%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU729^1 : 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.4gkZcQzibA true
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:55:59 PM UTC 2025
% Result : Theorem 119.59s 15.63s
% Output : Refutation 119.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU729^1 : TPTP v9.2.0. Released v3.7.0.
% 0.11/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.4gkZcQzibA true
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 1 16:11:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Running portfolio for 300 s
% 0.12/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Number of cores: 8
% 0.12/0.33 % Python version: Python 3.6.8
% 0.12/0.33 % Running in HO mode
% 0.49/0.63 % Total configuration time : 828
% 0.49/0.63 % Estimated wc time : 1656
% 0.49/0.63 % Estimated cpu time (8 cpus) : 207.0
% 0.50/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.50/0.70 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.51/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.51/0.72 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.51/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.51/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.51/0.72 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.51/0.72 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 119.59/15.63 % Solved by lams/40_c_ic.sh.
% 119.59/15.63 % done 3211 iterations in 14.858s
% 119.59/15.63 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 119.59/15.63 % SZS output start Refutation
% 119.59/15.63 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 119.59/15.63 thf(notdexE_type, type, notdexE: $o).
% 119.59/15.63 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 119.59/15.63 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 119.59/15.63 thf(setunionAx_type, type, setunionAx: $o).
% 119.59/15.63 thf(setminusELneg_type, type, setminusELneg: $o).
% 119.59/15.63 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 119.59/15.63 thf(ex1E1_type, type, ex1E1: $o).
% 119.59/15.63 thf(powersetE_type, type, powersetE: $o).
% 119.59/15.63 thf(omegaSAx_type, type, omegaSAx: $o).
% 119.59/15.63 thf(exuI1_type, type, exuI1: $o).
% 119.59/15.63 thf(exuI2_type, type, exuI2: $o).
% 119.59/15.63 thf(notequalI2_type, type, notequalI2: $o).
% 119.59/15.63 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 119.59/15.63 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 119.59/15.63 thf(upairsubunion_type, type, upairsubunion: $o).
% 119.59/15.63 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 119.59/15.63 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 119.59/15.63 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 119.59/15.63 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 119.59/15.63 thf(setminusILneg_type, type, setminusILneg: $o).
% 119.59/15.63 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 119.59/15.63 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 119.59/15.63 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 119.59/15.63 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 119.59/15.63 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 119.59/15.63 thf(iftrue_type, type, iftrue: $o).
% 119.59/15.63 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 119.59/15.63 thf(ifSingleton_type, type, ifSingleton: $o).
% 119.59/15.63 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 119.59/15.63 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 119.59/15.63 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 119.59/15.63 thf(lamProp_type, type, lamProp: $o).
% 119.59/15.63 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 119.59/15.63 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 119.59/15.63 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 119.59/15.63 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 119.59/15.63 thf(setukpairIR_type, type, setukpairIR: $o).
% 119.59/15.63 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 119.59/15.63 thf(lam2p_type, type, lam2p: $o).
% 119.59/15.63 thf(binunionE_type, type, binunionE: $o).
% 119.59/15.63 thf(setext_type, type, setext: $o).
% 119.59/15.63 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 119.59/15.63 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 119.59/15.63 thf(descr__Cong_type, type, descr__Cong: $o).
% 119.59/15.63 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 119.59/15.63 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 119.59/15.63 thf(eqbreln_type, type, eqbreln: $o).
% 119.59/15.63 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 119.59/15.63 thf(in_type, type, in: $i > $i > $o).
% 119.59/15.63 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 119.59/15.63 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 119.59/15.63 thf(complementT_lem_type, type, complementT_lem: $o).
% 119.59/15.63 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 119.59/15.63 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 119.59/15.63 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 119.59/15.63 thf(beta1_type, type, beta1: $o).
% 119.59/15.63 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 119.59/15.63 thf(powersetTE1_type, type, powersetTE1: $o).
% 119.59/15.63 thf(symdiffI2_type, type, symdiffI2: $o).
% 119.59/15.63 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 119.59/15.63 thf(upairset2IR_type, type, upairset2IR: $o).
% 119.59/15.63 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 119.59/15.63 thf(subsetE_type, type, subsetE: $o).
% 119.59/15.63 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 119.59/15.63 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 119.59/15.63 thf(setbeta_type, type, setbeta: $o).
% 119.59/15.63 thf(eqinunit_type, type, eqinunit: $o).
% 119.59/15.63 thf(upairsetIL_type, type, upairsetIL: $o).
% 119.59/15.63 thf(powersetI1_type, type, powersetI1: $o).
% 119.59/15.63 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 119.59/15.63 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 119.59/15.63 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 119.59/15.63 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 119.59/15.63 thf(powersetAx_type, type, powersetAx: $o).
% 119.59/15.63 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 119.59/15.63 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 119.59/15.63 thf(powersetI_type, type, powersetI: $o).
% 119.59/15.63 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 119.59/15.63 thf(upairsetIR_type, type, upairsetIR: $o).
% 119.59/15.63 thf(lamp_type, type, lamp: $o).
% 119.59/15.63 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 119.59/15.63 thf(inCongP_type, type, inCongP: $o).
% 119.59/15.63 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 119.59/15.63 thf(exuE3e_type, type, exuE3e: $o).
% 119.59/15.63 thf(emptysetE_type, type, emptysetE: $o).
% 119.59/15.63 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 119.59/15.63 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 119.59/15.63 thf(setunionI_type, type, setunionI: $o).
% 119.59/15.63 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 119.59/15.63 thf(prop2setI_type, type, prop2setI: $o).
% 119.59/15.63 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 119.59/15.63 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 119.59/15.63 thf(setminusER_type, type, setminusER: $o).
% 119.59/15.63 thf(exuE2_type, type, exuE2: $o).
% 119.59/15.63 thf(emptyset_type, type, emptyset: $i).
% 119.59/15.63 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 119.59/15.63 thf(sk__147_type, type, sk__147: $i > $i > $i).
% 119.59/15.63 thf(ex1I_type, type, ex1I: $o).
% 119.59/15.63 thf(ex1E2_type, type, ex1E2: $o).
% 119.59/15.63 thf(setminus_type, type, setminus: $i > $i > $i).
% 119.59/15.63 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 119.59/15.63 thf(powersetsubset_type, type, powersetsubset: $o).
% 119.59/15.63 thf(subPowSU_type, type, subPowSU: $o).
% 119.59/15.63 thf(notequalI1_type, type, notequalI1: $o).
% 119.59/15.63 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 119.59/15.63 thf(sk__143_type, type, sk__143: $i).
% 119.59/15.63 thf(notinemptyset_type, type, notinemptyset: $o).
% 119.59/15.63 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 119.59/15.63 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 119.59/15.63 thf(subsetTrans_type, type, subsetTrans: $o).
% 119.59/15.63 thf(kpairp_type, type, kpairp: $o).
% 119.59/15.63 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 119.59/15.63 thf(setminusI_type, type, setminusI: $o).
% 119.59/15.63 thf(binunionIL_type, type, binunionIL: $o).
% 119.59/15.63 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 119.59/15.63 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 119.59/15.63 thf(subsetE2_type, type, subsetE2: $o).
% 119.59/15.63 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 119.59/15.63 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 119.59/15.63 thf(beta2_type, type, beta2: $o).
% 119.59/15.63 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 119.59/15.63 thf(setextsub_type, type, setextsub: $o).
% 119.59/15.63 thf(binunionLsub_type, type, binunionLsub: $o).
% 119.59/15.63 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 119.59/15.63 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 119.59/15.63 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 119.59/15.63 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 119.59/15.63 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 119.59/15.63 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 119.59/15.63 thf(setunionE_type, type, setunionE: $o).
% 119.59/15.63 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 119.59/15.63 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 119.59/15.63 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 119.59/15.63 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 119.59/15.63 thf(binunionIR_type, type, binunionIR: $o).
% 119.59/15.63 thf(theeq_type, type, theeq: $o).
% 119.59/15.63 thf(setadjoinE_type, type, setadjoinE: $o).
% 119.59/15.63 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 119.59/15.63 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 119.59/15.63 thf(ap2p_type, type, ap2p: $o).
% 119.59/15.63 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 119.59/15.63 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 119.59/15.63 thf(exuE1_type, type, exuE1: $o).
% 119.59/15.63 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 119.59/15.63 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 119.59/15.63 thf(setminusLsub_type, type, setminusLsub: $o).
% 119.59/15.63 thf(funcextLem_type, type, funcextLem: $o).
% 119.59/15.63 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 119.59/15.63 thf(notinsingleton_type, type, notinsingleton: $o).
% 119.59/15.63 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 119.59/15.63 thf(exuEu_type, type, exuEu: $o).
% 119.59/15.63 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 119.59/15.63 thf(upairsetE_type, type, upairsetE: $o).
% 119.59/15.63 thf(omega0Ax_type, type, omega0Ax: $o).
% 119.59/15.63 thf(subsetTI_type, type, subsetTI: $o).
% 119.59/15.63 thf(notsubsetI_type, type, notsubsetI: $o).
% 119.59/15.63 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 119.59/15.63 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 119.59/15.63 thf(setextAx_type, type, setextAx: $o).
% 119.59/15.63 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 119.59/15.63 thf(powersetE1_type, type, powersetE1: $o).
% 119.59/15.63 thf(bs114d_type, type, bs114d: $o).
% 119.59/15.63 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 119.59/15.63 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 119.59/15.63 thf(sk__144_type, type, sk__144: $i).
% 119.59/15.63 thf(ifp_type, type, ifp: $o).
% 119.59/15.63 thf(powersetTI1_type, type, powersetTI1: $o).
% 119.59/15.63 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 119.59/15.63 thf(subsetI1_type, type, subsetI1: $o).
% 119.59/15.63 thf(symdiffE_type, type, symdiffE: $o).
% 119.59/15.63 thf(descrp_type, type, descrp: $o).
% 119.59/15.63 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 119.59/15.63 thf(foundationAx_type, type, foundationAx: $o).
% 119.59/15.63 thf(emptysetAx_type, type, emptysetAx: $o).
% 119.59/15.63 thf(emptyI_type, type, emptyI: $o).
% 119.59/15.63 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 119.59/15.63 thf(eta2_type, type, eta2: $o).
% 119.59/15.63 thf(binintersectEL_type, type, binintersectEL: $o).
% 119.59/15.63 thf(emptyE1_type, type, emptyE1: $o).
% 119.59/15.63 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 119.59/15.63 thf(complementTI1_type, type, complementTI1: $o).
% 119.59/15.63 thf(vacuousDall_type, type, vacuousDall: $o).
% 119.59/15.63 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 119.59/15.63 thf(binintersectI_type, type, binintersectI: $o).
% 119.59/15.63 thf(funcext_type, type, funcext: $o).
% 119.59/15.63 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 119.59/15.63 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 119.59/15.63 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 119.59/15.63 thf(brelnall2_type, type, brelnall2: $o).
% 119.59/15.63 thf(setextT_type, type, setextT: $o).
% 119.59/15.63 thf(ex1I2_type, type, ex1I2: $o).
% 119.59/15.63 thf(symdiffI1_type, type, symdiffI1: $o).
% 119.59/15.64 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 119.59/15.64 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 119.59/15.64 thf(theprop_type, type, theprop: $o).
% 119.59/15.64 thf(subsetI2_type, type, subsetI2: $o).
% 119.59/15.64 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 119.59/15.64 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 119.59/15.64 thf(setminusERneg_type, type, setminusERneg: $o).
% 119.59/15.64 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 119.59/15.64 thf(omega__Cong_type, type, omega__Cong: $o).
% 119.59/15.64 thf(subsetRefl_type, type, subsetRefl: $o).
% 119.59/15.64 thf(uniqinunit_type, type, uniqinunit: $o).
% 119.59/15.64 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 119.59/15.64 thf(prop2setE_type, type, prop2setE: $o).
% 119.59/15.64 thf(binunionEcases_type, type, binunionEcases: $o).
% 119.59/15.64 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 119.59/15.64 thf(complementTE1_type, type, complementTE1: $o).
% 119.59/15.64 thf(nonemptyI_type, type, nonemptyI: $o).
% 119.59/15.64 thf(app_type, type, app: $o).
% 119.59/15.64 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 119.59/15.64 thf(exuE3u_type, type, exuE3u: $o).
% 119.59/15.64 thf(eta1_type, type, eta1: $o).
% 119.59/15.64 thf(setminusEL_type, type, setminusEL: $o).
% 119.59/15.64 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 119.59/15.64 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 119.59/15.64 thf(sepSubset_type, type, sepSubset: $o).
% 119.59/15.64 thf(upairset2E_type, type, upairset2E: $o).
% 119.59/15.64 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 119.59/15.64 thf(exuI3_type, type, exuI3: $o).
% 119.59/15.64 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 119.59/15.64 thf(apProp_type, type, apProp: $o).
% 119.59/15.64 thf(notdallE_type, type, notdallE: $o).
% 119.59/15.64 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 119.59/15.64 thf(binintersectER_type, type, binintersectER: $o).
% 119.59/15.64 thf(brelnall1_type, type, brelnall1: $o).
% 119.59/15.64 thf(powerset_type, type, powerset: $i > $i).
% 119.59/15.64 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 119.59/15.64 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 119.59/15.64 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 119.59/15.64 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 119.59/15.64 thf(exu__Cong_type, type, exu__Cong: $o).
% 119.59/15.64 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 119.59/15.64 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 119.59/15.64 thf(secondinupair_type, type, secondinupair: $o).
% 119.59/15.64 thf(singletonprop_type, type, singletonprop: $o).
% 119.59/15.64 thf(singletonsubset_type, type, singletonsubset: $o).
% 119.59/15.64 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 119.59/15.64 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 119.59/15.64 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 119.59/15.64 thf(replAx_type, type, replAx: $o).
% 119.59/15.64 thf(upairequniteq_type, type, upairequniteq: $o).
% 119.59/15.64 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 119.59/15.64 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 119.59/15.64 thf(setukpairIL_type, type, setukpairIL: $o).
% 119.59/15.64 thf(setunionE2_type, type, setunionE2: $o).
% 119.59/15.64 thf(inPowerset_type, type, inPowerset: $o).
% 119.59/15.64 thf(iffalse_type, type, iffalse: $o).
% 119.59/15.64 thf(funcext2_type, type, funcext2: $o).
% 119.59/15.64 thf(subset_type, type, subset: $i > $i > $o).
% 119.59/15.64 thf(subbreln_type, type, subbreln: $o).
% 119.59/15.64 thf(in__Cong_type, type, in__Cong: $o).
% 119.59/15.64 thf(binunionRsub_type, type, binunionRsub: $o).
% 119.59/15.64 thf(subset2powerset_type, type, subset2powerset: $o).
% 119.59/15.64 thf(doubleComplementE1, axiom, doubleComplementE1 =
% 119.59/15.64 (![A:$i,X:$i]:
% 119.59/15.64 ( ( in @ X @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ![Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ A ) =>
% 119.59/15.64 ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) =>
% 119.59/15.64 ( in @ Xx @ X ) ) ) ) ))).
% 119.59/15.64 thf('0', plain,
% 119.59/15.64 (( doubleComplementE1 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ![X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ X4 ) =>
% 119.59/15.64 ( ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) =>
% 119.59/15.64 ( in @ X8 @ X6 ) ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(doubleComplementI1, axiom, doubleComplementI1 =
% 119.59/15.64 (![A:$i,X:$i]:
% 119.59/15.64 ( ( in @ X @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ![Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ A ) =>
% 119.59/15.64 ( ( in @ Xx @ X ) =>
% 119.59/15.64 ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 119.59/15.64 thf('1', plain,
% 119.59/15.64 (( doubleComplementI1 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ![X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ X4 ) =>
% 119.59/15.64 ( ( in @ X8 @ X6 ) =>
% 119.59/15.64 ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(contrasubsetT3, axiom, contrasubsetT3 =
% 119.59/15.64 (![A:$i,X:$i]:
% 119.59/15.64 ( ( in @ X @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ![Y:$i]:
% 119.59/15.64 ( ( in @ Y @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) =>
% 119.59/15.64 ( subset @ X @ Y ) ) ) ) ))).
% 119.59/15.64 thf('2', plain,
% 119.59/15.64 (( contrasubsetT3 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ![X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) =>
% 119.59/15.64 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(contrasubsetT2, axiom, contrasubsetT2 =
% 119.59/15.64 (![A:$i,X:$i]:
% 119.59/15.64 ( ( in @ X @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ![Y:$i]:
% 119.59/15.64 ( ( in @ Y @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ( subset @ X @ Y ) =>
% 119.59/15.64 ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ))).
% 119.59/15.64 thf('3', plain,
% 119.59/15.64 (( contrasubsetT2 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ![X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ( subset @ X6 @ X8 ) =>
% 119.59/15.64 ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(contrasubsetT1, axiom, contrasubsetT1 =
% 119.59/15.64 (![A:$i,X:$i]:
% 119.59/15.64 ( ( in @ X @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ![Y:$i]:
% 119.59/15.64 ( ( in @ Y @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ![Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ A ) =>
% 119.59/15.64 ( ( subset @ X @ Y ) =>
% 119.59/15.64 ( ( ~( in @ Xx @ Y ) ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 119.59/15.64 thf('4', plain,
% 119.59/15.64 (( contrasubsetT1 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ![X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ![X10:$i]:
% 119.59/15.64 ( ( in @ X10 @ X4 ) =>
% 119.59/15.64 ( ( subset @ X6 @ X8 ) =>
% 119.59/15.64 ( ( ~( in @ X10 @ X8 ) ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(contrasubsetT, axiom, contrasubsetT =
% 119.59/15.64 (![A:$i,X:$i]:
% 119.59/15.64 ( ( in @ X @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ![Y:$i]:
% 119.59/15.64 ( ( in @ Y @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ![Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ A ) =>
% 119.59/15.64 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 119.59/15.64 ( ( in @ Xx @ Y ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 119.59/15.64 thf('5', plain,
% 119.59/15.64 (( contrasubsetT ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ![X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ![X10:$i]:
% 119.59/15.64 ( ( in @ X10 @ X4 ) =>
% 119.59/15.64 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 119.59/15.64 ( ( in @ X10 @ X8 ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(complementTE1, axiom, complementTE1 =
% 119.59/15.64 (![A:$i,X:$i]:
% 119.59/15.64 ( ( in @ X @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ![Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ A ) =>
% 119.59/15.64 ( ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) => ( in @ Xx @ X ) ) ) ) ))).
% 119.59/15.64 thf('6', plain,
% 119.59/15.64 (( complementTE1 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ![X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ X4 ) =>
% 119.59/15.64 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) => ( in @ X8 @ X6 ) ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(complementTI1, axiom, complementTI1 =
% 119.59/15.64 (![A:$i,X:$i]:
% 119.59/15.64 ( ( in @ X @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ![Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ A ) =>
% 119.59/15.64 ( ( in @ Xx @ X ) => ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 119.59/15.64 thf('7', plain,
% 119.59/15.64 (( complementTI1 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ![X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ X4 ) =>
% 119.59/15.64 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(powersetTE1, axiom, powersetTE1 =
% 119.59/15.64 (![A:$i,X:$i]:
% 119.59/15.64 ( ( in @ X @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ![Y:$i]:
% 119.59/15.64 ( ( in @ Y @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ![Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ A ) =>
% 119.59/15.64 ( ( in @ X @ ( powerset @ Y ) ) =>
% 119.59/15.64 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 119.59/15.64 thf('8', plain,
% 119.59/15.64 (( powersetTE1 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ![X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ![X10:$i]:
% 119.59/15.64 ( ( in @ X10 @ X4 ) =>
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 119.59/15.64 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(powersetTI1, axiom, powersetTI1 =
% 119.59/15.64 (![A:$i,X:$i]:
% 119.59/15.64 ( ( in @ X @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ![Y:$i]:
% 119.59/15.64 ( ( in @ Y @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ( ![Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 119.59/15.64 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 119.59/15.64 thf('9', plain,
% 119.59/15.64 (( powersetTI1 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ![X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ( ![X10:$i]:
% 119.59/15.64 ( ( in @ X10 @ X4 ) =>
% 119.59/15.64 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 119.59/15.64 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(subsetTI, axiom, subsetTI =
% 119.59/15.64 (![A:$i,X:$i]:
% 119.59/15.64 ( ( in @ X @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ![Y:$i]:
% 119.59/15.64 ( ( in @ Y @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ( ![Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 119.59/15.64 ( subset @ X @ Y ) ) ) ) ))).
% 119.59/15.64 thf('10', plain,
% 119.59/15.64 (( subsetTI ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ![X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ( ![X10:$i]:
% 119.59/15.64 ( ( in @ X10 @ X4 ) =>
% 119.59/15.64 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 119.59/15.64 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(setextT, axiom, setextT =
% 119.59/15.64 (![A:$i,X:$i]:
% 119.59/15.64 ( ( in @ X @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ![Y:$i]:
% 119.59/15.64 ( ( in @ Y @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ( ![Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 119.59/15.64 ( ( ![Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 119.59/15.64 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 119.59/15.64 thf('11', plain,
% 119.59/15.64 (( setextT ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ![X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ( ![X10:$i]:
% 119.59/15.64 ( ( in @ X10 @ X4 ) =>
% 119.59/15.64 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 119.59/15.64 ( ( ![X12:$i]:
% 119.59/15.64 ( ( in @ X12 @ X4 ) =>
% 119.59/15.64 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 119.59/15.64 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(complementT_lem, axiom, complementT_lem =
% 119.59/15.64 (![A:$i,X:$i]:
% 119.59/15.64 ( ( in @ X @ ( powerset @ A ) ) =>
% 119.59/15.64 ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ))).
% 119.59/15.64 thf('12', plain,
% 119.59/15.64 (( complementT_lem ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( in @ ( setminus @ X4 @ X6 ) @ ( powerset @ X4 ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(setminusT_lem, axiom, setminusT_lem =
% 119.59/15.64 (![A:$i,X:$i]:
% 119.59/15.64 ( ( in @ X @ ( powerset @ A ) ) =>
% 119.59/15.64 ( ![Y:$i]:
% 119.59/15.64 ( ( in @ Y @ ( powerset @ A ) ) =>
% 119.59/15.64 ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 119.59/15.64 thf('13', plain,
% 119.59/15.64 (( setminusT_lem ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ![X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( in @ ( setminus @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(powersetT_lem, axiom, powersetT_lem =
% 119.59/15.64 (![A:$i,X:$i]:
% 119.59/15.64 ( ( in @ X @ ( powerset @ A ) ) =>
% 119.59/15.64 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 119.59/15.64 thf('14', plain,
% 119.59/15.64 (( powersetT_lem ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(singletoninpowerset, axiom, singletoninpowerset =
% 119.59/15.64 (![A:$i,Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ A ) =>
% 119.59/15.64 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 119.59/15.64 thf('15', plain,
% 119.59/15.64 (( singletoninpowerset ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ X4 ) =>
% 119.59/15.64 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(singletonsubset, axiom, singletonsubset =
% 119.59/15.64 (![A:$i,Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ A ) => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ))).
% 119.59/15.64 thf('16', plain,
% 119.59/15.64 (( singletonsubset ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ X4 ) => ( subset @ ( setadjoin @ X6 @ emptyset ) @ X4 ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(setminusSubset1, axiom, setminusSubset1 =
% 119.59/15.64 (![A:$i,B:$i]:
% 119.59/15.64 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))).
% 119.59/15.64 thf('17', plain,
% 119.59/15.64 (( setminusSubset1 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(setminusLsub, axiom, setminusLsub =
% 119.59/15.64 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))).
% 119.59/15.64 thf('18', plain,
% 119.59/15.64 (( setminusLsub ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(setminusIRneg, axiom, setminusIRneg =
% 119.59/15.64 (![A:$i,B:$i,Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 119.59/15.64 thf('19', plain,
% 119.59/15.64 (( setminusIRneg ) =
% 119.59/15.64 ( ![X4:$i,X6:$i,X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(setminusILneg, axiom, setminusILneg =
% 119.59/15.64 (![A:$i,B:$i,Xx:$i]:
% 119.59/15.64 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 119.59/15.64 thf('20', plain,
% 119.59/15.64 (( setminusILneg ) =
% 119.59/15.64 ( ![X4:$i,X6:$i,X8:$i]:
% 119.59/15.64 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(setminusELneg, axiom, setminusELneg =
% 119.59/15.64 (![A:$i,B:$i,Xx:$i]:
% 119.59/15.64 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 119.59/15.64 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 119.59/15.64 thf('21', plain,
% 119.59/15.64 (( setminusELneg ) =
% 119.59/15.64 ( ![X4:$i,X6:$i,X8:$i]:
% 119.59/15.64 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 119.59/15.64 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(setminusERneg, axiom, setminusERneg =
% 119.59/15.64 (![A:$i,B:$i,Xx:$i]:
% 119.59/15.64 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 119.59/15.64 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 119.59/15.64 thf('22', plain,
% 119.59/15.64 (( setminusERneg ) =
% 119.59/15.64 ( ![X4:$i,X6:$i,X8:$i]:
% 119.59/15.64 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 119.59/15.64 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(setminusSubset2, axiom, setminusSubset2 =
% 119.59/15.64 (![A:$i,B:$i]:
% 119.59/15.64 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))).
% 119.59/15.64 thf('23', plain,
% 119.59/15.64 (( setminusSubset2 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(setminusER, axiom, setminusER =
% 119.59/15.64 (![A:$i,B:$i,Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))).
% 119.59/15.64 thf('24', plain,
% 119.59/15.64 (( setminusER ) =
% 119.59/15.64 ( ![X4:$i,X6:$i,X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(setminusEL, axiom, setminusEL =
% 119.59/15.64 (![A:$i,B:$i,Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 119.59/15.64 thf('25', plain,
% 119.59/15.64 (( setminusEL ) =
% 119.59/15.64 ( ![X4:$i,X6:$i,X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(setminusI, axiom, setminusI =
% 119.59/15.64 (![A:$i,B:$i,Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ A ) =>
% 119.59/15.64 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 119.59/15.64 thf('26', plain,
% 119.59/15.64 (( setminusI ) =
% 119.59/15.64 ( ![X4:$i,X6:$i,X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ X4 ) =>
% 119.59/15.64 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(powersetsubset, axiom, powersetsubset =
% 119.59/15.64 (![A:$i,B:$i]:
% 119.59/15.64 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 119.59/15.64 thf('27', plain,
% 119.59/15.64 (( powersetsubset ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( subset @ X4 @ X6 ) =>
% 119.59/15.64 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 119.59/15.64 thf('28', plain,
% 119.59/15.64 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(powersetE1, axiom, powersetE1 =
% 119.59/15.64 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 119.59/15.64 thf('29', plain,
% 119.59/15.64 (( powersetE1 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(powersetI1, axiom, powersetI1 =
% 119.59/15.64 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 119.59/15.64 thf('30', plain,
% 119.59/15.64 (( powersetI1 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq =
% 119.59/15.64 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))).
% 119.59/15.64 thf('31', plain,
% 119.59/15.64 (( subsetemptysetimpeq ) =
% 119.59/15.64 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(setextsub, axiom, setextsub =
% 119.59/15.64 (![A:$i,B:$i]:
% 119.59/15.64 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))).
% 119.59/15.64 thf('32', plain,
% 119.59/15.64 (( setextsub ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( subset @ X4 @ X6 ) =>
% 119.59/15.64 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(subset2powerset, axiom, subset2powerset =
% 119.59/15.64 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 119.59/15.64 thf('33', plain,
% 119.59/15.64 (( subset2powerset ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(setadjoinSub2, axiom, setadjoinSub2 =
% 119.59/15.64 (![A:$i,Xx:$i,B:$i]:
% 119.59/15.64 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))).
% 119.59/15.64 thf('34', plain,
% 119.59/15.64 (( setadjoinSub2 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i,X8:$i]:
% 119.59/15.64 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(setadjoinSub, axiom, setadjoinSub =
% 119.59/15.64 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))).
% 119.59/15.64 thf('35', plain,
% 119.59/15.64 (( setadjoinSub ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(subsetTrans, axiom, subsetTrans =
% 119.59/15.64 (![A:$i,B:$i,C:$i]:
% 119.59/15.64 ( ( subset @ A @ B ) => ( ( subset @ B @ C ) => ( subset @ A @ C ) ) ))).
% 119.59/15.64 thf('36', plain,
% 119.59/15.64 (( subsetTrans ) =
% 119.59/15.64 ( ![X4:$i,X6:$i,X8:$i]:
% 119.59/15.64 ( ( subset @ X4 @ X6 ) =>
% 119.59/15.64 ( ( subset @ X6 @ X8 ) => ( subset @ X4 @ X8 ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(subsetRefl, axiom, subsetRefl = (![A:$i]: ( subset @ A @ A ))).
% 119.59/15.64 thf('37', plain, (( subsetRefl ) = ( ![X4:$i]: ( subset @ X4 @ X4 ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(notequalI1, axiom, notequalI1 =
% 119.59/15.64 (![A:$i,B:$i]: ( ( ~( subset @ A @ B ) ) => ( ( A ) != ( B ) ) ))).
% 119.59/15.64 thf('38', plain,
% 119.59/15.64 (( notequalI1 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]: ( ( ~( subset @ X4 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(notsubsetI, axiom, notsubsetI =
% 119.59/15.64 (![A:$i,B:$i,Xx:$i]:
% 119.59/15.64 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ~( subset @ A @ B ) ) ) ))).
% 119.59/15.64 thf('39', plain,
% 119.59/15.64 (( notsubsetI ) =
% 119.59/15.64 ( ![X4:$i,X6:$i,X8:$i]:
% 119.59/15.64 ( ( in @ X8 @ X4 ) =>
% 119.59/15.64 ( ( ~( in @ X8 @ X6 ) ) => ( ~( subset @ X4 @ X6 ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(subsetE2, axiom, subsetE2 =
% 119.59/15.64 (![A:$i,B:$i,Xx:$i]:
% 119.59/15.64 ( ( subset @ A @ B ) => ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 119.59/15.64 thf('40', plain,
% 119.59/15.64 (( subsetE2 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i,X8:$i]:
% 119.59/15.64 ( ( subset @ X4 @ X6 ) =>
% 119.59/15.64 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(subsetE, axiom, subsetE =
% 119.59/15.64 (![A:$i,B:$i,Xx:$i]:
% 119.59/15.64 ( ( subset @ A @ B ) => ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 119.59/15.64 thf('41', plain,
% 119.59/15.64 (( subsetE ) =
% 119.59/15.64 ( ![X4:$i,X6:$i,X8:$i]:
% 119.59/15.64 ( ( subset @ X4 @ X6 ) => ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(emptysetsubset, axiom, emptysetsubset =
% 119.59/15.64 (![A:$i]: ( subset @ emptyset @ A ))).
% 119.59/15.64 thf('42', plain,
% 119.59/15.64 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(subsetI2, axiom, subsetI2 =
% 119.59/15.64 (![A:$i,B:$i]:
% 119.59/15.64 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 119.59/15.64 ( subset @ A @ B ) ))).
% 119.59/15.64 thf('43', plain,
% 119.59/15.64 (( subsetI2 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 119.59/15.64 ( subset @ X4 @ X6 ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(eqimpsubset1, axiom, eqimpsubset1 =
% 119.59/15.64 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ A @ B ) ))).
% 119.59/15.64 thf('44', plain,
% 119.59/15.64 (( eqimpsubset1 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X4 @ X6 ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(eqimpsubset2, axiom, eqimpsubset2 =
% 119.59/15.64 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ B @ A ) ))).
% 119.59/15.64 thf('45', plain,
% 119.59/15.64 (( eqimpsubset2 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(subsetI1, axiom, subsetI1 =
% 119.59/15.64 (![A:$i,B:$i]:
% 119.59/15.64 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 119.59/15.64 ( subset @ A @ B ) ))).
% 119.59/15.64 thf('46', plain,
% 119.59/15.64 (( subsetI1 ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 119.59/15.64 ( subset @ X4 @ X6 ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(powerset__Cong, axiom, powerset__Cong =
% 119.59/15.64 (![A:$i,B:$i]:
% 119.59/15.64 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 119.59/15.64 thf('47', plain,
% 119.59/15.64 (( powerset__Cong ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(powersetE, axiom, powersetE =
% 119.59/15.64 (![A:$i,B:$i,Xx:$i]:
% 119.59/15.64 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 119.59/15.64 thf('48', plain,
% 119.59/15.64 (( powersetE ) =
% 119.59/15.64 ( ![X4:$i,X6:$i,X8:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 119.59/15.64 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(emptyInPowerset, axiom, emptyInPowerset =
% 119.59/15.64 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 119.59/15.64 thf('49', plain,
% 119.59/15.64 (( emptyInPowerset ) =
% 119.59/15.64 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(emptyinPowerset, axiom, emptyinPowerset =
% 119.59/15.64 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 119.59/15.64 thf('50', plain,
% 119.59/15.64 (( emptyinPowerset ) =
% 119.59/15.64 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(powersetI, axiom, powersetI =
% 119.59/15.64 (![A:$i,B:$i]:
% 119.59/15.64 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 119.59/15.64 ( in @ B @ ( powerset @ A ) ) ))).
% 119.59/15.64 thf('51', plain,
% 119.59/15.64 (( powersetI ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 119.59/15.64 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(powersetAx, axiom, powersetAx =
% 119.59/15.64 (![A:$i,B:$i]:
% 119.59/15.64 ( ( in @ B @ ( powerset @ A ) ) <=>
% 119.59/15.64 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 119.59/15.64 thf('52', plain,
% 119.59/15.64 (( powersetAx ) =
% 119.59/15.64 ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 119.59/15.64 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 119.59/15.64 define([status(thm)])).
% 119.59/15.64 thf(doubleComplementSub1, conjecture,
% 119.59/15.64 (( setextAx ) =>
% 119.59/15.64 ( ( emptysetAx ) =>
% 119.59/15.64 ( ( setadjoinAx ) =>
% 119.59/15.64 ( ( powersetAx ) =>
% 119.59/15.64 ( ( setunionAx ) =>
% 119.59/15.64 ( ( omega0Ax ) =>
% 119.59/15.64 ( ( omegaSAx ) =>
% 119.59/15.64 ( ( omegaIndAx ) =>
% 119.59/15.64 ( ( replAx ) =>
% 119.59/15.64 ( ( foundationAx ) =>
% 119.59/15.64 ( ( wellorderingAx ) =>
% 119.59/15.64 ( ( descrp ) =>
% 119.59/15.64 ( ( dsetconstrI ) =>
% 119.59/15.64 ( ( dsetconstrEL ) =>
% 119.59/15.64 ( ( dsetconstrER ) =>
% 119.59/15.64 ( ( exuE1 ) =>
% 119.59/15.64 ( ( prop2setE ) =>
% 119.59/15.64 ( ( emptysetE ) =>
% 119.59/15.64 ( ( emptysetimpfalse ) =>
% 119.59/15.64 ( ( notinemptyset ) =>
% 119.59/15.64 ( ( exuE3e ) =>
% 119.59/15.64 ( ( setext ) =>
% 119.59/15.64 ( ( emptyI ) =>
% 119.59/15.64 ( ( noeltsimpempty ) =>
% 119.59/15.64 ( ( setbeta ) =>
% 119.59/15.64 ( ( nonemptyE1 ) =>
% 119.59/15.64 ( ( nonemptyI ) =>
% 119.59/15.64 ( ( nonemptyI1 ) =>
% 119.59/15.64 ( ( setadjoinIL ) =>
% 119.59/15.64 ( ( emptyinunitempty ) =>
% 119.59/15.64 ( ( setadjoinIR ) =>
% 119.59/15.64 ( ( setadjoinE ) =>
% 119.59/15.64 ( (
% 119.59/15.64 setadjoinOr ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setoftrueEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 powersetI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 emptyinPowerset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 emptyInPowerset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 powersetE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunionI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunionE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subPowSU ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuE2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 nonemptyImpWitness ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 uniqinunit ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 notinsingleton ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 eqinunit ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 singletonsswitch ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairsetE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairsetIL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairsetIR ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 emptyE1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 vacuousDall ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 quantDeMorgan1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 quantDeMorgan2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 quantDeMorgan3 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 quantDeMorgan4 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 prop2setI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 prop2set2propI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 notdexE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 notdallE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuI1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuI3 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuI2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 inCongP ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuE3u ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exu__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 emptyset__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setadjoin__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 powerset__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunion__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 omega__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuEu ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 descr__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 dsetconstr__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subsetI1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 eqimpsubset2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 eqimpsubset1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subsetI2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 emptysetsubset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subsetE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subsetE2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 notsubsetI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 notequalI1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 notequalI2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subsetRefl ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subsetTrans ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setadjoinSub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setadjoinSub2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset2powerset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setextsub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subsetemptysetimpeq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 powersetI1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 powersetE1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 inPowerset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 powersetsubset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 sepInPowerset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 sepSubset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionIL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairset2IR ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionIR ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionEcases ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionLsub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionRsub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectSubset5 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectEL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectLsub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectSubset2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectSubset3 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectER ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 disjointsetsI1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectRsub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectSubset4 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectSubset1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 bs114d ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setminusI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setminusEL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setminusER ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setminusSubset2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setminusERneg ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setminusELneg ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setminusILneg ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setminusIRneg ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setminusLsub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setminusSubset1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 symdiffE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 symdiffI1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 symdiffI2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 symdiffIneg1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 symdiffIneg2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 secondinupair ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairIL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairIR ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 kpairiskpair ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 kpairp ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 singletonsubset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 singletoninpowerset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 singletoninpowunion ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairset2E ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairsubunion ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairinpowunion ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ubforcartprodlem1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ubforcartprodlem2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ubforcartprodlem3 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodpairin ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodmempair1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodmempair ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunionE2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunionsingleton1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunionsingleton2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunionsingleton ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 singletonprop ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ex1E1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ex1I ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ex1I2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 singletonsuniq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairinjL1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 kfstsingleton ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 theprop ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 kfstpairEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodfstin ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairinjL2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairinjL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairinjR11 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairinjR12 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairinjR1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairequniteq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairinjR2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairinjR ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ksndsingleton ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ksndpairEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 kpairsurjEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodsndin ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodpairmemEL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodpairmemER ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodmempaircEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodfstpairEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodsndpairEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodpairsurjEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 dpsetconstrI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 dpsetconstrSub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setOfPairsIsBReln ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 dpsetconstrERa ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 dpsetconstrEL1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 dpsetconstrEL2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 dpsetconstrER ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcImageSingleton ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 apProp ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 app ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 infuncsetfunc ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ap2p ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcinfuncset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 lamProp ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 lamp ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 lam2p ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 brelnall1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 brelnall2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ex1E2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcGraphProp1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcGraphProp3 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcGraphProp2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcextLem ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcGraphProp4 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subbreln ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 eqbreln ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcext ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcext2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ap2apEq1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ap2apEq2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 beta1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 eta1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 lam2lamEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 beta2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 eta2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 iffalseProp1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 iffalseProp2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 iftrueProp1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 iftrueProp2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ifSingleton ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ifp ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 theeq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 iftrue ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 iffalse ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 iftrueorfalse ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectT_lem ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionT_lem ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 powersetT_lem ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setminusT_lem ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 complementT_lem ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setextT ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subsetTI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 powersetTI1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 powersetTE1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 complementTI1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 complementTE1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectTELcontra ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectTERcontra ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 contrasubsetT ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 contrasubsetT1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 contrasubsetT2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 contrasubsetT3 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 doubleComplementI1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 doubleComplementE1 ) =>
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 A:$i,X:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 A ) ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 A @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 A @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 119.59/15.64 thf(zf_stmt_0, conjecture,
% 119.59/15.64 (( setextAx ) =>
% 119.59/15.64 ( ( emptysetAx ) =>
% 119.59/15.64 ( ( setadjoinAx ) =>
% 119.59/15.64 ( ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 119.59/15.64 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 119.59/15.64 ( ( setunionAx ) =>
% 119.59/15.64 ( ( omega0Ax ) =>
% 119.59/15.64 ( ( omegaSAx ) =>
% 119.59/15.64 ( ( omegaIndAx ) =>
% 119.59/15.64 ( ( replAx ) =>
% 119.59/15.64 ( ( foundationAx ) =>
% 119.59/15.64 ( ( wellorderingAx ) =>
% 119.59/15.64 ( ( descrp ) =>
% 119.59/15.64 ( ( dsetconstrI ) =>
% 119.59/15.64 ( ( dsetconstrEL ) =>
% 119.59/15.64 ( ( dsetconstrER ) =>
% 119.59/15.64 ( ( exuE1 ) =>
% 119.59/15.64 ( ( prop2setE ) =>
% 119.59/15.64 ( ( emptysetE ) =>
% 119.59/15.64 ( ( emptysetimpfalse ) =>
% 119.59/15.64 ( ( notinemptyset ) =>
% 119.59/15.64 ( ( exuE3e ) =>
% 119.59/15.64 ( ( setext ) =>
% 119.59/15.64 ( ( emptyI ) =>
% 119.59/15.64 ( ( noeltsimpempty ) =>
% 119.59/15.64 ( ( setbeta ) =>
% 119.59/15.64 ( ( nonemptyE1 ) =>
% 119.59/15.64 ( ( nonemptyI ) =>
% 119.59/15.64 ( ( nonemptyI1 ) =>
% 119.59/15.64 ( ( setadjoinIL ) =>
% 119.59/15.64 ( ( emptyinunitempty ) =>
% 119.59/15.64 ( ( setadjoinIR ) =>
% 119.59/15.64 ( ( setadjoinE ) =>
% 119.59/15.64 ( (
% 119.59/15.64 setadjoinOr ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setoftrueEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X10:$i,
% 119.59/15.64 X12:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X14:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X14 @ X12 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X14 @ X10 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X12 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X10 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X16:$i]:
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 emptyset @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X16 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X18:$i]:
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 emptyset @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X18 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X20:$i,
% 119.59/15.64 X22:$i,
% 119.59/15.64 X24:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X22 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X20 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X24 @ X22 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X24 @ X20 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunionI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunionE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subPowSU ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuE2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 nonemptyImpWitness ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 uniqinunit ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 notinsingleton ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 eqinunit ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 singletonsswitch ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairsetE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairsetIL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairsetIR ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 emptyE1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 vacuousDall ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 quantDeMorgan1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 quantDeMorgan2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 quantDeMorgan3 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 quantDeMorgan4 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 prop2setI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 prop2set2propI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 notdexE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 notdallE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuI1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuI3 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuI2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 inCongP ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuE3u ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exu__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 emptyset__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setadjoin__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X26:$i,
% 119.59/15.64 X28:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 X26 ) =
% 119.59/15.64 (
% 119.59/15.64 X28 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X26 ) =
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X28 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunion__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 omega__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuEu ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 descr__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 dsetconstr__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X30:$i,
% 119.59/15.64 X32:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X34:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X34 @ X30 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X34 @ X32 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X30 @ X32 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X36:$i,
% 119.59/15.64 X38:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 X36 ) =
% 119.59/15.64 (
% 119.59/15.64 X38 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X38 @ X36 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X40:$i,
% 119.59/15.64 X42:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 X40 ) =
% 119.59/15.64 (
% 119.59/15.64 X42 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X40 @ X42 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X44:$i,
% 119.59/15.64 X46:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X48:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X48 @ X44 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X48 @ X46 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X44 @ X46 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X50:$i]:
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 emptyset @
% 119.59/15.64 X50 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X52:$i,
% 119.59/15.64 X54:$i,
% 119.59/15.64 X56:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X52 @ X54 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X56 @ X52 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X56 @ X54 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X58:$i,
% 119.59/15.64 X60:$i,
% 119.59/15.64 X62:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X58 @ X60 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X62 @ X60 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X62 @ X58 ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X64:$i,
% 119.59/15.64 X66:$i,
% 119.59/15.64 X68:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X68 @ X64 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X68 @ X66 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 subset @
% 119.59/15.64 X64 @ X66 ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X70:$i,
% 119.59/15.64 X72:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 subset @
% 119.59/15.64 X70 @ X72 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 X70 ) !=
% 119.59/15.64 (
% 119.59/15.64 X72 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 notequalI2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X74:$i]:
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X74 @ X74 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X76:$i,
% 119.59/15.64 X78:$i,
% 119.59/15.64 X80:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X76 @ X78 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X78 @ X80 ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X76 @ X80 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X82:$i,
% 119.59/15.64 X84:$i]:
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X84 @
% 119.59/15.64 (
% 119.59/15.64 setadjoin
% 119.59/15.64 @
% 119.59/15.64 X82 @ X84 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X86:$i,
% 119.59/15.64 X88:$i,
% 119.59/15.64 X90:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X86 @ X90 ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X86 @
% 119.59/15.64 (
% 119.59/15.64 setadjoin
% 119.59/15.64 @
% 119.59/15.64 X88 @ X90 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X92:$i,
% 119.59/15.64 X94:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X92 @ X94 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X92 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X94 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X96:$i,
% 119.59/15.64 X98:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X96 @ X98 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X98 @ X96 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 X96 ) =
% 119.59/15.64 (
% 119.59/15.64 X98 ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X100:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X100 @
% 119.59/15.64 emptyset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 X100 ) =
% 119.59/15.64 (
% 119.59/15.64 emptyset ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X102:$i,
% 119.59/15.64 X104:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X104 @
% 119.59/15.64 X102 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X104 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X102 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X106:$i,
% 119.59/15.64 X108:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X108 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X106 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X108 @
% 119.59/15.64 X106 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X110:$i]:
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X110 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X110 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X112:$i,
% 119.59/15.64 X114:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X112 @
% 119.59/15.64 X114 ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X112 ) @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X114 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 sepInPowerset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 sepSubset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionIL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairset2IR ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionIR ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionEcases ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionLsub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionRsub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectSubset5 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectEL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectLsub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectSubset2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectSubset3 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectER ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 disjointsetsI1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectRsub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectSubset4 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectSubset1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 bs114d ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X116:$i,
% 119.59/15.64 X118:$i,
% 119.59/15.64 X120:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X120 @
% 119.59/15.64 X116 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X120 @
% 119.59/15.64 X118 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X120 @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X116 @
% 119.59/15.64 X118 ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X122:$i,
% 119.59/15.64 X124:$i,
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% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X126 @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X122 @
% 119.59/15.64 X124 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X126 @
% 119.59/15.64 X122 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X128:$i,
% 119.59/15.64 X130:$i,
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% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X132 @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X128 @
% 119.59/15.64 X130 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X132 @
% 119.59/15.64 X130 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X134:$i,
% 119.59/15.64 X136:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X134 @
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% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X134 @
% 119.59/15.64 X136 ) =
% 119.59/15.64 (
% 119.59/15.64 emptyset ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
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% 119.59/15.64 X138:$i,
% 119.59/15.64 X140:$i,
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% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X142 @
% 119.59/15.64 (
% 119.59/15.64 setminus
% 119.59/15.64 @
% 119.59/15.64 X138 @
% 119.59/15.64 X140 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X142 @
% 119.59/15.64 X138 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X142 @
% 119.59/15.64 X140 ) ) ) ) =>
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% 119.59/15.64 X144:$i,
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% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X148 @
% 119.59/15.64 (
% 119.59/15.64 setminus
% 119.59/15.64 @
% 119.59/15.64 X144 @
% 119.59/15.64 X146 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X148 @
% 119.59/15.64 X146 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X148 @
% 119.59/15.64 X144 ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X150:$i,
% 119.59/15.64 X152:$i,
% 119.59/15.64 X154:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X154 @
% 119.59/15.64 X150 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X154 @
% 119.59/15.64 (
% 119.59/15.64 setminus
% 119.59/15.64 @
% 119.59/15.64 X150 @
% 119.59/15.64 X152 ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X156:$i,
% 119.59/15.64 X158:$i,
% 119.59/15.64 X160:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X160 @
% 119.59/15.64 X158 ) =>
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X160 @
% 119.59/15.64 (
% 119.59/15.64 setminus
% 119.59/15.64 @
% 119.59/15.64 X156 @
% 119.59/15.64 X158 ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X162:$i,
% 119.59/15.64 X164:$i]:
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X162 @
% 119.59/15.64 X164 ) @
% 119.59/15.64 X162 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X166:$i,
% 119.59/15.64 X168:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X166 @
% 119.59/15.64 X168 ) =
% 119.59/15.64 (
% 119.59/15.64 emptyset ) ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X166 @
% 119.59/15.64 X168 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 symdiffE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 symdiffI1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 symdiffI2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 symdiffIneg1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 symdiffIneg2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 secondinupair ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairIL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairIR ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 kpairiskpair ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 kpairp ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X170:$i,
% 119.59/15.64 X172:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X172 @
% 119.59/15.64 X170 ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 (
% 119.59/15.64 setadjoin
% 119.59/15.64 @
% 119.59/15.64 X172 @
% 119.59/15.64 emptyset ) @
% 119.59/15.64 X170 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X174:$i,
% 119.59/15.64 X176:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X176 @
% 119.59/15.64 X174 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 (
% 119.59/15.64 setadjoin
% 119.59/15.64 @
% 119.59/15.64 X176 @
% 119.59/15.64 emptyset ) @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X174 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 singletoninpowunion ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairset2E ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairsubunion ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairinpowunion ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ubforcartprodlem1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ubforcartprodlem2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ubforcartprodlem3 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodpairin ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodmempair1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodmempair ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunionE2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunionsingleton1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunionsingleton2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunionsingleton ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 singletonprop ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ex1E1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ex1I ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ex1I2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 singletonsuniq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairinjL1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 kfstsingleton ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 theprop ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 kfstpairEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodfstin ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairinjL2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairinjL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairinjR11 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairinjR12 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairinjR1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairequniteq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairinjR2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairinjR ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ksndsingleton ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ksndpairEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 kpairsurjEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodsndin ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodpairmemEL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodpairmemER ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodmempaircEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodfstpairEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodsndpairEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 cartprodpairsurjEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 dpsetconstrI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 dpsetconstrSub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setOfPairsIsBReln ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 dpsetconstrERa ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 dpsetconstrEL1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 dpsetconstrEL2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 dpsetconstrER ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcImageSingleton ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 apProp ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 app ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 infuncsetfunc ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ap2p ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcinfuncset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 lamProp ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 lamp ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 lam2p ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 brelnall1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 brelnall2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ex1E2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcGraphProp1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcGraphProp3 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcGraphProp2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcextLem ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcGraphProp4 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subbreln ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 eqbreln ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcext ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 funcext2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ap2apEq1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ap2apEq2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 beta1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 eta1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 lam2lamEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 beta2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 eta2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 iffalseProp1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 iffalseProp2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 iftrueProp1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 iftrueProp2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ifSingleton ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ifp ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 theeq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 iftrue ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 iffalse ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 iftrueorfalse ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectT_lem ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionT_lem ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X178:$i,
% 119.59/15.64 X180:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X180 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X178 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X180 ) @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X178 ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X182:$i,
% 119.59/15.64 X184:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X184 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X182 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X186:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
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% 119.59/15.64 powerset @
% 119.59/15.64 X182 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X184 @
% 119.59/15.64 X186 ) @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X182 ) ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X188:$i,
% 119.59/15.64 X190:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X190 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X188 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X188 @
% 119.59/15.64 X190 ) @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X188 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
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% 119.59/15.64 X194:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X194 @
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% 119.59/15.64 powerset @
% 119.59/15.64 X192 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X196:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X196 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X192 ) ) =>
% 119.59/15.64 (
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% 119.59/15.64 (
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% 119.59/15.64 X198 @
% 119.59/15.64 X196 ) ) ) ) =>
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% 119.59/15.64 ![
% 119.59/15.64 X200:$i]:
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% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X200 @
% 119.59/15.64 X194 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 X194 ) =
% 119.59/15.64 (
% 119.59/15.64 X196 ) ) ) ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
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% 119.59/15.64 X204:$i]:
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% 119.59/15.64 (
% 119.59/15.64 in @
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% 119.59/15.64 (
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% 119.59/15.64 (
% 119.59/15.64 in @
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% 119.59/15.64 X202 ) ) =>
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% 119.59/15.64 (
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% 119.59/15.64 (
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% 119.59/15.64 in @
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% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X208 @
% 119.59/15.64 X206 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X204 @
% 119.59/15.64 X206 ) ) ) ) ) ) =>
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% 119.59/15.64 X214 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X212 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X214 ) ) ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X218:$i,
% 119.59/15.64 X220:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X220 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X218 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X222:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X222 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X218 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X224:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X224 @
% 119.59/15.64 X218 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X220 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X222 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X224 @
% 119.59/15.64 X220 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X224 @
% 119.59/15.64 X222 ) ) ) ) ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X226:$i,
% 119.59/15.64 X228:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X228 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X226 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X230:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X230 @
% 119.59/15.64 X226 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X230 @
% 119.59/15.64 X228 ) =>
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X230 @
% 119.59/15.64 (
% 119.59/15.64 setminus
% 119.59/15.64 @
% 119.59/15.64 X226 @
% 119.59/15.64 X228 ) ) ) ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X232:$i,
% 119.59/15.64 X234:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X234 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X232 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X236:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X236 @
% 119.59/15.64 X232 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X236 @
% 119.59/15.64 (
% 119.59/15.64 setminus
% 119.59/15.64 @
% 119.59/15.64 X232 @
% 119.59/15.64 X234 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X236 @
% 119.59/15.64 X234 ) ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectTELcontra ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectTERcontra ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X238:$i,
% 119.59/15.64 X240:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X240 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X238 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X242:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X242 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X238 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X244:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X244 @
% 119.59/15.64 X238 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X240 @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X238 @
% 119.59/15.64 X242 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X244 @
% 119.59/15.64 X242 ) =>
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X244 @
% 119.59/15.64 X240 ) ) ) ) ) ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X246:$i,
% 119.59/15.64 X248:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X248 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X246 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X250:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X250 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X246 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X252:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X252 @
% 119.59/15.64 X246 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X248 @
% 119.59/15.64 X250 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X252 @
% 119.59/15.64 X250 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X252 @
% 119.59/15.64 X248 ) ) ) ) ) ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X254:$i,
% 119.59/15.64 X256:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X256 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X254 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X258:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X258 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X254 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X256 @
% 119.59/15.64 X258 ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X254 @
% 119.59/15.64 X258 ) @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X254 @
% 119.59/15.64 X256 ) ) ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X260:$i,
% 119.59/15.64 X262:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X262 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X260 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X264:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X264 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X260 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X260 @
% 119.59/15.64 X264 ) @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X260 @
% 119.59/15.64 X262 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X262 @
% 119.59/15.64 X264 ) ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X266:$i,
% 119.59/15.64 X268:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X268 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X266 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X270:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X270 @
% 119.59/15.64 X266 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X270 @
% 119.59/15.64 X268 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X270 @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X266 @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X266 @
% 119.59/15.64 X268 ) ) ) ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X272:$i,
% 119.59/15.64 X274:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X274 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X272 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X276:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X276 @
% 119.59/15.64 X272 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X276 @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X272 @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X272 @
% 119.59/15.64 X274 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X276 @
% 119.59/15.64 X274 ) ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X278:$i,
% 119.59/15.64 X280:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X280 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X278 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X280 @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X278 @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X278 @
% 119.59/15.64 X280 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 119.59/15.64 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 119.59/15.64 thf(zf_stmt_2, axiom,
% 119.59/15.64 (![X8:$i,X6:$i,X4:$i]:
% 119.59/15.64 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 119.59/15.64 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 119.59/15.64 thf(zf_stmt_3, conjecture,
% 119.59/15.64 (( setextAx ) =>
% 119.59/15.64 ( ( emptysetAx ) =>
% 119.59/15.64 ( ( setadjoinAx ) =>
% 119.59/15.64 ( ( ![X4:$i,X6:$i]:
% 119.59/15.64 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 119.59/15.64 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 119.59/15.64 ( ( setunionAx ) =>
% 119.59/15.64 ( ( omega0Ax ) =>
% 119.59/15.64 ( ( omegaSAx ) =>
% 119.59/15.64 ( ( omegaIndAx ) =>
% 119.59/15.64 ( ( replAx ) =>
% 119.59/15.64 ( ( foundationAx ) =>
% 119.59/15.64 ( ( wellorderingAx ) =>
% 119.59/15.64 ( ( descrp ) =>
% 119.59/15.64 ( ( dsetconstrI ) =>
% 119.59/15.64 ( ( dsetconstrEL ) =>
% 119.59/15.64 ( ( dsetconstrER ) =>
% 119.59/15.64 ( ( exuE1 ) =>
% 119.59/15.64 ( ( prop2setE ) =>
% 119.59/15.64 ( ( emptysetE ) =>
% 119.59/15.64 ( ( emptysetimpfalse ) =>
% 119.59/15.64 ( ( notinemptyset ) =>
% 119.59/15.64 ( ( exuE3e ) =>
% 119.59/15.64 ( ( setext ) =>
% 119.59/15.64 ( ( emptyI ) =>
% 119.59/15.64 ( ( noeltsimpempty ) =>
% 119.59/15.64 ( ( setbeta ) =>
% 119.59/15.64 ( ( nonemptyE1 ) =>
% 119.59/15.64 ( ( nonemptyI ) =>
% 119.59/15.64 ( ( nonemptyI1 ) =>
% 119.59/15.64 ( ( setadjoinIL ) =>
% 119.59/15.64 ( ( emptyinunitempty ) =>
% 119.59/15.64 ( ( setadjoinIR ) =>
% 119.59/15.64 ( ( setadjoinE ) =>
% 119.59/15.64 ( (
% 119.59/15.64 setadjoinOr ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setoftrueEq ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X10:$i,
% 119.59/15.64 X12:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X14:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X14 @ X12 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X14 @ X10 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X12 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X10 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X16:$i]:
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 emptyset @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X16 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X18:$i]:
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 emptyset @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X18 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X20:$i,
% 119.59/15.64 X22:$i,
% 119.59/15.64 X24:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X22 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X20 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X24 @ X22 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X24 @ X20 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunionI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunionE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subPowSU ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuE2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 nonemptyImpWitness ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 uniqinunit ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 notinsingleton ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 eqinunit ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 singletonsswitch ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairsetE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairsetIL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairsetIR ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 emptyE1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 vacuousDall ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 quantDeMorgan1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 quantDeMorgan2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 quantDeMorgan3 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 quantDeMorgan4 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 prop2setI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 prop2set2propI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 notdexE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 notdallE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuI1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuI3 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuI2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 inCongP ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuE3u ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exu__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 emptyset__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setadjoin__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X26:$i,
% 119.59/15.64 X28:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 X26 ) =
% 119.59/15.64 (
% 119.59/15.64 X28 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X26 ) =
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X28 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setunion__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 omega__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 exuEu ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 descr__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 dsetconstr__Cong ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X30:$i,
% 119.59/15.64 X32:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X34:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X34 @ X30 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X34 @ X32 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X30 @ X32 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X36:$i,
% 119.59/15.64 X38:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 X36 ) =
% 119.59/15.64 (
% 119.59/15.64 X38 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X38 @ X36 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X40:$i,
% 119.59/15.64 X42:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 X40 ) =
% 119.59/15.64 (
% 119.59/15.64 X42 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X40 @ X42 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X44:$i,
% 119.59/15.64 X46:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X48:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X48 @ X44 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X48 @ X46 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X44 @ X46 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X50:$i]:
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 emptyset @
% 119.59/15.64 X50 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X52:$i,
% 119.59/15.64 X54:$i,
% 119.59/15.64 X56:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X52 @ X54 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X56 @ X52 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X56 @ X54 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X58:$i,
% 119.59/15.64 X60:$i,
% 119.59/15.64 X62:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X58 @ X60 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X62 @ X60 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X62 @ X58 ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X64:$i,
% 119.59/15.64 X66:$i,
% 119.59/15.64 X68:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X68 @ X64 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X68 @ X66 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 subset @
% 119.59/15.64 X64 @ X66 ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X70:$i,
% 119.59/15.64 X72:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 subset @
% 119.59/15.64 X70 @ X72 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 X70 ) !=
% 119.59/15.64 (
% 119.59/15.64 X72 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 notequalI2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X74:$i]:
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X74 @ X74 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X76:$i,
% 119.59/15.64 X78:$i,
% 119.59/15.64 X80:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X76 @ X78 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X78 @ X80 ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X76 @ X80 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X82:$i,
% 119.59/15.64 X84:$i]:
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X84 @
% 119.59/15.64 (
% 119.59/15.64 setadjoin
% 119.59/15.64 @
% 119.59/15.64 X82 @ X84 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X86:$i,
% 119.59/15.64 X88:$i,
% 119.59/15.64 X90:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X86 @ X90 ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X86 @
% 119.59/15.64 (
% 119.59/15.64 setadjoin
% 119.59/15.64 @
% 119.59/15.64 X88 @ X90 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X92:$i,
% 119.59/15.64 X94:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X92 @ X94 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X92 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X94 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X96:$i,
% 119.59/15.64 X98:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X96 @ X98 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X98 @ X96 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 X96 ) =
% 119.59/15.64 (
% 119.59/15.64 X98 ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X100:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X100 @
% 119.59/15.64 emptyset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 X100 ) =
% 119.59/15.64 (
% 119.59/15.64 emptyset ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X102:$i,
% 119.59/15.64 X104:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X104 @
% 119.59/15.64 X102 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X104 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X102 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X106:$i,
% 119.59/15.64 X108:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X108 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X106 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X108 @
% 119.59/15.64 X106 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X110:$i]:
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X110 @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X110 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X112:$i,
% 119.59/15.64 X114:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X112 @
% 119.59/15.64 X114 ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X112 ) @
% 119.59/15.64 (
% 119.59/15.64 powerset @
% 119.59/15.64 X114 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 sepInPowerset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 sepSubset ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionIL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 upairset2IR ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionIR ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionEcases ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionLsub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binunionRsub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectI ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectSubset5 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectEL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectLsub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectSubset2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectSubset3 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectER ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 disjointsetsI1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectRsub ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectSubset4 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 binintersectSubset1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 bs114d ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X116:$i,
% 119.59/15.64 X118:$i,
% 119.59/15.64 X120:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X120 @
% 119.59/15.64 X116 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X120 @
% 119.59/15.64 X118 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X120 @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X116 @
% 119.59/15.64 X118 ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X122:$i,
% 119.59/15.64 X124:$i,
% 119.59/15.64 X126:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X126 @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X122 @
% 119.59/15.64 X124 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X126 @
% 119.59/15.64 X122 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X128:$i,
% 119.59/15.64 X130:$i,
% 119.59/15.64 X132:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X132 @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X128 @
% 119.59/15.64 X130 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X132 @
% 119.59/15.64 X130 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X134:$i,
% 119.59/15.64 X136:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X134 @
% 119.59/15.64 X136 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X134 @
% 119.59/15.64 X136 ) =
% 119.59/15.64 (
% 119.59/15.64 emptyset ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X138:$i,
% 119.59/15.64 X140:$i,
% 119.59/15.64 X142:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X142 @
% 119.59/15.64 (
% 119.59/15.64 setminus
% 119.59/15.64 @
% 119.59/15.64 X138 @
% 119.59/15.64 X140 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X142 @
% 119.59/15.64 X138 ) =>
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X142 @
% 119.59/15.64 X140 ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X144:$i,
% 119.59/15.64 X146:$i,
% 119.59/15.64 X148:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X148 @
% 119.59/15.64 (
% 119.59/15.64 setminus
% 119.59/15.64 @
% 119.59/15.64 X144 @
% 119.59/15.64 X146 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X148 @
% 119.59/15.64 X146 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X148 @
% 119.59/15.64 X144 ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X150:$i,
% 119.59/15.64 X152:$i,
% 119.59/15.64 X154:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X154 @
% 119.59/15.64 X150 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X154 @
% 119.59/15.64 (
% 119.59/15.64 setminus
% 119.59/15.64 @
% 119.59/15.64 X150 @
% 119.59/15.64 X152 ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X156:$i,
% 119.59/15.64 X158:$i,
% 119.59/15.64 X160:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X160 @
% 119.59/15.64 X158 ) =>
% 119.59/15.64 (
% 119.59/15.64 ~(
% 119.59/15.64 in @
% 119.59/15.64 X160 @
% 119.59/15.64 (
% 119.59/15.64 setminus
% 119.59/15.64 @
% 119.59/15.64 X156 @
% 119.59/15.64 X158 ) ) ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X162:$i,
% 119.59/15.64 X164:$i]:
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X162 @
% 119.59/15.64 X164 ) @
% 119.59/15.64 X162 ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X166:$i,
% 119.59/15.64 X168:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setminus @
% 119.59/15.64 X166 @
% 119.59/15.64 X168 ) =
% 119.59/15.64 (
% 119.59/15.64 emptyset ) ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 X166 @
% 119.59/15.64 X168 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 symdiffE ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 symdiffI1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 symdiffI2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 symdiffIneg1 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 symdiffIneg2 ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 secondinupair ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairIL ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 setukpairIR ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 kpairiskpair ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 kpairp ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X170:$i,
% 119.59/15.64 X172:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X172 @
% 119.59/15.64 X170 ) =>
% 119.59/15.64 (
% 119.59/15.64 subset @
% 119.59/15.64 (
% 119.59/15.64 setadjoin
% 119.59/15.64 @
% 119.59/15.64 X172 @
% 119.59/15.64 emptyset ) @
% 119.59/15.64 X170 ) ) ) =>
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 ![
% 119.59/15.64 X174:$i,
% 119.59/15.64 X176:$i]:
% 119.59/15.64 (
% 119.59/15.64 (
% 119.59/15.64 in @
% 119.59/15.64 X176 @
% 119.59/15.64 X174 ) =>
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% 119.59/15.65 powerset @
% 119.59/15.65 X238 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X244:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X244 @
% 119.59/15.65 X238 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 X240 @
% 119.59/15.65 (
% 119.59/15.65 setminus @
% 119.59/15.65 X238 @
% 119.59/15.65 X242 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X244 @
% 119.59/15.65 X242 ) =>
% 119.59/15.65 (
% 119.59/15.65 ~(
% 119.59/15.65 in @
% 119.59/15.65 X244 @
% 119.59/15.65 X240 ) ) ) ) ) ) ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X246:$i,
% 119.59/15.65 X248:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X248 @
% 119.59/15.65 (
% 119.59/15.65 powerset @
% 119.59/15.65 X246 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X250:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X250 @
% 119.59/15.65 (
% 119.59/15.65 powerset @
% 119.59/15.65 X246 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X252:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X252 @
% 119.59/15.65 X246 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 X248 @
% 119.59/15.65 X250 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ~(
% 119.59/15.65 in @
% 119.59/15.65 X252 @
% 119.59/15.65 X250 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 ~(
% 119.59/15.65 in @
% 119.59/15.65 X252 @
% 119.59/15.65 X248 ) ) ) ) ) ) ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X254:$i,
% 119.59/15.65 X256:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X256 @
% 119.59/15.65 (
% 119.59/15.65 powerset @
% 119.59/15.65 X254 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X258:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X258 @
% 119.59/15.65 (
% 119.59/15.65 powerset @
% 119.59/15.65 X254 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 X256 @
% 119.59/15.65 X258 ) =>
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 (
% 119.59/15.65 setminus @
% 119.59/15.65 X254 @
% 119.59/15.65 X258 ) @
% 119.59/15.65 (
% 119.59/15.65 setminus @
% 119.59/15.65 X254 @
% 119.59/15.65 X256 ) ) ) ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X260:$i,
% 119.59/15.65 X262:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X262 @
% 119.59/15.65 (
% 119.59/15.65 powerset @
% 119.59/15.65 X260 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X264:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X264 @
% 119.59/15.65 (
% 119.59/15.65 powerset @
% 119.59/15.65 X260 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 (
% 119.59/15.65 setminus @
% 119.59/15.65 X260 @
% 119.59/15.65 X264 ) @
% 119.59/15.65 (
% 119.59/15.65 setminus @
% 119.59/15.65 X260 @
% 119.59/15.65 X262 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 X262 @
% 119.59/15.65 X264 ) ) ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X266:$i,
% 119.59/15.65 X268:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X268 @
% 119.59/15.65 (
% 119.59/15.65 powerset @
% 119.59/15.65 X266 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X270:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X270 @
% 119.59/15.65 X266 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X270 @
% 119.59/15.65 X268 ) =>
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X270 @
% 119.59/15.65 (
% 119.59/15.65 setminus @
% 119.59/15.65 X266 @
% 119.59/15.65 (
% 119.59/15.65 setminus @
% 119.59/15.65 X266 @
% 119.59/15.65 X268 ) ) ) ) ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X272:$i,
% 119.59/15.65 X274:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X274 @
% 119.59/15.65 (
% 119.59/15.65 powerset @
% 119.59/15.65 X272 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X276:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X276 @
% 119.59/15.65 X272 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X276 @
% 119.59/15.65 (
% 119.59/15.65 setminus @
% 119.59/15.65 X272 @
% 119.59/15.65 (
% 119.59/15.65 setminus @
% 119.59/15.65 X272 @
% 119.59/15.65 X274 ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X276 @
% 119.59/15.65 X274 ) ) ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X278:$i,
% 119.59/15.65 X280:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X280 @
% 119.59/15.65 (
% 119.59/15.65 powerset @
% 119.59/15.65 X278 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 X280 @
% 119.59/15.65 (
% 119.59/15.65 setminus @
% 119.59/15.65 X278 @
% 119.59/15.65 (
% 119.59/15.65 setminus @
% 119.59/15.65 X278 @
% 119.59/15.65 X280 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 119.59/15.65 thf(zf_stmt_4, negated_conjecture,
% 119.59/15.65 (~( ( setextAx ) =>
% 119.59/15.65 ( ( emptysetAx ) =>
% 119.59/15.65 ( ( setadjoinAx ) =>
% 119.59/15.65 ( ( ![X4:$i,X6:$i]:
% 119.59/15.65 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 119.59/15.65 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 119.59/15.65 ( ( setunionAx ) =>
% 119.59/15.65 ( ( omega0Ax ) =>
% 119.59/15.65 ( ( omegaSAx ) =>
% 119.59/15.65 ( ( omegaIndAx ) =>
% 119.59/15.65 ( ( replAx ) =>
% 119.59/15.65 ( ( foundationAx ) =>
% 119.59/15.65 ( ( wellorderingAx ) =>
% 119.59/15.65 ( ( descrp ) =>
% 119.59/15.65 ( ( dsetconstrI ) =>
% 119.59/15.65 ( ( dsetconstrEL ) =>
% 119.59/15.65 ( ( dsetconstrER ) =>
% 119.59/15.65 ( ( exuE1 ) =>
% 119.59/15.65 ( ( prop2setE ) =>
% 119.59/15.65 ( ( emptysetE ) =>
% 119.59/15.65 ( ( emptysetimpfalse ) =>
% 119.59/15.65 ( ( notinemptyset ) =>
% 119.59/15.65 ( ( exuE3e ) =>
% 119.59/15.65 ( ( setext ) =>
% 119.59/15.65 ( ( emptyI ) =>
% 119.59/15.65 ( ( noeltsimpempty ) =>
% 119.59/15.65 ( ( setbeta ) =>
% 119.59/15.65 ( ( nonemptyE1 ) =>
% 119.59/15.65 ( ( nonemptyI ) =>
% 119.59/15.65 ( ( nonemptyI1 ) =>
% 119.59/15.65 ( ( setadjoinIL ) =>
% 119.59/15.65 ( ( emptyinunitempty ) =>
% 119.59/15.65 ( ( setadjoinIR ) =>
% 119.59/15.65 ( (
% 119.59/15.65 setadjoinE ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 setadjoinOr ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 setoftrueEq ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X10:$i,
% 119.59/15.65 X12:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X14:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X14 @ X12 ) =>
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X14 @ X10 ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X12 @
% 119.59/15.65 (
% 119.59/15.65 powerset
% 119.59/15.65 @
% 119.59/15.65 X10 ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X16:$i]:
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 emptyset @
% 119.59/15.65 (
% 119.59/15.65 powerset
% 119.59/15.65 @
% 119.59/15.65 X16 ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X18:$i]:
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 emptyset @
% 119.59/15.65 (
% 119.59/15.65 powerset
% 119.59/15.65 @
% 119.59/15.65 X18 ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X20:$i,
% 119.59/15.65 X22:$i,
% 119.59/15.65 X24:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X22 @
% 119.59/15.65 (
% 119.59/15.65 powerset
% 119.59/15.65 @
% 119.59/15.65 X20 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X24 @ X22 ) =>
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X24 @ X20 ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 setunionI ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 setunionE ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 subPowSU ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 exuE2 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 nonemptyImpWitness ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 uniqinunit ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 notinsingleton ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 eqinunit ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 singletonsswitch ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 upairsetE ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 upairsetIL ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 upairsetIR ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 emptyE1 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 vacuousDall ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 quantDeMorgan1 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 quantDeMorgan2 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 quantDeMorgan3 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 quantDeMorgan4 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 prop2setI ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 prop2set2propI ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 notdexE ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 notdallE ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 exuI1 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 exuI3 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 exuI2 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 inCongP ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in__Cong ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 exuE3u ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 exu__Cong ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 emptyset__Cong ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 setadjoin__Cong ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X26:$i,
% 119.59/15.65 X28:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 X26 ) =
% 119.59/15.65 (
% 119.59/15.65 X28 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 powerset
% 119.59/15.65 @
% 119.59/15.65 X26 ) =
% 119.59/15.65 (
% 119.59/15.65 powerset
% 119.59/15.65 @
% 119.59/15.65 X28 ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 setunion__Cong ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 omega__Cong ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 exuEu ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 descr__Cong ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 dsetconstr__Cong ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X30:$i,
% 119.59/15.65 X32:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X34:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X34 @ X30 ) =>
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X34 @ X32 ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 X30 @ X32 ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X36:$i,
% 119.59/15.65 X38:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 X36 ) =
% 119.59/15.65 (
% 119.59/15.65 X38 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 X38 @ X36 ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X40:$i,
% 119.59/15.65 X42:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 X40 ) =
% 119.59/15.65 (
% 119.59/15.65 X42 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 X40 @ X42 ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X44:$i,
% 119.59/15.65 X46:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X48:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X48 @ X44 ) =>
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X48 @ X46 ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 X44 @ X46 ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X50:$i]:
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 emptyset @
% 119.59/15.65 X50 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X52:$i,
% 119.59/15.65 X54:$i,
% 119.59/15.65 X56:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 X52 @ X54 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X56 @ X52 ) =>
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X56 @ X54 ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X58:$i,
% 119.59/15.65 X60:$i,
% 119.59/15.65 X62:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 X58 @ X60 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ~
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X62 @ X60 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 ~
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X62 @ X58 ) ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X64:$i,
% 119.59/15.65 X66:$i,
% 119.59/15.65 X68:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X68 @ X64 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ~
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X68 @ X66 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 ~
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 X64 @ X66 ) ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X70:$i,
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% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 sepInPowerset ) =>
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% 119.59/15.65 (
% 119.59/15.65 sepSubset ) =>
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% 119.59/15.65 binunionIL ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 upairset2IR ) =>
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% 119.59/15.65 (
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% 119.59/15.65 (
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% 119.59/15.65 (
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% 119.59/15.65 (
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% 119.59/15.65 (
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% 119.59/15.65 (
% 119.59/15.65 disjointsetsI1 ) =>
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% 119.59/15.65 (
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% 119.59/15.65 (
% 119.59/15.65 binintersectSubset4 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 binintersectSubset1 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 bs114d ) =>
% 119.59/15.65 (
% 119.59/15.65 (
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% 119.59/15.65 X118:$i,
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% 119.59/15.65 (
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% 119.59/15.65 X124:$i,
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% 119.59/15.65 ![
% 119.59/15.65 X128:$i,
% 119.59/15.65 X130:$i,
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% 119.59/15.65 (
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% 119.59/15.65 (
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% 119.59/15.65 ![
% 119.59/15.65 X134:$i,
% 119.59/15.65 X136:$i]:
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% 119.59/15.65 (
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% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X138:$i,
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% 119.59/15.65 (
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% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X156:$i,
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% 119.59/15.65 (
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% 119.59/15.65 in @
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% 119.59/15.65 ![
% 119.59/15.65 X162:$i,
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% 119.59/15.65 X166:$i,
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% 119.59/15.65 (
% 119.59/15.65 setminus
% 119.59/15.65 @
% 119.59/15.65 X166 @
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% 119.59/15.65 (
% 119.59/15.65 emptyset ) ) =>
% 119.59/15.65 (
% 119.59/15.65 subset @
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% 119.59/15.65 (
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% 119.59/15.65 symdiffE ) =>
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% 119.59/15.65 (
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% 119.59/15.65 (
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% 119.59/15.65 (
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% 119.59/15.65 (
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% 119.59/15.65 (
% 119.59/15.65 secondinupair ) =>
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% 119.59/15.65 (
% 119.59/15.65 setukpairIL ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 setukpairIR ) =>
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% 119.59/15.65 (
% 119.59/15.65 kpairiskpair ) =>
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% 119.59/15.65 in @
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% 119.59/15.65 subset @
% 119.59/15.65 (
% 119.59/15.65 setadjoin
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% 119.59/15.65 (
% 119.59/15.65 (
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% 119.59/15.65 X174:$i,
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% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X176 @
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% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 (
% 119.59/15.65 setadjoin
% 119.59/15.65 @
% 119.59/15.65 X176 @
% 119.59/15.65 emptyset ) @
% 119.59/15.65 (
% 119.59/15.65 powerset
% 119.59/15.65 @
% 119.59/15.65 X174 ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 singletoninpowunion ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 upairset2E ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 upairsubunion ) =>
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% 119.59/15.65 (
% 119.59/15.65 upairinpowunion ) =>
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% 119.59/15.65 (
% 119.59/15.65 ubforcartprodlem1 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ubforcartprodlem2 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ubforcartprodlem3 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 cartprodpairin ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 cartprodmempair1 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 cartprodmempair ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 setunionE2 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 setunionsingleton1 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 setunionsingleton2 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 setunionsingleton ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 singletonprop ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ex1E1 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ex1I ) =>
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% 119.59/15.65 (
% 119.59/15.65 ex1I2 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 singletonsuniq ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 setukpairinjL1 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 kfstsingleton ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 theprop ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 kfstpairEq ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 cartprodfstin ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 setukpairinjL2 ) =>
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% 119.59/15.65 (
% 119.59/15.65 setukpairinjL ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 setukpairinjR11 ) =>
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% 119.59/15.65 (
% 119.59/15.65 setukpairinjR12 ) =>
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% 119.59/15.65 (
% 119.59/15.65 setukpairinjR1 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 upairequniteq ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 setukpairinjR2 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 setukpairinjR ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ksndsingleton ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ksndpairEq ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 kpairsurjEq ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 cartprodsndin ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 cartprodpairmemEL ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 cartprodpairmemER ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 cartprodmempaircEq ) =>
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% 119.59/15.65 @
% 119.59/15.65 X254 @
% 119.59/15.65 X258 ) @
% 119.59/15.65 (
% 119.59/15.65 setminus
% 119.59/15.65 @
% 119.59/15.65 X254 @
% 119.59/15.65 X256 ) ) ) ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X260:$i,
% 119.59/15.65 X262:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X262 @
% 119.59/15.65 (
% 119.59/15.65 powerset
% 119.59/15.65 @
% 119.59/15.65 X260 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X264:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X264 @
% 119.59/15.65 (
% 119.59/15.65 powerset
% 119.59/15.65 @
% 119.59/15.65 X260 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 (
% 119.59/15.65 setminus
% 119.59/15.65 @
% 119.59/15.65 X260 @
% 119.59/15.65 X264 ) @
% 119.59/15.65 (
% 119.59/15.65 setminus
% 119.59/15.65 @
% 119.59/15.65 X260 @
% 119.59/15.65 X262 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 X262 @
% 119.59/15.65 X264 ) ) ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X266:$i,
% 119.59/15.65 X268:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X268 @
% 119.59/15.65 (
% 119.59/15.65 powerset
% 119.59/15.65 @
% 119.59/15.65 X266 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X270:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X270 @
% 119.59/15.65 X266 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X270 @
% 119.59/15.65 X268 ) =>
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X270 @
% 119.59/15.65 (
% 119.59/15.65 setminus
% 119.59/15.65 @
% 119.59/15.65 X266 @
% 119.59/15.65 (
% 119.59/15.65 setminus
% 119.59/15.65 @
% 119.59/15.65 X266 @
% 119.59/15.65 X268 ) ) ) ) ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X272:$i,
% 119.59/15.65 X274:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X274 @
% 119.59/15.65 (
% 119.59/15.65 powerset
% 119.59/15.65 @
% 119.59/15.65 X272 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X276:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X276 @
% 119.59/15.65 X272 ) =>
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X276 @
% 119.59/15.65 (
% 119.59/15.65 setminus
% 119.59/15.65 @
% 119.59/15.65 X272 @
% 119.59/15.65 (
% 119.59/15.65 setminus
% 119.59/15.65 @
% 119.59/15.65 X272 @
% 119.59/15.65 X274 ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X276 @
% 119.59/15.65 X274 ) ) ) ) ) ) =>
% 119.59/15.65 (
% 119.59/15.65 ![
% 119.59/15.65 X278:$i,
% 119.59/15.65 X280:$i]:
% 119.59/15.65 (
% 119.59/15.65 (
% 119.59/15.65 in @
% 119.59/15.65 X280 @
% 119.59/15.65 (
% 119.59/15.65 powerset
% 119.59/15.65 @
% 119.59/15.65 X278 ) ) =>
% 119.59/15.65 (
% 119.59/15.65 subset @
% 119.59/15.65 X280 @
% 119.59/15.65 (
% 119.59/15.65 setminus
% 119.59/15.65 @
% 119.59/15.65 X278 @
% 119.59/15.65 (
% 119.59/15.65 setminus
% 119.59/15.65 @
% 119.59/15.65 X278 @
% 119.59/15.65 X280 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 119.59/15.65 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 119.59/15.65 thf(zip_derived_cl67, plain,
% 119.59/15.65 (![X32 : $i, X33 : $i, X34 : $i]:
% 119.59/15.65 (~ (in @ X32 @ (setminus @ X33 @ X34)) | ~ (in @ X32 @ X34))),
% 119.59/15.65 inference('cnf', [status(esa)], [zf_stmt_4])).
% 119.59/15.65 thf(zip_derived_cl20, plain,
% 119.59/15.65 (![X0 : $i, X1 : $i]:
% 119.59/15.65 ( (in @ X0 @ (powerset @ X1)) | ~ (in @ (sk__147 @ X0 @ X1) @ X1))),
% 119.59/15.65 inference('cnf', [status(esa)], [zf_stmt_4])).
% 119.59/15.65 thf(zip_derived_cl203, plain,
% 119.59/15.65 (![X92 : $i, X93 : $i, X94 : $i]:
% 119.59/15.65 (~ (in @ X92 @ X93)
% 119.59/15.65 | (in @ X92 @ X94)
% 119.59/15.65 | (in @ X92 @ (setminus @ X93 @ X94)))),
% 119.59/15.65 inference('cnf', [status(esa)], [zf_stmt_4])).
% 119.59/15.65 thf(zip_derived_cl21, plain,
% 119.59/15.65 (![X0 : $i, X1 : $i]:
% 119.59/15.65 ( (in @ X0 @ (powerset @ X1)) | (in @ (sk__147 @ X0 @ X1) @ X0))),
% 119.59/15.65 inference('cnf', [status(esa)], [zf_stmt_4])).
% 119.59/15.65 thf(zip_derived_cl217, plain,
% 119.59/15.65 (![X103 : $i, X104 : $i]:
% 119.59/15.65 ( (subset @ X103 @ X104) | ~ (in @ X103 @ (powerset @ X104)))),
% 119.59/15.65 inference('cnf', [status(esa)], [zf_stmt_4])).
% 119.59/15.65 thf(zip_derived_cl130, plain,
% 119.59/15.65 (~ (subset @ sk__144 @
% 119.59/15.65 (setminus @ sk__143 @ (setminus @ sk__143 @ sk__144)))),
% 119.59/15.65 inference('cnf', [status(esa)], [zf_stmt_4])).
% 119.59/15.65 thf(zip_derived_cl423, plain,
% 119.59/15.65 (~ (in @ sk__144 @
% 119.59/15.65 (powerset @ (setminus @ sk__143 @ (setminus @ sk__143 @ sk__144))))),
% 119.59/15.65 inference('sup-', [status(thm)], [zip_derived_cl217, zip_derived_cl130])).
% 119.59/15.65 thf(zip_derived_cl131, plain, ( (in @ sk__144 @ (powerset @ sk__143))),
% 119.59/15.65 inference('cnf', [status(esa)], [zf_stmt_4])).
% 119.59/15.65 thf(zip_derived_cl246, plain,
% 119.59/15.65 (![X123 : $i, X124 : $i, X125 : $i]:
% 119.59/15.65 (~ (in @ X123 @ (powerset @ X124))
% 119.59/15.65 | (in @ X125 @ X124)
% 119.59/15.65 | ~ (in @ X125 @ X123))),
% 119.59/15.65 inference('cnf', [status(esa)], [zf_stmt_4])).
% 119.59/15.65 thf(zip_derived_cl635, plain,
% 119.59/15.65 (![X0 : $i]: (~ (in @ X0 @ sk__144) | (in @ X0 @ sk__143))),
% 119.59/15.65 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl246])).
% 119.59/15.65 thf(zip_derived_cl15187, plain, ($false),
% 119.59/15.65 inference('eprover', [status(thm)],
% 119.59/15.65 [zip_derived_cl67, zip_derived_cl20, zip_derived_cl203,
% 119.59/15.65 zip_derived_cl21, zip_derived_cl423, zip_derived_cl635])).
% 119.59/15.65
% 119.59/15.65 % SZS output end Refutation
% 119.59/15.65
% 119.59/15.65
% 119.59/15.65 % Terminating...
% 119.59/15.65 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 120.13/15.86 % Runner terminated.
% 120.13/15.87 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------