38:$i,
% 46.16/9.47 X40:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X40 @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X38 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X40 @ X38 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X42:$i]:
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X42 @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X42 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X44:$i,
% 46.16/9.47 X46:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X44 @ X46 ) =>
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X44 ) @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X46 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X48:$i,
% 46.16/9.47 X50:(
% 46.16/9.47 $i > $o )]:
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 (
% 46.16/9.47 dsetconstr
% 46.16/9.47 @
% 46.16/9.47 X48 @
% 46.16/9.47 (
% 46.16/9.47 ^[
% 46.16/9.47 V_1:$i]:
% 46.16/9.47 (
% 46.16/9.47 X50 @ V_1 ) ) ) @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X48 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 sepSubset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionIL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairset2IR ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionIR ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionEcases ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionLsub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binunionRsub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X52:$i,
% 46.16/9.47 X54:$i,
% 46.16/9.47 X56:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X56 @ X52 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X56 @ X54 ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X56 @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X52 @ X54 ) ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X58:$i,
% 46.16/9.47 X60:$i,
% 46.16/9.47 X62:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X62 @ X58 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X62 @ X60 ) =>
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X62 @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X58 @ X60 ) ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X64:$i,
% 46.16/9.47 X66:$i,
% 46.16/9.47 X68:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X68 @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X64 @ X66 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X68 @ X64 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X70:$i,
% 46.16/9.47 X72:$i]:
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X70 @ X72 ) @
% 46.16/9.47 X70 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X74:$i,
% 46.16/9.47 X76:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X74 @ X76 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X74 @ X76 ) =
% 46.16/9.47 (
% 46.16/9.47 X74 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X78:$i,
% 46.16/9.47 X80:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X78 @ X80 ) =
% 46.16/9.47 (
% 46.16/9.47 X80 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X80 @ X78 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X82:$i,
% 46.16/9.47 X84:$i,
% 46.16/9.47 X86:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X86 @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X82 @ X84 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X86 @ X84 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X88:$i,
% 46.16/9.47 X90:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ~(
% 46.16/9.47 ?[
% 46.16/9.47 X92:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X92 @ X90 ) &
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X92 @ X88 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X88 @ X90 ) =
% 46.16/9.47 (
% 46.16/9.47 emptyset ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X94:$i,
% 46.16/9.47 X96:$i]:
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X94 @ X96 ) @
% 46.16/9.47 X96 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X98:$i,
% 46.16/9.47 X100:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X100 @ X98 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X98 @ X100 ) =
% 46.16/9.47 (
% 46.16/9.47 X100 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X102:$i,
% 46.16/9.47 X104:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X102 @
% 46.16/9.47 X104 ) =
% 46.16/9.47 (
% 46.16/9.47 X102 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 subset @
% 46.16/9.47 X102 @
% 46.16/9.47 X104 ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X106:$i,
% 46.16/9.47 X108:$i,
% 46.16/9.47 X110:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X106 @
% 46.16/9.47 (
% 46.16/9.47 binunion @
% 46.16/9.47 X108 @
% 46.16/9.47 X110 ) ) =
% 46.16/9.47 (
% 46.16/9.47 binunion @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X106 @
% 46.16/9.47 X108 ) @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X106 @
% 46.16/9.47 X110 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusEL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusER ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusSubset2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusERneg ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusELneg ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusILneg ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusIRneg ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusLsub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setminusSubset1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 symdiffE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 symdiffI1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 symdiffI2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 symdiffIneg1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 symdiffIneg2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 secondinupair ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairIL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairIR ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kpairiskpair ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kpairp ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletonsubset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X112:$i,
% 46.16/9.47 X114:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X114 @
% 46.16/9.47 X112 ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 (
% 46.16/9.47 setadjoin
% 46.16/9.47 @
% 46.16/9.47 X114 @
% 46.16/9.47 emptyset ) @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X112 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletoninpowunion ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairset2E ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairsubunion ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairinpowunion ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ubforcartprodlem1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ubforcartprodlem2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ubforcartprodlem3 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodpairin ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodmempair1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodmempair ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionE2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionsingleton1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionsingleton2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionsingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletonprop ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ex1E1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ex1I ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ex1I2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletonsuniq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjL1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kfstsingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 theprop ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kfstpairEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodfstin ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjL2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR11 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR12 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairequniteq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ksndsingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ksndpairEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kpairsurjEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodsndin ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodpairmemEL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodpairmemER ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodmempaircEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodfstpairEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodsndpairEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodpairsurjEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrI ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrSub ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setOfPairsIsBReln ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrERa ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrEL1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrEL2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 dpsetconstrER ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcImageSingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 apProp ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 app ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 infuncsetfunc ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ap2p ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcinfuncset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 lamProp ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 lamp ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 lam2p ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 brelnall1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 brelnall2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ex1E2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcGraphProp1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcGraphProp3 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcGraphProp2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcextLem ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcGraphProp4 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 subbreln ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eqbreln ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcext ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 funcext2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ap2apEq1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ap2apEq2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 beta1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eta1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 lam2lamEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 beta2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 eta2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iffalseProp1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iffalseProp2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iftrueProp1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iftrueProp2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ifSingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ifp ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 theeq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iftrue ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iffalse ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 iftrueorfalse ) =>
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X116:$i,
% 46.16/9.47 X118:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X118 @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X116 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X120:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X120 @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X116 ) ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 (
% 46.16/9.47 binintersect
% 46.16/9.47 @
% 46.16/9.47 X118 @
% 46.16/9.47 X120 ) @
% 46.16/9.47 (
% 46.16/9.47 powerset @
% 46.16/9.47 X116 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 46.16/9.47 thf(zf_stmt_4, negated_conjecture,
% 46.16/9.47 (~( ( setextAx ) =>
% 46.16/9.47 ( ( emptysetAx ) =>
% 46.16/9.47 ( ( setadjoinAx ) =>
% 46.16/9.47 ( ( ![X4:$i,X6:$i]:
% 46.16/9.47 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 46.16/9.47 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 46.16/9.47 ( ( setunionAx ) =>
% 46.16/9.47 ( ( omega0Ax ) =>
% 46.16/9.47 ( ( omegaSAx ) =>
% 46.16/9.47 ( ( omegaIndAx ) =>
% 46.16/9.47 ( ( replAx ) =>
% 46.16/9.47 ( ( foundationAx ) =>
% 46.16/9.47 ( ( wellorderingAx ) =>
% 46.16/9.47 ( ( descrp ) =>
% 46.16/9.47 ( ( dsetconstrI ) =>
% 46.16/9.47 ( ( dsetconstrEL ) =>
% 46.16/9.47 ( ( dsetconstrER ) =>
% 46.16/9.47 ( ( exuE1 ) =>
% 46.16/9.47 ( ( prop2setE ) =>
% 46.16/9.47 ( ( emptysetE ) =>
% 46.16/9.47 ( ( emptysetimpfalse ) =>
% 46.16/9.47 ( ( notinemptyset ) =>
% 46.16/9.47 ( ( exuE3e ) =>
% 46.16/9.47 ( ( setext ) =>
% 46.16/9.47 ( ( emptyI ) =>
% 46.16/9.47 ( ( noeltsimpempty ) =>
% 46.16/9.47 ( ( setbeta ) =>
% 46.16/9.47 ( ( nonemptyE1 ) =>
% 46.16/9.47 ( ( nonemptyI ) =>
% 46.16/9.47 ( ( nonemptyI1 ) =>
% 46.16/9.47 ( ( setadjoinIL ) =>
% 46.16/9.47 ( ( emptyinunitempty ) =>
% 46.16/9.47 ( ( setadjoinIR ) =>
% 46.16/9.47 ( (
% 46.16/9.47 setadjoinE ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setadjoinOr ) =>
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% 46.16/9.47 X30 @
% 46.16/9.47 (
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% 46.16/9.47 X32 ) ) ) ) =>
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% 46.16/9.47 $i > $o )]:
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% 46.16/9.47 (
% 46.16/9.47 binunion
% 46.16/9.47 @
% 46.16/9.47 (
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% 46.16/9.47 setukpairIR ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kpairiskpair ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kpairp ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletonsubset ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ![
% 46.16/9.47 X112:$i,
% 46.16/9.47 X114:$i]:
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 X114 @
% 46.16/9.47 X112 ) =>
% 46.16/9.47 (
% 46.16/9.47 in @
% 46.16/9.47 (
% 46.16/9.47 setadjoin
% 46.16/9.47 @
% 46.16/9.47 X114 @
% 46.16/9.47 emptyset ) @
% 46.16/9.47 (
% 46.16/9.47 powerset
% 46.16/9.47 @
% 46.16/9.47 X112 ) ) ) ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletoninpowunion ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairset2E ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairsubunion ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairinpowunion ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ubforcartprodlem1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ubforcartprodlem2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ubforcartprodlem3 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodpairin ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodmempair1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodmempair ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionE2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionsingleton1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionsingleton2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setunionsingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletonprop ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ex1E1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ex1I ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 ex1I2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 singletonsuniq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjL1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kfstsingleton ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 theprop ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 kfstpairEq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 cartprodfstin ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjL2 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjL ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR11 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR12 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR1 ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 upairequniteq ) =>
% 46.16/9.47 (
% 46.16/9.47 (
% 46.16/9.47 setukpairinjR2 ) =>
% 46.16/9.47 (
% 46.16/9.48 (
% 46.16/9.48 setukpairinjR ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 ksndsingleton ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 ksndpairEq ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 kpairsurjEq ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 cartprodsndin ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 cartprodpairmemEL ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 cartprodpairmemER ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 cartprodmempaircEq ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 cartprodfstpairEq ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 cartprodsndpairEq ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 cartprodpairsurjEq ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 dpsetconstrI ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 dpsetconstrSub ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 setOfPairsIsBReln ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 dpsetconstrERa ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 dpsetconstrEL1 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 dpsetconstrEL2 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 dpsetconstrER ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 funcImageSingleton ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 apProp ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 app ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 infuncsetfunc ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 ap2p ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 funcinfuncset ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 lamProp ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 lamp ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 lam2p ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 brelnall1 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 brelnall2 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 ex1E2 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 funcGraphProp1 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 funcGraphProp3 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 funcGraphProp2 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 funcextLem ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 funcGraphProp4 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 subbreln ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 eqbreln ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 funcext ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 funcext2 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 ap2apEq1 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 ap2apEq2 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 beta1 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 eta1 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 lam2lamEq ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 beta2 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 eta2 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 iffalseProp1 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 iffalseProp2 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 iftrueProp1 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 iftrueProp2 ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 ifSingleton ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 ifp ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 theeq ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 iftrue ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 iffalse ) =>
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 iftrueorfalse ) =>
% 46.16/9.48 (
% 46.16/9.48 ![
% 46.16/9.48 X116:$i,
% 46.16/9.48 X118:$i]:
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 in @
% 46.16/9.48 X118 @
% 46.16/9.48 (
% 46.16/9.48 powerset
% 46.16/9.48 @
% 46.16/9.48 X116 ) ) =>
% 46.16/9.48 (
% 46.16/9.48 ![
% 46.16/9.48 X120:$i]:
% 46.16/9.48 (
% 46.16/9.48 (
% 46.16/9.48 in @
% 46.16/9.48 X120 @
% 46.16/9.48 (
% 46.16/9.48 powerset
% 46.16/9.48 @
% 46.16/9.48 X116 ) ) =>
% 46.16/9.48 (
% 46.16/9.48 in @
% 46.16/9.48 (
% 46.16/9.48 binintersect
% 46.16/9.48 @
% 46.16/9.48 X118 @
% 46.16/9.48 X120 ) @
% 46.16/9.48 (
% 46.16/9.48 powerset
% 46.16/9.48 @
% 46.16/9.48 X116 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 46.16/9.48 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 46.16/9.48 thf(zip_derived_cl119, plain,
% 46.16/9.48 (~ (in @ (binintersect @ sk__59 @ sk__60) @ (powerset @ sk__58))),
% 46.16/9.48 inference('cnf', [status(esa)], [zf_stmt_4])).
% 46.16/9.48 thf(zip_derived_cl177, plain,
% 46.16/9.48 (![X26 : $i, X27 : $i]: (subset @ (binintersect @ X26 @ X27) @ X27)),
% 46.16/9.48 inference('cnf', [status(esa)], [zf_stmt_4])).
% 46.16/9.48 thf(zip_derived_cl50, plain,
% 46.16/9.48 (![X3 : $i, X4 : $i]:
% 46.16/9.48 ( (in @ X3 @ (powerset @ X4)) | ~ (subset @ X3 @ X4))),
% 46.16/9.48 inference('cnf', [status(esa)], [zf_stmt_4])).
% 46.16/9.48 thf(zip_derived_cl315, plain,
% 46.16/9.48 (![X0 : $i, X1 : $i]: (in @ (binintersect @ X1 @ X0) @ (powerset @ X0))),
% 46.16/9.48 inference('sup-', [status(thm)], [zip_derived_cl177, zip_derived_cl50])).
% 46.16/9.48 thf(zip_derived_cl118, plain, ( (in @ sk__60 @ (powerset @ sk__58))),
% 46.16/9.48 inference('cnf', [status(esa)], [zf_stmt_4])).
% 46.16/9.48 thf(zip_derived_cl180, plain,
% 46.16/9.48 (![X33 : $i, X34 : $i, X35 : $i]:
% 46.16/9.48 ( (in @ X33 @ X34) | ~ (in @ X33 @ (binintersect @ X34 @ X35)))),
% 46.16/9.48 inference('cnf', [status(esa)], [zf_stmt_4])).
% 46.16/9.48 thf(zip_derived_cl186, plain,
% 46.16/9.48 (![X39 : $i, X40 : $i]:
% 46.16/9.48 ( (subset @ (powerset @ X39) @ (powerset @ X40))
% 46.16/9.48 | ~ (subset @ X39 @ X40))),
% 46.16/9.48 inference('cnf', [status(esa)], [zf_stmt_4])).
% 46.16/9.48 thf(zip_derived_cl62, plain,
% 46.16/9.48 (![X17 : $i, X18 : $i]:
% 46.16/9.48 (((binintersect @ X18 @ X17) = (X17)) | ~ (subset @ X17 @ X18))),
% 46.16/9.48 inference('cnf', [status(esa)], [zf_stmt_4])).
% 46.16/9.48 thf(zip_derived_cl524, plain,
% 46.16/9.48 (![X0 : $i, X1 : $i]:
% 46.16/9.48 (~ (subset @ X1 @ X0)
% 46.16/9.48 | ((binintersect @ (powerset @ X0) @ (powerset @ X1))
% 46.16/9.48 = (powerset @ X1)))),
% 46.16/9.48 inference('sup-', [status(thm)], [zip_derived_cl186, zip_derived_cl62])).
% 46.16/9.48 thf(zip_derived_cl187, plain,
% 46.16/9.48 (![X41 : $i, X42 : $i]:
% 46.16/9.48 ( (subset @ X41 @ X42) | ~ (in @ X41 @ (powerset @ X42)))),
% 46.16/9.48 inference('cnf', [status(esa)], [zf_stmt_4])).
% 46.16/9.48 thf(zip_derived_cl17905, plain, ($false),
% 46.16/9.48 inference('eprover', [status(thm)],
% 46.16/9.48 [zip_derived_cl119, zip_derived_cl315, zip_derived_cl118,
% 46.16/9.48 zip_derived_cl180, zip_derived_cl524, zip_derived_cl187])).
% 46.16/9.48
% 46.16/9.48 % SZS output end Refutation
% 46.16/9.48
% 46.16/9.48
% 46.16/9.48 % Terminating...
% 46.62/9.69 % Runner terminated.
% 46.62/9.69 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------