%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU717^1 : 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.N9R73knsLB true
% Computer : n008.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 04:55:56 PM UTC 2025
% Result : Theorem 12.99s 2.63s
% Output : Refutation 12.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU717^1 : TPTP v9.2.0. Released v3.7.0.
% 0.08/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.N9R73knsLB true
% 0.12/0.32 % Computer : n008.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Oct 1 16:09:23 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.12/0.32 % Running portfolio for 300 s
% 0.12/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Number of cores: 8
% 0.12/0.33 % Python version: Python 3.6.8
% 0.12/0.33 % Running in HO mode
% 0.52/0.65 % Total configuration time : 828
% 0.52/0.65 % Estimated wc time : 1656
% 0.52/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.54/0.78 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.54/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.54/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.54/0.79 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 12.99/2.63 % Solved by lams/40_c_ic.sh.
% 12.99/2.63 % done 931 iterations in 1.804s
% 12.99/2.63 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 12.99/2.63 % SZS output start Refutation
% 12.99/2.63 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 12.99/2.63 thf(notdexE_type, type, notdexE: $o).
% 12.99/2.63 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 12.99/2.63 thf(setunionAx_type, type, setunionAx: $o).
% 12.99/2.63 thf(setminusELneg_type, type, setminusELneg: $o).
% 12.99/2.63 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 12.99/2.63 thf(ex1E1_type, type, ex1E1: $o).
% 12.99/2.63 thf(powersetE_type, type, powersetE: $o).
% 12.99/2.63 thf(omegaSAx_type, type, omegaSAx: $o).
% 12.99/2.63 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 12.99/2.63 thf(exuI1_type, type, exuI1: $o).
% 12.99/2.63 thf(exuI2_type, type, exuI2: $o).
% 12.99/2.63 thf(notequalI2_type, type, notequalI2: $o).
% 12.99/2.63 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 12.99/2.63 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 12.99/2.63 thf(upairsubunion_type, type, upairsubunion: $o).
% 12.99/2.63 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 12.99/2.63 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 12.99/2.63 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 12.99/2.63 thf(setminusILneg_type, type, setminusILneg: $o).
% 12.99/2.63 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 12.99/2.63 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 12.99/2.63 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 12.99/2.63 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 12.99/2.63 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 12.99/2.63 thf(iftrue_type, type, iftrue: $o).
% 12.99/2.63 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 12.99/2.63 thf(ifSingleton_type, type, ifSingleton: $o).
% 12.99/2.63 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 12.99/2.63 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 12.99/2.63 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 12.99/2.63 thf(lamProp_type, type, lamProp: $o).
% 12.99/2.63 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 12.99/2.63 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 12.99/2.63 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 12.99/2.63 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 12.99/2.63 thf(setukpairIR_type, type, setukpairIR: $o).
% 12.99/2.63 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 12.99/2.63 thf(lam2p_type, type, lam2p: $o).
% 12.99/2.63 thf(binunionE_type, type, binunionE: $o).
% 12.99/2.63 thf(setext_type, type, setext: $o).
% 12.99/2.63 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 12.99/2.63 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 12.99/2.63 thf(descr__Cong_type, type, descr__Cong: $o).
% 12.99/2.63 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 12.99/2.63 thf(eqbreln_type, type, eqbreln: $o).
% 12.99/2.63 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 12.99/2.63 thf(in_type, type, in: $i > $i > $o).
% 12.99/2.63 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 12.99/2.63 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 12.99/2.63 thf(complementT_lem_type, type, complementT_lem: $o).
% 12.99/2.63 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 12.99/2.63 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 12.99/2.63 thf(beta1_type, type, beta1: $o).
% 12.99/2.63 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 12.99/2.63 thf(symdiffI2_type, type, symdiffI2: $o).
% 12.99/2.63 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 12.99/2.63 thf(upairset2IR_type, type, upairset2IR: $o).
% 12.99/2.63 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 12.99/2.63 thf(subsetE_type, type, subsetE: $o).
% 12.99/2.63 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 12.99/2.63 thf(sk__39_type, type, sk__39: $i).
% 12.99/2.63 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 12.99/2.63 thf(setbeta_type, type, setbeta: $o).
% 12.99/2.63 thf(eqinunit_type, type, eqinunit: $o).
% 12.99/2.63 thf(upairsetIL_type, type, upairsetIL: $o).
% 12.99/2.63 thf(powersetI1_type, type, powersetI1: $o).
% 12.99/2.63 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 12.99/2.63 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 12.99/2.63 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 12.99/2.63 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 12.99/2.63 thf(powersetAx_type, type, powersetAx: $o).
% 12.99/2.63 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 12.99/2.63 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 12.99/2.63 thf(powersetI_type, type, powersetI: $o).
% 12.99/2.63 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 12.99/2.63 thf(upairsetIR_type, type, upairsetIR: $o).
% 12.99/2.63 thf(lamp_type, type, lamp: $o).
% 12.99/2.63 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 12.99/2.63 thf(inCongP_type, type, inCongP: $o).
% 12.99/2.63 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 12.99/2.63 thf(exuE3e_type, type, exuE3e: $o).
% 12.99/2.63 thf(emptysetE_type, type, emptysetE: $o).
% 12.99/2.63 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 12.99/2.63 thf(setunionI_type, type, setunionI: $o).
% 12.99/2.63 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 12.99/2.63 thf(prop2setI_type, type, prop2setI: $o).
% 12.99/2.63 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 12.99/2.63 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 12.99/2.63 thf(setminusER_type, type, setminusER: $o).
% 12.99/2.63 thf(exuE2_type, type, exuE2: $o).
% 12.99/2.63 thf(emptyset_type, type, emptyset: $i).
% 12.99/2.63 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 12.99/2.63 thf(ex1I_type, type, ex1I: $o).
% 12.99/2.63 thf(ex1E2_type, type, ex1E2: $o).
% 12.99/2.63 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 12.99/2.63 thf(powersetsubset_type, type, powersetsubset: $o).
% 12.99/2.63 thf(subPowSU_type, type, subPowSU: $o).
% 12.99/2.63 thf(notequalI1_type, type, notequalI1: $o).
% 12.99/2.63 thf(notinemptyset_type, type, notinemptyset: $o).
% 12.99/2.63 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 12.99/2.63 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 12.99/2.63 thf(subsetTrans_type, type, subsetTrans: $o).
% 12.99/2.63 thf(kpairp_type, type, kpairp: $o).
% 12.99/2.63 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 12.99/2.63 thf(setminusI_type, type, setminusI: $o).
% 12.99/2.63 thf(binunionIL_type, type, binunionIL: $o).
% 12.99/2.63 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 12.99/2.63 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 12.99/2.63 thf(subsetE2_type, type, subsetE2: $o).
% 12.99/2.63 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 12.99/2.63 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 12.99/2.63 thf(beta2_type, type, beta2: $o).
% 12.99/2.63 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 12.99/2.63 thf(setextsub_type, type, setextsub: $o).
% 12.99/2.63 thf(binunionLsub_type, type, binunionLsub: $o).
% 12.99/2.63 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 12.99/2.63 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 12.99/2.63 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 12.99/2.63 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 12.99/2.63 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 12.99/2.63 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 12.99/2.63 thf(setunionE_type, type, setunionE: $o).
% 12.99/2.63 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 12.99/2.63 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 12.99/2.63 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 12.99/2.63 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 12.99/2.63 thf(binunionIR_type, type, binunionIR: $o).
% 12.99/2.63 thf(theeq_type, type, theeq: $o).
% 12.99/2.63 thf(sk__41_type, type, sk__41: $i).
% 12.99/2.63 thf(setadjoinE_type, type, setadjoinE: $o).
% 12.99/2.63 thf(sk__43_type, type, sk__43: $i > $i > $i).
% 12.99/2.63 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 12.99/2.63 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 12.99/2.63 thf(ap2p_type, type, ap2p: $o).
% 12.99/2.63 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 12.99/2.63 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 12.99/2.63 thf(exuE1_type, type, exuE1: $o).
% 12.99/2.63 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 12.99/2.63 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 12.99/2.63 thf(setminusLsub_type, type, setminusLsub: $o).
% 12.99/2.63 thf(funcextLem_type, type, funcextLem: $o).
% 12.99/2.63 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 12.99/2.63 thf(notinsingleton_type, type, notinsingleton: $o).
% 12.99/2.63 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 12.99/2.63 thf(exuEu_type, type, exuEu: $o).
% 12.99/2.63 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 12.99/2.63 thf(upairsetE_type, type, upairsetE: $o).
% 12.99/2.63 thf(omega0Ax_type, type, omega0Ax: $o).
% 12.99/2.63 thf(subsetTI_type, type, subsetTI: $o).
% 12.99/2.63 thf(notsubsetI_type, type, notsubsetI: $o).
% 12.99/2.63 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 12.99/2.63 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 12.99/2.63 thf(setextAx_type, type, setextAx: $o).
% 12.99/2.63 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 12.99/2.63 thf(powersetE1_type, type, powersetE1: $o).
% 12.99/2.63 thf(bs114d_type, type, bs114d: $o).
% 12.99/2.63 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 12.99/2.63 thf(ifp_type, type, ifp: $o).
% 12.99/2.63 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 12.99/2.63 thf(subsetI1_type, type, subsetI1: $o).
% 12.99/2.63 thf(symdiffE_type, type, symdiffE: $o).
% 12.99/2.63 thf(descrp_type, type, descrp: $o).
% 12.99/2.63 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 12.99/2.63 thf(foundationAx_type, type, foundationAx: $o).
% 12.99/2.63 thf(emptysetAx_type, type, emptysetAx: $o).
% 12.99/2.63 thf(emptyI_type, type, emptyI: $o).
% 12.99/2.63 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 12.99/2.63 thf(eta2_type, type, eta2: $o).
% 12.99/2.63 thf(binintersectEL_type, type, binintersectEL: $o).
% 12.99/2.63 thf(emptyE1_type, type, emptyE1: $o).
% 12.99/2.63 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 12.99/2.63 thf(vacuousDall_type, type, vacuousDall: $o).
% 12.99/2.63 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 12.99/2.63 thf(binintersectI_type, type, binintersectI: $o).
% 12.99/2.63 thf(funcext_type, type, funcext: $o).
% 12.99/2.63 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 12.99/2.63 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 12.99/2.63 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 12.99/2.63 thf(brelnall2_type, type, brelnall2: $o).
% 12.99/2.63 thf(setextT_type, type, setextT: $o).
% 12.99/2.63 thf(ex1I2_type, type, ex1I2: $o).
% 12.99/2.63 thf(symdiffI1_type, type, symdiffI1: $o).
% 12.99/2.63 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 12.99/2.63 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 12.99/2.63 thf(theprop_type, type, theprop: $o).
% 12.99/2.63 thf(subsetI2_type, type, subsetI2: $o).
% 12.99/2.63 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 12.99/2.63 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 12.99/2.63 thf(setminusERneg_type, type, setminusERneg: $o).
% 12.99/2.63 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 12.99/2.63 thf(omega__Cong_type, type, omega__Cong: $o).
% 12.99/2.63 thf(subsetRefl_type, type, subsetRefl: $o).
% 12.99/2.63 thf(uniqinunit_type, type, uniqinunit: $o).
% 12.99/2.63 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 12.99/2.63 thf(prop2setE_type, type, prop2setE: $o).
% 12.99/2.63 thf(binunionEcases_type, type, binunionEcases: $o).
% 12.99/2.63 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 12.99/2.63 thf(nonemptyI_type, type, nonemptyI: $o).
% 12.99/2.63 thf(app_type, type, app: $o).
% 12.99/2.63 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 12.99/2.63 thf(sk__40_type, type, sk__40: $i).
% 12.99/2.63 thf(exuE3u_type, type, exuE3u: $o).
% 12.99/2.63 thf(eta1_type, type, eta1: $o).
% 12.99/2.63 thf(setminusEL_type, type, setminusEL: $o).
% 12.99/2.63 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 12.99/2.63 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 12.99/2.63 thf(sepSubset_type, type, sepSubset: $o).
% 12.99/2.63 thf(upairset2E_type, type, upairset2E: $o).
% 12.99/2.63 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 12.99/2.63 thf(exuI3_type, type, exuI3: $o).
% 12.99/2.63 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 12.99/2.63 thf(apProp_type, type, apProp: $o).
% 12.99/2.63 thf(notdallE_type, type, notdallE: $o).
% 12.99/2.63 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 12.99/2.63 thf(binintersectER_type, type, binintersectER: $o).
% 12.99/2.63 thf(brelnall1_type, type, brelnall1: $o).
% 12.99/2.63 thf(powerset_type, type, powerset: $i > $i).
% 12.99/2.63 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 12.99/2.63 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 12.99/2.63 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 12.99/2.63 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 12.99/2.63 thf(exu__Cong_type, type, exu__Cong: $o).
% 12.99/2.63 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 12.99/2.63 thf(secondinupair_type, type, secondinupair: $o).
% 12.99/2.63 thf(singletonprop_type, type, singletonprop: $o).
% 12.99/2.63 thf(singletonsubset_type, type, singletonsubset: $o).
% 12.99/2.63 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 12.99/2.63 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 12.99/2.63 thf(replAx_type, type, replAx: $o).
% 12.99/2.63 thf(upairequniteq_type, type, upairequniteq: $o).
% 12.99/2.63 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 12.99/2.63 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 12.99/2.63 thf(setukpairIL_type, type, setukpairIL: $o).
% 12.99/2.63 thf(setunionE2_type, type, setunionE2: $o).
% 12.99/2.63 thf(inPowerset_type, type, inPowerset: $o).
% 12.99/2.63 thf(iffalse_type, type, iffalse: $o).
% 12.99/2.63 thf(funcext2_type, type, funcext2: $o).
% 12.99/2.63 thf(subset_type, type, subset: $i > $i > $o).
% 12.99/2.63 thf(subbreln_type, type, subbreln: $o).
% 12.99/2.63 thf(in__Cong_type, type, in__Cong: $o).
% 12.99/2.63 thf(binunionRsub_type, type, binunionRsub: $o).
% 12.99/2.63 thf(subset2powerset_type, type, subset2powerset: $o).
% 12.99/2.63 thf(subsetTI, axiom, subsetTI =
% 12.99/2.63 (![A:$i,X:$i]:
% 12.99/2.63 ( ( in @ X @ ( powerset @ A ) ) =>
% 12.99/2.63 ( ![Y:$i]:
% 12.99/2.63 ( ( in @ Y @ ( powerset @ A ) ) =>
% 12.99/2.63 ( ( ![Xx:$i]:
% 12.99/2.63 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 12.99/2.63 ( subset @ X @ Y ) ) ) ) ))).
% 12.99/2.63 thf('0', plain,
% 12.99/2.63 (( subsetTI ) =
% 12.99/2.63 ( ![X4:$i,X6:$i]:
% 12.99/2.63 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 12.99/2.63 ( ![X8:$i]:
% 12.99/2.63 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 12.99/2.63 ( ( ![X10:$i]:
% 12.99/2.63 ( ( in @ X10 @ X4 ) =>
% 12.99/2.63 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 12.99/2.63 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 12.99/2.63 define([status(thm)])).
% 12.99/2.63 thf(setextT, axiom, setextT =
% 12.99/2.63 (![A:$i,X:$i]:
% 12.99/2.63 ( ( in @ X @ ( powerset @ A ) ) =>
% 12.99/2.63 ( ![Y:$i]:
% 12.99/2.63 ( ( in @ Y @ ( powerset @ A ) ) =>
% 12.99/2.63 ( ( ![Xx:$i]:
% 12.99/2.63 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 12.99/2.63 ( ( ![Xx:$i]:
% 12.99/2.63 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 12.99/2.63 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 12.99/2.63 thf('1', plain,
% 12.99/2.63 (( setextT ) =
% 12.99/2.63 ( ![X4:$i,X6:$i]:
% 12.99/2.63 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 12.99/2.63 ( ![X8:$i]:
% 12.99/2.63 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 12.99/2.63 ( ( ![X10:$i]:
% 12.99/2.63 ( ( in @ X10 @ X4 ) =>
% 12.99/2.63 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 12.99/2.63 ( ( ![X12:$i]:
% 12.99/2.63 ( ( in @ X12 @ X4 ) =>
% 12.99/2.63 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 12.99/2.63 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 12.99/2.63 define([status(thm)])).
% 12.99/2.63 thf(powersetT_lem, axiom, powersetT_lem =
% 12.99/2.63 (![A:$i,X:$i]:
% 12.99/2.63 ( ( in @ X @ ( powerset @ A ) ) =>
% 12.99/2.63 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 12.99/2.63 thf('2', plain,
% 12.99/2.63 (( powersetT_lem ) =
% 12.99/2.63 ( ![X4:$i,X6:$i]:
% 12.99/2.63 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 12.99/2.63 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 12.99/2.63 define([status(thm)])).
% 12.99/2.63 thf(singletoninpowerset, axiom, singletoninpowerset =
% 12.99/2.63 (![A:$i,Xx:$i]:
% 12.99/2.63 ( ( in @ Xx @ A ) =>
% 12.99/2.63 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 12.99/2.63 thf('3', plain,
% 12.99/2.63 (( singletoninpowerset ) =
% 12.99/2.63 ( ![X4:$i,X6:$i]:
% 12.99/2.63 ( ( in @ X6 @ X4 ) =>
% 12.99/2.63 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 12.99/2.63 define([status(thm)])).
% 12.99/2.63 thf(powersetsubset, axiom, powersetsubset =
% 12.99/2.63 (![A:$i,B:$i]:
% 12.99/2.63 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 12.99/2.63 thf('4', plain,
% 12.99/2.63 (( powersetsubset ) =
% 12.99/2.63 ( ![X4:$i,X6:$i]:
% 12.99/2.63 ( ( subset @ X4 @ X6 ) =>
% 12.99/2.63 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 12.99/2.63 define([status(thm)])).
% 12.99/2.63 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 12.99/2.63 thf('5', plain,
% 12.99/2.63 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 12.99/2.63 define([status(thm)])).
% 12.99/2.63 thf(powersetE1, axiom, powersetE1 =
% 12.99/2.63 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 12.99/2.63 thf('6', plain,
% 12.99/2.63 (( powersetE1 ) =
% 12.99/2.63 ( ![X4:$i,X6:$i]:
% 12.99/2.63 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 12.99/2.63 define([status(thm)])).
% 12.99/2.63 thf(powersetI1, axiom, powersetI1 =
% 12.99/2.63 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 12.99/2.63 thf('7', plain,
% 12.99/2.63 (( powersetI1 ) =
% 12.99/2.63 ( ![X4:$i,X6:$i]:
% 12.99/2.63 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 12.99/2.63 define([status(thm)])).
% 12.99/2.63 thf(subset2powerset, axiom, subset2powerset =
% 12.99/2.63 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 12.99/2.63 thf('8', plain,
% 12.99/2.63 (( subset2powerset ) =
% 12.99/2.63 ( ![X4:$i,X6:$i]:
% 12.99/2.63 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 12.99/2.63 define([status(thm)])).
% 12.99/2.63 thf(powerset__Cong, axiom, powerset__Cong =
% 12.99/2.63 (![A:$i,B:$i]:
% 12.99/2.63 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 12.99/2.63 thf('9', plain,
% 12.99/2.63 (( powerset__Cong ) =
% 12.99/2.63 ( ![X4:$i,X6:$i]:
% 12.99/2.63 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 12.99/2.63 define([status(thm)])).
% 12.99/2.63 thf(powersetE, axiom, powersetE =
% 12.99/2.63 (![A:$i,B:$i,Xx:$i]:
% 12.99/2.63 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 12.99/2.63 thf('10', plain,
% 12.99/2.63 (( powersetE ) =
% 12.99/2.63 ( ![X4:$i,X6:$i,X8:$i]:
% 12.99/2.63 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 12.99/2.63 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 12.99/2.63 define([status(thm)])).
% 12.99/2.63 thf(emptyInPowerset, axiom, emptyInPowerset =
% 12.99/2.63 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 12.99/2.63 thf('11', plain,
% 12.99/2.63 (( emptyInPowerset ) =
% 12.99/2.63 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 12.99/2.63 define([status(thm)])).
% 12.99/2.63 thf(emptyinPowerset, axiom, emptyinPowerset =
% 12.99/2.63 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 12.99/2.63 thf('12', plain,
% 12.99/2.63 (( emptyinPowerset ) =
% 12.99/2.63 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 12.99/2.63 define([status(thm)])).
% 12.99/2.63 thf(powersetI, axiom, powersetI =
% 12.99/2.63 (![A:$i,B:$i]:
% 12.99/2.63 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 12.99/2.63 ( in @ B @ ( powerset @ A ) ) ))).
% 12.99/2.63 thf('13', plain,
% 12.99/2.63 (( powersetI ) =
% 12.99/2.63 ( ![X4:$i,X6:$i]:
% 12.99/2.63 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 12.99/2.63 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 12.99/2.63 define([status(thm)])).
% 12.99/2.63 thf(powersetAx, axiom, powersetAx =
% 12.99/2.63 (![A:$i,B:$i]:
% 12.99/2.63 ( ( in @ B @ ( powerset @ A ) ) <=>
% 12.99/2.63 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 12.99/2.63 thf('14', plain,
% 12.99/2.63 (( powersetAx ) =
% 12.99/2.63 ( ![X4:$i,X6:$i]:
% 12.99/2.63 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 12.99/2.63 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 12.99/2.63 define([status(thm)])).
% 12.99/2.63 thf(powersetTI1, conjecture,
% 12.99/2.63 (( setextAx ) =>
% 12.99/2.63 ( ( emptysetAx ) =>
% 12.99/2.63 ( ( setadjoinAx ) =>
% 12.99/2.63 ( ( powersetAx ) =>
% 12.99/2.63 ( ( setunionAx ) =>
% 12.99/2.63 ( ( omega0Ax ) =>
% 12.99/2.63 ( ( omegaSAx ) =>
% 12.99/2.63 ( ( omegaIndAx ) =>
% 12.99/2.63 ( ( replAx ) =>
% 12.99/2.63 ( ( foundationAx ) =>
% 12.99/2.63 ( ( wellorderingAx ) =>
% 12.99/2.63 ( ( descrp ) =>
% 12.99/2.63 ( ( dsetconstrI ) =>
% 12.99/2.63 ( ( dsetconstrEL ) =>
% 12.99/2.63 ( ( dsetconstrER ) =>
% 12.99/2.63 ( ( exuE1 ) =>
% 12.99/2.63 ( ( prop2setE ) =>
% 12.99/2.63 ( ( emptysetE ) =>
% 12.99/2.63 ( ( emptysetimpfalse ) =>
% 12.99/2.63 ( ( notinemptyset ) =>
% 12.99/2.63 ( ( exuE3e ) =>
% 12.99/2.63 ( ( setext ) =>
% 12.99/2.63 ( ( emptyI ) =>
% 12.99/2.63 ( ( noeltsimpempty ) =>
% 12.99/2.63 ( ( setbeta ) =>
% 12.99/2.63 ( ( nonemptyE1 ) =>
% 12.99/2.63 ( ( nonemptyI ) =>
% 12.99/2.63 ( ( nonemptyI1 ) =>
% 12.99/2.63 ( ( setadjoinIL ) =>
% 12.99/2.63 ( ( emptyinunitempty ) =>
% 12.99/2.63 ( ( setadjoinIR ) =>
% 12.99/2.63 ( ( setadjoinE ) =>
% 12.99/2.63 ( (
% 12.99/2.63 setadjoinOr ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setoftrueEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 powersetI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 emptyinPowerset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 emptyInPowerset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 powersetE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunionI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunionE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subPowSU ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuE2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 nonemptyImpWitness ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 uniqinunit ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notinsingleton ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 eqinunit ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 singletonsswitch ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairsetE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairsetIL ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairsetIR ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 emptyE1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 vacuousDall ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 quantDeMorgan1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 quantDeMorgan2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 quantDeMorgan3 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 quantDeMorgan4 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 prop2setI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 prop2set2propI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notdexE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notdallE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuI1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuI3 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuI2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 inCongP ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuE3u ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exu__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 emptyset__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setadjoin__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 powerset__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunion__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 omega__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuEu ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 descr__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 dsetconstr__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetI1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 eqimpsubset2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 eqimpsubset1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetI2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 emptysetsubset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetE2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notsubsetI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notequalI1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notequalI2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetRefl ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetTrans ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setadjoinSub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setadjoinSub2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subset2powerset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setextsub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetemptysetimpeq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 powersetI1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 powersetE1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 inPowerset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 powersetsubset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 sepInPowerset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 sepSubset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binunionIL ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairset2IR ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binunionIR ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binunionEcases ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binunionE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binunionLsub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binunionRsub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectSubset5 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectEL ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectLsub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectSubset2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectSubset3 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectER ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 disjointsetsI1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectRsub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectSubset4 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectSubset1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 bs114d ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusEL ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusER ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusSubset2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusERneg ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusELneg ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusILneg ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusIRneg ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusLsub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusSubset1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 symdiffE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 symdiffI1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 symdiffI2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 symdiffIneg1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 symdiffIneg2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 secondinupair ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairIL ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairIR ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 kpairiskpair ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 kpairp ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 singletonsubset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 singletoninpowerset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 singletoninpowunion ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairset2E ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairsubunion ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairinpowunion ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ubforcartprodlem1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ubforcartprodlem2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ubforcartprodlem3 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodpairin ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodmempair1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodmempair ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunionE2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunionsingleton1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunionsingleton2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunionsingleton ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 singletonprop ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ex1E1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ex1I ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ex1I2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 singletonsuniq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairinjL1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 kfstsingleton ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 theprop ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 kfstpairEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodfstin ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairinjL2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairinjL ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairinjR11 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairinjR12 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairinjR1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairequniteq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairinjR2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairinjR ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ksndsingleton ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ksndpairEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 kpairsurjEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodsndin ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodpairmemEL ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodpairmemER ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodmempaircEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodfstpairEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodsndpairEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodpairsurjEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 dpsetconstrI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 dpsetconstrSub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setOfPairsIsBReln ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 dpsetconstrERa ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 dpsetconstrEL1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 dpsetconstrEL2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 dpsetconstrER ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcImageSingleton ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 apProp ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 app ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 infuncsetfunc ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ap2p ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcinfuncset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 lamProp ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 lamp ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 lam2p ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 brelnall1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 brelnall2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ex1E2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcGraphProp1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcGraphProp3 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcGraphProp2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcextLem ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcGraphProp4 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subbreln ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 eqbreln ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcext ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcext2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ap2apEq1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ap2apEq2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 beta1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 eta1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 lam2lamEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 beta2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 eta2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 iffalseProp1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 iffalseProp2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 iftrueProp1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 iftrueProp2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ifSingleton ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ifp ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 theeq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 iftrue ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 iffalse ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 iftrueorfalse ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectT_lem ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binunionT_lem ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 powersetT_lem ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusT_lem ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 complementT_lem ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setextT ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetTI ) =>
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 A:$i,X:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 A ) ) =>
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 Y:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 Y @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 A ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 Xx:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 Xx @ A ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 Xx @ X ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 Xx @ Y ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 12.99/2.63 thf(zf_stmt_0, conjecture,
% 12.99/2.63 (( setextAx ) =>
% 12.99/2.63 ( ( emptysetAx ) =>
% 12.99/2.63 ( ( setadjoinAx ) =>
% 12.99/2.63 ( ( ![X4:$i,X6:$i]:
% 12.99/2.63 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 12.99/2.63 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 12.99/2.63 ( ( setunionAx ) =>
% 12.99/2.63 ( ( omega0Ax ) =>
% 12.99/2.63 ( ( omegaSAx ) =>
% 12.99/2.63 ( ( omegaIndAx ) =>
% 12.99/2.63 ( ( replAx ) =>
% 12.99/2.63 ( ( foundationAx ) =>
% 12.99/2.63 ( ( wellorderingAx ) =>
% 12.99/2.63 ( ( descrp ) =>
% 12.99/2.63 ( ( dsetconstrI ) =>
% 12.99/2.63 ( ( dsetconstrEL ) =>
% 12.99/2.63 ( ( dsetconstrER ) =>
% 12.99/2.63 ( ( exuE1 ) =>
% 12.99/2.63 ( ( prop2setE ) =>
% 12.99/2.63 ( ( emptysetE ) =>
% 12.99/2.63 ( ( emptysetimpfalse ) =>
% 12.99/2.63 ( ( notinemptyset ) =>
% 12.99/2.63 ( ( exuE3e ) =>
% 12.99/2.63 ( ( setext ) =>
% 12.99/2.63 ( ( emptyI ) =>
% 12.99/2.63 ( ( noeltsimpempty ) =>
% 12.99/2.63 ( ( setbeta ) =>
% 12.99/2.63 ( ( nonemptyE1 ) =>
% 12.99/2.63 ( ( nonemptyI ) =>
% 12.99/2.63 ( ( nonemptyI1 ) =>
% 12.99/2.63 ( ( setadjoinIL ) =>
% 12.99/2.63 ( ( emptyinunitempty ) =>
% 12.99/2.63 ( ( setadjoinIR ) =>
% 12.99/2.63 ( ( setadjoinE ) =>
% 12.99/2.63 ( (
% 12.99/2.63 setadjoinOr ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setoftrueEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X10:$i,
% 12.99/2.63 X12:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X14:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X14 @ X12 ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X14 @ X10 ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X12 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X10 ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X16:$i]:
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 emptyset @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X16 ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X18:$i]:
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 emptyset @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X18 ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X20:$i,
% 12.99/2.63 X22:$i,
% 12.99/2.63 X24:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X22 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X20 ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X24 @ X22 ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X24 @ X20 ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunionI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunionE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subPowSU ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuE2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 nonemptyImpWitness ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 uniqinunit ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notinsingleton ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 eqinunit ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 singletonsswitch ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairsetE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairsetIL ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairsetIR ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 emptyE1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 vacuousDall ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 quantDeMorgan1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 quantDeMorgan2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 quantDeMorgan3 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 quantDeMorgan4 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 prop2setI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 prop2set2propI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notdexE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notdallE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuI1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuI3 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuI2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 inCongP ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuE3u ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exu__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 emptyset__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setadjoin__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X26:$i,
% 12.99/2.63 X28:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 X26 ) =
% 12.99/2.63 (
% 12.99/2.63 X28 ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X26 ) =
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X28 ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunion__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 omega__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuEu ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 descr__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 dsetconstr__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetI1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 eqimpsubset2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 eqimpsubset1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetI2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 emptysetsubset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetE2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notsubsetI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notequalI1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notequalI2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetRefl ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetTrans ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setadjoinSub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setadjoinSub2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X30:$i,
% 12.99/2.63 X32:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subset @
% 12.99/2.63 X30 @ X32 ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X30 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X32 ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setextsub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetemptysetimpeq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X34:$i,
% 12.99/2.63 X36:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subset @
% 12.99/2.63 X36 @ X34 ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X36 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X34 ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X38:$i,
% 12.99/2.63 X40:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X40 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X38 ) ) =>
% 12.99/2.63 (
% 12.99/2.63 subset @
% 12.99/2.63 X40 @ X38 ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X42:$i]:
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X42 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X42 ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X44:$i,
% 12.99/2.63 X46:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subset @
% 12.99/2.63 X44 @ X46 ) =>
% 12.99/2.63 (
% 12.99/2.63 subset @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X44 ) @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X46 ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 sepInPowerset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 sepSubset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binunionIL ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairset2IR ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binunionIR ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binunionEcases ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binunionE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binunionLsub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binunionRsub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectSubset5 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectEL ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectLsub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectSubset2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectSubset3 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectER ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 disjointsetsI1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectRsub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectSubset4 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectSubset1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 bs114d ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusEL ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusER ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusSubset2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusERneg ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusELneg ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusILneg ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusIRneg ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusLsub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusSubset1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 symdiffE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 symdiffI1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 symdiffI2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 symdiffIneg1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 symdiffIneg2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 secondinupair ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairIL ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairIR ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 kpairiskpair ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 kpairp ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 singletonsubset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X48:$i,
% 12.99/2.63 X50:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X50 @ X48 ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 (
% 12.99/2.63 setadjoin
% 12.99/2.63 @
% 12.99/2.63 X50 @
% 12.99/2.63 emptyset ) @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X48 ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 singletoninpowunion ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairset2E ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairsubunion ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairinpowunion ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ubforcartprodlem1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ubforcartprodlem2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ubforcartprodlem3 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodpairin ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodmempair1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodmempair ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunionE2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunionsingleton1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunionsingleton2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunionsingleton ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 singletonprop ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ex1E1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ex1I ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ex1I2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 singletonsuniq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairinjL1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 kfstsingleton ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 theprop ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 kfstpairEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodfstin ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairinjL2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairinjL ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairinjR11 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairinjR12 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairinjR1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairequniteq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairinjR2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setukpairinjR ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ksndsingleton ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ksndpairEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 kpairsurjEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodsndin ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodpairmemEL ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodpairmemER ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodmempaircEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodfstpairEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodsndpairEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 cartprodpairsurjEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 dpsetconstrI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 dpsetconstrSub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setOfPairsIsBReln ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 dpsetconstrERa ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 dpsetconstrEL1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 dpsetconstrEL2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 dpsetconstrER ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcImageSingleton ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 apProp ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 app ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 infuncsetfunc ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ap2p ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcinfuncset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 lamProp ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 lamp ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 lam2p ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 brelnall1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 brelnall2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ex1E2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcGraphProp1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcGraphProp3 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcGraphProp2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcextLem ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcGraphProp4 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subbreln ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 eqbreln ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcext ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 funcext2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ap2apEq1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ap2apEq2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 beta1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 eta1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 lam2lamEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 beta2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 eta2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 iffalseProp1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 iffalseProp2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 iftrueProp1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 iftrueProp2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ifSingleton ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ifp ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 theeq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 iftrue ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 iffalse ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 iftrueorfalse ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binintersectT_lem ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 binunionT_lem ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X52:$i,
% 12.99/2.63 X54:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X54 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X52 ) ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X54 ) @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X52 ) ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setminusT_lem ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 complementT_lem ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X56:$i,
% 12.99/2.63 X58:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X58 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X56 ) ) =>
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X60:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X60 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X56 ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X62:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X62 @ X56 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X62 @ X58 ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X62 @ X60 ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X64:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X64 @ X56 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X64 @ X60 ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X64 @ X58 ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 X58 ) =
% 12.99/2.63 (
% 12.99/2.63 X60 ) ) ) ) ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X66:$i,
% 12.99/2.63 X68:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X68 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X66 ) ) =>
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X70:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X70 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X66 ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X72:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X72 @ X66 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X72 @ X68 ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X72 @ X70 ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 subset @
% 12.99/2.63 X68 @ X70 ) ) ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X74:$i,
% 12.99/2.63 X76:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X76 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X74 ) ) =>
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X78:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X78 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X74 ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X80:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X80 @ X74 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X80 @ X76 ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X80 @ X78 ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X76 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X78 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 12.99/2.63 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 12.99/2.63 thf(zf_stmt_2, axiom,
% 12.99/2.63 (![X8:$i,X6:$i,X4:$i]:
% 12.99/2.63 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 12.99/2.63 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 12.99/2.63 thf(zf_stmt_3, conjecture,
% 12.99/2.63 (( setextAx ) =>
% 12.99/2.63 ( ( emptysetAx ) =>
% 12.99/2.63 ( ( setadjoinAx ) =>
% 12.99/2.63 ( ( ![X4:$i,X6:$i]:
% 12.99/2.63 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 12.99/2.63 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 12.99/2.63 ( ( setunionAx ) =>
% 12.99/2.63 ( ( omega0Ax ) =>
% 12.99/2.63 ( ( omegaSAx ) =>
% 12.99/2.63 ( ( omegaIndAx ) =>
% 12.99/2.63 ( ( replAx ) =>
% 12.99/2.63 ( ( foundationAx ) =>
% 12.99/2.63 ( ( wellorderingAx ) =>
% 12.99/2.63 ( ( descrp ) =>
% 12.99/2.63 ( ( dsetconstrI ) =>
% 12.99/2.63 ( ( dsetconstrEL ) =>
% 12.99/2.63 ( ( dsetconstrER ) =>
% 12.99/2.63 ( ( exuE1 ) =>
% 12.99/2.63 ( ( prop2setE ) =>
% 12.99/2.63 ( ( emptysetE ) =>
% 12.99/2.63 ( ( emptysetimpfalse ) =>
% 12.99/2.63 ( ( notinemptyset ) =>
% 12.99/2.63 ( ( exuE3e ) =>
% 12.99/2.63 ( ( setext ) =>
% 12.99/2.63 ( ( emptyI ) =>
% 12.99/2.63 ( ( noeltsimpempty ) =>
% 12.99/2.63 ( ( setbeta ) =>
% 12.99/2.63 ( ( nonemptyE1 ) =>
% 12.99/2.63 ( ( nonemptyI ) =>
% 12.99/2.63 ( ( nonemptyI1 ) =>
% 12.99/2.63 ( ( setadjoinIL ) =>
% 12.99/2.63 ( ( emptyinunitempty ) =>
% 12.99/2.63 ( ( setadjoinIR ) =>
% 12.99/2.63 ( ( setadjoinE ) =>
% 12.99/2.63 ( (
% 12.99/2.63 setadjoinOr ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setoftrueEq ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X10:$i,
% 12.99/2.63 X12:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X14:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X14 @ X12 ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X14 @ X10 ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X12 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X10 ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X16:$i]:
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 emptyset @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X16 ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X18:$i]:
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 emptyset @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X18 ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X20:$i,
% 12.99/2.63 X22:$i,
% 12.99/2.63 X24:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X22 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X20 ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X24 @ X22 ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X24 @ X20 ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunionI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunionE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subPowSU ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuE2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 nonemptyImpWitness ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 uniqinunit ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notinsingleton ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 eqinunit ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 singletonsswitch ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairsetE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairsetIL ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 upairsetIR ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 emptyE1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 vacuousDall ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 quantDeMorgan1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 quantDeMorgan2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 quantDeMorgan3 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 quantDeMorgan4 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 prop2setI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 prop2set2propI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notdexE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notdallE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuI1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuI3 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuI2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 inCongP ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 in__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuE3u ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exu__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 emptyset__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setadjoin__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X26:$i,
% 12.99/2.63 X28:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 X26 ) =
% 12.99/2.63 (
% 12.99/2.63 X28 ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X26 ) =
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X28 ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setunion__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 omega__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 exuEu ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 descr__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 dsetconstr__Cong ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetI1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 eqimpsubset2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 eqimpsubset1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetI2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 emptysetsubset ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetE ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetE2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notsubsetI ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notequalI1 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 notequalI2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetRefl ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subsetTrans ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setadjoinSub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setadjoinSub2 ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 ![
% 12.99/2.63 X30:$i,
% 12.99/2.63 X32:$i]:
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 subset @
% 12.99/2.63 X30 @ X32 ) =>
% 12.99/2.63 (
% 12.99/2.63 in @
% 12.99/2.63 X30 @
% 12.99/2.63 (
% 12.99/2.63 powerset @
% 12.99/2.63 X32 ) ) ) ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.63 setextsub ) =>
% 12.99/2.63 (
% 12.99/2.63 (
% 12.99/2.64 subsetemptysetimpeq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X34:$i,
% 12.99/2.64 X36:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 subset @
% 12.99/2.64 X36 @ X34 ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X36 @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 X34 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X38:$i,
% 12.99/2.64 X40:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X40 @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 X38 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 subset @
% 12.99/2.64 X40 @ X38 ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X42:$i]:
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X42 @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 X42 ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X44:$i,
% 12.99/2.64 X46:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 subset @
% 12.99/2.64 X44 @ X46 ) =>
% 12.99/2.64 (
% 12.99/2.64 subset @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 X44 ) @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 X46 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 sepInPowerset ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 sepSubset ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binunionIL ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 upairset2IR ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binunionIR ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binunionEcases ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binunionE ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binunionLsub ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binunionRsub ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectI ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectSubset5 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectEL ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectLsub ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectSubset2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectSubset3 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectER ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 disjointsetsI1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectRsub ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectSubset4 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectSubset1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 bs114d ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusI ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusEL ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusER ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusSubset2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusERneg ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusELneg ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusILneg ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusIRneg ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusLsub ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusSubset1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 symdiffE ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 symdiffI1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 symdiffI2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 symdiffIneg1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 symdiffIneg2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 secondinupair ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairIL ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairIR ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 kpairiskpair ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 kpairp ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 singletonsubset ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X48:$i,
% 12.99/2.64 X50:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X50 @ X48 ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 (
% 12.99/2.64 setadjoin
% 12.99/2.64 @
% 12.99/2.64 X50 @
% 12.99/2.64 emptyset ) @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 X48 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 singletoninpowunion ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 upairset2E ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 upairsubunion ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 upairinpowunion ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ubforcartprodlem1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ubforcartprodlem2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ubforcartprodlem3 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodpairin ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodmempair1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodmempair ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setunionE2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setunionsingleton1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setunionsingleton2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setunionsingleton ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 singletonprop ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ex1E1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ex1I ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ex1I2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 singletonsuniq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairinjL1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 kfstsingleton ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 theprop ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 kfstpairEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodfstin ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairinjL2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairinjL ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairinjR11 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairinjR12 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairinjR1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 upairequniteq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairinjR2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairinjR ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ksndsingleton ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ksndpairEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 kpairsurjEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodsndin ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodpairmemEL ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodpairmemER ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodmempaircEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodfstpairEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodsndpairEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodpairsurjEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 dpsetconstrI ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 dpsetconstrSub ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setOfPairsIsBReln ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 dpsetconstrERa ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 dpsetconstrEL1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 dpsetconstrEL2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 dpsetconstrER ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcImageSingleton ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 apProp ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 app ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 infuncsetfunc ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ap2p ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcinfuncset ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 lamProp ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 lamp ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 lam2p ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 brelnall1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 brelnall2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ex1E2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcGraphProp1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcGraphProp3 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcGraphProp2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcextLem ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcGraphProp4 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 subbreln ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 eqbreln ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcext ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcext2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ap2apEq1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ap2apEq2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 beta1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 eta1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 lam2lamEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 beta2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 eta2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 iffalseProp1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 iffalseProp2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 iftrueProp1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 iftrueProp2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ifSingleton ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ifp ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 theeq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 iftrue ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 iffalse ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 iftrueorfalse ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectT_lem ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binunionT_lem ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X52:$i,
% 12.99/2.64 X54:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X54 @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 X52 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 X54 ) @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 X52 ) ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusT_lem ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 complementT_lem ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X56:$i,
% 12.99/2.64 X58:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X58 @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 X56 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X60:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X60 @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 X56 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X62:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X62 @ X56 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X62 @ X58 ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X62 @ X60 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X64:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X64 @ X56 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X64 @ X60 ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X64 @ X58 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 X58 ) =
% 12.99/2.64 (
% 12.99/2.64 X60 ) ) ) ) ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X66:$i,
% 12.99/2.64 X68:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X68 @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 X66 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X70:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X70 @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 X66 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X72:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X72 @ X66 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X72 @ X68 ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X72 @ X70 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 subset @
% 12.99/2.64 X68 @ X70 ) ) ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X74:$i,
% 12.99/2.64 X76:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X76 @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 X74 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X78:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X78 @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 X74 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X80:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X80 @ X74 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X80 @ X76 ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X80 @ X78 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X76 @
% 12.99/2.64 (
% 12.99/2.64 powerset @
% 12.99/2.64 X78 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 12.99/2.64 thf(zf_stmt_4, negated_conjecture,
% 12.99/2.64 (~( ( setextAx ) =>
% 12.99/2.64 ( ( emptysetAx ) =>
% 12.99/2.64 ( ( setadjoinAx ) =>
% 12.99/2.64 ( ( ![X4:$i,X6:$i]:
% 12.99/2.64 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 12.99/2.64 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 12.99/2.64 ( ( setunionAx ) =>
% 12.99/2.64 ( ( omega0Ax ) =>
% 12.99/2.64 ( ( omegaSAx ) =>
% 12.99/2.64 ( ( omegaIndAx ) =>
% 12.99/2.64 ( ( replAx ) =>
% 12.99/2.64 ( ( foundationAx ) =>
% 12.99/2.64 ( ( wellorderingAx ) =>
% 12.99/2.64 ( ( descrp ) =>
% 12.99/2.64 ( ( dsetconstrI ) =>
% 12.99/2.64 ( ( dsetconstrEL ) =>
% 12.99/2.64 ( ( dsetconstrER ) =>
% 12.99/2.64 ( ( exuE1 ) =>
% 12.99/2.64 ( ( prop2setE ) =>
% 12.99/2.64 ( ( emptysetE ) =>
% 12.99/2.64 ( ( emptysetimpfalse ) =>
% 12.99/2.64 ( ( notinemptyset ) =>
% 12.99/2.64 ( ( exuE3e ) =>
% 12.99/2.64 ( ( setext ) =>
% 12.99/2.64 ( ( emptyI ) =>
% 12.99/2.64 ( ( noeltsimpempty ) =>
% 12.99/2.64 ( ( setbeta ) =>
% 12.99/2.64 ( ( nonemptyE1 ) =>
% 12.99/2.64 ( ( nonemptyI ) =>
% 12.99/2.64 ( ( nonemptyI1 ) =>
% 12.99/2.64 ( ( setadjoinIL ) =>
% 12.99/2.64 ( ( emptyinunitempty ) =>
% 12.99/2.64 ( ( setadjoinIR ) =>
% 12.99/2.64 ( (
% 12.99/2.64 setadjoinE ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setadjoinOr ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setoftrueEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X10:$i,
% 12.99/2.64 X12:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X14:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X14 @ X12 ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X14 @ X10 ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X12 @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X10 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X16:$i]:
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 emptyset @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X16 ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X18:$i]:
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 emptyset @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X18 ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X20:$i,
% 12.99/2.64 X22:$i,
% 12.99/2.64 X24:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X22 @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X20 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X24 @ X22 ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X24 @ X20 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setunionI ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setunionE ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 subPowSU ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 exuE2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 nonemptyImpWitness ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 uniqinunit ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 notinsingleton ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 eqinunit ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 singletonsswitch ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 upairsetE ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 upairsetIL ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 upairsetIR ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 emptyE1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 vacuousDall ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 quantDeMorgan1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 quantDeMorgan2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 quantDeMorgan3 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 quantDeMorgan4 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 prop2setI ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 prop2set2propI ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 notdexE ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 notdallE ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 exuI1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 exuI3 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 exuI2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 inCongP ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in__Cong ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 exuE3u ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 exu__Cong ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 emptyset__Cong ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setadjoin__Cong ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X26:$i,
% 12.99/2.64 X28:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 X26 ) =
% 12.99/2.64 (
% 12.99/2.64 X28 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X26 ) =
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X28 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setunion__Cong ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 omega__Cong ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 exuEu ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 descr__Cong ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 dsetconstr__Cong ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 subsetI1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 eqimpsubset2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 eqimpsubset1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 subsetI2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 emptysetsubset ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 subsetE ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 subsetE2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 notsubsetI ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 notequalI1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 notequalI2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 subsetRefl ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 subsetTrans ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setadjoinSub ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setadjoinSub2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X30:$i,
% 12.99/2.64 X32:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 subset @
% 12.99/2.64 X30 @ X32 ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X30 @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X32 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setextsub ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 subsetemptysetimpeq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X34:$i,
% 12.99/2.64 X36:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 subset @
% 12.99/2.64 X36 @ X34 ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X36 @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X34 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X38:$i,
% 12.99/2.64 X40:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X40 @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X38 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 subset @
% 12.99/2.64 X40 @ X38 ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X42:$i]:
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X42 @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X42 ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X44:$i,
% 12.99/2.64 X46:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 subset @
% 12.99/2.64 X44 @ X46 ) =>
% 12.99/2.64 (
% 12.99/2.64 subset @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X44 ) @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X46 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 sepInPowerset ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 sepSubset ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binunionIL ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 upairset2IR ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binunionIR ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binunionEcases ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binunionE ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binunionLsub ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binunionRsub ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectI ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectSubset5 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectEL ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectLsub ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectSubset2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectSubset3 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectER ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 disjointsetsI1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectRsub ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectSubset4 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectSubset1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 bs114d ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusI ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusEL ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusER ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusSubset2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusERneg ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusELneg ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusILneg ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusIRneg ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusLsub ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusSubset1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 symdiffE ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 symdiffI1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 symdiffI2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 symdiffIneg1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 symdiffIneg2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 secondinupair ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairIL ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairIR ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 kpairiskpair ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 kpairp ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 singletonsubset ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X48:$i,
% 12.99/2.64 X50:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X50 @ X48 ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 (
% 12.99/2.64 setadjoin
% 12.99/2.64 @
% 12.99/2.64 X50 @
% 12.99/2.64 emptyset ) @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X48 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 singletoninpowunion ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 upairset2E ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 upairsubunion ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 upairinpowunion ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ubforcartprodlem1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ubforcartprodlem2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ubforcartprodlem3 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodpairin ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodmempair1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodmempair ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setunionE2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setunionsingleton1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setunionsingleton2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setunionsingleton ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 singletonprop ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ex1E1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ex1I ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ex1I2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 singletonsuniq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairinjL1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 kfstsingleton ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 theprop ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 kfstpairEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodfstin ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairinjL2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairinjL ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairinjR11 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairinjR12 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairinjR1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 upairequniteq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairinjR2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setukpairinjR ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ksndsingleton ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ksndpairEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 kpairsurjEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodsndin ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodpairmemEL ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodpairmemER ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodmempaircEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodfstpairEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodsndpairEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 cartprodpairsurjEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 dpsetconstrI ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 dpsetconstrSub ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setOfPairsIsBReln ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 dpsetconstrERa ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 dpsetconstrEL1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 dpsetconstrEL2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 dpsetconstrER ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcImageSingleton ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 apProp ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 app ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 infuncsetfunc ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ap2p ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcinfuncset ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 lamProp ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 lamp ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 lam2p ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 brelnall1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 brelnall2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ex1E2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcGraphProp1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcGraphProp3 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcGraphProp2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcextLem ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcGraphProp4 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 subbreln ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 eqbreln ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcext ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 funcext2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ap2apEq1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ap2apEq2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 beta1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 eta1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 lam2lamEq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 beta2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 eta2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 iffalseProp1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 iffalseProp2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 iftrueProp1 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 iftrueProp2 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ifSingleton ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ifp ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 theeq ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 iftrue ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 iffalse ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 iftrueorfalse ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binintersectT_lem ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 binunionT_lem ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X52:$i,
% 12.99/2.64 X54:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X54 @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X52 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X54 ) @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X52 ) ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 setminusT_lem ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 complementT_lem ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X56:$i,
% 12.99/2.64 X58:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X58 @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X56 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X60:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X60 @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X56 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X62:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X62 @ X56 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X62 @ X58 ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X62 @ X60 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X64:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X64 @ X56 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X64 @ X60 ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X64 @ X58 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 X58 ) =
% 12.99/2.64 (
% 12.99/2.64 X60 ) ) ) ) ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X66:$i,
% 12.99/2.64 X68:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X68 @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X66 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X70:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X70 @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X66 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X72:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X72 @ X66 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X72 @ X68 ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X72 @ X70 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 subset @
% 12.99/2.64 X68 @ X70 ) ) ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X74:$i,
% 12.99/2.64 X76:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X76 @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X74 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X78:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X78 @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X74 ) ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 ![
% 12.99/2.64 X80:$i]:
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X80 @ X74 ) =>
% 12.99/2.64 (
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X80 @ X76 ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X80 @ X78 ) ) ) ) =>
% 12.99/2.64 (
% 12.99/2.64 in @
% 12.99/2.64 X76 @
% 12.99/2.64 (
% 12.99/2.64 powerset
% 12.99/2.64 @
% 12.99/2.64 X78 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 12.99/2.64 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 12.99/2.64 thf(zip_derived_cl124, plain, (~ (in @ sk__40 @ (powerset @ sk__41))),
% 12.99/2.64 inference('cnf', [status(esa)], [zf_stmt_4])).
% 12.99/2.64 thf(zip_derived_cl21, plain,
% 12.99/2.64 (![X0 : $i, X1 : $i]:
% 12.99/2.64 ( (in @ X0 @ (powerset @ X1)) | (in @ (sk__43 @ X0 @ X1) @ X0))),
% 12.99/2.64 inference('cnf', [status(esa)], [zf_stmt_4])).
% 12.99/2.64 thf(zip_derived_cl125, plain,
% 12.99/2.64 (![X13 : $i]:
% 12.99/2.64 (~ (in @ X13 @ sk__40) | (in @ X13 @ sk__41) | ~ (in @ X13 @ sk__39))),
% 12.99/2.64 inference('cnf', [status(esa)], [zf_stmt_4])).
% 12.99/2.64 thf(zip_derived_cl20, plain,
% 12.99/2.64 (![X0 : $i, X1 : $i]:
% 12.99/2.64 ( (in @ X0 @ (powerset @ X1)) | ~ (in @ (sk__43 @ X0 @ X1) @ X1))),
% 12.99/2.64 inference('cnf', [status(esa)], [zf_stmt_4])).
% 12.99/2.64 thf(zip_derived_cl297, plain,
% 12.99/2.64 (![X0 : $i]:
% 12.99/2.64 (~ (in @ (sk__43 @ X0 @ sk__41) @ sk__39)
% 12.99/2.64 | ~ (in @ (sk__43 @ X0 @ sk__41) @ sk__40)
% 12.99/2.64 | (in @ X0 @ (powerset @ sk__41)))),
% 12.99/2.64 inference('sup-', [status(thm)], [zip_derived_cl125, zip_derived_cl20])).
% 12.99/2.64 thf(zip_derived_cl126, plain, ( (in @ sk__40 @ (powerset @ sk__39))),
% 12.99/2.64 inference('cnf', [status(esa)], [zf_stmt_4])).
% 12.99/2.64 thf(zip_derived_cl232, plain,
% 12.99/2.64 (![X25 : $i, X26 : $i, X27 : $i]:
% 12.99/2.64 (~ (in @ X25 @ (powerset @ X26))
% 12.99/2.64 | (in @ X27 @ X26)
% 12.99/2.64 | ~ (in @ X27 @ X25))),
% 12.99/2.64 inference('cnf', [status(esa)], [zf_stmt_4])).
% 12.99/2.64 thf(zip_derived_cl305, plain,
% 12.99/2.64 (![X0 : $i]: (~ (in @ X0 @ sk__40) | (in @ X0 @ sk__39))),
% 12.99/2.64 inference('sup-', [status(thm)], [zip_derived_cl126, zip_derived_cl232])).
% 12.99/2.64 thf(zip_derived_cl2974, plain,
% 12.99/2.64 (![X0 : $i]:
% 12.99/2.64 ( (in @ X0 @ (powerset @ sk__41))
% 12.99/2.64 | ~ (in @ (sk__43 @ X0 @ sk__41) @ sk__40))),
% 12.99/2.64 inference('clc', [status(thm)], [zip_derived_cl297, zip_derived_cl305])).
% 12.99/2.64 thf(zip_derived_cl2977, plain,
% 12.99/2.64 (( (in @ sk__40 @ (powerset @ sk__41))
% 12.99/2.64 | (in @ sk__40 @ (powerset @ sk__41)))),
% 12.99/2.64 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl2974])).
% 12.99/2.64 thf(zip_derived_cl2983, plain, ( (in @ sk__40 @ (powerset @ sk__41))),
% 12.99/2.64 inference('simplify', [status(thm)], [zip_derived_cl2977])).
% 12.99/2.64 thf(zip_derived_cl2987, plain, ($false),
% 12.99/2.64 inference('demod', [status(thm)], [zip_derived_cl124, zip_derived_cl2983])).
% 12.99/2.64
% 12.99/2.64 % SZS output end Refutation
% 12.99/2.64
% 12.99/2.64
% 12.99/2.64 % Terminating...
% 14.02/2.86 % Runner terminated.
% 14.02/2.88 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------