%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU735^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.suPZDZFZyM true
% Computer : n023.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 04:56:02 PM UTC 2025
% Result : Theorem 61.67s 9.51s
% Output : Refutation 61.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU735^1 : TPTP v9.2.0. Released v3.7.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.suPZDZFZyM true
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 1 16:13:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Running portfolio for 300 s
% 0.12/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % 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
% 0.53/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.53/0.73 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.53/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.53/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.53/0.74 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.53/0.75 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.54/0.81 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.54/0.86 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 61.67/9.51 % Solved by lams/40_c_ic.sh.
% 61.67/9.51 % done 3458 iterations in 8.646s
% 61.67/9.51 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 61.67/9.51 % SZS output start Refutation
% 61.67/9.51 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 61.67/9.51 thf(notdexE_type, type, notdexE: $o).
% 61.67/9.51 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 61.67/9.51 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 61.67/9.51 thf(setunionAx_type, type, setunionAx: $o).
% 61.67/9.51 thf(setminusELneg_type, type, setminusELneg: $o).
% 61.67/9.51 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 61.67/9.51 thf(ex1E1_type, type, ex1E1: $o).
% 61.67/9.51 thf(powersetE_type, type, powersetE: $o).
% 61.67/9.51 thf(omegaSAx_type, type, omegaSAx: $o).
% 61.67/9.51 thf(exuI1_type, type, exuI1: $o).
% 61.67/9.51 thf(exuI2_type, type, exuI2: $o).
% 61.67/9.51 thf(notequalI2_type, type, notequalI2: $o).
% 61.67/9.51 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 61.67/9.51 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 61.67/9.51 thf(upairsubunion_type, type, upairsubunion: $o).
% 61.67/9.51 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 61.67/9.51 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 61.67/9.51 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 61.67/9.51 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 61.67/9.51 thf(setminusILneg_type, type, setminusILneg: $o).
% 61.67/9.51 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 61.67/9.51 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 61.67/9.51 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 61.67/9.51 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 61.67/9.51 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 61.67/9.51 thf(iftrue_type, type, iftrue: $o).
% 61.67/9.51 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 61.67/9.51 thf(ifSingleton_type, type, ifSingleton: $o).
% 61.67/9.51 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 61.67/9.51 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 61.67/9.51 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 61.67/9.51 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 61.67/9.51 thf(lamProp_type, type, lamProp: $o).
% 61.67/9.51 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 61.67/9.51 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 61.67/9.51 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 61.67/9.51 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 61.67/9.51 thf(setukpairIR_type, type, setukpairIR: $o).
% 61.67/9.51 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 61.67/9.51 thf(lam2p_type, type, lam2p: $o).
% 61.67/9.51 thf(binunionE_type, type, binunionE: $o).
% 61.67/9.51 thf(setext_type, type, setext: $o).
% 61.67/9.51 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 61.67/9.51 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 61.67/9.51 thf(descr__Cong_type, type, descr__Cong: $o).
% 61.67/9.51 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 61.67/9.51 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 61.67/9.51 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 61.67/9.51 thf(eqbreln_type, type, eqbreln: $o).
% 61.67/9.51 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 61.67/9.51 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 61.67/9.51 $o).
% 61.67/9.51 thf(in_type, type, in: $i > $i > $o).
% 61.67/9.51 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 61.67/9.51 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 61.67/9.51 thf(complementT_lem_type, type, complementT_lem: $o).
% 61.67/9.51 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 61.67/9.51 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 61.67/9.51 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 61.67/9.51 thf(beta1_type, type, beta1: $o).
% 61.67/9.51 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 61.67/9.51 thf(powersetTE1_type, type, powersetTE1: $o).
% 61.67/9.51 thf(symdiffI2_type, type, symdiffI2: $o).
% 61.67/9.51 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 61.67/9.51 thf(upairset2IR_type, type, upairset2IR: $o).
% 61.67/9.51 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 61.67/9.51 thf(subsetE_type, type, subsetE: $o).
% 61.67/9.51 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 61.67/9.51 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 61.67/9.51 thf(setbeta_type, type, setbeta: $o).
% 61.67/9.51 thf(eqinunit_type, type, eqinunit: $o).
% 61.67/9.51 thf(upairsetIL_type, type, upairsetIL: $o).
% 61.67/9.51 thf(powersetI1_type, type, powersetI1: $o).
% 61.67/9.51 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 61.67/9.51 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 61.67/9.51 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 61.67/9.51 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 61.67/9.51 thf(powersetAx_type, type, powersetAx: $o).
% 61.67/9.51 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 61.67/9.51 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 61.67/9.51 thf(powersetI_type, type, powersetI: $o).
% 61.67/9.51 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 61.67/9.51 thf(upairsetIR_type, type, upairsetIR: $o).
% 61.67/9.51 thf(lamp_type, type, lamp: $o).
% 61.67/9.51 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 61.67/9.51 thf(inCongP_type, type, inCongP: $o).
% 61.67/9.51 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 61.67/9.51 thf(exuE3e_type, type, exuE3e: $o).
% 61.67/9.51 thf(emptysetE_type, type, emptysetE: $o).
% 61.67/9.51 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 61.67/9.51 thf(setunionI_type, type, setunionI: $o).
% 61.67/9.51 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 61.67/9.51 thf(prop2setI_type, type, prop2setI: $o).
% 61.67/9.51 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 61.67/9.51 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 61.67/9.51 thf(setminusER_type, type, setminusER: $o).
% 61.67/9.51 thf(exuE2_type, type, exuE2: $o).
% 61.67/9.51 thf(emptyset_type, type, emptyset: $i).
% 61.67/9.51 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 61.67/9.51 thf(ex1I_type, type, ex1I: $o).
% 61.67/9.51 thf(ex1E2_type, type, ex1E2: $o).
% 61.67/9.51 thf(setminus_type, type, setminus: $i > $i > $i).
% 61.67/9.51 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 61.67/9.51 thf(powersetsubset_type, type, powersetsubset: $o).
% 61.67/9.51 thf(subPowSU_type, type, subPowSU: $o).
% 61.67/9.51 thf(notequalI1_type, type, notequalI1: $o).
% 61.67/9.51 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 61.67/9.51 thf(notinemptyset_type, type, notinemptyset: $o).
% 61.67/9.51 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 61.67/9.51 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 61.67/9.51 thf(subsetTrans_type, type, subsetTrans: $o).
% 61.67/9.51 thf(kpairp_type, type, kpairp: $o).
% 61.67/9.51 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 61.67/9.51 thf(setminusI_type, type, setminusI: $o).
% 61.67/9.51 thf(binunionIL_type, type, binunionIL: $o).
% 61.67/9.51 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 61.67/9.51 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 61.67/9.51 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 61.67/9.51 thf(subsetE2_type, type, subsetE2: $o).
% 61.67/9.51 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 61.67/9.51 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 61.67/9.51 thf(beta2_type, type, beta2: $o).
% 61.67/9.51 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 61.67/9.51 thf(setextsub_type, type, setextsub: $o).
% 61.67/9.51 thf(binunionLsub_type, type, binunionLsub: $o).
% 61.67/9.51 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 61.67/9.51 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 61.67/9.51 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 61.67/9.51 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 61.67/9.51 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 61.67/9.51 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 61.67/9.51 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 61.67/9.51 thf(setunionE_type, type, setunionE: $o).
% 61.67/9.51 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 61.67/9.51 thf(sk__162_type, type, sk__162: $i).
% 61.67/9.51 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 61.67/9.51 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 61.67/9.51 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 61.67/9.51 thf(binunionIR_type, type, binunionIR: $o).
% 61.67/9.51 thf(theeq_type, type, theeq: $o).
% 61.67/9.51 thf(setadjoinE_type, type, setadjoinE: $o).
% 61.67/9.51 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 61.67/9.51 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 61.67/9.51 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 61.67/9.51 thf(ap2p_type, type, ap2p: $o).
% 61.67/9.51 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 61.67/9.51 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 61.67/9.51 thf(exuE1_type, type, exuE1: $o).
% 61.67/9.51 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 61.67/9.51 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 61.67/9.51 thf(setminusLsub_type, type, setminusLsub: $o).
% 61.67/9.51 thf(funcextLem_type, type, funcextLem: $o).
% 61.67/9.51 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 61.67/9.51 thf(notinsingleton_type, type, notinsingleton: $o).
% 61.67/9.51 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 61.67/9.51 thf(exuEu_type, type, exuEu: $o).
% 61.67/9.51 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 61.67/9.51 thf(upairsetE_type, type, upairsetE: $o).
% 61.67/9.51 thf(omega0Ax_type, type, omega0Ax: $o).
% 61.67/9.51 thf(subsetTI_type, type, subsetTI: $o).
% 61.67/9.51 thf(sk__163_type, type, sk__163: $i).
% 61.67/9.51 thf(notsubsetI_type, type, notsubsetI: $o).
% 61.67/9.51 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 61.67/9.51 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 61.67/9.51 thf(setextAx_type, type, setextAx: $o).
% 61.67/9.51 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 61.67/9.51 thf(powersetE1_type, type, powersetE1: $o).
% 61.67/9.51 thf(bs114d_type, type, bs114d: $o).
% 61.67/9.51 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 61.67/9.51 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 61.67/9.51 thf(ifp_type, type, ifp: $o).
% 61.67/9.51 thf(powersetTI1_type, type, powersetTI1: $o).
% 61.67/9.51 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 61.67/9.51 thf(subsetI1_type, type, subsetI1: $o).
% 61.67/9.51 thf(symdiffE_type, type, symdiffE: $o).
% 61.67/9.51 thf(descrp_type, type, descrp: $o).
% 61.67/9.51 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 61.67/9.51 thf(foundationAx_type, type, foundationAx: $o).
% 61.67/9.51 thf(emptysetAx_type, type, emptysetAx: $o).
% 61.67/9.51 thf(emptyI_type, type, emptyI: $o).
% 61.67/9.51 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 61.67/9.51 thf(eta2_type, type, eta2: $o).
% 61.67/9.51 thf(binintersectEL_type, type, binintersectEL: $o).
% 61.67/9.51 thf(emptyE1_type, type, emptyE1: $o).
% 61.67/9.51 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 61.67/9.51 thf(complementTI1_type, type, complementTI1: $o).
% 61.67/9.51 thf(vacuousDall_type, type, vacuousDall: $o).
% 61.67/9.51 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 61.67/9.51 thf(binintersectI_type, type, binintersectI: $o).
% 61.67/9.51 thf(funcext_type, type, funcext: $o).
% 61.67/9.51 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 61.67/9.51 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 61.67/9.51 thf(sk__161_type, type, sk__161: $i).
% 61.67/9.51 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 61.67/9.51 thf(brelnall2_type, type, brelnall2: $o).
% 61.67/9.51 thf(setextT_type, type, setextT: $o).
% 61.67/9.51 thf(ex1I2_type, type, ex1I2: $o).
% 61.67/9.51 thf(symdiffI1_type, type, symdiffI1: $o).
% 61.67/9.51 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 61.67/9.51 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 61.67/9.51 thf(theprop_type, type, theprop: $o).
% 61.67/9.51 thf(subsetI2_type, type, subsetI2: $o).
% 61.67/9.51 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 61.67/9.51 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 61.67/9.51 thf(setminusERneg_type, type, setminusERneg: $o).
% 61.67/9.51 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 61.67/9.51 thf(omega__Cong_type, type, omega__Cong: $o).
% 61.67/9.51 thf(subsetRefl_type, type, subsetRefl: $o).
% 61.67/9.51 thf(uniqinunit_type, type, uniqinunit: $o).
% 61.67/9.51 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 61.67/9.51 $o).
% 61.67/9.51 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 61.67/9.51 thf(prop2setE_type, type, prop2setE: $o).
% 61.67/9.51 thf(binunionEcases_type, type, binunionEcases: $o).
% 61.67/9.51 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 61.67/9.51 thf(complementTE1_type, type, complementTE1: $o).
% 61.67/9.51 thf(nonemptyI_type, type, nonemptyI: $o).
% 61.67/9.51 thf(app_type, type, app: $o).
% 61.67/9.51 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 61.67/9.51 thf(exuE3u_type, type, exuE3u: $o).
% 61.67/9.51 thf(eta1_type, type, eta1: $o).
% 61.67/9.51 thf(setminusEL_type, type, setminusEL: $o).
% 61.67/9.51 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 61.67/9.51 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 61.67/9.51 thf(sepSubset_type, type, sepSubset: $o).
% 61.67/9.51 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 61.67/9.51 thf(upairset2E_type, type, upairset2E: $o).
% 61.67/9.51 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 61.67/9.51 thf(exuI3_type, type, exuI3: $o).
% 61.67/9.51 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 61.67/9.51 thf(apProp_type, type, apProp: $o).
% 61.67/9.51 thf(notdallE_type, type, notdallE: $o).
% 61.67/9.51 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 61.67/9.51 thf(binintersectER_type, type, binintersectER: $o).
% 61.67/9.51 thf(brelnall1_type, type, brelnall1: $o).
% 61.67/9.51 thf(powerset_type, type, powerset: $i > $i).
% 61.67/9.51 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 61.67/9.51 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 61.67/9.51 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 61.67/9.51 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 61.67/9.51 thf(exu__Cong_type, type, exu__Cong: $o).
% 61.67/9.51 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 61.67/9.51 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 61.67/9.51 thf(secondinupair_type, type, secondinupair: $o).
% 61.67/9.51 thf(singletonprop_type, type, singletonprop: $o).
% 61.67/9.51 thf(singletonsubset_type, type, singletonsubset: $o).
% 61.67/9.51 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 61.67/9.51 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 61.67/9.51 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 61.67/9.51 thf(replAx_type, type, replAx: $o).
% 61.67/9.51 thf(upairequniteq_type, type, upairequniteq: $o).
% 61.67/9.51 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 61.67/9.51 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 61.67/9.51 thf(setukpairIL_type, type, setukpairIL: $o).
% 61.67/9.51 thf(setunionE2_type, type, setunionE2: $o).
% 61.67/9.51 thf(inPowerset_type, type, inPowerset: $o).
% 61.67/9.51 thf(iffalse_type, type, iffalse: $o).
% 61.67/9.51 thf(funcext2_type, type, funcext2: $o).
% 61.67/9.51 thf(subset_type, type, subset: $i > $i > $o).
% 61.67/9.51 thf(subbreln_type, type, subbreln: $o).
% 61.67/9.51 thf(in__Cong_type, type, in__Cong: $o).
% 61.67/9.51 thf(binunionRsub_type, type, binunionRsub: $o).
% 61.67/9.51 thf(subset2powerset_type, type, subset2powerset: $o).
% 61.67/9.51 thf(complementSubsetComplementIntersect, axiom,
% 61.67/9.51 complementSubsetComplementIntersect =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Y:$i]:
% 61.67/9.51 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.67/9.51 ( subset @
% 61.67/9.51 ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ))).
% 61.67/9.51 thf('0', plain,
% 61.67/9.51 (( complementSubsetComplementIntersect ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( subset @
% 61.67/9.51 ( setminus @ X4 @ X6 ) @
% 61.67/9.51 ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(complementImpComplementIntersect, axiom,
% 61.67/9.51 complementImpComplementIntersect =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Y:$i]:
% 61.67/9.51 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) =>
% 61.67/9.51 ( ( in @ Xx @ ( setminus @ A @ X ) ) =>
% 61.67/9.51 ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 61.67/9.51 thf('1', plain,
% 61.67/9.51 (( complementImpComplementIntersect ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X10:$i]:
% 61.67/9.51 ( ( in @ X10 @ X4 ) =>
% 61.67/9.51 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) =>
% 61.67/9.51 ( in @
% 61.67/9.51 X10 @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(complementTnotintersectT, axiom, complementTnotintersectT =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Y:$i]:
% 61.67/9.51 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) =>
% 61.67/9.51 ( ( in @ Xx @ ( setminus @ A @ X ) ) =>
% 61.67/9.51 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 61.67/9.51 thf('2', plain,
% 61.67/9.51 (( complementTnotintersectT ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X10:$i]:
% 61.67/9.51 ( ( in @ X10 @ X4 ) =>
% 61.67/9.51 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) =>
% 61.67/9.51 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(doubleComplementEq, axiom, doubleComplementEq =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ( X ) = ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 61.67/9.51 thf('3', plain,
% 61.67/9.51 (( doubleComplementEq ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ( X6 ) = ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(doubleComplementSub2, axiom, doubleComplementSub2 =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ))).
% 61.67/9.51 thf('4', plain,
% 61.67/9.51 (( doubleComplementSub2 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) @ X6 ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(doubleComplementSub1, axiom, doubleComplementSub1 =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 61.67/9.51 thf('5', plain,
% 61.67/9.51 (( doubleComplementSub1 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( subset @ X6 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(doubleComplementE1, axiom, doubleComplementE1 =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) =>
% 61.67/9.51 ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) =>
% 61.67/9.51 ( in @ Xx @ X ) ) ) ) ))).
% 61.67/9.51 thf('6', plain,
% 61.67/9.51 (( doubleComplementE1 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ X4 ) =>
% 61.67/9.51 ( ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) =>
% 61.67/9.51 ( in @ X8 @ X6 ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(doubleComplementI1, axiom, doubleComplementI1 =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) =>
% 61.67/9.51 ( ( in @ Xx @ X ) =>
% 61.67/9.51 ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 61.67/9.51 thf('7', plain,
% 61.67/9.51 (( doubleComplementI1 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ X4 ) =>
% 61.67/9.51 ( ( in @ X8 @ X6 ) =>
% 61.67/9.51 ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(contrasubsetT3, axiom, contrasubsetT3 =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Y:$i]:
% 61.67/9.51 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) =>
% 61.67/9.51 ( subset @ X @ Y ) ) ) ) ))).
% 61.67/9.51 thf('8', plain,
% 61.67/9.51 (( contrasubsetT3 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) =>
% 61.67/9.51 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(contrasubsetT2, axiom, contrasubsetT2 =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Y:$i]:
% 61.67/9.51 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ( subset @ X @ Y ) =>
% 61.67/9.51 ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ))).
% 61.67/9.51 thf('9', plain,
% 61.67/9.51 (( contrasubsetT2 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ( subset @ X6 @ X8 ) =>
% 61.67/9.51 ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(contrasubsetT1, axiom, contrasubsetT1 =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Y:$i]:
% 61.67/9.51 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) =>
% 61.67/9.51 ( ( subset @ X @ Y ) =>
% 61.67/9.51 ( ( ~( in @ Xx @ Y ) ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 61.67/9.51 thf('10', plain,
% 61.67/9.51 (( contrasubsetT1 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X10:$i]:
% 61.67/9.51 ( ( in @ X10 @ X4 ) =>
% 61.67/9.51 ( ( subset @ X6 @ X8 ) =>
% 61.67/9.51 ( ( ~( in @ X10 @ X8 ) ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(contrasubsetT, axiom, contrasubsetT =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Y:$i]:
% 61.67/9.51 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) =>
% 61.67/9.51 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 61.67/9.51 ( ( in @ Xx @ Y ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 61.67/9.51 thf('11', plain,
% 61.67/9.51 (( contrasubsetT ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X10:$i]:
% 61.67/9.51 ( ( in @ X10 @ X4 ) =>
% 61.67/9.51 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 61.67/9.51 ( ( in @ X10 @ X8 ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(binintersectTERcontra, axiom, binintersectTERcontra =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Y:$i]:
% 61.67/9.51 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) =>
% 61.67/9.51 ( ( ~( in @ Xx @ Y ) ) =>
% 61.67/9.51 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 61.67/9.51 thf('12', plain,
% 61.67/9.51 (( binintersectTERcontra ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X10:$i]:
% 61.67/9.51 ( ( in @ X10 @ X4 ) =>
% 61.67/9.51 ( ( ~( in @ X10 @ X8 ) ) =>
% 61.67/9.51 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(binintersectTELcontra, axiom, binintersectTELcontra =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Y:$i]:
% 61.67/9.51 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) =>
% 61.67/9.51 ( ( ~( in @ Xx @ X ) ) =>
% 61.67/9.51 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 61.67/9.51 thf('13', plain,
% 61.67/9.51 (( binintersectTELcontra ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X10:$i]:
% 61.67/9.51 ( ( in @ X10 @ X4 ) =>
% 61.67/9.51 ( ( ~( in @ X10 @ X6 ) ) =>
% 61.67/9.51 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(complementTE1, axiom, complementTE1 =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) =>
% 61.67/9.51 ( ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) => ( in @ Xx @ X ) ) ) ) ))).
% 61.67/9.51 thf('14', plain,
% 61.67/9.51 (( complementTE1 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ X4 ) =>
% 61.67/9.51 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) => ( in @ X8 @ X6 ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(complementTI1, axiom, complementTI1 =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) =>
% 61.67/9.51 ( ( in @ Xx @ X ) => ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 61.67/9.51 thf('15', plain,
% 61.67/9.51 (( complementTI1 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ X4 ) =>
% 61.67/9.51 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(powersetTE1, axiom, powersetTE1 =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Y:$i]:
% 61.67/9.51 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) =>
% 61.67/9.51 ( ( in @ X @ ( powerset @ Y ) ) =>
% 61.67/9.51 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 61.67/9.51 thf('16', plain,
% 61.67/9.51 (( powersetTE1 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X10:$i]:
% 61.67/9.51 ( ( in @ X10 @ X4 ) =>
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 61.67/9.51 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(powersetTI1, axiom, powersetTI1 =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Y:$i]:
% 61.67/9.51 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ( ![Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 61.67/9.51 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 61.67/9.51 thf('17', plain,
% 61.67/9.51 (( powersetTI1 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ( ![X10:$i]:
% 61.67/9.51 ( ( in @ X10 @ X4 ) =>
% 61.67/9.51 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 61.67/9.51 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(subsetTI, axiom, subsetTI =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Y:$i]:
% 61.67/9.51 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ( ![Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 61.67/9.51 ( subset @ X @ Y ) ) ) ) ))).
% 61.67/9.51 thf('18', plain,
% 61.67/9.51 (( subsetTI ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ( ![X10:$i]:
% 61.67/9.51 ( ( in @ X10 @ X4 ) =>
% 61.67/9.51 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 61.67/9.51 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(setextT, axiom, setextT =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Y:$i]:
% 61.67/9.51 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ( ![Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 61.67/9.51 ( ( ![Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 61.67/9.51 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 61.67/9.51 thf('19', plain,
% 61.67/9.51 (( setextT ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ( ![X10:$i]:
% 61.67/9.51 ( ( in @ X10 @ X4 ) =>
% 61.67/9.51 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 61.67/9.51 ( ( ![X12:$i]:
% 61.67/9.51 ( ( in @ X12 @ X4 ) =>
% 61.67/9.51 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 61.67/9.51 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(complementT_lem, axiom, complementT_lem =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ))).
% 61.67/9.51 thf('20', plain,
% 61.67/9.51 (( complementT_lem ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( in @ ( setminus @ X4 @ X6 ) @ ( powerset @ X4 ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(setminusT_lem, axiom, setminusT_lem =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Y:$i]:
% 61.67/9.51 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.67/9.51 ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 61.67/9.51 thf('21', plain,
% 61.67/9.51 (( setminusT_lem ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( in @ ( setminus @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(powersetT_lem, axiom, powersetT_lem =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 61.67/9.51 thf('22', plain,
% 61.67/9.51 (( powersetT_lem ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(binintersectT_lem, axiom, binintersectT_lem =
% 61.67/9.51 (![A:$i,X:$i]:
% 61.67/9.51 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.67/9.51 ( ![Y:$i]:
% 61.67/9.51 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.67/9.51 ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 61.67/9.51 thf('23', plain,
% 61.67/9.51 (( binintersectT_lem ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ![X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( in @ ( binintersect @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(singletoninpowerset, axiom, singletoninpowerset =
% 61.67/9.51 (![A:$i,Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) =>
% 61.67/9.51 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 61.67/9.51 thf('24', plain,
% 61.67/9.51 (( singletoninpowerset ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ X4 ) =>
% 61.67/9.51 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(setminusSubset1, axiom, setminusSubset1 =
% 61.67/9.51 (![A:$i,B:$i]:
% 61.67/9.51 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))).
% 61.67/9.51 thf('25', plain,
% 61.67/9.51 (( setminusSubset1 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(setminusLsub, axiom, setminusLsub =
% 61.67/9.51 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))).
% 61.67/9.51 thf('26', plain,
% 61.67/9.51 (( setminusLsub ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(setminusIRneg, axiom, setminusIRneg =
% 61.67/9.51 (![A:$i,B:$i,Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 61.67/9.51 thf('27', plain,
% 61.67/9.51 (( setminusIRneg ) =
% 61.67/9.51 ( ![X4:$i,X6:$i,X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(setminusILneg, axiom, setminusILneg =
% 61.67/9.51 (![A:$i,B:$i,Xx:$i]:
% 61.67/9.51 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 61.67/9.51 thf('28', plain,
% 61.67/9.51 (( setminusILneg ) =
% 61.67/9.51 ( ![X4:$i,X6:$i,X8:$i]:
% 61.67/9.51 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(setminusELneg, axiom, setminusELneg =
% 61.67/9.51 (![A:$i,B:$i,Xx:$i]:
% 61.67/9.51 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 61.67/9.51 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 61.67/9.51 thf('29', plain,
% 61.67/9.51 (( setminusELneg ) =
% 61.67/9.51 ( ![X4:$i,X6:$i,X8:$i]:
% 61.67/9.51 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 61.67/9.51 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(setminusERneg, axiom, setminusERneg =
% 61.67/9.51 (![A:$i,B:$i,Xx:$i]:
% 61.67/9.51 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 61.67/9.51 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 61.67/9.51 thf('30', plain,
% 61.67/9.51 (( setminusERneg ) =
% 61.67/9.51 ( ![X4:$i,X6:$i,X8:$i]:
% 61.67/9.51 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 61.67/9.51 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(setminusSubset2, axiom, setminusSubset2 =
% 61.67/9.51 (![A:$i,B:$i]:
% 61.67/9.51 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))).
% 61.67/9.51 thf('31', plain,
% 61.67/9.51 (( setminusSubset2 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(setminusER, axiom, setminusER =
% 61.67/9.51 (![A:$i,B:$i,Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))).
% 61.67/9.51 thf('32', plain,
% 61.67/9.51 (( setminusER ) =
% 61.67/9.51 ( ![X4:$i,X6:$i,X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(setminusEL, axiom, setminusEL =
% 61.67/9.51 (![A:$i,B:$i,Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 61.67/9.51 thf('33', plain,
% 61.67/9.51 (( setminusEL ) =
% 61.67/9.51 ( ![X4:$i,X6:$i,X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(setminusI, axiom, setminusI =
% 61.67/9.51 (![A:$i,B:$i,Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) =>
% 61.67/9.51 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 61.67/9.51 thf('34', plain,
% 61.67/9.51 (( setminusI ) =
% 61.67/9.51 ( ![X4:$i,X6:$i,X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ X4 ) =>
% 61.67/9.51 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(binintersectSubset1, axiom, binintersectSubset1 =
% 61.67/9.51 (![A:$i,B:$i]:
% 61.67/9.51 ( ( ( binintersect @ A @ B ) = ( A ) ) => ( subset @ A @ B ) ))).
% 61.67/9.51 thf('35', plain,
% 61.67/9.51 (( binintersectSubset1 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) => ( subset @ X4 @ X6 ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(binintersectSubset4, axiom, binintersectSubset4 =
% 61.67/9.51 (![A:$i,B:$i]:
% 61.67/9.51 ( ( subset @ B @ A ) => ( ( binintersect @ A @ B ) = ( B ) ) ))).
% 61.67/9.51 thf('36', plain,
% 61.67/9.51 (( binintersectSubset4 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( subset @ X6 @ X4 ) => ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(binintersectRsub, axiom, binintersectRsub =
% 61.67/9.51 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ B ))).
% 61.67/9.51 thf('37', plain,
% 61.67/9.51 (( binintersectRsub ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X6 ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(disjointsetsI1, axiom, disjointsetsI1 =
% 61.67/9.51 (![A:$i,B:$i]:
% 61.67/9.51 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ B ) & ( in @ Xx @ A ) ) ) ) =>
% 61.67/9.51 ( ( binintersect @ A @ B ) = ( emptyset ) ) ))).
% 61.67/9.51 thf('38', plain,
% 61.67/9.51 (( disjointsetsI1 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( ~( ?[X8:$i]: ( ( in @ X8 @ X6 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 61.67/9.51 ( ( binintersect @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(binintersectER, axiom, binintersectER =
% 61.67/9.51 (![A:$i,B:$i,Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ B ) ))).
% 61.67/9.51 thf('39', plain,
% 61.67/9.51 (( binintersectER ) =
% 61.67/9.51 ( ![X4:$i,X6:$i,X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X6 ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(binintersectSubset3, axiom, binintersectSubset3 =
% 61.67/9.51 (![A:$i,B:$i]:
% 61.67/9.51 ( ( ( binintersect @ A @ B ) = ( B ) ) => ( subset @ B @ A ) ))).
% 61.67/9.51 thf('40', plain,
% 61.67/9.51 (( binintersectSubset3 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(binintersectSubset2, axiom, binintersectSubset2 =
% 61.67/9.51 (![A:$i,B:$i]:
% 61.67/9.51 ( ( subset @ A @ B ) => ( ( binintersect @ A @ B ) = ( A ) ) ))).
% 61.67/9.51 thf('41', plain,
% 61.67/9.51 (( binintersectSubset2 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( subset @ X4 @ X6 ) => ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(binintersectLsub, axiom, binintersectLsub =
% 61.67/9.51 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ A ))).
% 61.67/9.51 thf('42', plain,
% 61.67/9.51 (( binintersectLsub ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X4 ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(binintersectEL, axiom, binintersectEL =
% 61.67/9.51 (![A:$i,B:$i,Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 61.67/9.51 thf('43', plain,
% 61.67/9.51 (( binintersectEL ) =
% 61.67/9.51 ( ![X4:$i,X6:$i,X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(binintersectSubset5, axiom, binintersectSubset5 =
% 61.67/9.51 (![A:$i,B:$i,C:$i]:
% 61.67/9.51 ( ( subset @ C @ A ) =>
% 61.67/9.51 ( ( subset @ C @ B ) => ( subset @ C @ ( binintersect @ A @ B ) ) ) ))).
% 61.67/9.51 thf('44', plain,
% 61.67/9.51 (( binintersectSubset5 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i,X8:$i]:
% 61.67/9.51 ( ( subset @ X8 @ X4 ) =>
% 61.67/9.51 ( ( subset @ X8 @ X6 ) =>
% 61.67/9.51 ( subset @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(binintersectI, axiom, binintersectI =
% 61.67/9.51 (![A:$i,B:$i,Xx:$i]:
% 61.67/9.51 ( ( in @ Xx @ A ) =>
% 61.67/9.51 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ))).
% 61.67/9.51 thf('45', plain,
% 61.67/9.51 (( binintersectI ) =
% 61.67/9.51 ( ![X4:$i,X6:$i,X8:$i]:
% 61.67/9.51 ( ( in @ X8 @ X4 ) =>
% 61.67/9.51 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(powersetsubset, axiom, powersetsubset =
% 61.67/9.51 (![A:$i,B:$i]:
% 61.67/9.51 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 61.67/9.51 thf('46', plain,
% 61.67/9.51 (( powersetsubset ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( subset @ X4 @ X6 ) =>
% 61.67/9.51 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 61.67/9.51 thf('47', plain,
% 61.67/9.51 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(powersetE1, axiom, powersetE1 =
% 61.67/9.51 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 61.67/9.51 thf('48', plain,
% 61.67/9.51 (( powersetE1 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(powersetI1, axiom, powersetI1 =
% 61.67/9.51 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 61.67/9.51 thf('49', plain,
% 61.67/9.51 (( powersetI1 ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(subset2powerset, axiom, subset2powerset =
% 61.67/9.51 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 61.67/9.51 thf('50', plain,
% 61.67/9.51 (( subset2powerset ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(powerset__Cong, axiom, powerset__Cong =
% 61.67/9.51 (![A:$i,B:$i]:
% 61.67/9.51 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 61.67/9.51 thf('51', plain,
% 61.67/9.51 (( powerset__Cong ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(powersetE, axiom, powersetE =
% 61.67/9.51 (![A:$i,B:$i,Xx:$i]:
% 61.67/9.51 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 61.67/9.51 thf('52', plain,
% 61.67/9.51 (( powersetE ) =
% 61.67/9.51 ( ![X4:$i,X6:$i,X8:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.67/9.51 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(emptyInPowerset, axiom, emptyInPowerset =
% 61.67/9.51 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 61.67/9.51 thf('53', plain,
% 61.67/9.51 (( emptyInPowerset ) =
% 61.67/9.51 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(emptyinPowerset, axiom, emptyinPowerset =
% 61.67/9.51 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 61.67/9.51 thf('54', plain,
% 61.67/9.51 (( emptyinPowerset ) =
% 61.67/9.51 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(powersetI, axiom, powersetI =
% 61.67/9.51 (![A:$i,B:$i]:
% 61.67/9.51 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 61.67/9.51 ( in @ B @ ( powerset @ A ) ) ))).
% 61.67/9.51 thf('55', plain,
% 61.67/9.51 (( powersetI ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 61.67/9.51 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(powersetAx, axiom, powersetAx =
% 61.67/9.51 (![A:$i,B:$i]:
% 61.67/9.51 ( ( in @ B @ ( powerset @ A ) ) <=>
% 61.67/9.51 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 61.67/9.51 thf('56', plain,
% 61.67/9.51 (( powersetAx ) =
% 61.67/9.51 ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 61.67/9.51 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 61.67/9.51 define([status(thm)])).
% 61.67/9.51 thf(complementInPowersetComplementIntersect, conjecture,
% 61.67/9.51 (( setextAx ) =>
% 61.67/9.51 ( ( emptysetAx ) =>
% 61.67/9.51 ( ( setadjoinAx ) =>
% 61.67/9.51 ( ( powersetAx ) =>
% 61.67/9.51 ( ( setunionAx ) =>
% 61.67/9.51 ( ( omega0Ax ) =>
% 61.67/9.51 ( ( omegaSAx ) =>
% 61.67/9.51 ( ( omegaIndAx ) =>
% 61.67/9.51 ( ( replAx ) =>
% 61.67/9.51 ( ( foundationAx ) =>
% 61.67/9.51 ( ( wellorderingAx ) =>
% 61.67/9.51 ( ( descrp ) =>
% 61.67/9.51 ( ( dsetconstrI ) =>
% 61.67/9.51 ( ( dsetconstrEL ) =>
% 61.67/9.51 ( ( dsetconstrER ) =>
% 61.67/9.51 ( ( exuE1 ) =>
% 61.67/9.51 ( ( prop2setE ) =>
% 61.67/9.51 ( ( emptysetE ) =>
% 61.67/9.51 ( ( emptysetimpfalse ) =>
% 61.67/9.51 ( ( notinemptyset ) =>
% 61.67/9.51 ( ( exuE3e ) =>
% 61.67/9.51 ( ( setext ) =>
% 61.67/9.51 ( ( emptyI ) =>
% 61.67/9.51 ( ( noeltsimpempty ) =>
% 61.67/9.51 ( ( setbeta ) =>
% 61.67/9.51 ( ( nonemptyE1 ) =>
% 61.67/9.51 ( ( nonemptyI ) =>
% 61.67/9.51 ( ( nonemptyI1 ) =>
% 61.67/9.51 ( ( setadjoinIL ) =>
% 61.67/9.51 ( ( emptyinunitempty ) =>
% 61.67/9.51 ( ( setadjoinIR ) =>
% 61.67/9.51 ( ( setadjoinE ) =>
% 61.67/9.51 ( (
% 61.67/9.51 setadjoinOr ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setoftrueEq ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 powersetI ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 emptyinPowerset ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 emptyInPowerset ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 powersetE ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setunionI ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setunionE ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 subPowSU ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 exuE2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 nonemptyImpWitness ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 uniqinunit ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 notinsingleton ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 eqinunit ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 singletonsswitch ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 upairsetE ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 upairsetIL ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 upairsetIR ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 emptyE1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 vacuousDall ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 quantDeMorgan1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 quantDeMorgan2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 quantDeMorgan3 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 quantDeMorgan4 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 prop2setI ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 prop2set2propI ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 notdexE ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 notdallE ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 exuI1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 exuI3 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 exuI2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 inCongP ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 in__Cong ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 exuE3u ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 exu__Cong ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 emptyset__Cong ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setadjoin__Cong ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 powerset__Cong ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setunion__Cong ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 omega__Cong ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 exuEu ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 descr__Cong ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 dsetconstr__Cong ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 subsetI1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 eqimpsubset2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 eqimpsubset1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 subsetI2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 emptysetsubset ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 subsetE ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 subsetE2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 notsubsetI ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 notequalI1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 notequalI2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 subsetRefl ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 subsetTrans ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setadjoinSub ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setadjoinSub2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 subset2powerset ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setextsub ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 subsetemptysetimpeq ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 powersetI1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 powersetE1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 inPowerset ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 powersetsubset ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 sepInPowerset ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 sepSubset ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binunionIL ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 upairset2IR ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binunionIR ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binunionEcases ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binunionE ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binunionLsub ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binunionRsub ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binintersectI ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binintersectSubset5 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binintersectEL ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binintersectLsub ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binintersectSubset2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binintersectSubset3 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binintersectER ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 disjointsetsI1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binintersectRsub ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binintersectSubset4 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binintersectSubset1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 bs114d ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setminusI ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setminusEL ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setminusER ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setminusSubset2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setminusERneg ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setminusELneg ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setminusILneg ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setminusIRneg ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setminusLsub ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setminusSubset1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 symdiffE ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 symdiffI1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 symdiffI2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 symdiffIneg1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 symdiffIneg2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 secondinupair ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setukpairIL ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setukpairIR ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 kpairiskpair ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 kpairp ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 singletonsubset ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 singletoninpowerset ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 singletoninpowunion ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 upairset2E ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 upairsubunion ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 upairinpowunion ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 ubforcartprodlem1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 ubforcartprodlem2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 ubforcartprodlem3 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 cartprodpairin ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 cartprodmempair1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 cartprodmempair ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setunionE2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setunionsingleton1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setunionsingleton2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setunionsingleton ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 singletonprop ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 ex1E1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 ex1I ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 ex1I2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 singletonsuniq ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setukpairinjL1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 kfstsingleton ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 theprop ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 kfstpairEq ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 cartprodfstin ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setukpairinjL2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setukpairinjL ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setukpairinjR11 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setukpairinjR12 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setukpairinjR1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 upairequniteq ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setukpairinjR2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setukpairinjR ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 ksndsingleton ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 ksndpairEq ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 kpairsurjEq ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 cartprodsndin ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 cartprodpairmemEL ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 cartprodpairmemER ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 cartprodmempaircEq ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 cartprodfstpairEq ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 cartprodsndpairEq ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 cartprodpairsurjEq ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 dpsetconstrI ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 dpsetconstrSub ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setOfPairsIsBReln ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 dpsetconstrERa ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 dpsetconstrEL1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 dpsetconstrEL2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 dpsetconstrER ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 funcImageSingleton ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 apProp ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 app ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 infuncsetfunc ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 ap2p ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 funcinfuncset ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 lamProp ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 lamp ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 lam2p ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 brelnall1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 brelnall2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 ex1E2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 funcGraphProp1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 funcGraphProp3 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 funcGraphProp2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 funcextLem ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 funcGraphProp4 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 subbreln ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 eqbreln ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 funcext ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 funcext2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 ap2apEq1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 ap2apEq2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 beta1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 eta1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 lam2lamEq ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 beta2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 eta2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 iffalseProp1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 iffalseProp2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 iftrueProp1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 iftrueProp2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 ifSingleton ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 ifp ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 theeq ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 iftrue ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 iffalse ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 iftrueorfalse ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binintersectT_lem ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binunionT_lem ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 powersetT_lem ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setminusT_lem ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 complementT_lem ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 setextT ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 subsetTI ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 powersetTI1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 powersetTE1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 complementTI1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 complementTE1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binintersectTELcontra ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 binintersectTERcontra ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 contrasubsetT ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 contrasubsetT1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 contrasubsetT2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 contrasubsetT3 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 doubleComplementI1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 doubleComplementE1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 doubleComplementSub1 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 doubleComplementSub2 ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 doubleComplementEq ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 complementTnotintersectT ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 complementImpComplementIntersect ) =>
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 complementSubsetComplementIntersect ) =>
% 61.67/9.51 (
% 61.67/9.51 ![
% 61.67/9.51 A:$i,X:$i]:
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 in @
% 61.67/9.51 X @
% 61.67/9.51 (
% 61.67/9.51 powerset @
% 61.67/9.51 A ) ) =>
% 61.67/9.51 (
% 61.67/9.51 ![
% 61.67/9.51 Y:$i]:
% 61.67/9.51 (
% 61.67/9.51 (
% 61.67/9.51 in @
% 61.67/9.51 Y @
% 61.67/9.51 (
% 61.67/9.51 powerset @
% 61.67/9.51 A ) ) =>
% 61.67/9.51 (
% 61.67/9.51 in @
% 61.67/9.51 (
% 61.67/9.51 setminus @
% 61.67/9.51 A @ X ) @
% 61.67/9.51 (
% 61.67/9.51 powerset @
% 61.67/9.51 (
% 61.67/9.51 setminus @
% 61.67/9.51 A @
% 61.67/9.51 (
% 61.67/9.51 binintersect
% 61.67/9.51 @
% 61.67/9.51 X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 61.67/9.51 thf(zf_stmt_0, conjecture,
% 61.67/9.51 (( setextAx ) =>
% 61.67/9.51 ( ( emptysetAx ) =>
% 61.67/9.51 ( ( setadjoinAx ) =>
% 61.67/9.51 ( ( ![X4:$i,X6:$i]:
% 61.67/9.51 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 61.67/9.51 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 61.67/9.51 ( ( setunionAx ) =>
% 61.67/9.51 ( ( omega0Ax ) =>
% 61.67/9.51 ( ( omegaSAx ) =>
% 61.67/9.51 ( ( omegaIndAx ) =>
% 61.67/9.51 ( ( replAx ) =>
% 61.67/9.51 ( ( foundationAx ) =>
% 61.67/9.51 ( ( wellorderingAx ) =>
% 61.67/9.51 ( ( descrp ) =>
% 61.67/9.51 ( ( dsetconstrI ) =>
% 61.67/9.51 ( ( dsetconstrEL ) =>
% 61.67/9.51 ( ( dsetconstrER ) =>
% 61.67/9.52 ( ( exuE1 ) =>
% 61.67/9.52 ( ( prop2setE ) =>
% 61.67/9.52 ( ( emptysetE ) =>
% 61.67/9.52 ( ( emptysetimpfalse ) =>
% 61.67/9.52 ( ( notinemptyset ) =>
% 61.67/9.52 ( ( exuE3e ) =>
% 61.67/9.52 ( ( setext ) =>
% 61.67/9.52 ( ( emptyI ) =>
% 61.67/9.52 ( ( noeltsimpempty ) =>
% 61.67/9.52 ( ( setbeta ) =>
% 61.67/9.52 ( ( nonemptyE1 ) =>
% 61.67/9.52 ( ( nonemptyI ) =>
% 61.67/9.52 ( ( nonemptyI1 ) =>
% 61.67/9.52 ( ( setadjoinIL ) =>
% 61.67/9.52 ( ( emptyinunitempty ) =>
% 61.67/9.52 ( ( setadjoinIR ) =>
% 61.67/9.52 ( ( setadjoinE ) =>
% 61.67/9.52 ( (
% 61.67/9.52 setadjoinOr ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setoftrueEq ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X10:$i,
% 61.67/9.52 X12:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X14:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X14 @ X12 ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X14 @ X10 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X12 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X10 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X16:$i]:
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 emptyset @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X16 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X18:$i]:
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 emptyset @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X18 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X20:$i,
% 61.67/9.52 X22:$i,
% 61.67/9.52 X24:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X22 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X20 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X24 @ X22 ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X24 @ X20 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setunionI ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setunionE ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subPowSU ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 exuE2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 nonemptyImpWitness ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 uniqinunit ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 notinsingleton ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 eqinunit ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 singletonsswitch ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 upairsetE ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 upairsetIL ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 upairsetIR ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 emptyE1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 vacuousDall ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 quantDeMorgan1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 quantDeMorgan2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 quantDeMorgan3 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 quantDeMorgan4 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 prop2setI ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 prop2set2propI ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 notdexE ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 notdallE ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 exuI1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 exuI3 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 exuI2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 inCongP ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in__Cong ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 exuE3u ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 exu__Cong ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 emptyset__Cong ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setadjoin__Cong ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X26:$i,
% 61.67/9.52 X28:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 X26 ) =
% 61.67/9.52 (
% 61.67/9.52 X28 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X26 ) =
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X28 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setunion__Cong ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 omega__Cong ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 exuEu ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 descr__Cong ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 dsetconstr__Cong ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subsetI1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 eqimpsubset2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 eqimpsubset1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subsetI2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 emptysetsubset ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subsetE ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subsetE2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 notsubsetI ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 notequalI1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 notequalI2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subsetRefl ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subsetTrans ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setadjoinSub ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setadjoinSub2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X30:$i,
% 61.67/9.52 X32:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X30 @ X32 ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X30 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X32 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setextsub ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subsetemptysetimpeq ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X34:$i,
% 61.67/9.52 X36:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X36 @ X34 ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X36 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X34 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X38:$i,
% 61.67/9.52 X40:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X40 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X38 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X40 @ X38 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X42:$i]:
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X42 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X42 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X44:$i,
% 61.67/9.52 X46:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X44 @ X46 ) =>
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X44 ) @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X46 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 sepInPowerset ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 sepSubset ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binunionIL ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 upairset2IR ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binunionIR ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binunionEcases ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binunionE ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binunionLsub ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binunionRsub ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X48:$i,
% 61.67/9.52 X50:$i,
% 61.67/9.52 X52:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X52 @ X48 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X52 @ X50 ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X52 @
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X48 @ X50 ) ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X54:$i,
% 61.67/9.52 X56:$i,
% 61.67/9.52 X58:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X58 @ X54 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X58 @ X56 ) =>
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X58 @
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X54 @ X56 ) ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X60:$i,
% 61.67/9.52 X62:$i,
% 61.67/9.52 X64:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X64 @
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X60 @ X62 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X64 @ X60 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X66:$i,
% 61.67/9.52 X68:$i]:
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X66 @ X68 ) @
% 61.67/9.52 X66 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X70:$i,
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% 61.67/9.52 X76 @ X74 ) ) ) =>
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% 61.67/9.52 X78 @ X80 ) ) =>
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% 61.67/9.52 X104 ) ) ) ) ) =>
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% 61.67/9.52 X114 @
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% 61.67/9.52 in @
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% 61.67/9.52 X116 ) ) ) ) =>
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% 61.67/9.52 X130 ) ) ) ) ) =>
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% 61.67/9.52 in @
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% 61.67/9.52 @
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% 61.67/9.52 ![
% 61.67/9.52 X142:$i,
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% 61.67/9.52 ~(
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% 61.67/9.52 X148 ) ) =>
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% 61.67/9.52 (
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% 61.67/9.52 emptyset ) ) =>
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X152 @
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% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 symdiffE ) =>
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% 61.67/9.52 (
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% 61.67/9.52 (
% 61.67/9.52 secondinupair ) =>
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% 61.67/9.52 (
% 61.67/9.52 setukpairIL ) =>
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% 61.67/9.52 (
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% 61.67/9.52 kpairiskpair ) =>
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% 61.67/9.52 kpairp ) =>
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% 61.67/9.52 (
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% 61.67/9.52 in @
% 61.67/9.52 X158 @
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% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 (
% 61.67/9.52 setadjoin
% 61.67/9.52 @
% 61.67/9.52 X158 @
% 61.67/9.52 emptyset ) @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X156 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 singletoninpowunion ) =>
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% 61.67/9.52 (
% 61.67/9.52 upairset2E ) =>
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% 61.67/9.52 ubforcartprodlem2 ) =>
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% 61.67/9.52 (
% 61.67/9.52 ubforcartprodlem3 ) =>
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% 61.67/9.52 cartprodpairin ) =>
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% 61.67/9.52 cartprodmempair1 ) =>
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% 61.67/9.52 X274 @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X270 @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X270 @
% 61.67/9.52 X272 ) ) ) ) ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X276:$i,
% 61.67/9.52 X278:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X278 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X276 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X280:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X280 @
% 61.67/9.52 X276 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X280 @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X276 @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X276 @
% 61.67/9.52 X278 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X280 @
% 61.67/9.52 X278 ) ) ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X282:$i,
% 61.67/9.52 X284:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X284 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X282 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X284 @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X282 @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X282 @
% 61.67/9.52 X284 ) ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X286:$i,
% 61.67/9.52 X288:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X288 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X286 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X286 @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X286 @
% 61.67/9.52 X288 ) ) @
% 61.67/9.52 X288 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X290:$i,
% 61.67/9.52 X292:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X292 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X290 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 X292 ) =
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X290 @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X290 @
% 61.67/9.52 X292 ) ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X294:$i,
% 61.67/9.52 X296:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X296 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X294 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X298:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X298 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X294 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X300:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X300 @
% 61.67/9.52 X294 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X300 @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X294 @
% 61.67/9.52 X296 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 ~(
% 61.67/9.52 in @
% 61.67/9.52 X300 @
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X296 @
% 61.67/9.52 X298 ) ) ) ) ) ) ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X302:$i,
% 61.67/9.52 X304:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X304 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X302 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X306:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X306 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X302 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X308:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X308 @
% 61.67/9.52 X302 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X308 @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X302 @
% 61.67/9.52 X304 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X308 @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X302 @
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X304 @
% 61.67/9.52 X306 ) ) ) ) ) ) ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X310:$i,
% 61.67/9.52 X312:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X312 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X310 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X314:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X314 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X310 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X310 @
% 61.67/9.52 X312 ) @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X310 @
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X312 @
% 61.67/9.52 X314 ) ) ) ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X316:$i,
% 61.67/9.52 X318:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X318 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X316 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X320:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X320 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X316 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X316 @
% 61.67/9.52 X318 ) @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X316 @
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X318 @
% 61.67/9.52 X320 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 61.67/9.52 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 61.67/9.52 thf(zf_stmt_2, axiom,
% 61.67/9.52 (![X8:$i,X6:$i,X4:$i]:
% 61.67/9.52 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 61.67/9.52 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 61.67/9.52 thf(zf_stmt_3, conjecture,
% 61.67/9.52 (( setextAx ) =>
% 61.67/9.52 ( ( emptysetAx ) =>
% 61.67/9.52 ( ( setadjoinAx ) =>
% 61.67/9.52 ( ( ![X4:$i,X6:$i]:
% 61.67/9.52 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 61.67/9.52 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 61.67/9.52 ( ( setunionAx ) =>
% 61.67/9.52 ( ( omega0Ax ) =>
% 61.67/9.52 ( ( omegaSAx ) =>
% 61.67/9.52 ( ( omegaIndAx ) =>
% 61.67/9.52 ( ( replAx ) =>
% 61.67/9.52 ( ( foundationAx ) =>
% 61.67/9.52 ( ( wellorderingAx ) =>
% 61.67/9.52 ( ( descrp ) =>
% 61.67/9.52 ( ( dsetconstrI ) =>
% 61.67/9.52 ( ( dsetconstrEL ) =>
% 61.67/9.52 ( ( dsetconstrER ) =>
% 61.67/9.52 ( ( exuE1 ) =>
% 61.67/9.52 ( ( prop2setE ) =>
% 61.67/9.52 ( ( emptysetE ) =>
% 61.67/9.52 ( ( emptysetimpfalse ) =>
% 61.67/9.52 ( ( notinemptyset ) =>
% 61.67/9.52 ( ( exuE3e ) =>
% 61.67/9.52 ( ( setext ) =>
% 61.67/9.52 ( ( emptyI ) =>
% 61.67/9.52 ( ( noeltsimpempty ) =>
% 61.67/9.52 ( ( setbeta ) =>
% 61.67/9.52 ( ( nonemptyE1 ) =>
% 61.67/9.52 ( ( nonemptyI ) =>
% 61.67/9.52 ( ( nonemptyI1 ) =>
% 61.67/9.52 ( ( setadjoinIL ) =>
% 61.67/9.52 ( ( emptyinunitempty ) =>
% 61.67/9.52 ( ( setadjoinIR ) =>
% 61.67/9.52 ( ( setadjoinE ) =>
% 61.67/9.52 ( (
% 61.67/9.52 setadjoinOr ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setoftrueEq ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X10:$i,
% 61.67/9.52 X12:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X14:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X14 @ X12 ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X14 @ X10 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X12 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X10 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X16:$i]:
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 emptyset @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X16 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X18:$i]:
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 emptyset @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X18 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X20:$i,
% 61.67/9.52 X22:$i,
% 61.67/9.52 X24:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X22 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X20 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X24 @ X22 ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X24 @ X20 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setunionI ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setunionE ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subPowSU ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 exuE2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 nonemptyImpWitness ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 uniqinunit ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 notinsingleton ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 eqinunit ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 singletonsswitch ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 upairsetE ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 upairsetIL ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 upairsetIR ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 emptyE1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 vacuousDall ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 quantDeMorgan1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 quantDeMorgan2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 quantDeMorgan3 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 quantDeMorgan4 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 prop2setI ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 prop2set2propI ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 notdexE ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 notdallE ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 exuI1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 exuI3 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 exuI2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 inCongP ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in__Cong ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 exuE3u ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 exu__Cong ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 emptyset__Cong ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setadjoin__Cong ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X26:$i,
% 61.67/9.52 X28:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 X26 ) =
% 61.67/9.52 (
% 61.67/9.52 X28 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X26 ) =
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X28 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setunion__Cong ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 omega__Cong ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 exuEu ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 descr__Cong ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 dsetconstr__Cong ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subsetI1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 eqimpsubset2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 eqimpsubset1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subsetI2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 emptysetsubset ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subsetE ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subsetE2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 notsubsetI ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 notequalI1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 notequalI2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subsetRefl ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subsetTrans ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setadjoinSub ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setadjoinSub2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X30:$i,
% 61.67/9.52 X32:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X30 @ X32 ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X30 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X32 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setextsub ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subsetemptysetimpeq ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X34:$i,
% 61.67/9.52 X36:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X36 @ X34 ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X36 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X34 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X38:$i,
% 61.67/9.52 X40:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X40 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X38 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X40 @ X38 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X42:$i]:
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X42 @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X42 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X44:$i,
% 61.67/9.52 X46:$i]:
% 61.67/9.52 (
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% 61.67/9.52 subset @
% 61.67/9.52 X44 @ X46 ) =>
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X44 ) @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X46 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 sepInPowerset ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 sepSubset ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binunionIL ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 upairset2IR ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binunionIR ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binunionEcases ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binunionE ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binunionLsub ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binunionRsub ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
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% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X52 @ X48 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X52 @ X50 ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X52 @
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X48 @ X50 ) ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
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% 61.67/9.52 X56:$i,
% 61.67/9.52 X58:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X58 @ X54 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X58 @ X56 ) =>
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X58 @
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X54 @ X56 ) ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X60:$i,
% 61.67/9.52 X62:$i,
% 61.67/9.52 X64:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X64 @
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X60 @ X62 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X64 @ X60 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X66:$i,
% 61.67/9.52 X68:$i]:
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X66 @ X68 ) @
% 61.67/9.52 X66 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X70:$i,
% 61.67/9.52 X72:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X70 @ X72 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X70 @ X72 ) =
% 61.67/9.52 (
% 61.67/9.52 X70 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X74:$i,
% 61.67/9.52 X76:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X74 @ X76 ) =
% 61.67/9.52 (
% 61.67/9.52 X76 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X76 @ X74 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X78:$i,
% 61.67/9.52 X80:$i,
% 61.67/9.52 X82:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X82 @
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X78 @ X80 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X82 @ X80 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X84:$i,
% 61.67/9.52 X86:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ~(
% 61.67/9.52 ?[
% 61.67/9.52 X88:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X88 @ X86 ) &
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X88 @ X84 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X84 @ X86 ) =
% 61.67/9.52 (
% 61.67/9.52 emptyset ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X90:$i,
% 61.67/9.52 X92:$i]:
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X90 @ X92 ) @
% 61.67/9.52 X92 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X94:$i,
% 61.67/9.52 X96:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X96 @ X94 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X94 @ X96 ) =
% 61.67/9.52 (
% 61.67/9.52 X96 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X98:$i,
% 61.67/9.52 X100:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 binintersect
% 61.67/9.52 @
% 61.67/9.52 X98 @ X100 ) =
% 61.67/9.52 (
% 61.67/9.52 X98 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X98 @ X100 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 bs114d ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X102:$i,
% 61.67/9.52 X104:$i,
% 61.67/9.52 X106:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X106 @
% 61.67/9.52 X102 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ~(
% 61.67/9.52 in @
% 61.67/9.52 X106 @
% 61.67/9.52 X104 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X106 @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X102 @
% 61.67/9.52 X104 ) ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X108:$i,
% 61.67/9.52 X110:$i,
% 61.67/9.52 X112:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X112 @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X108 @
% 61.67/9.52 X110 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X112 @
% 61.67/9.52 X108 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X114:$i,
% 61.67/9.52 X116:$i,
% 61.67/9.52 X118:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X118 @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X114 @
% 61.67/9.52 X116 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 ~(
% 61.67/9.52 in @
% 61.67/9.52 X118 @
% 61.67/9.52 X116 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X120:$i,
% 61.67/9.52 X122:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X120 @
% 61.67/9.52 X122 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X120 @
% 61.67/9.52 X122 ) =
% 61.67/9.52 (
% 61.67/9.52 emptyset ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X124:$i,
% 61.67/9.52 X126:$i,
% 61.67/9.52 X128:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ~(
% 61.67/9.52 in @
% 61.67/9.52 X128 @
% 61.67/9.52 (
% 61.67/9.52 setminus
% 61.67/9.52 @
% 61.67/9.52 X124 @
% 61.67/9.52 X126 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X128 @
% 61.67/9.52 X124 ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X128 @
% 61.67/9.52 X126 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X130:$i,
% 61.67/9.52 X132:$i,
% 61.67/9.52 X134:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ~(
% 61.67/9.52 in @
% 61.67/9.52 X134 @
% 61.67/9.52 (
% 61.67/9.52 setminus
% 61.67/9.52 @
% 61.67/9.52 X130 @
% 61.67/9.52 X132 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ~(
% 61.67/9.52 in @
% 61.67/9.52 X134 @
% 61.67/9.52 X132 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 ~(
% 61.67/9.52 in @
% 61.67/9.52 X134 @
% 61.67/9.52 X130 ) ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X136:$i,
% 61.67/9.52 X138:$i,
% 61.67/9.52 X140:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ~(
% 61.67/9.52 in @
% 61.67/9.52 X140 @
% 61.67/9.52 X136 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 ~(
% 61.67/9.52 in @
% 61.67/9.52 X140 @
% 61.67/9.52 (
% 61.67/9.52 setminus
% 61.67/9.52 @
% 61.67/9.52 X136 @
% 61.67/9.52 X138 ) ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X142:$i,
% 61.67/9.52 X144:$i,
% 61.67/9.52 X146:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X146 @
% 61.67/9.52 X144 ) =>
% 61.67/9.52 (
% 61.67/9.52 ~(
% 61.67/9.52 in @
% 61.67/9.52 X146 @
% 61.67/9.52 (
% 61.67/9.52 setminus
% 61.67/9.52 @
% 61.67/9.52 X142 @
% 61.67/9.52 X144 ) ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X148:$i,
% 61.67/9.52 X150:$i]:
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X148 @
% 61.67/9.52 X150 ) @
% 61.67/9.52 X148 ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X152:$i,
% 61.67/9.52 X154:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setminus @
% 61.67/9.52 X152 @
% 61.67/9.52 X154 ) =
% 61.67/9.52 (
% 61.67/9.52 emptyset ) ) =>
% 61.67/9.52 (
% 61.67/9.52 subset @
% 61.67/9.52 X152 @
% 61.67/9.52 X154 ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 symdiffE ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 symdiffI1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 symdiffI2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 symdiffIneg1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 symdiffIneg2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 secondinupair ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setukpairIL ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setukpairIR ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 kpairiskpair ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 kpairp ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 singletonsubset ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ![
% 61.67/9.52 X156:$i,
% 61.67/9.52 X158:$i]:
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 X158 @
% 61.67/9.52 X156 ) =>
% 61.67/9.52 (
% 61.67/9.52 in @
% 61.67/9.52 (
% 61.67/9.52 setadjoin
% 61.67/9.52 @
% 61.67/9.52 X158 @
% 61.67/9.52 emptyset ) @
% 61.67/9.52 (
% 61.67/9.52 powerset @
% 61.67/9.52 X156 ) ) ) ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 singletoninpowunion ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 upairset2E ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 upairsubunion ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 upairinpowunion ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ubforcartprodlem1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ubforcartprodlem2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ubforcartprodlem3 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 cartprodpairin ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 cartprodmempair1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 cartprodmempair ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setunionE2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setunionsingleton1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setunionsingleton2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setunionsingleton ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 singletonprop ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ex1E1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ex1I ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ex1I2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 singletonsuniq ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setukpairinjL1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 kfstsingleton ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 theprop ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 kfstpairEq ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 cartprodfstin ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setukpairinjL2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setukpairinjL ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setukpairinjR11 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setukpairinjR12 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setukpairinjR1 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 upairequniteq ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setukpairinjR2 ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setukpairinjR ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ksndsingleton ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 ksndpairEq ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 kpairsurjEq ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 cartprodsndin ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 cartprodpairmemEL ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 cartprodpairmemER ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 cartprodmempaircEq ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 cartprodfstpairEq ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 cartprodsndpairEq ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 cartprodpairsurjEq ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 dpsetconstrI ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 dpsetconstrSub ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 setOfPairsIsBReln ) =>
% 61.67/9.52 (
% 61.67/9.52 (
% 61.67/9.52 dpsetconstrERa ) =>
% 61.67/9.52 (
% 61.67/9.52 (
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% 61.67/9.53 (
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% 61.67/9.53 X254 @
% 61.67/9.53 (
% 61.67/9.53 powerset @
% 61.67/9.53 X250 ) ) =>
% 61.67/9.53 (
% 61.67/9.53 ![
% 61.67/9.53 X256:$i]:
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 X256 @
% 61.67/9.53 X250 ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 subset @
% 61.67/9.53 X252 @
% 61.67/9.53 X254 ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 ~(
% 61.67/9.53 in @
% 61.67/9.53 X256 @
% 61.67/9.53 X254 ) ) =>
% 61.67/9.53 (
% 61.67/9.53 ~(
% 61.67/9.53 in @
% 61.67/9.53 X256 @
% 61.67/9.53 X252 ) ) ) ) ) ) ) ) ) ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 ![
% 61.67/9.53 X258:$i,
% 61.67/9.53 X260:$i]:
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% 61.67/9.53 X258 ) ) =>
% 61.67/9.53 (
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% 61.67/9.53 (
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% 61.67/9.53 X258 @
% 61.67/9.53 X262 ) @
% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X258 @
% 61.67/9.53 X260 ) ) ) ) ) ) ) =>
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% 61.67/9.53 X264 ) ) =>
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% 61.67/9.53 (
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% 61.67/9.53 X264 ) ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 subset @
% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X264 @
% 61.67/9.53 X268 ) @
% 61.67/9.53 (
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% 61.67/9.53 X264 @
% 61.67/9.53 X266 ) ) =>
% 61.67/9.53 (
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% 61.67/9.53 X266 @
% 61.67/9.53 X268 ) ) ) ) ) ) =>
% 61.67/9.53 (
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% 61.67/9.53 (
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% 61.67/9.53 (
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% 61.67/9.53 (
% 61.67/9.53 (
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% 61.67/9.53 X272 ) =>
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 X274 @
% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X270 @
% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X270 @
% 61.67/9.53 X272 ) ) ) ) ) ) ) ) =>
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% 61.67/9.53 (
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% 61.67/9.53 (
% 61.67/9.53 (
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% 61.67/9.53 X276 @
% 61.67/9.53 X278 ) ) ) =>
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 X280 @
% 61.67/9.53 X278 ) ) ) ) ) ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 ![
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% 61.67/9.53 (
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% 61.67/9.53 X282 ) ) =>
% 61.67/9.53 (
% 61.67/9.53 subset @
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% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X282 @
% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X282 @
% 61.67/9.53 X284 ) ) ) ) ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 ![
% 61.67/9.53 X286:$i,
% 61.67/9.53 X288:$i]:
% 61.67/9.53 (
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% 61.67/9.53 in @
% 61.67/9.53 X288 @
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% 61.67/9.53 powerset @
% 61.67/9.53 X286 ) ) =>
% 61.67/9.53 (
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% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X286 @
% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X286 @
% 61.67/9.53 X288 ) ) @
% 61.67/9.53 X288 ) ) ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 ![
% 61.67/9.53 X290:$i,
% 61.67/9.53 X292:$i]:
% 61.67/9.53 (
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% 61.67/9.53 in @
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% 61.67/9.53 (
% 61.67/9.53 powerset @
% 61.67/9.53 X290 ) ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 X292 ) =
% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X290 @
% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X290 @
% 61.67/9.53 X292 ) ) ) ) ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 ![
% 61.67/9.53 X294:$i,
% 61.67/9.53 X296:$i]:
% 61.67/9.53 (
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% 61.67/9.53 powerset @
% 61.67/9.53 X294 ) ) =>
% 61.67/9.53 (
% 61.67/9.53 ![
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% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 in @
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% 61.67/9.53 (
% 61.67/9.53 powerset @
% 61.67/9.53 X294 ) ) =>
% 61.67/9.53 (
% 61.67/9.53 ![
% 61.67/9.53 X300:$i]:
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 X300 @
% 61.67/9.53 X294 ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 X300 @
% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X294 @
% 61.67/9.53 X296 ) ) =>
% 61.67/9.53 (
% 61.67/9.53 ~(
% 61.67/9.53 in @
% 61.67/9.53 X300 @
% 61.67/9.53 (
% 61.67/9.53 binintersect
% 61.67/9.53 @
% 61.67/9.53 X296 @
% 61.67/9.53 X298 ) ) ) ) ) ) ) ) ) ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 ![
% 61.67/9.53 X302:$i,
% 61.67/9.53 X304:$i]:
% 61.67/9.53 (
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% 61.67/9.53 powerset @
% 61.67/9.53 X302 ) ) =>
% 61.67/9.53 (
% 61.67/9.53 ![
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% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 X306 @
% 61.67/9.53 (
% 61.67/9.53 powerset @
% 61.67/9.53 X302 ) ) =>
% 61.67/9.53 (
% 61.67/9.53 ![
% 61.67/9.53 X308:$i]:
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 X308 @
% 61.67/9.53 X302 ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 X308 @
% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X302 @
% 61.67/9.53 X304 ) ) =>
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 X308 @
% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X302 @
% 61.67/9.53 (
% 61.67/9.53 binintersect
% 61.67/9.53 @
% 61.67/9.53 X304 @
% 61.67/9.53 X306 ) ) ) ) ) ) ) ) ) ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 ![
% 61.67/9.53 X310:$i,
% 61.67/9.53 X312:$i]:
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 X312 @
% 61.67/9.53 (
% 61.67/9.53 powerset @
% 61.67/9.53 X310 ) ) =>
% 61.67/9.53 (
% 61.67/9.53 ![
% 61.67/9.53 X314:$i]:
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 X314 @
% 61.67/9.53 (
% 61.67/9.53 powerset @
% 61.67/9.53 X310 ) ) =>
% 61.67/9.53 (
% 61.67/9.53 subset @
% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X310 @
% 61.67/9.53 X312 ) @
% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X310 @
% 61.67/9.53 (
% 61.67/9.53 binintersect
% 61.67/9.53 @
% 61.67/9.53 X312 @
% 61.67/9.53 X314 ) ) ) ) ) ) ) =>
% 61.67/9.53 (
% 61.67/9.53 ![
% 61.67/9.53 X316:$i,
% 61.67/9.53 X318:$i]:
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 X318 @
% 61.67/9.53 (
% 61.67/9.53 powerset @
% 61.67/9.53 X316 ) ) =>
% 61.67/9.53 (
% 61.67/9.53 ![
% 61.67/9.53 X320:$i]:
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 X320 @
% 61.67/9.53 (
% 61.67/9.53 powerset @
% 61.67/9.53 X316 ) ) =>
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X316 @
% 61.67/9.53 X318 ) @
% 61.67/9.53 (
% 61.67/9.53 powerset @
% 61.67/9.53 (
% 61.67/9.53 setminus @
% 61.67/9.53 X316 @
% 61.67/9.53 (
% 61.67/9.53 binintersect
% 61.67/9.53 @
% 61.67/9.53 X318 @
% 61.67/9.53 X320 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 61.67/9.53 thf(zf_stmt_4, negated_conjecture,
% 61.67/9.53 (~( ( setextAx ) =>
% 61.67/9.53 ( ( emptysetAx ) =>
% 61.67/9.53 ( ( setadjoinAx ) =>
% 61.67/9.53 ( ( ![X4:$i,X6:$i]:
% 61.67/9.53 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 61.67/9.53 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 61.67/9.53 ( ( setunionAx ) =>
% 61.67/9.53 ( ( omega0Ax ) =>
% 61.67/9.53 ( ( omegaSAx ) =>
% 61.67/9.53 ( ( omegaIndAx ) =>
% 61.67/9.53 ( ( replAx ) =>
% 61.67/9.53 ( ( foundationAx ) =>
% 61.67/9.53 ( ( wellorderingAx ) =>
% 61.67/9.53 ( ( descrp ) =>
% 61.67/9.53 ( ( dsetconstrI ) =>
% 61.67/9.53 ( ( dsetconstrEL ) =>
% 61.67/9.53 ( ( dsetconstrER ) =>
% 61.67/9.53 ( ( exuE1 ) =>
% 61.67/9.53 ( ( prop2setE ) =>
% 61.67/9.53 ( ( emptysetE ) =>
% 61.67/9.53 ( ( emptysetimpfalse ) =>
% 61.67/9.53 ( ( notinemptyset ) =>
% 61.67/9.53 ( ( exuE3e ) =>
% 61.67/9.53 ( ( setext ) =>
% 61.67/9.53 ( ( emptyI ) =>
% 61.67/9.53 ( ( noeltsimpempty ) =>
% 61.67/9.53 ( ( setbeta ) =>
% 61.67/9.53 ( ( nonemptyE1 ) =>
% 61.67/9.53 ( ( nonemptyI ) =>
% 61.67/9.53 ( ( nonemptyI1 ) =>
% 61.67/9.53 ( ( setadjoinIL ) =>
% 61.67/9.53 ( ( emptyinunitempty ) =>
% 61.67/9.53 ( ( setadjoinIR ) =>
% 61.67/9.53 ( (
% 61.67/9.53 setadjoinE ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 setadjoinOr ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 setoftrueEq ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 ![
% 61.67/9.53 X10:$i,
% 61.67/9.53 X12:$i]:
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 ![
% 61.67/9.53 X14:$i]:
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 X14 @ X12 ) =>
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 X14 @ X10 ) ) ) =>
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 X12 @
% 61.67/9.53 (
% 61.67/9.53 powerset
% 61.67/9.53 @
% 61.67/9.53 X10 ) ) ) ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 ![
% 61.67/9.53 X16:$i]:
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 emptyset @
% 61.67/9.53 (
% 61.67/9.53 powerset
% 61.67/9.53 @
% 61.67/9.53 X16 ) ) ) =>
% 61.67/9.53 (
% 61.67/9.53 (
% 61.67/9.53 ![
% 61.67/9.53 X18:$i]:
% 61.67/9.53 (
% 61.67/9.53 in @
% 61.67/9.53 emptyset @
% 61.67/9.53 (
% 61.67/9.53 powerset
% 61.89/9.53 @
% 61.89/9.53 X18 ) ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X20:$i,
% 61.89/9.53 X22:$i,
% 61.89/9.53 X24:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X22 @
% 61.89/9.53 (
% 61.89/9.53 powerset
% 61.89/9.53 @
% 61.89/9.53 X20 ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X24 @ X22 ) =>
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X24 @ X20 ) ) ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 setunionI ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 setunionE ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 subPowSU ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 exuE2 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 nonemptyImpWitness ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 uniqinunit ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 notinsingleton ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 eqinunit ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 singletonsswitch ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 upairsetE ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 upairsetIL ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 upairsetIR ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 emptyE1 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 vacuousDall ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 quantDeMorgan1 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 quantDeMorgan2 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 quantDeMorgan3 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 quantDeMorgan4 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 prop2setI ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 prop2set2propI ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 notdexE ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 notdallE ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 exuI1 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 exuI3 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 exuI2 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 inCongP ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 in__Cong ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 exuE3u ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 exu__Cong ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 emptyset__Cong ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 setadjoin__Cong ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X26:$i,
% 61.89/9.53 X28:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 X26 ) =
% 61.89/9.53 (
% 61.89/9.53 X28 ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 powerset
% 61.89/9.53 @
% 61.89/9.53 X26 ) =
% 61.89/9.53 (
% 61.89/9.53 powerset
% 61.89/9.53 @
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% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 setunion__Cong ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 omega__Cong ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 exuEu ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 descr__Cong ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 dsetconstr__Cong ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 subsetI1 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 eqimpsubset2 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 eqimpsubset1 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 subsetI2 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 emptysetsubset ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 subsetE ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 subsetE2 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 notsubsetI ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 notequalI1 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 notequalI2 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 subsetRefl ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 subsetTrans ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 setadjoinSub ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 setadjoinSub2 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X30:$i,
% 61.89/9.53 X32:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 subset @
% 61.89/9.53 X30 @ X32 ) =>
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X30 @
% 61.89/9.53 (
% 61.89/9.53 powerset
% 61.89/9.53 @
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% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 setextsub ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 subsetemptysetimpeq ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X34:$i,
% 61.89/9.53 X36:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 subset @
% 61.89/9.53 X36 @ X34 ) =>
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X36 @
% 61.89/9.53 (
% 61.89/9.53 powerset
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% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X38:$i,
% 61.89/9.53 X40:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X40 @
% 61.89/9.53 (
% 61.89/9.53 powerset
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% 61.89/9.53 X38 ) ) =>
% 61.89/9.53 (
% 61.89/9.53 subset @
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% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X42:$i]:
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X42 @
% 61.89/9.53 (
% 61.89/9.53 powerset
% 61.89/9.53 @
% 61.89/9.53 X42 ) ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X44:$i,
% 61.89/9.53 X46:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 subset @
% 61.89/9.53 X44 @ X46 ) =>
% 61.89/9.53 (
% 61.89/9.53 subset @
% 61.89/9.53 (
% 61.89/9.53 powerset
% 61.89/9.53 @
% 61.89/9.53 X44 ) @
% 61.89/9.53 (
% 61.89/9.53 powerset
% 61.89/9.53 @
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% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 sepInPowerset ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 sepSubset ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 binunionIL ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 upairset2IR ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 binunionIR ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 binunionEcases ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 binunionE ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 binunionLsub ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 binunionRsub ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X48:$i,
% 61.89/9.53 X50:$i,
% 61.89/9.53 X52:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X52 @ X48 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X52 @ X50 ) =>
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X52 @
% 61.89/9.53 (
% 61.89/9.53 binintersect
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% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X54:$i,
% 61.89/9.53 X56:$i,
% 61.89/9.53 X58:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 subset @
% 61.89/9.53 X58 @ X54 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 subset @
% 61.89/9.53 X58 @ X56 ) =>
% 61.89/9.53 (
% 61.89/9.53 subset @
% 61.89/9.53 X58 @
% 61.89/9.53 (
% 61.89/9.53 binintersect
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% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X60:$i,
% 61.89/9.53 X62:$i,
% 61.89/9.53 X64:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X64 @
% 61.89/9.53 (
% 61.89/9.53 binintersect
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% 61.89/9.53 X60 @ X62 ) ) =>
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X64 @ X60 ) ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X66:$i,
% 61.89/9.53 X68:$i]:
% 61.89/9.53 (
% 61.89/9.53 subset @
% 61.89/9.53 (
% 61.89/9.53 binintersect
% 61.89/9.53 @
% 61.89/9.53 X66 @ X68 ) @
% 61.89/9.53 X66 ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X70:$i,
% 61.89/9.53 X72:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 subset @
% 61.89/9.53 X70 @ X72 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 binintersect
% 61.89/9.53 @
% 61.89/9.53 X70 @ X72 ) =
% 61.89/9.53 (
% 61.89/9.53 X70 ) ) ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X74:$i,
% 61.89/9.53 X76:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 binintersect
% 61.89/9.53 @
% 61.89/9.53 X74 @ X76 ) =
% 61.89/9.53 (
% 61.89/9.53 X76 ) ) =>
% 61.89/9.53 (
% 61.89/9.53 subset @
% 61.89/9.53 X76 @ X74 ) ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X78:$i,
% 61.89/9.53 X80:$i,
% 61.89/9.53 X82:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X82 @
% 61.89/9.53 (
% 61.89/9.53 binintersect
% 61.89/9.53 @
% 61.89/9.53 X78 @ X80 ) ) =>
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X82 @ X80 ) ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X84:$i,
% 61.89/9.53 X86:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ~
% 61.89/9.53 (
% 61.89/9.53 ?[
% 61.89/9.53 X88:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X88 @ X86 ) &
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X88 @ X84 ) ) ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 binintersect
% 61.89/9.53 @
% 61.89/9.53 X84 @ X86 ) =
% 61.89/9.53 (
% 61.89/9.53 emptyset ) ) ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X90:$i,
% 61.89/9.53 X92:$i]:
% 61.89/9.53 (
% 61.89/9.53 subset @
% 61.89/9.53 (
% 61.89/9.53 binintersect
% 61.89/9.53 @
% 61.89/9.53 X90 @ X92 ) @
% 61.89/9.53 X92 ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X94:$i,
% 61.89/9.53 X96:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 subset @
% 61.89/9.53 X96 @ X94 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 binintersect
% 61.89/9.53 @
% 61.89/9.53 X94 @ X96 ) =
% 61.89/9.53 (
% 61.89/9.53 X96 ) ) ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X98:$i,
% 61.89/9.53 X100:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 binintersect
% 61.89/9.53 @
% 61.89/9.53 X98 @
% 61.89/9.53 X100 ) =
% 61.89/9.53 (
% 61.89/9.53 X98 ) ) =>
% 61.89/9.53 (
% 61.89/9.53 subset @
% 61.89/9.53 X98 @
% 61.89/9.53 X100 ) ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 bs114d ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X102:$i,
% 61.89/9.53 X104:$i,
% 61.89/9.53 X106:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X106 @
% 61.89/9.53 X102 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ~
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X106 @
% 61.89/9.53 X104 ) ) =>
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X106 @
% 61.89/9.53 (
% 61.89/9.53 setminus
% 61.89/9.53 @
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% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X108:$i,
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% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X112 @
% 61.89/9.53 (
% 61.89/9.53 setminus
% 61.89/9.53 @
% 61.89/9.53 X108 @
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% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X112 @
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% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X114:$i,
% 61.89/9.53 X116:$i,
% 61.89/9.53 X118:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X118 @
% 61.89/9.53 (
% 61.89/9.53 setminus
% 61.89/9.53 @
% 61.89/9.53 X114 @
% 61.89/9.53 X116 ) ) =>
% 61.89/9.53 (
% 61.89/9.53 ~
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X118 @
% 61.89/9.53 X116 ) ) ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X120:$i,
% 61.89/9.53 X122:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 subset @
% 61.89/9.53 X120 @
% 61.89/9.53 X122 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 setminus
% 61.89/9.53 @
% 61.89/9.53 X120 @
% 61.89/9.53 X122 ) =
% 61.89/9.53 (
% 61.89/9.53 emptyset ) ) ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X124:$i,
% 61.89/9.53 X126:$i,
% 61.89/9.53 X128:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ~
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X128 @
% 61.89/9.53 (
% 61.89/9.53 setminus
% 61.89/9.53 @
% 61.89/9.53 X124 @
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% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X128 @
% 61.89/9.53 X124 ) =>
% 61.89/9.53 (
% 61.89/9.53 in @
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% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X130:$i,
% 61.89/9.53 X132:$i,
% 61.89/9.53 X134:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ~
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X134 @
% 61.89/9.53 (
% 61.89/9.53 setminus
% 61.89/9.53 @
% 61.89/9.53 X130 @
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% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ~
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X134 @
% 61.89/9.53 X132 ) ) =>
% 61.89/9.53 (
% 61.89/9.53 ~
% 61.89/9.53 (
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% 61.89/9.53 X134 @
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% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X136:$i,
% 61.89/9.53 X138:$i,
% 61.89/9.53 X140:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ~
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X140 @
% 61.89/9.53 X136 ) ) =>
% 61.89/9.53 (
% 61.89/9.53 ~
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X140 @
% 61.89/9.53 (
% 61.89/9.53 setminus
% 61.89/9.53 @
% 61.89/9.53 X136 @
% 61.89/9.53 X138 ) ) ) ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X142:$i,
% 61.89/9.53 X144:$i,
% 61.89/9.53 X146:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X146 @
% 61.89/9.53 X144 ) =>
% 61.89/9.53 (
% 61.89/9.53 ~
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X146 @
% 61.89/9.53 (
% 61.89/9.53 setminus
% 61.89/9.53 @
% 61.89/9.53 X142 @
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% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X148:$i,
% 61.89/9.53 X150:$i]:
% 61.89/9.53 (
% 61.89/9.53 subset @
% 61.89/9.53 (
% 61.89/9.53 setminus
% 61.89/9.53 @
% 61.89/9.53 X148 @
% 61.89/9.53 X150 ) @
% 61.89/9.53 X148 ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X152:$i,
% 61.89/9.53 X154:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 setminus
% 61.89/9.53 @
% 61.89/9.53 X152 @
% 61.89/9.53 X154 ) =
% 61.89/9.53 (
% 61.89/9.53 emptyset ) ) =>
% 61.89/9.53 (
% 61.89/9.53 subset @
% 61.89/9.53 X152 @
% 61.89/9.53 X154 ) ) ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 symdiffE ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 symdiffI1 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 symdiffI2 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 symdiffIneg1 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 symdiffIneg2 ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 secondinupair ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 setukpairIL ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 setukpairIR ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 kpairiskpair ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 kpairp ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 singletonsubset ) =>
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 ![
% 61.89/9.53 X156:$i,
% 61.89/9.53 X158:$i]:
% 61.89/9.53 (
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 X158 @
% 61.89/9.53 X156 ) =>
% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 (
% 61.89/9.53 setadjoin
% 61.89/9.53 @
% 61.89/9.53 X158 @
% 61.89/9.53 emptyset ) @
% 61.89/9.53 (
% 61.89/9.53 powerset
% 61.89/9.53 @
% 61.89/9.53 X156 ) ) ) ) =>
% 61.89/9.53 (
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% 61.89/9.53 (
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% 61.89/9.53 (
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% 61.89/9.53 (
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% 61.89/9.53 (
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% 61.89/9.53 (
% 61.89/9.53 (
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% 61.89/9.53 (
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% 61.89/9.53 (
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% 61.89/9.53 (
% 61.89/9.53 dpsetconstrSub ) =>
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% 61.89/9.53 (
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% 61.89/9.53 (
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% 61.89/9.53 (
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% 61.89/9.53 (
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% 61.89/9.53 ![
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% 61.89/9.53 (
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% 61.89/9.53 (
% 61.89/9.53 in @
% 61.89/9.53 (
% 61.89/9.53 setminus
% 61.89/9.53 @
% 61.89/9.53 X316 @
% 61.89/9.53 X318 ) @
% 61.89/9.53 (
% 61.89/9.53 powerset
% 61.89/9.53 @
% 61.89/9.53 (
% 61.89/9.53 setminus
% 61.89/9.53 @
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% 61.89/9.53 (
% 61.89/9.53 binintersect
% 61.89/9.53 @
% 61.89/9.53 X318 @
% 61.89/9.53 X320 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 61.89/9.53 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 61.89/9.53 thf(zip_derived_cl135, plain, ( (in @ sk__162 @ (powerset @ sk__161))),
% 61.89/9.53 inference('cnf', [status(esa)], [zf_stmt_4])).
% 61.89/9.53 thf(zip_derived_cl58, plain,
% 61.89/9.53 (![X9 : $i, X10 : $i]: (subset @ (binintersect @ X9 @ X10) @ X9)),
% 61.89/9.53 inference('cnf', [status(esa)], [zf_stmt_4])).
% 61.89/9.53 thf(zip_derived_cl50, plain,
% 61.89/9.53 (![X3 : $i, X4 : $i]:
% 61.89/9.53 ( (in @ X3 @ (powerset @ X4)) | ~ (subset @ X3 @ X4))),
% 61.89/9.53 inference('cnf', [status(esa)], [zf_stmt_4])).
% 61.89/9.53 thf(zip_derived_cl288, plain,
% 61.89/9.53 (![X0 : $i, X1 : $i]: (in @ (binintersect @ X0 @ X1) @ (powerset @ X0))),
% 61.89/9.53 inference('sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl50])).
% 61.89/9.53 thf(zip_derived_cl58, plain,
% 61.89/9.53 (![X9 : $i, X10 : $i]: (subset @ (binintersect @ X9 @ X10) @ X9)),
% 61.89/9.53 inference('cnf', [status(esa)], [zf_stmt_4])).
% 61.89/9.53 thf(zip_derived_cl134, plain,
% 61.89/9.53 (~ (in @ (setminus @ sk__161 @ sk__162) @
% 61.89/9.53 (powerset @ (setminus @ sk__161 @ (binintersect @ sk__162 @ sk__163))))),
% 61.89/9.53 inference('cnf', [status(esa)], [zf_stmt_4])).
% 61.89/9.53 thf(zip_derived_cl119, plain,
% 61.89/9.53 (![X35 : $i, X36 : $i]:
% 61.89/9.53 ( (in @ (powerset @ X35) @ (powerset @ (powerset @ X36)))
% 61.89/9.53 | ~ (in @ X35 @ (powerset @ X36)))),
% 61.89/9.53 inference('cnf', [status(esa)], [zf_stmt_4])).
% 61.89/9.53 thf(zip_derived_cl252, plain,
% 61.89/9.53 (![X143 : $i, X144 : $i, X145 : $i]:
% 61.89/9.53 (~ (in @ X143 @ (powerset @ X144))
% 61.89/9.53 | (in @ X145 @ X144)
% 61.89/9.53 | ~ (in @ X145 @ X143))),
% 61.89/9.53 inference('cnf', [status(esa)], [zf_stmt_4])).
% 61.89/9.53 thf(zip_derived_cl636, plain,
% 61.89/9.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 61.89/9.53 (~ (in @ X1 @ (powerset @ X0))
% 61.89/9.53 | ~ (in @ X2 @ (powerset @ X1))
% 61.89/9.53 | (in @ X2 @ (powerset @ X0)))),
% 61.89/9.53 inference('sup-', [status(thm)], [zip_derived_cl119, zip_derived_cl252])).
% 61.89/9.53 thf(zip_derived_cl140, plain,
% 61.89/9.53 (![X83 : $i, X84 : $i, X85 : $i]:
% 61.89/9.53 (~ (in @ X83 @ (powerset @ X84))
% 61.89/9.53 | (subset @ (setminus @ X84 @ X83) @ (setminus @ X84 @ X85))
% 61.89/9.53 | ~ (subset @ X85 @ X83)
% 61.89/9.53 | ~ (in @ X85 @ (powerset @ X84)))),
% 61.89/9.53 inference('cnf', [status(esa)], [zf_stmt_4])).
% 61.89/9.53 thf(zip_derived_cl226, plain,
% 61.89/9.53 (![X139 : $i, X140 : $i]:
% 61.89/9.53 ( (in @ X139 @ (powerset @ X140)) | ~ (subset @ X139 @ X140))),
% 61.89/9.53 inference('cnf', [status(esa)], [zf_stmt_4])).
% 61.89/9.53 thf(zip_derived_cl13470, plain, ($false),
% 61.89/9.53 inference('eprover', [status(thm)],
% 61.89/9.53 [zip_derived_cl135, zip_derived_cl288, zip_derived_cl58,
% 61.89/9.53 zip_derived_cl134, zip_derived_cl636, zip_derived_cl140,
% 61.89/9.53 zip_derived_cl226])).
% 61.89/9.53
% 61.89/9.53 % SZS output end Refutation
% 61.89/9.53
% 61.89/9.53
% 61.89/9.53 % Terminating...
% 61.89/9.66 % Runner terminated.
% 61.94/9.69 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------