%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU737^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.p6I6RF4aNH true
% Computer : n016.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 04:56:03 PM UTC 2025
% Result : Theorem 61.50s 8.99s
% Output : Refutation 62.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SEU737^1 : TPTP v9.2.0. Released v3.7.0.
% 0.09/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.p6I6RF4aNH true
% 0.11/0.35 % Computer : n016.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8042.1875MB
% 0.11/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Wed Oct 1 16:15:23 EDT 2025
% 0.11/0.35 % CPUTime :
% 0.11/0.35 % Running portfolio for 300 s
% 0.11/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Number of cores: 8
% 0.11/0.36 % Python version: Python 3.6.8
% 0.11/0.36 % Running in HO mode
% 0.47/0.63 % Total configuration time : 828
% 0.47/0.63 % Estimated wc time : 1656
% 0.47/0.63 % Estimated cpu time (8 cpus) : 207.0
% 0.48/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.48/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.48/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.48/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.48/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.49/0.83 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.49/0.84 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.49/0.85 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 61.50/8.99 % Solved by lams/40_c_ic.sh.
% 61.50/8.99 % done 3794 iterations in 8.139s
% 61.50/8.99 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 61.50/8.99 % SZS output start Refutation
% 61.50/8.99 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 61.50/8.99 thf(notdexE_type, type, notdexE: $o).
% 61.50/8.99 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 61.50/8.99 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 61.50/8.99 thf(setunionAx_type, type, setunionAx: $o).
% 61.50/8.99 thf(setminusELneg_type, type, setminusELneg: $o).
% 61.50/8.99 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 61.50/8.99 thf(ex1E1_type, type, ex1E1: $o).
% 61.50/8.99 thf(powersetE_type, type, powersetE: $o).
% 61.50/8.99 thf(omegaSAx_type, type, omegaSAx: $o).
% 61.50/8.99 thf(exuI1_type, type, exuI1: $o).
% 61.50/8.99 thf(exuI2_type, type, exuI2: $o).
% 61.50/8.99 thf(notequalI2_type, type, notequalI2: $o).
% 61.50/8.99 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 61.50/8.99 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 61.50/8.99 thf(upairsubunion_type, type, upairsubunion: $o).
% 61.50/8.99 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 61.50/8.99 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 61.50/8.99 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 61.50/8.99 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 61.50/8.99 thf(setminusILneg_type, type, setminusILneg: $o).
% 61.50/8.99 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 61.50/8.99 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 61.50/8.99 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 61.50/8.99 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 61.50/8.99 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 61.50/8.99 thf(iftrue_type, type, iftrue: $o).
% 61.50/8.99 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 61.50/8.99 thf(ifSingleton_type, type, ifSingleton: $o).
% 61.50/8.99 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 61.50/8.99 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 61.50/8.99 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 61.50/8.99 thf(sk__147_type, type, sk__147: $i).
% 61.50/8.99 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 61.50/8.99 thf(lamProp_type, type, lamProp: $o).
% 61.50/8.99 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 61.50/8.99 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 61.50/8.99 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 61.50/8.99 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 61.50/8.99 thf(setukpairIR_type, type, setukpairIR: $o).
% 61.50/8.99 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 61.50/8.99 thf(lam2p_type, type, lam2p: $o).
% 61.50/8.99 thf(binunionE_type, type, binunionE: $o).
% 61.50/8.99 thf(setext_type, type, setext: $o).
% 61.50/8.99 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 61.50/8.99 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 61.50/8.99 thf(descr__Cong_type, type, descr__Cong: $o).
% 61.50/8.99 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 61.50/8.99 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 61.50/8.99 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 61.50/8.99 thf(eqbreln_type, type, eqbreln: $o).
% 61.50/8.99 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 61.50/8.99 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 61.50/8.99 $o).
% 61.50/8.99 thf(in_type, type, in: $i > $i > $o).
% 61.50/8.99 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 61.50/8.99 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 61.50/8.99 thf(complementT_lem_type, type, complementT_lem: $o).
% 61.50/8.99 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 61.50/8.99 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 61.50/8.99 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 61.50/8.99 thf(beta1_type, type, beta1: $o).
% 61.50/8.99 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 61.50/8.99 thf(powersetTE1_type, type, powersetTE1: $o).
% 61.50/8.99 thf(symdiffI2_type, type, symdiffI2: $o).
% 61.50/8.99 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 61.50/8.99 thf(upairset2IR_type, type, upairset2IR: $o).
% 61.50/8.99 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 61.50/8.99 thf(subsetE_type, type, subsetE: $o).
% 61.50/8.99 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 61.50/8.99 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 61.50/8.99 thf(setbeta_type, type, setbeta: $o).
% 61.50/8.99 thf(eqinunit_type, type, eqinunit: $o).
% 61.50/8.99 thf(upairsetIL_type, type, upairsetIL: $o).
% 61.50/8.99 thf(powersetI1_type, type, powersetI1: $o).
% 61.50/8.99 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 61.50/8.99 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 61.50/8.99 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 61.50/8.99 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 61.50/8.99 thf(powersetAx_type, type, powersetAx: $o).
% 61.50/8.99 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 61.50/8.99 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 61.50/8.99 thf(powersetI_type, type, powersetI: $o).
% 61.50/8.99 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 61.50/8.99 thf(upairsetIR_type, type, upairsetIR: $o).
% 61.50/8.99 thf(lamp_type, type, lamp: $o).
% 61.50/8.99 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 61.50/8.99 thf(inCongP_type, type, inCongP: $o).
% 61.50/8.99 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 61.50/8.99 thf(exuE3e_type, type, exuE3e: $o).
% 61.50/8.99 thf(emptysetE_type, type, emptysetE: $o).
% 61.50/8.99 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 61.50/8.99 thf(setunionI_type, type, setunionI: $o).
% 61.50/8.99 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 61.50/8.99 thf(prop2setI_type, type, prop2setI: $o).
% 61.50/8.99 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 61.50/8.99 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 61.50/8.99 thf(setminusER_type, type, setminusER: $o).
% 61.50/8.99 thf(exuE2_type, type, exuE2: $o).
% 61.50/8.99 thf(emptyset_type, type, emptyset: $i).
% 61.50/8.99 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 61.50/8.99 thf(ex1I_type, type, ex1I: $o).
% 61.50/8.99 thf(ex1E2_type, type, ex1E2: $o).
% 61.50/8.99 thf(setminus_type, type, setminus: $i > $i > $i).
% 61.50/8.99 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 61.50/8.99 thf(powersetsubset_type, type, powersetsubset: $o).
% 61.50/8.99 thf(subPowSU_type, type, subPowSU: $o).
% 61.50/8.99 thf(notequalI1_type, type, notequalI1: $o).
% 61.50/8.99 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 61.50/8.99 thf(notinemptyset_type, type, notinemptyset: $o).
% 61.50/8.99 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 61.50/8.99 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 61.50/8.99 thf(subsetTrans_type, type, subsetTrans: $o).
% 61.50/8.99 thf(kpairp_type, type, kpairp: $o).
% 61.50/8.99 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 61.50/8.99 thf(setminusI_type, type, setminusI: $o).
% 61.50/8.99 thf(binunionIL_type, type, binunionIL: $o).
% 61.50/8.99 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 61.50/8.99 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 61.50/8.99 thf(subsetE2_type, type, subsetE2: $o).
% 61.50/8.99 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 61.50/8.99 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 61.50/8.99 thf(beta2_type, type, beta2: $o).
% 61.50/8.99 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 61.50/8.99 thf(setextsub_type, type, setextsub: $o).
% 61.50/8.99 thf(binunionLsub_type, type, binunionLsub: $o).
% 61.50/8.99 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 61.50/8.99 thf(sk__148_type, type, sk__148: $i).
% 61.50/8.99 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 61.50/8.99 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 61.50/8.99 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 61.50/8.99 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 61.50/8.99 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 61.50/8.99 thf(setunionE_type, type, setunionE: $o).
% 61.50/8.99 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 61.50/8.99 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 61.50/8.99 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 61.50/8.99 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 61.50/8.99 thf(binunionIR_type, type, binunionIR: $o).
% 61.50/8.99 thf(theeq_type, type, theeq: $o).
% 61.50/8.99 thf(setadjoinE_type, type, setadjoinE: $o).
% 61.50/8.99 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 61.50/8.99 thf(sk__146_type, type, sk__146: $i).
% 61.50/8.99 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 61.50/8.99 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 61.50/8.99 thf(ap2p_type, type, ap2p: $o).
% 61.50/8.99 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 61.50/8.99 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 61.50/8.99 thf(exuE1_type, type, exuE1: $o).
% 61.50/8.99 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 61.50/8.99 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 61.50/8.99 thf(setminusLsub_type, type, setminusLsub: $o).
% 61.50/8.99 thf(funcextLem_type, type, funcextLem: $o).
% 61.50/8.99 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 61.50/8.99 thf(notinsingleton_type, type, notinsingleton: $o).
% 61.50/8.99 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 61.50/8.99 thf(exuEu_type, type, exuEu: $o).
% 61.50/8.99 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 61.50/8.99 thf(upairsetE_type, type, upairsetE: $o).
% 61.50/8.99 thf(omega0Ax_type, type, omega0Ax: $o).
% 61.50/8.99 thf(subsetTI_type, type, subsetTI: $o).
% 61.50/8.99 thf(notsubsetI_type, type, notsubsetI: $o).
% 61.50/8.99 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 61.50/8.99 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 61.50/8.99 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 61.50/8.99 thf(setextAx_type, type, setextAx: $o).
% 61.50/8.99 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 61.50/8.99 thf(powersetE1_type, type, powersetE1: $o).
% 61.50/8.99 thf(bs114d_type, type, bs114d: $o).
% 61.50/8.99 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 61.50/8.99 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 61.50/8.99 thf(ifp_type, type, ifp: $o).
% 61.50/8.99 thf(powersetTI1_type, type, powersetTI1: $o).
% 61.50/8.99 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 61.50/8.99 thf(subsetI1_type, type, subsetI1: $o).
% 61.50/8.99 thf(symdiffE_type, type, symdiffE: $o).
% 61.50/8.99 thf(descrp_type, type, descrp: $o).
% 61.50/8.99 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 61.50/8.99 thf(foundationAx_type, type, foundationAx: $o).
% 61.50/8.99 thf(emptysetAx_type, type, emptysetAx: $o).
% 61.50/8.99 thf(emptyI_type, type, emptyI: $o).
% 61.50/8.99 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 61.50/8.99 thf(eta2_type, type, eta2: $o).
% 61.50/8.99 thf(binintersectEL_type, type, binintersectEL: $o).
% 61.50/8.99 thf(emptyE1_type, type, emptyE1: $o).
% 61.50/8.99 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 61.50/8.99 thf(complementTI1_type, type, complementTI1: $o).
% 61.50/8.99 thf(vacuousDall_type, type, vacuousDall: $o).
% 61.50/8.99 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 61.50/8.99 thf(binintersectI_type, type, binintersectI: $o).
% 61.50/8.99 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 61.50/8.99 thf(funcext_type, type, funcext: $o).
% 61.50/8.99 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 61.50/8.99 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 61.50/8.99 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 61.50/8.99 thf(brelnall2_type, type, brelnall2: $o).
% 61.50/8.99 thf(setextT_type, type, setextT: $o).
% 61.50/8.99 thf(ex1I2_type, type, ex1I2: $o).
% 61.50/8.99 thf(symdiffI1_type, type, symdiffI1: $o).
% 61.50/8.99 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 61.50/8.99 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 61.50/8.99 thf(sk__142_type, type, sk__142: $i > $i > $i).
% 61.50/8.99 thf(theprop_type, type, theprop: $o).
% 61.50/8.99 thf(subsetI2_type, type, subsetI2: $o).
% 61.50/8.99 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 61.50/8.99 $o).
% 61.50/8.99 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 61.50/8.99 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 61.50/8.99 thf(setminusERneg_type, type, setminusERneg: $o).
% 61.50/8.99 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 61.50/8.99 thf(omega__Cong_type, type, omega__Cong: $o).
% 61.50/8.99 thf(subsetRefl_type, type, subsetRefl: $o).
% 61.50/8.99 thf(uniqinunit_type, type, uniqinunit: $o).
% 61.50/8.99 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 61.50/8.99 $o).
% 61.50/8.99 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 61.50/8.99 thf(prop2setE_type, type, prop2setE: $o).
% 61.50/8.99 thf(binunionEcases_type, type, binunionEcases: $o).
% 61.50/8.99 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 61.50/8.99 thf(complementTE1_type, type, complementTE1: $o).
% 61.50/8.99 thf(nonemptyI_type, type, nonemptyI: $o).
% 61.50/8.99 thf(app_type, type, app: $o).
% 61.50/8.99 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 61.50/8.99 thf(exuE3u_type, type, exuE3u: $o).
% 61.50/8.99 thf(eta1_type, type, eta1: $o).
% 61.50/8.99 thf(setminusEL_type, type, setminusEL: $o).
% 61.50/8.99 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 61.50/8.99 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 61.50/8.99 thf(sepSubset_type, type, sepSubset: $o).
% 61.50/8.99 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 61.50/8.99 thf(upairset2E_type, type, upairset2E: $o).
% 61.50/8.99 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 61.50/8.99 thf(exuI3_type, type, exuI3: $o).
% 61.50/8.99 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 61.50/8.99 thf(apProp_type, type, apProp: $o).
% 61.50/8.99 thf(notdallE_type, type, notdallE: $o).
% 61.50/8.99 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 61.50/8.99 thf(binintersectER_type, type, binintersectER: $o).
% 61.50/8.99 thf(brelnall1_type, type, brelnall1: $o).
% 61.50/8.99 thf(powerset_type, type, powerset: $i > $i).
% 61.50/8.99 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 61.50/8.99 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 61.50/8.99 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 61.50/8.99 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 61.50/8.99 thf(exu__Cong_type, type, exu__Cong: $o).
% 61.50/8.99 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 61.50/8.99 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 61.50/8.99 thf(secondinupair_type, type, secondinupair: $o).
% 61.50/8.99 thf(singletonprop_type, type, singletonprop: $o).
% 61.50/8.99 thf(singletonsubset_type, type, singletonsubset: $o).
% 61.50/8.99 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 61.50/8.99 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 61.50/8.99 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 61.50/8.99 thf(replAx_type, type, replAx: $o).
% 61.50/8.99 thf(upairequniteq_type, type, upairequniteq: $o).
% 61.50/8.99 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 61.50/8.99 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 61.50/8.99 thf(setukpairIL_type, type, setukpairIL: $o).
% 61.50/8.99 thf(setunionE2_type, type, setunionE2: $o).
% 61.50/8.99 thf(inPowerset_type, type, inPowerset: $o).
% 61.50/8.99 thf(iffalse_type, type, iffalse: $o).
% 61.50/8.99 thf(funcext2_type, type, funcext2: $o).
% 61.50/8.99 thf(subset_type, type, subset: $i > $i > $o).
% 61.50/8.99 thf(subbreln_type, type, subbreln: $o).
% 61.50/8.99 thf(in__Cong_type, type, in__Cong: $o).
% 61.50/8.99 thf(binunionRsub_type, type, binunionRsub: $o).
% 61.50/8.99 thf(subset2powerset_type, type, subset2powerset: $o).
% 61.50/8.99 thf(contraSubsetComplement, axiom, contraSubsetComplement =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Y:$i]:
% 61.50/8.99 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 61.50/8.99 ( ![Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ A ) =>
% 61.50/8.99 ( ( in @ Xx @ Y ) => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ))).
% 61.50/8.99 thf('0', plain,
% 61.50/8.99 (( contraSubsetComplement ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 61.50/8.99 ( ![X10:$i]:
% 61.50/8.99 ( ( in @ X10 @ X4 ) =>
% 61.50/8.99 ( ( in @ X10 @ X8 ) =>
% 61.50/8.99 ( in @ X10 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(doubleComplementEq, axiom, doubleComplementEq =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ( X ) = ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 61.50/8.99 thf('1', plain,
% 61.50/8.99 (( doubleComplementEq ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ( X6 ) = ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(doubleComplementSub2, axiom, doubleComplementSub2 =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ))).
% 61.50/8.99 thf('2', plain,
% 61.50/8.99 (( doubleComplementSub2 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) @ X6 ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(doubleComplementSub1, axiom, doubleComplementSub1 =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 61.50/8.99 thf('3', plain,
% 61.50/8.99 (( doubleComplementSub1 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( subset @ X6 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(doubleComplementE1, axiom, doubleComplementE1 =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ A ) =>
% 61.50/8.99 ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) =>
% 61.50/8.99 ( in @ Xx @ X ) ) ) ) ))).
% 61.50/8.99 thf('4', plain,
% 61.50/8.99 (( doubleComplementE1 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ X4 ) =>
% 61.50/8.99 ( ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) =>
% 61.50/8.99 ( in @ X8 @ X6 ) ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(doubleComplementI1, axiom, doubleComplementI1 =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ A ) =>
% 61.50/8.99 ( ( in @ Xx @ X ) =>
% 61.50/8.99 ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 61.50/8.99 thf('5', plain,
% 61.50/8.99 (( doubleComplementI1 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ X4 ) =>
% 61.50/8.99 ( ( in @ X8 @ X6 ) =>
% 61.50/8.99 ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(contrasubsetT3, axiom, contrasubsetT3 =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Y:$i]:
% 61.50/8.99 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) =>
% 61.50/8.99 ( subset @ X @ Y ) ) ) ) ))).
% 61.50/8.99 thf('6', plain,
% 61.50/8.99 (( contrasubsetT3 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) =>
% 61.50/8.99 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(contrasubsetT2, axiom, contrasubsetT2 =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Y:$i]:
% 61.50/8.99 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ( subset @ X @ Y ) =>
% 61.50/8.99 ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ))).
% 61.50/8.99 thf('7', plain,
% 61.50/8.99 (( contrasubsetT2 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ( subset @ X6 @ X8 ) =>
% 61.50/8.99 ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(contrasubsetT1, axiom, contrasubsetT1 =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Y:$i]:
% 61.50/8.99 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ A ) =>
% 61.50/8.99 ( ( subset @ X @ Y ) =>
% 61.50/8.99 ( ( ~( in @ Xx @ Y ) ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 61.50/8.99 thf('8', plain,
% 61.50/8.99 (( contrasubsetT1 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X10:$i]:
% 61.50/8.99 ( ( in @ X10 @ X4 ) =>
% 61.50/8.99 ( ( subset @ X6 @ X8 ) =>
% 61.50/8.99 ( ( ~( in @ X10 @ X8 ) ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(contrasubsetT, axiom, contrasubsetT =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Y:$i]:
% 61.50/8.99 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ A ) =>
% 61.50/8.99 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 61.50/8.99 ( ( in @ Xx @ Y ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 61.50/8.99 thf('9', plain,
% 61.50/8.99 (( contrasubsetT ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X10:$i]:
% 61.50/8.99 ( ( in @ X10 @ X4 ) =>
% 61.50/8.99 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 61.50/8.99 ( ( in @ X10 @ X8 ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(complementTE1, axiom, complementTE1 =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ A ) =>
% 61.50/8.99 ( ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) => ( in @ Xx @ X ) ) ) ) ))).
% 61.50/8.99 thf('10', plain,
% 61.50/8.99 (( complementTE1 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ X4 ) =>
% 61.50/8.99 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) => ( in @ X8 @ X6 ) ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(complementTI1, axiom, complementTI1 =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ A ) =>
% 61.50/8.99 ( ( in @ Xx @ X ) => ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 61.50/8.99 thf('11', plain,
% 61.50/8.99 (( complementTI1 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ X4 ) =>
% 61.50/8.99 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(powersetTE1, axiom, powersetTE1 =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Y:$i]:
% 61.50/8.99 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ A ) =>
% 61.50/8.99 ( ( in @ X @ ( powerset @ Y ) ) =>
% 61.50/8.99 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 61.50/8.99 thf('12', plain,
% 61.50/8.99 (( powersetTE1 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X10:$i]:
% 61.50/8.99 ( ( in @ X10 @ X4 ) =>
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 61.50/8.99 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(powersetTI1, axiom, powersetTI1 =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Y:$i]:
% 61.50/8.99 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ( ![Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 61.50/8.99 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 61.50/8.99 thf('13', plain,
% 61.50/8.99 (( powersetTI1 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ( ![X10:$i]:
% 61.50/8.99 ( ( in @ X10 @ X4 ) =>
% 61.50/8.99 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 61.50/8.99 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(subsetTI, axiom, subsetTI =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Y:$i]:
% 61.50/8.99 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ( ![Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 61.50/8.99 ( subset @ X @ Y ) ) ) ) ))).
% 61.50/8.99 thf('14', plain,
% 61.50/8.99 (( subsetTI ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ( ![X10:$i]:
% 61.50/8.99 ( ( in @ X10 @ X4 ) =>
% 61.50/8.99 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 61.50/8.99 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(setextT, axiom, setextT =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Y:$i]:
% 61.50/8.99 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ( ![Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 61.50/8.99 ( ( ![Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 61.50/8.99 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 61.50/8.99 thf('15', plain,
% 61.50/8.99 (( setextT ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ( ![X10:$i]:
% 61.50/8.99 ( ( in @ X10 @ X4 ) =>
% 61.50/8.99 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 61.50/8.99 ( ( ![X12:$i]:
% 61.50/8.99 ( ( in @ X12 @ X4 ) =>
% 61.50/8.99 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 61.50/8.99 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(complementT_lem, axiom, complementT_lem =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ))).
% 61.50/8.99 thf('16', plain,
% 61.50/8.99 (( complementT_lem ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( in @ ( setminus @ X4 @ X6 ) @ ( powerset @ X4 ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(setminusT_lem, axiom, setminusT_lem =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( ![Y:$i]:
% 61.50/8.99 ( ( in @ Y @ ( powerset @ A ) ) =>
% 61.50/8.99 ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 61.50/8.99 thf('17', plain,
% 61.50/8.99 (( setminusT_lem ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ![X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( in @ ( setminus @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(powersetT_lem, axiom, powersetT_lem =
% 61.50/8.99 (![A:$i,X:$i]:
% 61.50/8.99 ( ( in @ X @ ( powerset @ A ) ) =>
% 61.50/8.99 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 61.50/8.99 thf('18', plain,
% 61.50/8.99 (( powersetT_lem ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(singletoninpowerset, axiom, singletoninpowerset =
% 61.50/8.99 (![A:$i,Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ A ) =>
% 61.50/8.99 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 61.50/8.99 thf('19', plain,
% 61.50/8.99 (( singletoninpowerset ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ X4 ) =>
% 61.50/8.99 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(setminusSubset1, axiom, setminusSubset1 =
% 61.50/8.99 (![A:$i,B:$i]:
% 61.50/8.99 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))).
% 61.50/8.99 thf('20', plain,
% 61.50/8.99 (( setminusSubset1 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(setminusLsub, axiom, setminusLsub =
% 61.50/8.99 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))).
% 61.50/8.99 thf('21', plain,
% 61.50/8.99 (( setminusLsub ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(setminusIRneg, axiom, setminusIRneg =
% 61.50/8.99 (![A:$i,B:$i,Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 61.50/8.99 thf('22', plain,
% 61.50/8.99 (( setminusIRneg ) =
% 61.50/8.99 ( ![X4:$i,X6:$i,X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(setminusILneg, axiom, setminusILneg =
% 61.50/8.99 (![A:$i,B:$i,Xx:$i]:
% 61.50/8.99 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 61.50/8.99 thf('23', plain,
% 61.50/8.99 (( setminusILneg ) =
% 61.50/8.99 ( ![X4:$i,X6:$i,X8:$i]:
% 61.50/8.99 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(setminusELneg, axiom, setminusELneg =
% 61.50/8.99 (![A:$i,B:$i,Xx:$i]:
% 61.50/8.99 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 61.50/8.99 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 61.50/8.99 thf('24', plain,
% 61.50/8.99 (( setminusELneg ) =
% 61.50/8.99 ( ![X4:$i,X6:$i,X8:$i]:
% 61.50/8.99 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 61.50/8.99 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(setminusERneg, axiom, setminusERneg =
% 61.50/8.99 (![A:$i,B:$i,Xx:$i]:
% 61.50/8.99 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 61.50/8.99 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 61.50/8.99 thf('25', plain,
% 61.50/8.99 (( setminusERneg ) =
% 61.50/8.99 ( ![X4:$i,X6:$i,X8:$i]:
% 61.50/8.99 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 61.50/8.99 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(setminusSubset2, axiom, setminusSubset2 =
% 61.50/8.99 (![A:$i,B:$i]:
% 61.50/8.99 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))).
% 61.50/8.99 thf('26', plain,
% 61.50/8.99 (( setminusSubset2 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(setminusER, axiom, setminusER =
% 61.50/8.99 (![A:$i,B:$i,Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))).
% 61.50/8.99 thf('27', plain,
% 61.50/8.99 (( setminusER ) =
% 61.50/8.99 ( ![X4:$i,X6:$i,X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(setminusEL, axiom, setminusEL =
% 61.50/8.99 (![A:$i,B:$i,Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 61.50/8.99 thf('28', plain,
% 61.50/8.99 (( setminusEL ) =
% 61.50/8.99 ( ![X4:$i,X6:$i,X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(setminusI, axiom, setminusI =
% 61.50/8.99 (![A:$i,B:$i,Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ A ) =>
% 61.50/8.99 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 61.50/8.99 thf('29', plain,
% 61.50/8.99 (( setminusI ) =
% 61.50/8.99 ( ![X4:$i,X6:$i,X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ X4 ) =>
% 61.50/8.99 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(powersetsubset, axiom, powersetsubset =
% 61.50/8.99 (![A:$i,B:$i]:
% 61.50/8.99 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 61.50/8.99 thf('30', plain,
% 61.50/8.99 (( powersetsubset ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( subset @ X4 @ X6 ) =>
% 61.50/8.99 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 61.50/8.99 thf('31', plain,
% 61.50/8.99 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(powersetE1, axiom, powersetE1 =
% 61.50/8.99 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 61.50/8.99 thf('32', plain,
% 61.50/8.99 (( powersetE1 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(powersetI1, axiom, powersetI1 =
% 61.50/8.99 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 61.50/8.99 thf('33', plain,
% 61.50/8.99 (( powersetI1 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq =
% 61.50/8.99 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))).
% 61.50/8.99 thf('34', plain,
% 61.50/8.99 (( subsetemptysetimpeq ) =
% 61.50/8.99 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(setextsub, axiom, setextsub =
% 61.50/8.99 (![A:$i,B:$i]:
% 61.50/8.99 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))).
% 61.50/8.99 thf('35', plain,
% 61.50/8.99 (( setextsub ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( subset @ X4 @ X6 ) =>
% 61.50/8.99 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(subset2powerset, axiom, subset2powerset =
% 61.50/8.99 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 61.50/8.99 thf('36', plain,
% 61.50/8.99 (( subset2powerset ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(subsetTrans, axiom, subsetTrans =
% 61.50/8.99 (![A:$i,B:$i,C:$i]:
% 61.50/8.99 ( ( subset @ A @ B ) => ( ( subset @ B @ C ) => ( subset @ A @ C ) ) ))).
% 61.50/8.99 thf('37', plain,
% 61.50/8.99 (( subsetTrans ) =
% 61.50/8.99 ( ![X4:$i,X6:$i,X8:$i]:
% 61.50/8.99 ( ( subset @ X4 @ X6 ) =>
% 61.50/8.99 ( ( subset @ X6 @ X8 ) => ( subset @ X4 @ X8 ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(subsetRefl, axiom, subsetRefl = (![A:$i]: ( subset @ A @ A ))).
% 61.50/8.99 thf('38', plain, (( subsetRefl ) = ( ![X4:$i]: ( subset @ X4 @ X4 ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(notequalI1, axiom, notequalI1 =
% 61.50/8.99 (![A:$i,B:$i]: ( ( ~( subset @ A @ B ) ) => ( ( A ) != ( B ) ) ))).
% 61.50/8.99 thf('39', plain,
% 61.50/8.99 (( notequalI1 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]: ( ( ~( subset @ X4 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(notsubsetI, axiom, notsubsetI =
% 61.50/8.99 (![A:$i,B:$i,Xx:$i]:
% 61.50/8.99 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ~( subset @ A @ B ) ) ) ))).
% 61.50/8.99 thf('40', plain,
% 61.50/8.99 (( notsubsetI ) =
% 61.50/8.99 ( ![X4:$i,X6:$i,X8:$i]:
% 61.50/8.99 ( ( in @ X8 @ X4 ) =>
% 61.50/8.99 ( ( ~( in @ X8 @ X6 ) ) => ( ~( subset @ X4 @ X6 ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(subsetE2, axiom, subsetE2 =
% 61.50/8.99 (![A:$i,B:$i,Xx:$i]:
% 61.50/8.99 ( ( subset @ A @ B ) => ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 61.50/8.99 thf('41', plain,
% 61.50/8.99 (( subsetE2 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i,X8:$i]:
% 61.50/8.99 ( ( subset @ X4 @ X6 ) =>
% 61.50/8.99 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(subsetE, axiom, subsetE =
% 61.50/8.99 (![A:$i,B:$i,Xx:$i]:
% 61.50/8.99 ( ( subset @ A @ B ) => ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 61.50/8.99 thf('42', plain,
% 61.50/8.99 (( subsetE ) =
% 61.50/8.99 ( ![X4:$i,X6:$i,X8:$i]:
% 61.50/8.99 ( ( subset @ X4 @ X6 ) => ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(emptysetsubset, axiom, emptysetsubset =
% 61.50/8.99 (![A:$i]: ( subset @ emptyset @ A ))).
% 61.50/8.99 thf('43', plain,
% 61.50/8.99 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(subsetI2, axiom, subsetI2 =
% 61.50/8.99 (![A:$i,B:$i]:
% 61.50/8.99 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 61.50/8.99 ( subset @ A @ B ) ))).
% 61.50/8.99 thf('44', plain,
% 61.50/8.99 (( subsetI2 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 61.50/8.99 ( subset @ X4 @ X6 ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(eqimpsubset1, axiom, eqimpsubset1 =
% 61.50/8.99 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ A @ B ) ))).
% 61.50/8.99 thf('45', plain,
% 61.50/8.99 (( eqimpsubset1 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X4 @ X6 ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(eqimpsubset2, axiom, eqimpsubset2 =
% 61.50/8.99 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ B @ A ) ))).
% 61.50/8.99 thf('46', plain,
% 61.50/8.99 (( eqimpsubset2 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(subsetI1, axiom, subsetI1 =
% 61.50/8.99 (![A:$i,B:$i]:
% 61.50/8.99 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 61.50/8.99 ( subset @ A @ B ) ))).
% 61.50/8.99 thf('47', plain,
% 61.50/8.99 (( subsetI1 ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 61.50/8.99 ( subset @ X4 @ X6 ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(powerset__Cong, axiom, powerset__Cong =
% 61.50/8.99 (![A:$i,B:$i]:
% 61.50/8.99 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 61.50/8.99 thf('48', plain,
% 61.50/8.99 (( powerset__Cong ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(powersetE, axiom, powersetE =
% 61.50/8.99 (![A:$i,B:$i,Xx:$i]:
% 61.50/8.99 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 61.50/8.99 thf('49', plain,
% 61.50/8.99 (( powersetE ) =
% 61.50/8.99 ( ![X4:$i,X6:$i,X8:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 61.50/8.99 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(emptyInPowerset, axiom, emptyInPowerset =
% 61.50/8.99 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 61.50/8.99 thf('50', plain,
% 61.50/8.99 (( emptyInPowerset ) =
% 61.50/8.99 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(emptyinPowerset, axiom, emptyinPowerset =
% 61.50/8.99 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 61.50/8.99 thf('51', plain,
% 61.50/8.99 (( emptyinPowerset ) =
% 61.50/8.99 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(powersetI, axiom, powersetI =
% 61.50/8.99 (![A:$i,B:$i]:
% 61.50/8.99 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 61.50/8.99 ( in @ B @ ( powerset @ A ) ) ))).
% 61.50/8.99 thf('52', plain,
% 61.50/8.99 (( powersetI ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 61.50/8.99 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(powersetAx, axiom, powersetAx =
% 61.50/8.99 (![A:$i,B:$i]:
% 61.50/8.99 ( ( in @ B @ ( powerset @ A ) ) <=>
% 61.50/8.99 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 61.50/8.99 thf('53', plain,
% 61.50/8.99 (( powersetAx ) =
% 61.50/8.99 ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 61.50/8.99 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 61.50/8.99 define([status(thm)])).
% 61.50/8.99 thf(complementTcontraSubset, conjecture,
% 61.50/8.99 (( setextAx ) =>
% 61.50/8.99 ( ( emptysetAx ) =>
% 61.50/8.99 ( ( setadjoinAx ) =>
% 61.50/8.99 ( ( powersetAx ) =>
% 61.50/8.99 ( ( setunionAx ) =>
% 61.50/8.99 ( ( omega0Ax ) =>
% 61.50/8.99 ( ( omegaSAx ) =>
% 61.50/8.99 ( ( omegaIndAx ) =>
% 61.50/8.99 ( ( replAx ) =>
% 61.50/8.99 ( ( foundationAx ) =>
% 61.50/8.99 ( ( wellorderingAx ) =>
% 61.50/8.99 ( ( descrp ) =>
% 61.50/8.99 ( ( dsetconstrI ) =>
% 61.50/8.99 ( ( dsetconstrEL ) =>
% 61.50/8.99 ( ( dsetconstrER ) =>
% 61.50/8.99 ( ( exuE1 ) =>
% 61.50/8.99 ( ( prop2setE ) =>
% 61.50/8.99 ( ( emptysetE ) =>
% 61.50/8.99 ( ( emptysetimpfalse ) =>
% 61.50/8.99 ( ( notinemptyset ) =>
% 61.50/8.99 ( ( exuE3e ) =>
% 61.50/8.99 ( ( setext ) =>
% 61.50/8.99 ( ( emptyI ) =>
% 61.50/8.99 ( ( noeltsimpempty ) =>
% 61.50/8.99 ( ( setbeta ) =>
% 61.50/8.99 ( ( nonemptyE1 ) =>
% 61.50/8.99 ( ( nonemptyI ) =>
% 61.50/8.99 ( ( nonemptyI1 ) =>
% 61.50/8.99 ( ( setadjoinIL ) =>
% 61.50/8.99 ( ( emptyinunitempty ) =>
% 61.50/8.99 ( ( setadjoinIR ) =>
% 61.50/8.99 ( ( setadjoinE ) =>
% 61.50/8.99 ( (
% 61.50/8.99 setadjoinOr ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 setoftrueEq ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 powersetI ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 emptyinPowerset ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 emptyInPowerset ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 powersetE ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 setunionI ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 setunionE ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 subPowSU ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 exuE2 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 nonemptyImpWitness ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 uniqinunit ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 notinsingleton ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 eqinunit ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 singletonsswitch ) =>
% 61.50/8.99 (
% 61.50/8.99 (
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% 61.50/8.99 subset @
% 61.50/8.99 X @
% 61.50/8.99 (
% 61.50/8.99 setminus @
% 61.50/8.99 A @ Y ) ) =>
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 Y @
% 61.50/8.99 (
% 61.50/8.99 setminus @
% 61.50/8.99 A @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 61.50/8.99 thf(zf_stmt_0, conjecture,
% 61.50/8.99 (( setextAx ) =>
% 61.50/8.99 ( ( emptysetAx ) =>
% 61.50/8.99 ( ( setadjoinAx ) =>
% 61.50/8.99 ( ( ![X4:$i,X6:$i]:
% 61.50/8.99 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 61.50/8.99 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 61.50/8.99 ( ( setunionAx ) =>
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% 61.50/8.99 ( ( omegaSAx ) =>
% 61.50/8.99 ( ( omegaIndAx ) =>
% 61.50/8.99 ( ( replAx ) =>
% 61.50/8.99 ( ( foundationAx ) =>
% 61.50/8.99 ( ( wellorderingAx ) =>
% 61.50/8.99 ( ( descrp ) =>
% 61.50/8.99 ( ( dsetconstrI ) =>
% 61.50/8.99 ( ( dsetconstrEL ) =>
% 61.50/8.99 ( ( dsetconstrER ) =>
% 61.50/8.99 ( ( exuE1 ) =>
% 61.50/8.99 ( ( prop2setE ) =>
% 61.50/8.99 ( ( emptysetE ) =>
% 61.50/8.99 ( ( emptysetimpfalse ) =>
% 61.50/8.99 ( ( notinemptyset ) =>
% 61.50/8.99 ( ( exuE3e ) =>
% 61.50/8.99 ( ( setext ) =>
% 61.50/8.99 ( ( emptyI ) =>
% 61.50/8.99 ( ( noeltsimpempty ) =>
% 61.50/8.99 ( ( setbeta ) =>
% 61.50/8.99 ( ( nonemptyE1 ) =>
% 61.50/8.99 ( ( nonemptyI ) =>
% 61.50/8.99 ( ( nonemptyI1 ) =>
% 61.50/8.99 ( ( setadjoinIL ) =>
% 61.50/8.99 ( ( emptyinunitempty ) =>
% 61.50/8.99 ( ( setadjoinIR ) =>
% 61.50/8.99 ( ( setadjoinE ) =>
% 61.50/8.99 ( (
% 61.50/8.99 setadjoinOr ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 setoftrueEq ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X10:$i,
% 61.50/8.99 X12:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X14:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X14 @ X12 ) =>
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X14 @ X10 ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X12 @
% 61.50/8.99 (
% 61.50/8.99 powerset @
% 61.50/8.99 X10 ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X16:$i]:
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 emptyset @
% 61.50/8.99 (
% 61.50/8.99 powerset @
% 61.50/8.99 X16 ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X18:$i]:
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 emptyset @
% 61.50/8.99 (
% 61.50/8.99 powerset @
% 61.50/8.99 X18 ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X20:$i,
% 61.50/8.99 X22:$i,
% 61.50/8.99 X24:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X22 @
% 61.50/8.99 (
% 61.50/8.99 powerset @
% 61.50/8.99 X20 ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X24 @ X22 ) =>
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X24 @ X20 ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 setunionI ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 setunionE ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 subPowSU ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 exuE2 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 nonemptyImpWitness ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 uniqinunit ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 notinsingleton ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 eqinunit ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 singletonsswitch ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 upairsetE ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 upairsetIL ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 upairsetIR ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 emptyE1 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 vacuousDall ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 quantDeMorgan1 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 quantDeMorgan2 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 quantDeMorgan3 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 quantDeMorgan4 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 prop2setI ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 prop2set2propI ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 notdexE ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 notdallE ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 exuI1 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 exuI3 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 exuI2 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 inCongP ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 in__Cong ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 exuE3u ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 exu__Cong ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 emptyset__Cong ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 setadjoin__Cong ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X26:$i,
% 61.50/8.99 X28:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 X26 ) =
% 61.50/8.99 (
% 61.50/8.99 X28 ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 powerset @
% 61.50/8.99 X26 ) =
% 61.50/8.99 (
% 61.50/8.99 powerset @
% 61.50/8.99 X28 ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 setunion__Cong ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 omega__Cong ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 exuEu ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 descr__Cong ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 dsetconstr__Cong ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X30:$i,
% 61.50/8.99 X32:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X34:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X34 @ X30 ) =>
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X34 @ X32 ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X30 @ X32 ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X36:$i,
% 61.50/8.99 X38:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 X36 ) =
% 61.50/8.99 (
% 61.50/8.99 X38 ) ) =>
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X38 @ X36 ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X40:$i,
% 61.50/8.99 X42:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 X40 ) =
% 61.50/8.99 (
% 61.50/8.99 X42 ) ) =>
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X40 @ X42 ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X44:$i,
% 61.50/8.99 X46:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X48:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X48 @ X44 ) =>
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X48 @ X46 ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X44 @ X46 ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X50:$i]:
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 emptyset @
% 61.50/8.99 X50 ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X52:$i,
% 61.50/8.99 X54:$i,
% 61.50/8.99 X56:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X52 @ X54 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X56 @ X52 ) =>
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X56 @ X54 ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X58:$i,
% 61.50/8.99 X60:$i,
% 61.50/8.99 X62:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X58 @ X60 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ~(
% 61.50/8.99 in @
% 61.50/8.99 X62 @ X60 ) ) =>
% 61.50/8.99 (
% 61.50/8.99 ~(
% 61.50/8.99 in @
% 61.50/8.99 X62 @ X58 ) ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X64:$i,
% 61.50/8.99 X66:$i,
% 61.50/8.99 X68:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X68 @ X64 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ~(
% 61.50/8.99 in @
% 61.50/8.99 X68 @ X66 ) ) =>
% 61.50/8.99 (
% 61.50/8.99 ~(
% 61.50/8.99 subset @
% 61.50/8.99 X64 @ X66 ) ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X70:$i,
% 61.50/8.99 X72:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ~(
% 61.50/8.99 subset @
% 61.50/8.99 X70 @ X72 ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 X70 ) !=
% 61.50/8.99 (
% 61.50/8.99 X72 ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 notequalI2 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X74:$i]:
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X74 @ X74 ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X76:$i,
% 61.50/8.99 X78:$i,
% 61.50/8.99 X80:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X76 @ X78 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X78 @ X80 ) =>
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X76 @ X80 ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 setadjoinSub ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 setadjoinSub2 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X82:$i,
% 61.50/8.99 X84:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X82 @ X84 ) =>
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X82 @
% 61.50/8.99 (
% 61.50/8.99 powerset @
% 61.50/8.99 X84 ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X86:$i,
% 61.50/8.99 X88:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X86 @ X88 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X88 @ X86 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 X86 ) =
% 61.50/8.99 (
% 61.50/8.99 X88 ) ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X90:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X90 @
% 61.50/8.99 emptyset ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 X90 ) =
% 61.50/8.99 (
% 61.50/8.99 emptyset ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X92:$i,
% 61.50/8.99 X94:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X94 @ X92 ) =>
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X94 @
% 61.50/8.99 (
% 61.50/8.99 powerset @
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% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X96:$i,
% 61.50/8.99 X98:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X98 @
% 61.50/8.99 (
% 61.50/8.99 powerset @
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% 61.50/8.99 (
% 61.50/8.99 subset @
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% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X100:$i]:
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X100 @
% 61.50/8.99 (
% 61.50/8.99 powerset @
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% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X102:$i,
% 61.50/8.99 X104:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X102 @
% 61.50/8.99 X104 ) =>
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 (
% 61.50/8.99 powerset @
% 61.50/8.99 X102 ) @
% 61.50/8.99 (
% 61.50/8.99 powerset @
% 61.50/8.99 X104 ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 sepInPowerset ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 sepSubset ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 binunionIL ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 upairset2IR ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 binunionIR ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 binunionEcases ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 binunionE ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 binunionLsub ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 binunionRsub ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 binintersectI ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 binintersectSubset5 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 binintersectEL ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 binintersectLsub ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 binintersectSubset2 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 binintersectSubset3 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 binintersectER ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 disjointsetsI1 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 binintersectRsub ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 binintersectSubset4 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 binintersectSubset1 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 bs114d ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X106:$i,
% 61.50/8.99 X108:$i,
% 61.50/8.99 X110:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X110 @
% 61.50/8.99 X106 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ~(
% 61.50/8.99 in @
% 61.50/8.99 X110 @
% 61.50/8.99 X108 ) ) =>
% 61.50/8.99 (
% 61.50/8.99 in @
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% 61.50/8.99 (
% 61.50/8.99 setminus @
% 61.50/8.99 X106 @
% 61.50/8.99 X108 ) ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X112:$i,
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% 61.50/8.99 X112 @
% 61.50/8.99 X114 ) ) =>
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X116 @
% 61.50/8.99 X112 ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
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% 61.50/8.99 X120:$i,
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% 61.50/8.99 X122 @
% 61.50/8.99 (
% 61.50/8.99 setminus @
% 61.50/8.99 X118 @
% 61.50/8.99 X120 ) ) =>
% 61.50/8.99 (
% 61.50/8.99 ~(
% 61.50/8.99 in @
% 61.50/8.99 X122 @
% 61.50/8.99 X120 ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
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% 61.50/8.99 X126:$i]:
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% 61.50/8.99 (
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% 61.50/8.99 setminus @
% 61.50/8.99 X124 @
% 61.50/8.99 X126 ) =
% 61.50/8.99 (
% 61.50/8.99 emptyset ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X128:$i,
% 61.50/8.99 X130:$i,
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% 61.50/8.99 @
% 61.50/8.99 X128 @
% 61.50/8.99 X130 ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X132 @
% 61.50/8.99 X128 ) =>
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X132 @
% 61.50/8.99 X130 ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
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% 61.50/8.99 @
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% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ~(
% 61.50/8.99 in @
% 61.50/8.99 X138 @
% 61.50/8.99 X136 ) ) =>
% 61.50/8.99 (
% 61.50/8.99 ~(
% 61.50/8.99 in @
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% 61.50/8.99 X134 ) ) ) ) ) =>
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% 61.50/8.99 (
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% 61.50/8.99 (
% 61.50/8.99 ~(
% 61.50/8.99 in @
% 61.50/8.99 X144 @
% 61.50/8.99 (
% 61.50/8.99 setminus
% 61.50/8.99 @
% 61.50/8.99 X140 @
% 61.50/8.99 X142 ) ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X146:$i,
% 61.50/8.99 X148:$i,
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% 61.50/8.99 (
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% 61.50/8.99 X150 @
% 61.50/8.99 X148 ) =>
% 61.50/8.99 (
% 61.50/8.99 ~(
% 61.50/8.99 in @
% 61.50/8.99 X150 @
% 61.50/8.99 (
% 61.50/8.99 setminus
% 61.50/8.99 @
% 61.50/8.99 X146 @
% 61.50/8.99 X148 ) ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
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% 61.50/8.99 (
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% 61.50/8.99 X152 @
% 61.50/8.99 X154 ) @
% 61.50/8.99 X152 ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ![
% 61.50/8.99 X156:$i,
% 61.50/8.99 X158:$i]:
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 setminus @
% 61.50/8.99 X156 @
% 61.50/8.99 X158 ) =
% 61.50/8.99 (
% 61.50/8.99 emptyset ) ) =>
% 61.50/8.99 (
% 61.50/8.99 subset @
% 61.50/8.99 X156 @
% 61.50/8.99 X158 ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 symdiffE ) =>
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% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 symdiffIneg1 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 symdiffIneg2 ) =>
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% 61.50/8.99 (
% 61.50/8.99 secondinupair ) =>
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% 61.50/8.99 (
% 61.50/8.99 setukpairIL ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 setukpairIR ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 kpairiskpair ) =>
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% 61.50/8.99 (
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% 61.50/8.99 (
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% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 X162 @
% 61.50/8.99 X160 ) =>
% 61.50/8.99 (
% 61.50/8.99 in @
% 61.50/8.99 (
% 61.50/8.99 setadjoin
% 61.50/8.99 @
% 61.50/8.99 X162 @
% 61.50/8.99 emptyset ) @
% 61.50/8.99 (
% 61.50/8.99 powerset @
% 61.50/8.99 X160 ) ) ) ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 singletoninpowunion ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 upairset2E ) =>
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% 61.50/8.99 (
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% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 upairinpowunion ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ubforcartprodlem1 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ubforcartprodlem2 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 ubforcartprodlem3 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 cartprodpairin ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 cartprodmempair1 ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 cartprodmempair ) =>
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% 61.50/8.99 (
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% 61.50/8.99 (
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% 61.50/8.99 (
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% 61.50/8.99 (
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% 61.50/8.99 (
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% 61.50/8.99 (
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% 61.50/8.99 (
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% 61.50/8.99 (
% 61.50/8.99 singletonsuniq ) =>
% 61.50/8.99 (
% 61.50/8.99 (
% 61.50/8.99 setukpairinjL1 ) =>
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% 61.50/8.99 (
% 61.50/8.99 setukpairinjL ) =>
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% 61.50/8.99 (
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% 61.50/8.99 (
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% 61.50/9.00 (
% 61.50/9.00 (
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% 61.50/9.00 (
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% 61.50/9.00 in @
% 61.50/9.00 X190 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X188 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X192:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X192 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X188 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X194:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X194 @
% 61.50/9.00 X188 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X194 @
% 61.50/9.00 X190 ) =>
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X194 @
% 61.50/9.00 X192 ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 X190 @
% 61.50/9.00 X192 ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X196:$i,
% 61.50/9.00 X198:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X198 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X196 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X200:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X200 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X196 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X202:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X202 @
% 61.50/9.00 X196 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X202 @
% 61.50/9.00 X198 ) =>
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X202 @
% 61.50/9.00 X200 ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X198 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X200 ) ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X204:$i,
% 61.50/9.00 X206:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X206 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X204 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X208:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X208 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X204 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X210:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X210 @
% 61.50/9.00 X204 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X206 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X208 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X210 @
% 61.50/9.00 X206 ) =>
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X210 @
% 61.50/9.00 X208 ) ) ) ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X212:$i,
% 61.50/9.00 X214:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X214 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X212 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X216:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X216 @
% 61.50/9.00 X212 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X216 @
% 61.50/9.00 X214 ) =>
% 61.50/9.00 (
% 61.50/9.00 ~(
% 61.50/9.00 in @
% 61.50/9.00 X216 @
% 61.50/9.00 (
% 61.50/9.00 setminus
% 61.50/9.00 @
% 61.50/9.00 X212 @
% 61.50/9.00 X214 ) ) ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X218:$i,
% 61.50/9.00 X220:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X220 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X218 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X222:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X222 @
% 61.50/9.00 X218 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ~(
% 61.50/9.00 in @
% 61.50/9.00 X222 @
% 61.50/9.00 (
% 61.50/9.00 setminus
% 61.50/9.00 @
% 61.50/9.00 X218 @
% 61.50/9.00 X220 ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X222 @
% 61.50/9.00 X220 ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 binintersectTELcontra ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 binintersectTERcontra ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X224:$i,
% 61.50/9.00 X226:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X226 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X224 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X228:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X228 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X224 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X230:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X230 @
% 61.50/9.00 X224 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 X226 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X224 @
% 61.50/9.00 X228 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X230 @
% 61.50/9.00 X228 ) =>
% 61.50/9.00 (
% 61.50/9.00 ~(
% 61.50/9.00 in @
% 61.50/9.00 X230 @
% 61.50/9.00 X226 ) ) ) ) ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X232:$i,
% 61.50/9.00 X234:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X234 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X232 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X236:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X236 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X232 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X238:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X238 @
% 61.50/9.00 X232 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 X234 @
% 61.50/9.00 X236 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ~(
% 61.50/9.00 in @
% 61.50/9.00 X238 @
% 61.50/9.00 X236 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ~(
% 61.50/9.00 in @
% 61.50/9.00 X238 @
% 61.50/9.00 X234 ) ) ) ) ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X240:$i,
% 61.50/9.00 X242:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X242 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X240 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X244:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X244 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X240 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 X242 @
% 61.50/9.00 X244 ) =>
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X240 @
% 61.50/9.00 X244 ) @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X240 @
% 61.50/9.00 X242 ) ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X246:$i,
% 61.50/9.00 X248:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X248 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X246 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X250:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X250 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X246 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X246 @
% 61.50/9.00 X250 ) @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X246 @
% 61.50/9.00 X248 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 X248 @
% 61.50/9.00 X250 ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X252:$i,
% 61.50/9.00 X254:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X254 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X252 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X256:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X256 @
% 61.50/9.00 X252 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X256 @
% 61.50/9.00 X254 ) =>
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X256 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X252 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X252 @
% 61.50/9.00 X254 ) ) ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X258:$i,
% 61.50/9.00 X260:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X260 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X258 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X262:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X262 @
% 61.50/9.00 X258 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X262 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X258 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X258 @
% 61.50/9.00 X260 ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X262 @
% 61.50/9.00 X260 ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X264:$i,
% 61.50/9.00 X266:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X266 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X264 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 X266 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X264 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X264 @
% 61.50/9.00 X266 ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X268:$i,
% 61.50/9.00 X270:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X270 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X268 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X268 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X268 @
% 61.50/9.00 X270 ) ) @
% 61.50/9.00 X270 ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X272:$i,
% 61.50/9.00 X274:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X274 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X272 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 X274 ) =
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X272 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X272 @
% 61.50/9.00 X274 ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 complementTnotintersectT ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 complementImpComplementIntersect ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 complementSubsetComplementIntersect ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 complementInPowersetComplementIntersect ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X276:$i,
% 61.50/9.00 X278:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X278 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X276 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X280:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X280 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X276 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 X278 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X276 @
% 61.50/9.00 X280 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X282:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X282 @
% 61.50/9.00 X276 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X282 @
% 61.50/9.00 X280 ) =>
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X282 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X276 @
% 61.50/9.00 X278 ) ) ) ) ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X284:$i,
% 61.50/9.00 X286:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X286 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X284 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X288:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X288 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X284 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 X286 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X284 @
% 61.50/9.00 X288 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 X288 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X284 @
% 61.50/9.00 X286 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 61.50/9.00 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 61.50/9.00 thf(zf_stmt_2, axiom,
% 61.50/9.00 (![X8:$i,X6:$i,X4:$i]:
% 61.50/9.00 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 61.50/9.00 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 61.50/9.00 thf(zf_stmt_3, conjecture,
% 61.50/9.00 (( setextAx ) =>
% 61.50/9.00 ( ( emptysetAx ) =>
% 61.50/9.00 ( ( setadjoinAx ) =>
% 61.50/9.00 ( ( ![X4:$i,X6:$i]:
% 61.50/9.00 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 61.50/9.00 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 61.50/9.00 ( ( setunionAx ) =>
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% 61.50/9.00 X120 ) ) ) ) =>
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% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X124:$i,
% 61.50/9.00 X126:$i]:
% 61.50/9.00 (
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% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X124 @
% 61.50/9.00 X126 ) =
% 61.50/9.00 (
% 61.50/9.00 emptyset ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X128:$i,
% 61.50/9.00 X130:$i,
% 61.50/9.00 X132:$i]:
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% 61.50/9.00 (
% 61.50/9.00 ~(
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% 61.50/9.00 X128 @
% 61.50/9.00 X130 ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X132 @
% 61.50/9.00 X128 ) =>
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X132 @
% 61.50/9.00 X130 ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X134:$i,
% 61.50/9.00 X136:$i,
% 61.50/9.00 X138:$i]:
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% 61.50/9.00 @
% 61.50/9.00 X134 @
% 61.50/9.00 X136 ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ~(
% 61.50/9.00 in @
% 61.50/9.00 X138 @
% 61.50/9.00 X136 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ~(
% 61.50/9.00 in @
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% 61.50/9.00 X134 ) ) ) ) ) =>
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% 61.50/9.00 (
% 61.50/9.00 ~(
% 61.50/9.00 in @
% 61.50/9.00 X144 @
% 61.50/9.00 (
% 61.50/9.00 setminus
% 61.50/9.00 @
% 61.50/9.00 X140 @
% 61.50/9.00 X142 ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X146:$i,
% 61.50/9.00 X148:$i,
% 61.50/9.00 X150:$i]:
% 61.50/9.00 (
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% 61.50/9.00 X150 @
% 61.50/9.00 X148 ) =>
% 61.50/9.00 (
% 61.50/9.00 ~(
% 61.50/9.00 in @
% 61.50/9.00 X150 @
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% 61.50/9.00 setminus
% 61.50/9.00 @
% 61.50/9.00 X146 @
% 61.50/9.00 X148 ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
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% 61.50/9.00 setminus @
% 61.50/9.00 X152 @
% 61.50/9.00 X154 ) @
% 61.50/9.00 X152 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X156:$i,
% 61.50/9.00 X158:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X156 @
% 61.50/9.00 X158 ) =
% 61.50/9.00 (
% 61.50/9.00 emptyset ) ) =>
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 X156 @
% 61.50/9.00 X158 ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 symdiffE ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 symdiffI1 ) =>
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% 61.50/9.00 (
% 61.50/9.00 symdiffI2 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 symdiffIneg1 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 symdiffIneg2 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 secondinupair ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 setukpairIL ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 setukpairIR ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 kpairiskpair ) =>
% 61.50/9.00 (
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% 61.50/9.00 (
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% 61.50/9.00 X162 @
% 61.50/9.00 X160 ) =>
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 (
% 61.50/9.00 setadjoin
% 61.50/9.00 @
% 61.50/9.00 X162 @
% 61.50/9.00 emptyset ) @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X160 ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 singletoninpowunion ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 upairset2E ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 upairsubunion ) =>
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% 61.50/9.00 (
% 61.50/9.00 upairinpowunion ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ubforcartprodlem1 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ubforcartprodlem2 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ubforcartprodlem3 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 cartprodpairin ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 cartprodmempair1 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 cartprodmempair ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 setunionE2 ) =>
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% 61.50/9.00 (
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% 61.50/9.00 (
% 61.50/9.00 (
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% 61.50/9.00 (
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% 61.50/9.00 (
% 61.50/9.00 singletonprop ) =>
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% 61.50/9.00 ex1E1 ) =>
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% 61.50/9.00 (
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% 61.50/9.00 (
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% 61.50/9.00 (
% 61.50/9.00 singletonsuniq ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 setukpairinjL1 ) =>
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% 61.50/9.00 (
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% 61.50/9.00 (
% 61.50/9.00 setukpairinjL ) =>
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% 61.50/9.00 (
% 61.50/9.00 cartprodfstpairEq ) =>
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% 61.50/9.00 (
% 61.50/9.00 cartprodsndpairEq ) =>
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% 61.50/9.00 (
% 61.50/9.00 cartprodpairsurjEq ) =>
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% 61.50/9.00 (
% 61.50/9.00 dpsetconstrI ) =>
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% 61.50/9.00 (
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% 61.50/9.00 (
% 61.50/9.00 setOfPairsIsBReln ) =>
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% 61.50/9.00 (
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% 61.50/9.00 (
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% 61.50/9.00 (
% 61.50/9.00 dpsetconstrEL2 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 dpsetconstrER ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 funcImageSingleton ) =>
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% 61.50/9.00 (
% 61.50/9.00 apProp ) =>
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% 61.50/9.00 (
% 61.50/9.00 app ) =>
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% 61.50/9.00 (
% 61.50/9.00 infuncsetfunc ) =>
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% 61.50/9.00 lam2lamEq ) =>
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% 61.50/9.00 (
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% 61.50/9.00 X164 ) ) ) ) ) =>
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% 61.50/9.00 powerset @
% 61.50/9.00 X168 ) ) ) ) ) ) =>
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% 61.50/9.00 X174 @
% 61.50/9.00 X176 ) @
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% 61.50/9.00 powerset @
% 61.50/9.00 X174 ) ) ) ) =>
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% 61.50/9.00 (
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% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X200 ) ) ) ) ) ) ) =>
% 61.50/9.00 (
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% 61.50/9.00 X208 ) ) =>
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% 61.50/9.00 X206 ) =>
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X210 @
% 61.50/9.00 X208 ) ) ) ) ) ) ) ) ) =>
% 61.50/9.00 (
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% 61.50/9.00 X212 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X216:$i]:
% 61.50/9.00 (
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% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X216 @
% 61.50/9.00 X214 ) =>
% 61.50/9.00 (
% 61.50/9.00 ~(
% 61.50/9.00 in @
% 61.50/9.00 X216 @
% 61.50/9.00 (
% 61.50/9.00 setminus
% 61.50/9.00 @
% 61.50/9.00 X212 @
% 61.50/9.00 X214 ) ) ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
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% 61.50/9.00 (
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% 61.50/9.00 X220 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X218 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X222:$i]:
% 61.50/9.00 (
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% 61.50/9.00 in @
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% 61.50/9.00 X218 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ~(
% 61.50/9.00 in @
% 61.50/9.00 X222 @
% 61.50/9.00 (
% 61.50/9.00 setminus
% 61.50/9.00 @
% 61.50/9.00 X218 @
% 61.50/9.00 X220 ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X222 @
% 61.50/9.00 X220 ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 binintersectTELcontra ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 binintersectTERcontra ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X224:$i,
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% 61.50/9.00 (
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% 61.50/9.00 powerset @
% 61.50/9.00 X224 ) ) =>
% 61.50/9.00 (
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% 61.50/9.00 X224 ) ) =>
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% 61.50/9.00 (
% 61.50/9.00 (
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% 61.50/9.00 X230 @
% 61.50/9.00 X228 ) =>
% 61.50/9.00 (
% 61.50/9.00 ~(
% 61.50/9.00 in @
% 61.50/9.00 X230 @
% 61.50/9.00 X226 ) ) ) ) ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
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% 61.50/9.00 X232 ) ) =>
% 61.50/9.00 (
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% 61.50/9.00 (
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% 61.50/9.00 X232 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
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% 61.50/9.00 (
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% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ~(
% 61.50/9.00 in @
% 61.50/9.00 X238 @
% 61.50/9.00 X236 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ~(
% 61.50/9.00 in @
% 61.50/9.00 X238 @
% 61.50/9.00 X234 ) ) ) ) ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
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% 61.50/9.00 X240:$i,
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% 61.50/9.00 (
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% 61.50/9.00 X242 @
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% 61.50/9.00 X240 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X244:$i]:
% 61.50/9.00 (
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% 61.50/9.00 powerset @
% 61.50/9.00 X240 ) ) =>
% 61.50/9.00 (
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% 61.50/9.00 X242 @
% 61.50/9.00 X244 ) =>
% 61.50/9.00 (
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% 61.50/9.00 (
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% 61.50/9.00 X240 @
% 61.50/9.00 X244 ) @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X240 @
% 61.50/9.00 X242 ) ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X246:$i,
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% 61.50/9.00 X248 @
% 61.50/9.00 (
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% 61.50/9.00 X246 ) ) =>
% 61.50/9.00 (
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% 61.50/9.00 X246 ) ) =>
% 61.50/9.00 (
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% 61.50/9.00 X246 @
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% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X246 @
% 61.50/9.00 X248 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 X248 @
% 61.50/9.00 X250 ) ) ) ) ) ) =>
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% 61.50/9.00 (
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% 61.50/9.00 (
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% 61.50/9.00 (
% 61.50/9.00 (
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% 61.50/9.00 X254 ) =>
% 61.50/9.00 (
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% 61.50/9.00 X256 @
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% 61.50/9.00 X252 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X252 @
% 61.50/9.00 X254 ) ) ) ) ) ) ) ) =>
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% 61.50/9.00 (
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% 61.50/9.00 (
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% 61.50/9.00 X258 ) =>
% 61.50/9.00 (
% 61.50/9.00 (
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% 61.50/9.00 (
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% 61.50/9.00 X258 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X258 @
% 61.50/9.00 X260 ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X262 @
% 61.50/9.00 X260 ) ) ) ) ) ) =>
% 61.50/9.00 (
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% 61.50/9.00 X266:$i]:
% 61.50/9.00 (
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% 61.50/9.00 X264 ) ) =>
% 61.50/9.00 (
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% 61.50/9.00 (
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% 61.50/9.00 X264 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X264 @
% 61.50/9.00 X266 ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X268:$i,
% 61.50/9.00 X270:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
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% 61.50/9.00 X270 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X268 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X268 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X268 @
% 61.50/9.00 X270 ) ) @
% 61.50/9.00 X270 ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X272:$i,
% 61.50/9.00 X274:$i]:
% 61.50/9.00 (
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% 61.50/9.00 in @
% 61.50/9.00 X274 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X272 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 X274 ) =
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X272 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X272 @
% 61.50/9.00 X274 ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 complementTnotintersectT ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 complementImpComplementIntersect ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 complementSubsetComplementIntersect ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 complementInPowersetComplementIntersect ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X276:$i,
% 61.50/9.00 X278:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X278 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X276 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X280:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
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% 61.50/9.00 powerset @
% 61.50/9.00 X276 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 X278 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X276 @
% 61.50/9.00 X280 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X282:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X282 @
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% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X282 @
% 61.50/9.00 X280 ) =>
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X282 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X276 @
% 61.50/9.00 X278 ) ) ) ) ) ) ) ) ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X284:$i,
% 61.50/9.00 X286:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X286 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X284 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X288:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 in @
% 61.50/9.00 X288 @
% 61.50/9.00 (
% 61.50/9.00 powerset @
% 61.50/9.00 X284 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 X286 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X284 @
% 61.50/9.00 X288 ) ) =>
% 61.50/9.00 (
% 61.50/9.00 subset @
% 61.50/9.00 X288 @
% 61.50/9.00 (
% 61.50/9.00 setminus @
% 61.50/9.00 X284 @
% 61.50/9.00 X286 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 61.50/9.00 thf(zf_stmt_4, negated_conjecture,
% 61.50/9.00 (~( ( setextAx ) =>
% 61.50/9.00 ( ( emptysetAx ) =>
% 61.50/9.00 ( ( setadjoinAx ) =>
% 61.50/9.00 ( ( ![X4:$i,X6:$i]:
% 61.50/9.00 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 61.50/9.00 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 61.50/9.00 ( ( setunionAx ) =>
% 61.50/9.00 ( ( omega0Ax ) =>
% 61.50/9.00 ( ( omegaSAx ) =>
% 61.50/9.00 ( ( omegaIndAx ) =>
% 61.50/9.00 ( ( replAx ) =>
% 61.50/9.00 ( ( foundationAx ) =>
% 61.50/9.00 ( ( wellorderingAx ) =>
% 61.50/9.00 ( ( descrp ) =>
% 61.50/9.00 ( ( dsetconstrI ) =>
% 61.50/9.00 ( ( dsetconstrEL ) =>
% 61.50/9.00 ( ( dsetconstrER ) =>
% 61.50/9.00 ( ( exuE1 ) =>
% 61.50/9.00 ( ( prop2setE ) =>
% 61.50/9.00 ( ( emptysetE ) =>
% 61.50/9.00 ( ( emptysetimpfalse ) =>
% 61.50/9.00 ( ( notinemptyset ) =>
% 61.50/9.00 ( ( exuE3e ) =>
% 61.50/9.00 ( ( setext ) =>
% 61.50/9.00 ( ( emptyI ) =>
% 61.50/9.00 ( ( noeltsimpempty ) =>
% 61.50/9.00 ( ( setbeta ) =>
% 61.50/9.00 ( ( nonemptyE1 ) =>
% 61.50/9.00 ( ( nonemptyI ) =>
% 61.50/9.00 ( ( nonemptyI1 ) =>
% 61.50/9.00 ( ( setadjoinIL ) =>
% 61.50/9.00 ( ( emptyinunitempty ) =>
% 61.50/9.00 ( ( setadjoinIR ) =>
% 61.50/9.00 ( (
% 61.50/9.00 setadjoinE ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 setadjoinOr ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 setoftrueEq ) =>
% 61.50/9.00 (
% 61.50/9.00 (
% 61.50/9.00 ![
% 61.50/9.00 X10:$i,
% 61.50/9.00 X12:$i]:
% 61.50/9.00 (
% 61.50/9.00 (
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% 61.50/9.00 powerset
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% 62.18/9.01 (
% 62.18/9.01 (
% 62.18/9.01 complementTnotintersectT ) =>
% 62.18/9.01 (
% 62.18/9.01 (
% 62.18/9.01 complementImpComplementIntersect ) =>
% 62.18/9.01 (
% 62.18/9.01 (
% 62.18/9.01 complementSubsetComplementIntersect ) =>
% 62.18/9.01 (
% 62.18/9.01 (
% 62.18/9.01 complementInPowersetComplementIntersect ) =>
% 62.18/9.01 (
% 62.18/9.01 (
% 62.18/9.01 ![
% 62.18/9.01 X276:$i,
% 62.18/9.01 X278:$i]:
% 62.18/9.01 (
% 62.18/9.01 (
% 62.18/9.01 in @
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% 62.18/9.01 (
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% 62.18/9.01 in @
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% 62.18/9.01 (
% 62.18/9.01 ![
% 62.18/9.01 X284:$i,
% 62.18/9.01 X286:$i]:
% 62.18/9.01 (
% 62.18/9.01 (
% 62.18/9.01 in @
% 62.18/9.01 X286 @
% 62.18/9.01 (
% 62.18/9.01 powerset
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% 62.18/9.01 X284 ) ) =>
% 62.18/9.01 (
% 62.18/9.01 ![
% 62.18/9.01 X288:$i]:
% 62.18/9.01 (
% 62.18/9.01 (
% 62.18/9.01 in @
% 62.18/9.01 X288 @
% 62.18/9.01 (
% 62.18/9.01 powerset
% 62.18/9.01 @
% 62.18/9.01 X284 ) ) =>
% 62.18/9.01 (
% 62.18/9.01 (
% 62.18/9.01 subset @
% 62.18/9.01 X286 @
% 62.18/9.01 (
% 62.18/9.01 setminus
% 62.18/9.01 @
% 62.18/9.01 X284 @
% 62.18/9.01 X288 ) ) =>
% 62.18/9.01 (
% 62.18/9.01 subset @
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% 62.18/9.01 (
% 62.18/9.01 setminus
% 62.18/9.01 @
% 62.18/9.01 X284 @
% 62.18/9.01 X286 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 62.18/9.01 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 62.18/9.01 thf(zip_derived_cl135, plain,
% 62.18/9.01 (~ (subset @ sk__148 @ (setminus @ sk__146 @ sk__147))),
% 62.18/9.01 inference('cnf', [status(esa)], [zf_stmt_4])).
% 62.18/9.01 thf(zip_derived_cl237, plain,
% 62.18/9.01 (![X122 : $i, X123 : $i]:
% 62.18/9.01 ( (subset @ X122 @ X123) | (in @ (sk__142 @ X123 @ X122) @ X122))),
% 62.18/9.01 inference('cnf', [status(esa)], [zf_stmt_4])).
% 62.18/9.01 thf(zip_derived_cl136, plain,
% 62.18/9.01 ( (subset @ sk__147 @ (setminus @ sk__146 @ sk__148))),
% 62.18/9.01 inference('cnf', [status(esa)], [zf_stmt_4])).
% 62.18/9.01 thf(zip_derived_cl133, plain,
% 62.18/9.01 (![X62 : $i, X63 : $i, X64 : $i, X65 : $i]:
% 62.18/9.01 (~ (in @ X62 @ (powerset @ X63))
% 62.18/9.01 | ~ (in @ X64 @ X62)
% 62.18/9.01 | (in @ X64 @ (setminus @ X63 @ X65))
% 62.18/9.01 | ~ (in @ X64 @ X63)
% 62.18/9.01 | ~ (subset @ X65 @ (setminus @ X63 @ X62))
% 62.18/9.01 | ~ (in @ X65 @ (powerset @ X63)))),
% 62.18/9.01 inference('cnf', [status(esa)], [zf_stmt_4])).
% 62.18/9.01 thf(zip_derived_cl256, plain,
% 62.18/9.01 (![X126 : $i, X127 : $i, X128 : $i]:
% 62.18/9.01 (~ (in @ X126 @ (powerset @ X127))
% 62.18/9.01 | (in @ X128 @ X127)
% 62.18/9.01 | ~ (in @ X128 @ X126))),
% 62.18/9.01 inference('cnf', [status(esa)], [zf_stmt_4])).
% 62.18/9.01 thf(zip_derived_cl1090, plain,
% 62.18/9.01 (![X62 : $i, X63 : $i, X64 : $i, X65 : $i]:
% 62.18/9.01 (~ (in @ X65 @ (powerset @ X63))
% 62.18/9.01 | ~ (subset @ X65 @ (setminus @ X63 @ X62))
% 62.18/9.01 | (in @ X64 @ (setminus @ X63 @ X65))
% 62.18/9.01 | ~ (in @ X64 @ X62)
% 62.18/9.01 | ~ (in @ X62 @ (powerset @ X63)))),
% 62.18/9.01 inference('clc', [status(thm)], [zip_derived_cl133, zip_derived_cl256])).
% 62.18/9.01 thf(zip_derived_cl1095, plain,
% 62.18/9.01 (![X0 : $i]:
% 62.18/9.01 (~ (in @ sk__148 @ (powerset @ sk__146))
% 62.18/9.01 | ~ (in @ X0 @ sk__148)
% 62.18/9.01 | (in @ X0 @ (setminus @ sk__146 @ sk__147))
% 62.18/9.01 | ~ (in @ sk__147 @ (powerset @ sk__146)))),
% 62.18/9.01 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl1090])).
% 62.18/9.01 thf(zip_derived_cl134, plain, ( (in @ sk__148 @ (powerset @ sk__146))),
% 62.18/9.01 inference('cnf', [status(esa)], [zf_stmt_4])).
% 62.18/9.01 thf(zip_derived_cl137, plain, ( (in @ sk__147 @ (powerset @ sk__146))),
% 62.18/9.01 inference('cnf', [status(esa)], [zf_stmt_4])).
% 62.18/9.01 thf(zip_derived_cl1115, plain,
% 62.18/9.01 (![X0 : $i]:
% 62.18/9.01 (~ (in @ X0 @ sk__148) | (in @ X0 @ (setminus @ sk__146 @ sk__147)))),
% 62.18/9.01 inference('demod', [status(thm)],
% 62.18/9.01 [zip_derived_cl1095, zip_derived_cl134, zip_derived_cl137])).
% 62.18/9.01 thf(zip_derived_cl236, plain,
% 62.18/9.01 (![X122 : $i, X123 : $i]:
% 62.18/9.01 ( (subset @ X122 @ X123) | ~ (in @ (sk__142 @ X123 @ X122) @ X123))),
% 62.18/9.01 inference('cnf', [status(esa)], [zf_stmt_4])).
% 62.18/9.01 thf(zip_derived_cl17754, plain, ($false),
% 62.18/9.01 inference('eprover', [status(thm)],
% 62.18/9.01 [zip_derived_cl135, zip_derived_cl237, zip_derived_cl1115,
% 62.18/9.01 zip_derived_cl236])).
% 62.18/9.01
% 62.18/9.01 % SZS output end Refutation
% 62.18/9.01
% 62.18/9.01
% 62.18/9.01 % Terminating...
% 62.73/9.16 % Runner terminated.
% 62.73/9.17 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------