%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU730^1 : 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.qxnuKaprB7 true
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:56:00 PM UTC 2025
% Result : Theorem 45.98s 9.17s
% Output : Refutation 45.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SEU730^1 : TPTP v9.2.0. Released v3.7.0.
% 0.05/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.qxnuKaprB7 true
% 0.10/0.35 % Computer : n014.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8042.1875MB
% 0.10/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Wed Oct 1 16:02:53 EDT 2025
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Running portfolio for 300 s
% 0.10/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Number of cores: 8
% 0.10/0.35 % Python version: Python 3.6.8
% 0.10/0.36 % Running in HO mode
% 0.51/0.63 % Total configuration time : 828
% 0.51/0.63 % Estimated wc time : 1656
% 0.51/0.63 % Estimated cpu time (8 cpus) : 207.0
% 0.86/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.86/0.78 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.95/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.95/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.95/0.82 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.95/0.83 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.95/0.84 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.95/0.84 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 45.98/9.17 % Solved by lams/40_c_ic.sh.
% 45.98/9.17 % done 4046 iterations in 8.197s
% 45.98/9.17 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 45.98/9.17 % SZS output start Refutation
% 45.98/9.17 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 45.98/9.17 thf(notdexE_type, type, notdexE: $o).
% 45.98/9.17 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 45.98/9.17 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 45.98/9.17 thf(setunionAx_type, type, setunionAx: $o).
% 45.98/9.17 thf(setminusELneg_type, type, setminusELneg: $o).
% 45.98/9.17 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 45.98/9.17 thf(ex1E1_type, type, ex1E1: $o).
% 45.98/9.17 thf(powersetE_type, type, powersetE: $o).
% 45.98/9.17 thf(omegaSAx_type, type, omegaSAx: $o).
% 45.98/9.17 thf(exuI1_type, type, exuI1: $o).
% 45.98/9.17 thf(exuI2_type, type, exuI2: $o).
% 45.98/9.17 thf(notequalI2_type, type, notequalI2: $o).
% 45.98/9.17 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 45.98/9.17 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 45.98/9.17 thf(upairsubunion_type, type, upairsubunion: $o).
% 45.98/9.17 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 45.98/9.17 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 45.98/9.17 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 45.98/9.17 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 45.98/9.17 thf(setminusILneg_type, type, setminusILneg: $o).
% 45.98/9.17 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 45.98/9.17 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 45.98/9.17 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 45.98/9.17 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 45.98/9.17 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 45.98/9.17 thf(iftrue_type, type, iftrue: $o).
% 45.98/9.17 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 45.98/9.17 thf(ifSingleton_type, type, ifSingleton: $o).
% 45.98/9.17 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 45.98/9.17 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 45.98/9.17 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 45.98/9.17 thf(lamProp_type, type, lamProp: $o).
% 45.98/9.17 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 45.98/9.17 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 45.98/9.17 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 45.98/9.17 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 45.98/9.17 thf(setukpairIR_type, type, setukpairIR: $o).
% 45.98/9.17 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 45.98/9.17 thf(lam2p_type, type, lam2p: $o).
% 45.98/9.17 thf(binunionE_type, type, binunionE: $o).
% 45.98/9.17 thf(setext_type, type, setext: $o).
% 45.98/9.17 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 45.98/9.17 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 45.98/9.17 thf(descr__Cong_type, type, descr__Cong: $o).
% 45.98/9.17 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 45.98/9.17 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 45.98/9.17 thf(eqbreln_type, type, eqbreln: $o).
% 45.98/9.17 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 45.98/9.17 thf(in_type, type, in: $i > $i > $o).
% 45.98/9.17 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 45.98/9.17 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 45.98/9.17 thf(complementT_lem_type, type, complementT_lem: $o).
% 45.98/9.17 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 45.98/9.17 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 45.98/9.17 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 45.98/9.17 thf(beta1_type, type, beta1: $o).
% 45.98/9.17 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 45.98/9.17 thf(powersetTE1_type, type, powersetTE1: $o).
% 45.98/9.17 thf(symdiffI2_type, type, symdiffI2: $o).
% 45.98/9.17 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 45.98/9.17 thf(upairset2IR_type, type, upairset2IR: $o).
% 45.98/9.17 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 45.98/9.17 thf(subsetE_type, type, subsetE: $o).
% 45.98/9.17 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 45.98/9.17 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 45.98/9.17 thf(setbeta_type, type, setbeta: $o).
% 45.98/9.17 thf(eqinunit_type, type, eqinunit: $o).
% 45.98/9.17 thf(upairsetIL_type, type, upairsetIL: $o).
% 45.98/9.17 thf(powersetI1_type, type, powersetI1: $o).
% 45.98/9.17 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 45.98/9.17 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 45.98/9.17 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 45.98/9.17 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 45.98/9.17 thf(powersetAx_type, type, powersetAx: $o).
% 45.98/9.17 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 45.98/9.17 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 45.98/9.17 thf(powersetI_type, type, powersetI: $o).
% 45.98/9.17 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 45.98/9.17 thf(upairsetIR_type, type, upairsetIR: $o).
% 45.98/9.17 thf(lamp_type, type, lamp: $o).
% 45.98/9.17 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 45.98/9.17 thf(inCongP_type, type, inCongP: $o).
% 45.98/9.17 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 45.98/9.17 thf(exuE3e_type, type, exuE3e: $o).
% 45.98/9.17 thf(emptysetE_type, type, emptysetE: $o).
% 45.98/9.17 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 45.98/9.17 thf(setunionI_type, type, setunionI: $o).
% 45.98/9.17 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 45.98/9.17 thf(prop2setI_type, type, prop2setI: $o).
% 45.98/9.17 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 45.98/9.17 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 45.98/9.17 thf(setminusER_type, type, setminusER: $o).
% 45.98/9.17 thf(exuE2_type, type, exuE2: $o).
% 45.98/9.17 thf(emptyset_type, type, emptyset: $i).
% 45.98/9.17 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 45.98/9.17 thf(ex1I_type, type, ex1I: $o).
% 45.98/9.17 thf(ex1E2_type, type, ex1E2: $o).
% 45.98/9.17 thf(setminus_type, type, setminus: $i > $i > $i).
% 45.98/9.17 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 45.98/9.17 thf(powersetsubset_type, type, powersetsubset: $o).
% 45.98/9.17 thf(subPowSU_type, type, subPowSU: $o).
% 45.98/9.17 thf(notequalI1_type, type, notequalI1: $o).
% 45.98/9.17 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 45.98/9.17 thf(notinemptyset_type, type, notinemptyset: $o).
% 45.98/9.17 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 45.98/9.17 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 45.98/9.17 thf(subsetTrans_type, type, subsetTrans: $o).
% 45.98/9.17 thf(kpairp_type, type, kpairp: $o).
% 45.98/9.17 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 45.98/9.17 thf(setminusI_type, type, setminusI: $o).
% 45.98/9.17 thf(binunionIL_type, type, binunionIL: $o).
% 45.98/9.17 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 45.98/9.17 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 45.98/9.17 thf(subsetE2_type, type, subsetE2: $o).
% 45.98/9.17 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 45.98/9.17 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 45.98/9.17 thf(beta2_type, type, beta2: $o).
% 45.98/9.17 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 45.98/9.17 thf(setextsub_type, type, setextsub: $o).
% 45.98/9.17 thf(binunionLsub_type, type, binunionLsub: $o).
% 45.98/9.17 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 45.98/9.17 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 45.98/9.17 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 45.98/9.17 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 45.98/9.17 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 45.98/9.17 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 45.98/9.17 thf(setunionE_type, type, setunionE: $o).
% 45.98/9.17 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 45.98/9.17 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 45.98/9.17 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 45.98/9.17 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 45.98/9.17 thf(binunionIR_type, type, binunionIR: $o).
% 45.98/9.17 thf(theeq_type, type, theeq: $o).
% 45.98/9.17 thf(setadjoinE_type, type, setadjoinE: $o).
% 45.98/9.17 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 45.98/9.17 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 45.98/9.17 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 45.98/9.17 thf(ap2p_type, type, ap2p: $o).
% 45.98/9.17 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 45.98/9.17 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 45.98/9.17 thf(exuE1_type, type, exuE1: $o).
% 45.98/9.17 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 45.98/9.17 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 45.98/9.17 thf(setminusLsub_type, type, setminusLsub: $o).
% 45.98/9.17 thf(funcextLem_type, type, funcextLem: $o).
% 45.98/9.17 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 45.98/9.17 thf(notinsingleton_type, type, notinsingleton: $o).
% 45.98/9.17 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 45.98/9.17 thf(exuEu_type, type, exuEu: $o).
% 45.98/9.17 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 45.98/9.17 thf(upairsetE_type, type, upairsetE: $o).
% 45.98/9.17 thf(omega0Ax_type, type, omega0Ax: $o).
% 45.98/9.17 thf(subsetTI_type, type, subsetTI: $o).
% 45.98/9.17 thf(notsubsetI_type, type, notsubsetI: $o).
% 45.98/9.17 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 45.98/9.17 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 45.98/9.17 thf(setextAx_type, type, setextAx: $o).
% 45.98/9.17 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 45.98/9.17 thf(powersetE1_type, type, powersetE1: $o).
% 45.98/9.17 thf(bs114d_type, type, bs114d: $o).
% 45.98/9.17 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 45.98/9.17 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 45.98/9.17 thf(ifp_type, type, ifp: $o).
% 45.98/9.17 thf(powersetTI1_type, type, powersetTI1: $o).
% 45.98/9.17 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 45.98/9.17 thf(subsetI1_type, type, subsetI1: $o).
% 45.98/9.17 thf(symdiffE_type, type, symdiffE: $o).
% 45.98/9.17 thf(descrp_type, type, descrp: $o).
% 45.98/9.17 thf(sk__145_type, type, sk__145: $i).
% 45.98/9.17 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 45.98/9.17 thf(foundationAx_type, type, foundationAx: $o).
% 45.98/9.17 thf(emptysetAx_type, type, emptysetAx: $o).
% 45.98/9.17 thf(emptyI_type, type, emptyI: $o).
% 45.98/9.17 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 45.98/9.17 thf(eta2_type, type, eta2: $o).
% 45.98/9.17 thf(binintersectEL_type, type, binintersectEL: $o).
% 45.98/9.17 thf(emptyE1_type, type, emptyE1: $o).
% 45.98/9.17 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 45.98/9.17 thf(complementTI1_type, type, complementTI1: $o).
% 45.98/9.17 thf(vacuousDall_type, type, vacuousDall: $o).
% 45.98/9.17 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 45.98/9.17 thf(binintersectI_type, type, binintersectI: $o).
% 45.98/9.17 thf(funcext_type, type, funcext: $o).
% 45.98/9.17 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 45.98/9.17 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 45.98/9.17 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 45.98/9.17 thf(brelnall2_type, type, brelnall2: $o).
% 45.98/9.17 thf(setextT_type, type, setextT: $o).
% 45.98/9.17 thf(ex1I2_type, type, ex1I2: $o).
% 45.98/9.17 thf(symdiffI1_type, type, symdiffI1: $o).
% 45.98/9.17 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 45.98/9.17 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 45.98/9.17 thf(theprop_type, type, theprop: $o).
% 45.98/9.17 thf(subsetI2_type, type, subsetI2: $o).
% 45.98/9.17 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 45.98/9.17 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 45.98/9.17 thf(setminusERneg_type, type, setminusERneg: $o).
% 45.98/9.17 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 45.98/9.17 thf(omega__Cong_type, type, omega__Cong: $o).
% 45.98/9.17 thf(subsetRefl_type, type, subsetRefl: $o).
% 45.98/9.17 thf(uniqinunit_type, type, uniqinunit: $o).
% 45.98/9.17 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 45.98/9.17 thf(prop2setE_type, type, prop2setE: $o).
% 45.98/9.17 thf(binunionEcases_type, type, binunionEcases: $o).
% 45.98/9.17 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 45.98/9.17 thf(complementTE1_type, type, complementTE1: $o).
% 45.98/9.17 thf(nonemptyI_type, type, nonemptyI: $o).
% 45.98/9.17 thf(app_type, type, app: $o).
% 45.98/9.17 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 45.98/9.17 thf(exuE3u_type, type, exuE3u: $o).
% 45.98/9.17 thf(eta1_type, type, eta1: $o).
% 45.98/9.17 thf(setminusEL_type, type, setminusEL: $o).
% 45.98/9.17 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 45.98/9.17 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 45.98/9.17 thf(sepSubset_type, type, sepSubset: $o).
% 45.98/9.17 thf(upairset2E_type, type, upairset2E: $o).
% 45.98/9.17 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 45.98/9.17 thf(exuI3_type, type, exuI3: $o).
% 45.98/9.17 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 45.98/9.17 thf(apProp_type, type, apProp: $o).
% 45.98/9.17 thf(notdallE_type, type, notdallE: $o).
% 45.98/9.17 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 45.98/9.17 thf(binintersectER_type, type, binintersectER: $o).
% 45.98/9.17 thf(brelnall1_type, type, brelnall1: $o).
% 45.98/9.17 thf(powerset_type, type, powerset: $i > $i).
% 45.98/9.17 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 45.98/9.17 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 45.98/9.17 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 45.98/9.17 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 45.98/9.17 thf(exu__Cong_type, type, exu__Cong: $o).
% 45.98/9.17 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 45.98/9.17 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 45.98/9.17 thf(secondinupair_type, type, secondinupair: $o).
% 45.98/9.17 thf(singletonprop_type, type, singletonprop: $o).
% 45.98/9.17 thf(singletonsubset_type, type, singletonsubset: $o).
% 45.98/9.17 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 45.98/9.17 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 45.98/9.17 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 45.98/9.17 thf(replAx_type, type, replAx: $o).
% 45.98/9.17 thf(upairequniteq_type, type, upairequniteq: $o).
% 45.98/9.17 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 45.98/9.17 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 45.98/9.17 thf(setukpairIL_type, type, setukpairIL: $o).
% 45.98/9.17 thf(setunionE2_type, type, setunionE2: $o).
% 45.98/9.17 thf(inPowerset_type, type, inPowerset: $o).
% 45.98/9.17 thf(iffalse_type, type, iffalse: $o).
% 45.98/9.17 thf(funcext2_type, type, funcext2: $o).
% 45.98/9.17 thf(subset_type, type, subset: $i > $i > $o).
% 45.98/9.17 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 45.98/9.17 thf(subbreln_type, type, subbreln: $o).
% 45.98/9.17 thf(in__Cong_type, type, in__Cong: $o).
% 45.98/9.17 thf(binunionRsub_type, type, binunionRsub: $o).
% 45.98/9.17 thf(sk__146_type, type, sk__146: $i).
% 45.98/9.17 thf(subset2powerset_type, type, subset2powerset: $o).
% 45.98/9.17 thf(doubleComplementSub1, axiom, doubleComplementSub1 =
% 45.98/9.17 (![A:$i,X:$i]:
% 45.98/9.17 ( ( in @ X @ ( powerset @ A ) ) =>
% 45.98/9.17 ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 45.98/9.17 thf('0', plain,
% 45.98/9.17 (( doubleComplementSub1 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( subset @ X6 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(doubleComplementE1, axiom, doubleComplementE1 =
% 45.98/9.17 (![A:$i,X:$i]:
% 45.98/9.17 ( ( in @ X @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ![Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ A ) =>
% 45.98/9.17 ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) =>
% 45.98/9.17 ( in @ Xx @ X ) ) ) ) ))).
% 45.98/9.17 thf('1', plain,
% 45.98/9.17 (( doubleComplementE1 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ![X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ X4 ) =>
% 45.98/9.17 ( ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) =>
% 45.98/9.17 ( in @ X8 @ X6 ) ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(doubleComplementI1, axiom, doubleComplementI1 =
% 45.98/9.17 (![A:$i,X:$i]:
% 45.98/9.17 ( ( in @ X @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ![Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ A ) =>
% 45.98/9.17 ( ( in @ Xx @ X ) =>
% 45.98/9.17 ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 45.98/9.17 thf('2', plain,
% 45.98/9.17 (( doubleComplementI1 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ![X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ X4 ) =>
% 45.98/9.17 ( ( in @ X8 @ X6 ) =>
% 45.98/9.17 ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(contrasubsetT3, axiom, contrasubsetT3 =
% 45.98/9.17 (![A:$i,X:$i]:
% 45.98/9.17 ( ( in @ X @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ![Y:$i]:
% 45.98/9.17 ( ( in @ Y @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) =>
% 45.98/9.17 ( subset @ X @ Y ) ) ) ) ))).
% 45.98/9.17 thf('3', plain,
% 45.98/9.17 (( contrasubsetT3 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ![X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) =>
% 45.98/9.17 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(contrasubsetT2, axiom, contrasubsetT2 =
% 45.98/9.17 (![A:$i,X:$i]:
% 45.98/9.17 ( ( in @ X @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ![Y:$i]:
% 45.98/9.17 ( ( in @ Y @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ( subset @ X @ Y ) =>
% 45.98/9.17 ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ))).
% 45.98/9.17 thf('4', plain,
% 45.98/9.17 (( contrasubsetT2 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ![X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ( subset @ X6 @ X8 ) =>
% 45.98/9.17 ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(contrasubsetT1, axiom, contrasubsetT1 =
% 45.98/9.17 (![A:$i,X:$i]:
% 45.98/9.17 ( ( in @ X @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ![Y:$i]:
% 45.98/9.17 ( ( in @ Y @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ![Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ A ) =>
% 45.98/9.17 ( ( subset @ X @ Y ) =>
% 45.98/9.17 ( ( ~( in @ Xx @ Y ) ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 45.98/9.17 thf('5', plain,
% 45.98/9.17 (( contrasubsetT1 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ![X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ![X10:$i]:
% 45.98/9.17 ( ( in @ X10 @ X4 ) =>
% 45.98/9.17 ( ( subset @ X6 @ X8 ) =>
% 45.98/9.17 ( ( ~( in @ X10 @ X8 ) ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(contrasubsetT, axiom, contrasubsetT =
% 45.98/9.17 (![A:$i,X:$i]:
% 45.98/9.17 ( ( in @ X @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ![Y:$i]:
% 45.98/9.17 ( ( in @ Y @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ![Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ A ) =>
% 45.98/9.17 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 45.98/9.17 ( ( in @ Xx @ Y ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 45.98/9.17 thf('6', plain,
% 45.98/9.17 (( contrasubsetT ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ![X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ![X10:$i]:
% 45.98/9.17 ( ( in @ X10 @ X4 ) =>
% 45.98/9.17 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 45.98/9.17 ( ( in @ X10 @ X8 ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(complementTE1, axiom, complementTE1 =
% 45.98/9.17 (![A:$i,X:$i]:
% 45.98/9.17 ( ( in @ X @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ![Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ A ) =>
% 45.98/9.17 ( ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) => ( in @ Xx @ X ) ) ) ) ))).
% 45.98/9.17 thf('7', plain,
% 45.98/9.17 (( complementTE1 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ![X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ X4 ) =>
% 45.98/9.17 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) => ( in @ X8 @ X6 ) ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(complementTI1, axiom, complementTI1 =
% 45.98/9.17 (![A:$i,X:$i]:
% 45.98/9.17 ( ( in @ X @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ![Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ A ) =>
% 45.98/9.17 ( ( in @ Xx @ X ) => ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 45.98/9.17 thf('8', plain,
% 45.98/9.17 (( complementTI1 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ![X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ X4 ) =>
% 45.98/9.17 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(powersetTE1, axiom, powersetTE1 =
% 45.98/9.17 (![A:$i,X:$i]:
% 45.98/9.17 ( ( in @ X @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ![Y:$i]:
% 45.98/9.17 ( ( in @ Y @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ![Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ A ) =>
% 45.98/9.17 ( ( in @ X @ ( powerset @ Y ) ) =>
% 45.98/9.17 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 45.98/9.17 thf('9', plain,
% 45.98/9.17 (( powersetTE1 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ![X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ![X10:$i]:
% 45.98/9.17 ( ( in @ X10 @ X4 ) =>
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 45.98/9.17 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(powersetTI1, axiom, powersetTI1 =
% 45.98/9.17 (![A:$i,X:$i]:
% 45.98/9.17 ( ( in @ X @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ![Y:$i]:
% 45.98/9.17 ( ( in @ Y @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ( ![Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 45.98/9.17 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 45.98/9.17 thf('10', plain,
% 45.98/9.17 (( powersetTI1 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ![X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ( ![X10:$i]:
% 45.98/9.17 ( ( in @ X10 @ X4 ) =>
% 45.98/9.17 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 45.98/9.17 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(subsetTI, axiom, subsetTI =
% 45.98/9.17 (![A:$i,X:$i]:
% 45.98/9.17 ( ( in @ X @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ![Y:$i]:
% 45.98/9.17 ( ( in @ Y @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ( ![Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 45.98/9.17 ( subset @ X @ Y ) ) ) ) ))).
% 45.98/9.17 thf('11', plain,
% 45.98/9.17 (( subsetTI ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ![X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ( ![X10:$i]:
% 45.98/9.17 ( ( in @ X10 @ X4 ) =>
% 45.98/9.17 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 45.98/9.17 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(setextT, axiom, setextT =
% 45.98/9.17 (![A:$i,X:$i]:
% 45.98/9.17 ( ( in @ X @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ![Y:$i]:
% 45.98/9.17 ( ( in @ Y @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ( ![Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 45.98/9.17 ( ( ![Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 45.98/9.17 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 45.98/9.17 thf('12', plain,
% 45.98/9.17 (( setextT ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ![X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ( ![X10:$i]:
% 45.98/9.17 ( ( in @ X10 @ X4 ) =>
% 45.98/9.17 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 45.98/9.17 ( ( ![X12:$i]:
% 45.98/9.17 ( ( in @ X12 @ X4 ) =>
% 45.98/9.17 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 45.98/9.17 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(complementT_lem, axiom, complementT_lem =
% 45.98/9.17 (![A:$i,X:$i]:
% 45.98/9.17 ( ( in @ X @ ( powerset @ A ) ) =>
% 45.98/9.17 ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ))).
% 45.98/9.17 thf('13', plain,
% 45.98/9.17 (( complementT_lem ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( in @ ( setminus @ X4 @ X6 ) @ ( powerset @ X4 ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(setminusT_lem, axiom, setminusT_lem =
% 45.98/9.17 (![A:$i,X:$i]:
% 45.98/9.17 ( ( in @ X @ ( powerset @ A ) ) =>
% 45.98/9.17 ( ![Y:$i]:
% 45.98/9.17 ( ( in @ Y @ ( powerset @ A ) ) =>
% 45.98/9.17 ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 45.98/9.17 thf('14', plain,
% 45.98/9.17 (( setminusT_lem ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ![X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( in @ ( setminus @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(powersetT_lem, axiom, powersetT_lem =
% 45.98/9.17 (![A:$i,X:$i]:
% 45.98/9.17 ( ( in @ X @ ( powerset @ A ) ) =>
% 45.98/9.17 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 45.98/9.17 thf('15', plain,
% 45.98/9.17 (( powersetT_lem ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(singletoninpowerset, axiom, singletoninpowerset =
% 45.98/9.17 (![A:$i,Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ A ) =>
% 45.98/9.17 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 45.98/9.17 thf('16', plain,
% 45.98/9.17 (( singletoninpowerset ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ X4 ) =>
% 45.98/9.17 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(singletonsubset, axiom, singletonsubset =
% 45.98/9.17 (![A:$i,Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ A ) => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ))).
% 45.98/9.17 thf('17', plain,
% 45.98/9.17 (( singletonsubset ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ X4 ) => ( subset @ ( setadjoin @ X6 @ emptyset ) @ X4 ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(setminusSubset1, axiom, setminusSubset1 =
% 45.98/9.17 (![A:$i,B:$i]:
% 45.98/9.17 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))).
% 45.98/9.17 thf('18', plain,
% 45.98/9.17 (( setminusSubset1 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(setminusLsub, axiom, setminusLsub =
% 45.98/9.17 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))).
% 45.98/9.17 thf('19', plain,
% 45.98/9.17 (( setminusLsub ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(setminusIRneg, axiom, setminusIRneg =
% 45.98/9.17 (![A:$i,B:$i,Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 45.98/9.17 thf('20', plain,
% 45.98/9.17 (( setminusIRneg ) =
% 45.98/9.17 ( ![X4:$i,X6:$i,X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(setminusILneg, axiom, setminusILneg =
% 45.98/9.17 (![A:$i,B:$i,Xx:$i]:
% 45.98/9.17 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 45.98/9.17 thf('21', plain,
% 45.98/9.17 (( setminusILneg ) =
% 45.98/9.17 ( ![X4:$i,X6:$i,X8:$i]:
% 45.98/9.17 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(setminusELneg, axiom, setminusELneg =
% 45.98/9.17 (![A:$i,B:$i,Xx:$i]:
% 45.98/9.17 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 45.98/9.17 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 45.98/9.17 thf('22', plain,
% 45.98/9.17 (( setminusELneg ) =
% 45.98/9.17 ( ![X4:$i,X6:$i,X8:$i]:
% 45.98/9.17 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 45.98/9.17 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(setminusERneg, axiom, setminusERneg =
% 45.98/9.17 (![A:$i,B:$i,Xx:$i]:
% 45.98/9.17 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 45.98/9.17 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 45.98/9.17 thf('23', plain,
% 45.98/9.17 (( setminusERneg ) =
% 45.98/9.17 ( ![X4:$i,X6:$i,X8:$i]:
% 45.98/9.17 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 45.98/9.17 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(setminusSubset2, axiom, setminusSubset2 =
% 45.98/9.17 (![A:$i,B:$i]:
% 45.98/9.17 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))).
% 45.98/9.17 thf('24', plain,
% 45.98/9.17 (( setminusSubset2 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(setminusER, axiom, setminusER =
% 45.98/9.17 (![A:$i,B:$i,Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))).
% 45.98/9.17 thf('25', plain,
% 45.98/9.17 (( setminusER ) =
% 45.98/9.17 ( ![X4:$i,X6:$i,X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(setminusEL, axiom, setminusEL =
% 45.98/9.17 (![A:$i,B:$i,Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 45.98/9.17 thf('26', plain,
% 45.98/9.17 (( setminusEL ) =
% 45.98/9.17 ( ![X4:$i,X6:$i,X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(setminusI, axiom, setminusI =
% 45.98/9.17 (![A:$i,B:$i,Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ A ) =>
% 45.98/9.17 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 45.98/9.17 thf('27', plain,
% 45.98/9.17 (( setminusI ) =
% 45.98/9.17 ( ![X4:$i,X6:$i,X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ X4 ) =>
% 45.98/9.17 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(powersetsubset, axiom, powersetsubset =
% 45.98/9.17 (![A:$i,B:$i]:
% 45.98/9.17 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 45.98/9.17 thf('28', plain,
% 45.98/9.17 (( powersetsubset ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( subset @ X4 @ X6 ) =>
% 45.98/9.17 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 45.98/9.17 thf('29', plain,
% 45.98/9.17 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(powersetE1, axiom, powersetE1 =
% 45.98/9.17 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 45.98/9.17 thf('30', plain,
% 45.98/9.17 (( powersetE1 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(powersetI1, axiom, powersetI1 =
% 45.98/9.17 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 45.98/9.17 thf('31', plain,
% 45.98/9.17 (( powersetI1 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq =
% 45.98/9.17 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))).
% 45.98/9.17 thf('32', plain,
% 45.98/9.17 (( subsetemptysetimpeq ) =
% 45.98/9.17 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(setextsub, axiom, setextsub =
% 45.98/9.17 (![A:$i,B:$i]:
% 45.98/9.17 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))).
% 45.98/9.17 thf('33', plain,
% 45.98/9.17 (( setextsub ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( subset @ X4 @ X6 ) =>
% 45.98/9.17 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(subset2powerset, axiom, subset2powerset =
% 45.98/9.17 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 45.98/9.17 thf('34', plain,
% 45.98/9.17 (( subset2powerset ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(setadjoinSub2, axiom, setadjoinSub2 =
% 45.98/9.17 (![A:$i,Xx:$i,B:$i]:
% 45.98/9.17 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))).
% 45.98/9.17 thf('35', plain,
% 45.98/9.17 (( setadjoinSub2 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i,X8:$i]:
% 45.98/9.17 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(setadjoinSub, axiom, setadjoinSub =
% 45.98/9.17 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))).
% 45.98/9.17 thf('36', plain,
% 45.98/9.17 (( setadjoinSub ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(subsetTrans, axiom, subsetTrans =
% 45.98/9.17 (![A:$i,B:$i,C:$i]:
% 45.98/9.17 ( ( subset @ A @ B ) => ( ( subset @ B @ C ) => ( subset @ A @ C ) ) ))).
% 45.98/9.17 thf('37', plain,
% 45.98/9.17 (( subsetTrans ) =
% 45.98/9.17 ( ![X4:$i,X6:$i,X8:$i]:
% 45.98/9.17 ( ( subset @ X4 @ X6 ) =>
% 45.98/9.17 ( ( subset @ X6 @ X8 ) => ( subset @ X4 @ X8 ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(subsetRefl, axiom, subsetRefl = (![A:$i]: ( subset @ A @ A ))).
% 45.98/9.17 thf('38', plain, (( subsetRefl ) = ( ![X4:$i]: ( subset @ X4 @ X4 ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(notequalI1, axiom, notequalI1 =
% 45.98/9.17 (![A:$i,B:$i]: ( ( ~( subset @ A @ B ) ) => ( ( A ) != ( B ) ) ))).
% 45.98/9.17 thf('39', plain,
% 45.98/9.17 (( notequalI1 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]: ( ( ~( subset @ X4 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(notsubsetI, axiom, notsubsetI =
% 45.98/9.17 (![A:$i,B:$i,Xx:$i]:
% 45.98/9.17 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ~( subset @ A @ B ) ) ) ))).
% 45.98/9.17 thf('40', plain,
% 45.98/9.17 (( notsubsetI ) =
% 45.98/9.17 ( ![X4:$i,X6:$i,X8:$i]:
% 45.98/9.17 ( ( in @ X8 @ X4 ) =>
% 45.98/9.17 ( ( ~( in @ X8 @ X6 ) ) => ( ~( subset @ X4 @ X6 ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(subsetE2, axiom, subsetE2 =
% 45.98/9.17 (![A:$i,B:$i,Xx:$i]:
% 45.98/9.17 ( ( subset @ A @ B ) => ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 45.98/9.17 thf('41', plain,
% 45.98/9.17 (( subsetE2 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i,X8:$i]:
% 45.98/9.17 ( ( subset @ X4 @ X6 ) =>
% 45.98/9.17 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(subsetE, axiom, subsetE =
% 45.98/9.17 (![A:$i,B:$i,Xx:$i]:
% 45.98/9.17 ( ( subset @ A @ B ) => ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 45.98/9.17 thf('42', plain,
% 45.98/9.17 (( subsetE ) =
% 45.98/9.17 ( ![X4:$i,X6:$i,X8:$i]:
% 45.98/9.17 ( ( subset @ X4 @ X6 ) => ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(emptysetsubset, axiom, emptysetsubset =
% 45.98/9.17 (![A:$i]: ( subset @ emptyset @ A ))).
% 45.98/9.17 thf('43', plain,
% 45.98/9.17 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(subsetI2, axiom, subsetI2 =
% 45.98/9.17 (![A:$i,B:$i]:
% 45.98/9.17 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 45.98/9.17 ( subset @ A @ B ) ))).
% 45.98/9.17 thf('44', plain,
% 45.98/9.17 (( subsetI2 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 45.98/9.17 ( subset @ X4 @ X6 ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(eqimpsubset1, axiom, eqimpsubset1 =
% 45.98/9.17 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ A @ B ) ))).
% 45.98/9.17 thf('45', plain,
% 45.98/9.17 (( eqimpsubset1 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X4 @ X6 ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(eqimpsubset2, axiom, eqimpsubset2 =
% 45.98/9.17 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ B @ A ) ))).
% 45.98/9.17 thf('46', plain,
% 45.98/9.17 (( eqimpsubset2 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(subsetI1, axiom, subsetI1 =
% 45.98/9.17 (![A:$i,B:$i]:
% 45.98/9.17 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 45.98/9.17 ( subset @ A @ B ) ))).
% 45.98/9.17 thf('47', plain,
% 45.98/9.17 (( subsetI1 ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 45.98/9.17 ( subset @ X4 @ X6 ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(powerset__Cong, axiom, powerset__Cong =
% 45.98/9.17 (![A:$i,B:$i]:
% 45.98/9.17 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 45.98/9.17 thf('48', plain,
% 45.98/9.17 (( powerset__Cong ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(powersetE, axiom, powersetE =
% 45.98/9.17 (![A:$i,B:$i,Xx:$i]:
% 45.98/9.17 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 45.98/9.17 thf('49', plain,
% 45.98/9.17 (( powersetE ) =
% 45.98/9.17 ( ![X4:$i,X6:$i,X8:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 45.98/9.17 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(emptyInPowerset, axiom, emptyInPowerset =
% 45.98/9.17 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 45.98/9.17 thf('50', plain,
% 45.98/9.17 (( emptyInPowerset ) =
% 45.98/9.17 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(emptyinPowerset, axiom, emptyinPowerset =
% 45.98/9.17 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 45.98/9.17 thf('51', plain,
% 45.98/9.17 (( emptyinPowerset ) =
% 45.98/9.17 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(powersetI, axiom, powersetI =
% 45.98/9.17 (![A:$i,B:$i]:
% 45.98/9.17 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 45.98/9.17 ( in @ B @ ( powerset @ A ) ) ))).
% 45.98/9.17 thf('52', plain,
% 45.98/9.17 (( powersetI ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 45.98/9.17 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(powersetAx, axiom, powersetAx =
% 45.98/9.17 (![A:$i,B:$i]:
% 45.98/9.17 ( ( in @ B @ ( powerset @ A ) ) <=>
% 45.98/9.17 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 45.98/9.17 thf('53', plain,
% 45.98/9.17 (( powersetAx ) =
% 45.98/9.17 ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 45.98/9.17 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 45.98/9.17 define([status(thm)])).
% 45.98/9.17 thf(doubleComplementSub2, conjecture,
% 45.98/9.17 (( setextAx ) =>
% 45.98/9.17 ( ( emptysetAx ) =>
% 45.98/9.17 ( ( setadjoinAx ) =>
% 45.98/9.17 ( ( powersetAx ) =>
% 45.98/9.17 ( ( setunionAx ) =>
% 45.98/9.17 ( ( omega0Ax ) =>
% 45.98/9.17 ( ( omegaSAx ) =>
% 45.98/9.17 ( ( omegaIndAx ) =>
% 45.98/9.17 ( ( replAx ) =>
% 45.98/9.17 ( ( foundationAx ) =>
% 45.98/9.17 ( ( wellorderingAx ) =>
% 45.98/9.17 ( ( descrp ) =>
% 45.98/9.17 ( ( dsetconstrI ) =>
% 45.98/9.17 ( ( dsetconstrEL ) =>
% 45.98/9.17 ( ( dsetconstrER ) =>
% 45.98/9.17 ( ( exuE1 ) =>
% 45.98/9.17 ( ( prop2setE ) =>
% 45.98/9.17 ( ( emptysetE ) =>
% 45.98/9.17 ( ( emptysetimpfalse ) =>
% 45.98/9.17 ( ( notinemptyset ) =>
% 45.98/9.17 ( ( exuE3e ) =>
% 45.98/9.17 ( ( setext ) =>
% 45.98/9.17 ( ( emptyI ) =>
% 45.98/9.17 ( ( noeltsimpempty ) =>
% 45.98/9.17 ( ( setbeta ) =>
% 45.98/9.17 ( ( nonemptyE1 ) =>
% 45.98/9.17 ( ( nonemptyI ) =>
% 45.98/9.17 ( ( nonemptyI1 ) =>
% 45.98/9.17 ( ( setadjoinIL ) =>
% 45.98/9.17 ( ( emptyinunitempty ) =>
% 45.98/9.17 ( ( setadjoinIR ) =>
% 45.98/9.17 ( ( setadjoinE ) =>
% 45.98/9.17 ( (
% 45.98/9.17 setadjoinOr ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setoftrueEq ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 powersetI ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 emptyinPowerset ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 emptyInPowerset ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 powersetE ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setunionI ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setunionE ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 subPowSU ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 exuE2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 nonemptyImpWitness ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 uniqinunit ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 notinsingleton ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 eqinunit ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 singletonsswitch ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 upairsetE ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 upairsetIL ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 upairsetIR ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 emptyE1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 vacuousDall ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 quantDeMorgan1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 quantDeMorgan2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 quantDeMorgan3 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 quantDeMorgan4 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 prop2setI ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 prop2set2propI ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 notdexE ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 notdallE ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 exuI1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 exuI3 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 exuI2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 inCongP ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 in__Cong ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 exuE3u ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 exu__Cong ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 emptyset__Cong ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setadjoin__Cong ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 powerset__Cong ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setunion__Cong ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 omega__Cong ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 exuEu ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 descr__Cong ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 dsetconstr__Cong ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 subsetI1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 eqimpsubset2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 eqimpsubset1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 subsetI2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 emptysetsubset ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 subsetE ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 subsetE2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 notsubsetI ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 notequalI1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 notequalI2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 subsetRefl ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 subsetTrans ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setadjoinSub ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setadjoinSub2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 subset2powerset ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setextsub ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 subsetemptysetimpeq ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 powersetI1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 powersetE1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 inPowerset ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 powersetsubset ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 sepInPowerset ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 sepSubset ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binunionIL ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 upairset2IR ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binunionIR ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binunionEcases ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binunionE ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binunionLsub ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binunionRsub ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binintersectI ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binintersectSubset5 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binintersectEL ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binintersectLsub ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binintersectSubset2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binintersectSubset3 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binintersectER ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 disjointsetsI1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binintersectRsub ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binintersectSubset4 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binintersectSubset1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 bs114d ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setminusI ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setminusEL ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setminusER ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setminusSubset2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setminusERneg ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setminusELneg ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setminusILneg ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setminusIRneg ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setminusLsub ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setminusSubset1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 symdiffE ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 symdiffI1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 symdiffI2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 symdiffIneg1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 symdiffIneg2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 secondinupair ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setukpairIL ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setukpairIR ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 kpairiskpair ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 kpairp ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 singletonsubset ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 singletoninpowerset ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 singletoninpowunion ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 upairset2E ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 upairsubunion ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 upairinpowunion ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 ubforcartprodlem1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 ubforcartprodlem2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 ubforcartprodlem3 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 cartprodpairin ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 cartprodmempair1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 cartprodmempair ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setunionE2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setunionsingleton1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setunionsingleton2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setunionsingleton ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 singletonprop ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 ex1E1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 ex1I ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 ex1I2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 singletonsuniq ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setukpairinjL1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 kfstsingleton ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 theprop ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 kfstpairEq ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 cartprodfstin ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setukpairinjL2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setukpairinjL ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setukpairinjR11 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setukpairinjR12 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setukpairinjR1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 upairequniteq ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setukpairinjR2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setukpairinjR ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 ksndsingleton ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 ksndpairEq ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 kpairsurjEq ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 cartprodsndin ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 cartprodpairmemEL ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 cartprodpairmemER ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 cartprodmempaircEq ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 cartprodfstpairEq ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 cartprodsndpairEq ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 cartprodpairsurjEq ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 dpsetconstrI ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 dpsetconstrSub ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setOfPairsIsBReln ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 dpsetconstrERa ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 dpsetconstrEL1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 dpsetconstrEL2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 dpsetconstrER ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 funcImageSingleton ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 apProp ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 app ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 infuncsetfunc ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 ap2p ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 funcinfuncset ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 lamProp ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 lamp ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 lam2p ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 brelnall1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 brelnall2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 ex1E2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 funcGraphProp1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 funcGraphProp3 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 funcGraphProp2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 funcextLem ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 funcGraphProp4 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 subbreln ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 eqbreln ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 funcext ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 funcext2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 ap2apEq1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 ap2apEq2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 beta1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 eta1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 lam2lamEq ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 beta2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 eta2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 iffalseProp1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 iffalseProp2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 iftrueProp1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 iftrueProp2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 ifSingleton ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 ifp ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 theeq ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 iftrue ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 iffalse ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 iftrueorfalse ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binintersectT_lem ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binunionT_lem ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 powersetT_lem ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setminusT_lem ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 complementT_lem ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setextT ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 subsetTI ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 powersetTI1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 powersetTE1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 complementTI1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 complementTE1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binintersectTELcontra ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 binintersectTERcontra ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 contrasubsetT ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 contrasubsetT1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 contrasubsetT2 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 contrasubsetT3 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 doubleComplementI1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 doubleComplementE1 ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 doubleComplementSub1 ) =>
% 45.98/9.17 (
% 45.98/9.17 ![
% 45.98/9.17 A:$i,X:$i]:
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 in @
% 45.98/9.17 X @
% 45.98/9.17 (
% 45.98/9.17 powerset @
% 45.98/9.17 A ) ) =>
% 45.98/9.17 (
% 45.98/9.17 subset @
% 45.98/9.17 (
% 45.98/9.17 setminus @
% 45.98/9.17 A @
% 45.98/9.17 (
% 45.98/9.17 setminus @
% 45.98/9.17 A @ X ) ) @
% 45.98/9.17 X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 45.98/9.17 thf(zf_stmt_0, conjecture,
% 45.98/9.17 (( setextAx ) =>
% 45.98/9.17 ( ( emptysetAx ) =>
% 45.98/9.17 ( ( setadjoinAx ) =>
% 45.98/9.17 ( ( ![X4:$i,X6:$i]:
% 45.98/9.17 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 45.98/9.17 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 45.98/9.17 ( ( setunionAx ) =>
% 45.98/9.17 ( ( omega0Ax ) =>
% 45.98/9.17 ( ( omegaSAx ) =>
% 45.98/9.17 ( ( omegaIndAx ) =>
% 45.98/9.17 ( ( replAx ) =>
% 45.98/9.17 ( ( foundationAx ) =>
% 45.98/9.17 ( ( wellorderingAx ) =>
% 45.98/9.17 ( ( descrp ) =>
% 45.98/9.17 ( ( dsetconstrI ) =>
% 45.98/9.17 ( ( dsetconstrEL ) =>
% 45.98/9.17 ( ( dsetconstrER ) =>
% 45.98/9.17 ( ( exuE1 ) =>
% 45.98/9.17 ( ( prop2setE ) =>
% 45.98/9.17 ( ( emptysetE ) =>
% 45.98/9.17 ( ( emptysetimpfalse ) =>
% 45.98/9.17 ( ( notinemptyset ) =>
% 45.98/9.17 ( ( exuE3e ) =>
% 45.98/9.17 ( ( setext ) =>
% 45.98/9.17 ( ( emptyI ) =>
% 45.98/9.17 ( ( noeltsimpempty ) =>
% 45.98/9.17 ( ( setbeta ) =>
% 45.98/9.17 ( ( nonemptyE1 ) =>
% 45.98/9.17 ( ( nonemptyI ) =>
% 45.98/9.17 ( ( nonemptyI1 ) =>
% 45.98/9.17 ( ( setadjoinIL ) =>
% 45.98/9.17 ( ( emptyinunitempty ) =>
% 45.98/9.17 ( ( setadjoinIR ) =>
% 45.98/9.17 ( ( setadjoinE ) =>
% 45.98/9.17 ( (
% 45.98/9.17 setadjoinOr ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 setoftrueEq ) =>
% 45.98/9.17 (
% 45.98/9.17 (
% 45.98/9.17 ![
% 45.98/9.17 X10:$i,
% 45.98/9.17 X12:$i]:
% 45.98/9.17 (
% 45.98/9.17 (
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% 45.98/9.18 setminus
% 45.98/9.18 @
% 45.98/9.18 X138 @
% 45.98/9.18 X140 ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X142 @
% 45.98/9.18 X138 ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X142 @
% 45.98/9.18 X140 ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X144:$i,
% 45.98/9.18 X146:$i,
% 45.98/9.18 X148:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ~(
% 45.98/9.18 in @
% 45.98/9.18 X148 @
% 45.98/9.18 (
% 45.98/9.18 setminus
% 45.98/9.18 @
% 45.98/9.18 X144 @
% 45.98/9.18 X146 ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ~(
% 45.98/9.18 in @
% 45.98/9.18 X148 @
% 45.98/9.18 X146 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ~(
% 45.98/9.18 in @
% 45.98/9.18 X148 @
% 45.98/9.18 X144 ) ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X150:$i,
% 45.98/9.18 X152:$i,
% 45.98/9.18 X154:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ~(
% 45.98/9.18 in @
% 45.98/9.18 X154 @
% 45.98/9.18 X150 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ~(
% 45.98/9.18 in @
% 45.98/9.18 X154 @
% 45.98/9.18 (
% 45.98/9.18 setminus
% 45.98/9.18 @
% 45.98/9.18 X150 @
% 45.98/9.18 X152 ) ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X156:$i,
% 45.98/9.18 X158:$i,
% 45.98/9.18 X160:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X160 @
% 45.98/9.18 X158 ) =>
% 45.98/9.18 (
% 45.98/9.18 ~(
% 45.98/9.18 in @
% 45.98/9.18 X160 @
% 45.98/9.18 (
% 45.98/9.18 setminus
% 45.98/9.18 @
% 45.98/9.18 X156 @
% 45.98/9.18 X158 ) ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X162:$i,
% 45.98/9.18 X164:$i]:
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X162 @
% 45.98/9.18 X164 ) @
% 45.98/9.18 X162 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X166:$i,
% 45.98/9.18 X168:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X166 @
% 45.98/9.18 X168 ) =
% 45.98/9.18 (
% 45.98/9.18 emptyset ) ) =>
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 X166 @
% 45.98/9.18 X168 ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 symdiffE ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 symdiffI1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 symdiffI2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 symdiffIneg1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 symdiffIneg2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 secondinupair ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setukpairIL ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setukpairIR ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 kpairiskpair ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 kpairp ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X170:$i,
% 45.98/9.18 X172:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X172 @
% 45.98/9.18 X170 ) =>
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 (
% 45.98/9.18 setadjoin
% 45.98/9.18 @
% 45.98/9.18 X172 @
% 45.98/9.18 emptyset ) @
% 45.98/9.18 X170 ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X174:$i,
% 45.98/9.18 X176:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X176 @
% 45.98/9.18 X174 ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 (
% 45.98/9.18 setadjoin
% 45.98/9.18 @
% 45.98/9.18 X176 @
% 45.98/9.18 emptyset ) @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X174 ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 singletoninpowunion ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 upairset2E ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 upairsubunion ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 upairinpowunion ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ubforcartprodlem1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ubforcartprodlem2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ubforcartprodlem3 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 cartprodpairin ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 cartprodmempair1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 cartprodmempair ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setunionE2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setunionsingleton1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setunionsingleton2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setunionsingleton ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 singletonprop ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ex1E1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ex1I ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ex1I2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 singletonsuniq ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setukpairinjL1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 kfstsingleton ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 theprop ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 kfstpairEq ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 cartprodfstin ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setukpairinjL2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setukpairinjL ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setukpairinjR11 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setukpairinjR12 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setukpairinjR1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 upairequniteq ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setukpairinjR2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setukpairinjR ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ksndsingleton ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ksndpairEq ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 kpairsurjEq ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 cartprodsndin ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 cartprodpairmemEL ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 cartprodpairmemER ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 cartprodmempaircEq ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 cartprodfstpairEq ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 cartprodsndpairEq ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 cartprodpairsurjEq ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 dpsetconstrI ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 dpsetconstrSub ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setOfPairsIsBReln ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 dpsetconstrERa ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 dpsetconstrEL1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 dpsetconstrEL2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 dpsetconstrER ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 funcImageSingleton ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 apProp ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 app ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 infuncsetfunc ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ap2p ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 funcinfuncset ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 lamProp ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 lamp ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 lam2p ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 brelnall1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 brelnall2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ex1E2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 funcGraphProp1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 funcGraphProp3 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 funcGraphProp2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 funcextLem ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 funcGraphProp4 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 subbreln ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 eqbreln ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 funcext ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 funcext2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ap2apEq1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ap2apEq2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 beta1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 eta1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 lam2lamEq ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 beta2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 eta2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 iffalseProp1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 iffalseProp2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 iftrueProp1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 iftrueProp2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ifSingleton ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ifp ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 theeq ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 iftrue ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 iffalse ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 iftrueorfalse ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 binintersectT_lem ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 binunionT_lem ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X178:$i,
% 45.98/9.18 X180:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X180 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X178 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X180 ) @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 (
% 45.98/9.18 powerset @
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X182:$i,
% 45.98/9.18 X184:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X184 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X182 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X186:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X186 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X182 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X184 @
% 45.98/9.18 X186 ) @
% 45.98/9.18 (
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% 45.98/9.18 X182 ) ) ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X188:$i,
% 45.98/9.18 X190:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X190 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X188 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X188 @
% 45.98/9.18 X190 ) @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X188 ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X192:$i,
% 45.98/9.18 X194:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X194 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X192 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X196:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X196 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X192 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X198:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X198 @
% 45.98/9.18 X192 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X198 @
% 45.98/9.18 X194 ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X198 @
% 45.98/9.18 X196 ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X200:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X200 @
% 45.98/9.18 X192 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X200 @
% 45.98/9.18 X196 ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X200 @
% 45.98/9.18 X194 ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X202:$i,
% 45.98/9.18 X204:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X204 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X202 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X206:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X206 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X202 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X208:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
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% 45.98/9.18 X202 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X208 @
% 45.98/9.18 X204 ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X208 @
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% 45.98/9.18 (
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X210:$i,
% 45.98/9.18 X212:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X212 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X210 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ![
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X214 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X210 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X216:$i]:
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X216 @
% 45.98/9.18 X212 ) =>
% 45.98/9.18 (
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% 45.98/9.18 X216 @
% 45.98/9.18 X214 ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X218:$i,
% 45.98/9.18 X220:$i]:
% 45.98/9.18 (
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% 45.98/9.18 in @
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% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X218 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X222:$i]:
% 45.98/9.18 (
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% 45.98/9.18 in @
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% 45.98/9.18 X218 ) ) =>
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% 45.98/9.18 X224:$i]:
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% 45.98/9.18 X218 ) =>
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% 45.98/9.18 (
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% 45.98/9.18 X226:$i,
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% 45.98/9.18 in @
% 45.98/9.18 X228 @
% 45.98/9.18 (
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% 45.98/9.18 (
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% 45.98/9.18 X230:$i]:
% 45.98/9.18 (
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X230 @
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% 45.98/9.18 (
% 45.98/9.18 ~(
% 45.98/9.18 in @
% 45.98/9.18 X230 @
% 45.98/9.18 (
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% 45.98/9.18 (
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% 45.98/9.18 (
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% 45.98/9.18 X236:$i]:
% 45.98/9.18 (
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% 45.98/9.18 in @
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% 45.98/9.18 (
% 45.98/9.18 (
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% 45.98/9.18 in @
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 binintersectTELcontra ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 binintersectTERcontra ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X238:$i,
% 45.98/9.18 X240:$i]:
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% 45.98/9.18 (
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% 45.98/9.18 (
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% 45.98/9.18 X250:$i]:
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% 45.98/9.18 X254:$i,
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X260:$i,
% 45.98/9.18 X262:$i]:
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% 45.98/9.18 in @
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% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X264:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X264 @
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% 45.98/9.18 X260 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 subset @
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% 45.98/9.18 X260 @
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X266:$i,
% 45.98/9.18 X268:$i]:
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% 45.98/9.18 in @
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% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X270:$i]:
% 45.98/9.18 (
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% 45.98/9.18 X270 @
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
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% 45.98/9.18 X268 ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X270 @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X266 @
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X272:$i,
% 45.98/9.18 X274:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X274 @
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% 45.98/9.18 powerset @
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% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X276:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X276 @
% 45.98/9.18 X272 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X276 @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X272 @
% 45.98/9.18 (
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% 45.98/9.18 (
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X278:$i,
% 45.98/9.18 X280:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X280 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X278 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 X280 @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X278 @
% 45.98/9.18 (
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% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X282:$i,
% 45.98/9.18 X284:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X284 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X282 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X282 @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X282 @
% 45.98/9.18 X284 ) ) @
% 45.98/9.18 X284 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 45.98/9.18 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 45.98/9.18 thf(zf_stmt_2, axiom,
% 45.98/9.18 (![X8:$i,X6:$i,X4:$i]:
% 45.98/9.18 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 45.98/9.18 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 45.98/9.18 thf(zf_stmt_3, conjecture,
% 45.98/9.18 (( setextAx ) =>
% 45.98/9.18 ( ( emptysetAx ) =>
% 45.98/9.18 ( ( setadjoinAx ) =>
% 45.98/9.18 ( ( ![X4:$i,X6:$i]:
% 45.98/9.18 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 45.98/9.18 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 45.98/9.18 ( ( setunionAx ) =>
% 45.98/9.18 ( ( omega0Ax ) =>
% 45.98/9.18 ( ( omegaSAx ) =>
% 45.98/9.18 ( ( omegaIndAx ) =>
% 45.98/9.18 ( ( replAx ) =>
% 45.98/9.18 ( ( foundationAx ) =>
% 45.98/9.18 ( ( wellorderingAx ) =>
% 45.98/9.18 ( ( descrp ) =>
% 45.98/9.18 ( ( dsetconstrI ) =>
% 45.98/9.18 ( ( dsetconstrEL ) =>
% 45.98/9.18 ( ( dsetconstrER ) =>
% 45.98/9.18 ( ( exuE1 ) =>
% 45.98/9.18 ( ( prop2setE ) =>
% 45.98/9.18 ( ( emptysetE ) =>
% 45.98/9.18 ( ( emptysetimpfalse ) =>
% 45.98/9.18 ( ( notinemptyset ) =>
% 45.98/9.18 ( ( exuE3e ) =>
% 45.98/9.18 ( ( setext ) =>
% 45.98/9.18 ( ( emptyI ) =>
% 45.98/9.18 ( ( noeltsimpempty ) =>
% 45.98/9.18 ( ( setbeta ) =>
% 45.98/9.18 ( ( nonemptyE1 ) =>
% 45.98/9.18 ( ( nonemptyI ) =>
% 45.98/9.18 ( ( nonemptyI1 ) =>
% 45.98/9.18 ( ( setadjoinIL ) =>
% 45.98/9.18 ( ( emptyinunitempty ) =>
% 45.98/9.18 ( ( setadjoinIR ) =>
% 45.98/9.18 ( ( setadjoinE ) =>
% 45.98/9.18 ( (
% 45.98/9.18 setadjoinOr ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setoftrueEq ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X10:$i,
% 45.98/9.18 X12:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X14:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X14 @ X12 ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X14 @ X10 ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X12 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X10 ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X16:$i]:
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 emptyset @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X16 ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X18:$i]:
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 emptyset @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X18 ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X20:$i,
% 45.98/9.18 X22:$i,
% 45.98/9.18 X24:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X22 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X20 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X24 @ X22 ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X24 @ X20 ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setunionI ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setunionE ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 subPowSU ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 exuE2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 nonemptyImpWitness ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 uniqinunit ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 notinsingleton ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 eqinunit ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 singletonsswitch ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 upairsetE ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 upairsetIL ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 upairsetIR ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 emptyE1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 vacuousDall ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 quantDeMorgan1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 quantDeMorgan2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 quantDeMorgan3 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 quantDeMorgan4 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 prop2setI ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 prop2set2propI ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 notdexE ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 notdallE ) =>
% 45.98/9.18 (
% 45.98/9.18 (
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% 45.98/9.18 emptyset ) @
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% 45.98/9.18 (
% 45.98/9.18 powerset @
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% 45.98/9.18 (
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% 45.98/9.18 in @
% 45.98/9.18 X236 @
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% 45.98/9.18 (
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% 45.98/9.18 binintersectTELcontra ) =>
% 45.98/9.18 (
% 45.98/9.18 (
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% 45.98/9.18 (
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% 45.98/9.18 (
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% 45.98/9.18 (
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 subset @
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
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% 45.98/9.18 ![
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% 45.98/9.18 (
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% 45.98/9.18 (
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% 45.98/9.18 (
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% 45.98/9.18 in @
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% 45.98/9.18 (
% 45.98/9.18 ![
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 subset @
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ~(
% 45.98/9.18 in @
% 45.98/9.18 X252 @
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% 45.98/9.18 (
% 45.98/9.18 ~(
% 45.98/9.18 in @
% 45.98/9.18 X252 @
% 45.98/9.18 X248 ) ) ) ) ) ) ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X254:$i,
% 45.98/9.18 X256:$i]:
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% 45.98/9.18 (
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% 45.98/9.18 (
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% 45.98/9.18 in @
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 X256 @
% 45.98/9.18 X258 ) =>
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X254 @
% 45.98/9.18 X258 ) @
% 45.98/9.18 (
% 45.98/9.18 setminus @
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X260:$i,
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% 45.98/9.18 (
% 45.98/9.18 powerset @
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% 45.98/9.18 ![
% 45.98/9.18 X264:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X264 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X260 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X260 @
% 45.98/9.18 X264 ) @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X260 @
% 45.98/9.18 X262 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 X262 @
% 45.98/9.18 X264 ) ) ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X266:$i,
% 45.98/9.18 X268:$i]:
% 45.98/9.18 (
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% 45.98/9.18 in @
% 45.98/9.18 X268 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X266 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X270:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X270 @
% 45.98/9.18 X266 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X270 @
% 45.98/9.18 X268 ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X270 @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X266 @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X266 @
% 45.98/9.18 X268 ) ) ) ) ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X272:$i,
% 45.98/9.18 X274:$i]:
% 45.98/9.18 (
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% 45.98/9.18 in @
% 45.98/9.18 X274 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X272 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X276:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X276 @
% 45.98/9.18 X272 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X276 @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X272 @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X272 @
% 45.98/9.18 X274 ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X276 @
% 45.98/9.18 X274 ) ) ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X278:$i,
% 45.98/9.18 X280:$i]:
% 45.98/9.18 (
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% 45.98/9.18 in @
% 45.98/9.18 X280 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X278 ) ) =>
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% 45.98/9.18 subset @
% 45.98/9.18 X280 @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X278 @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X278 @
% 45.98/9.18 X280 ) ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X282:$i,
% 45.98/9.18 X284:$i]:
% 45.98/9.18 (
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% 45.98/9.18 in @
% 45.98/9.18 X284 @
% 45.98/9.18 (
% 45.98/9.18 powerset @
% 45.98/9.18 X282 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X282 @
% 45.98/9.18 (
% 45.98/9.18 setminus @
% 45.98/9.18 X282 @
% 45.98/9.18 X284 ) ) @
% 45.98/9.18 X284 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 45.98/9.18 thf(zf_stmt_4, negated_conjecture,
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% 45.98/9.18 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
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% 45.98/9.18 ( ( dsetconstrEL ) =>
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% 45.98/9.18 ( ( prop2setE ) =>
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% 45.98/9.18 setadjoinE ) =>
% 45.98/9.18 (
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% 45.98/9.18 setadjoinOr ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setoftrueEq ) =>
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% 45.98/9.18 ![
% 45.98/9.18 X10:$i,
% 45.98/9.18 X12:$i]:
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% 45.98/9.18 ![
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% 45.98/9.18 (
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% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X12 @
% 45.98/9.18 (
% 45.98/9.18 powerset
% 45.98/9.18 @
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X16:$i]:
% 45.98/9.18 (
% 45.98/9.18 in @
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% 45.98/9.18 powerset
% 45.98/9.18 @
% 45.98/9.18 X16 ) ) ) =>
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% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X18:$i]:
% 45.98/9.18 (
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% 45.98/9.18 @
% 45.98/9.18 X18 ) ) ) =>
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% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X20:$i,
% 45.98/9.18 X22:$i,
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% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
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% 45.98/9.18 (
% 45.98/9.18 setunionI ) =>
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% 45.98/9.18 setunionE ) =>
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% 45.98/9.18 subPowSU ) =>
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% 45.98/9.18 (
% 45.98/9.18 exuE2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 nonemptyImpWitness ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 uniqinunit ) =>
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% 45.98/9.18 notinsingleton ) =>
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% 45.98/9.18 upairsetIL ) =>
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% 45.98/9.18 (
% 45.98/9.18 upairsetIR ) =>
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% 45.98/9.18 (
% 45.98/9.18 emptyE1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 vacuousDall ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 quantDeMorgan1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 quantDeMorgan2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 quantDeMorgan3 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 quantDeMorgan4 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 prop2setI ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 prop2set2propI ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 notdexE ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 notdallE ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 exuI1 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 exuI3 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 exuI2 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 inCongP ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in__Cong ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 exuE3u ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 exu__Cong ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 emptyset__Cong ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setadjoin__Cong ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X26:$i,
% 45.98/9.18 X28:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 X26 ) =
% 45.98/9.18 (
% 45.98/9.18 X28 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 powerset
% 45.98/9.18 @
% 45.98/9.18 X26 ) =
% 45.98/9.18 (
% 45.98/9.18 powerset
% 45.98/9.18 @
% 45.98/9.18 X28 ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 setunion__Cong ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 omega__Cong ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 exuEu ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 descr__Cong ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 dsetconstr__Cong ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X30:$i,
% 45.98/9.18 X32:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X34:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X34 @ X30 ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X34 @ X32 ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 X30 @ X32 ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X36:$i,
% 45.98/9.18 X38:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 X36 ) =
% 45.98/9.18 (
% 45.98/9.18 X38 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 X38 @ X36 ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X40:$i,
% 45.98/9.18 X42:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 X40 ) =
% 45.98/9.18 (
% 45.98/9.18 X42 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 X40 @ X42 ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X44:$i,
% 45.98/9.18 X46:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X48:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X48 @ X44 ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X48 @ X46 ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 X44 @ X46 ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X50:$i]:
% 45.98/9.18 (
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% 45.98/9.18 (
% 45.98/9.18 (
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% 45.98/9.18 in @
% 45.98/9.18 X250 @
% 45.98/9.18 (
% 45.98/9.18 powerset
% 45.98/9.18 @
% 45.98/9.18 X246 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X252:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X252 @
% 45.98/9.18 X246 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 X248 @
% 45.98/9.18 X250 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ~
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X252 @
% 45.98/9.18 X250 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ~
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X252 @
% 45.98/9.18 X248 ) ) ) ) ) ) ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X254:$i,
% 45.98/9.18 X256:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X256 @
% 45.98/9.18 (
% 45.98/9.18 powerset
% 45.98/9.18 @
% 45.98/9.18 X254 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X258:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X258 @
% 45.98/9.18 (
% 45.98/9.18 powerset
% 45.98/9.18 @
% 45.98/9.18 X254 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 X256 @
% 45.98/9.18 X258 ) =>
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 (
% 45.98/9.18 setminus
% 45.98/9.18 @
% 45.98/9.18 X254 @
% 45.98/9.18 X258 ) @
% 45.98/9.18 (
% 45.98/9.18 setminus
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% 45.98/9.18 X254 @
% 45.98/9.18 X256 ) ) ) ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X260:$i,
% 45.98/9.18 X262:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X262 @
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% 45.98/9.18 @
% 45.98/9.18 X260 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X264:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X264 @
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% 45.98/9.18 powerset
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% 45.98/9.18 X260 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 (
% 45.98/9.18 setminus
% 45.98/9.18 @
% 45.98/9.18 X260 @
% 45.98/9.18 X264 ) @
% 45.98/9.18 (
% 45.98/9.18 setminus
% 45.98/9.18 @
% 45.98/9.18 X260 @
% 45.98/9.18 X262 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 X262 @
% 45.98/9.18 X264 ) ) ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X266:$i,
% 45.98/9.18 X268:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X268 @
% 45.98/9.18 (
% 45.98/9.18 powerset
% 45.98/9.18 @
% 45.98/9.18 X266 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X270:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X270 @
% 45.98/9.18 X266 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X270 @
% 45.98/9.18 X268 ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X270 @
% 45.98/9.18 (
% 45.98/9.18 setminus
% 45.98/9.18 @
% 45.98/9.18 X266 @
% 45.98/9.18 (
% 45.98/9.18 setminus
% 45.98/9.18 @
% 45.98/9.18 X266 @
% 45.98/9.18 X268 ) ) ) ) ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X272:$i,
% 45.98/9.18 X274:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X274 @
% 45.98/9.18 (
% 45.98/9.18 powerset
% 45.98/9.18 @
% 45.98/9.18 X272 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X276:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X276 @
% 45.98/9.18 X272 ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X276 @
% 45.98/9.18 (
% 45.98/9.18 setminus
% 45.98/9.18 @
% 45.98/9.18 X272 @
% 45.98/9.18 (
% 45.98/9.18 setminus
% 45.98/9.18 @
% 45.98/9.18 X272 @
% 45.98/9.18 X274 ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X276 @
% 45.98/9.18 X274 ) ) ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X278:$i,
% 45.98/9.18 X280:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X280 @
% 45.98/9.18 (
% 45.98/9.18 powerset
% 45.98/9.18 @
% 45.98/9.18 X278 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 X280 @
% 45.98/9.18 (
% 45.98/9.18 setminus
% 45.98/9.18 @
% 45.98/9.18 X278 @
% 45.98/9.18 (
% 45.98/9.18 setminus
% 45.98/9.18 @
% 45.98/9.18 X278 @
% 45.98/9.18 X280 ) ) ) ) ) =>
% 45.98/9.18 (
% 45.98/9.18 ![
% 45.98/9.18 X282:$i,
% 45.98/9.18 X284:$i]:
% 45.98/9.18 (
% 45.98/9.18 (
% 45.98/9.18 in @
% 45.98/9.18 X284 @
% 45.98/9.18 (
% 45.98/9.18 powerset
% 45.98/9.18 @
% 45.98/9.18 X282 ) ) =>
% 45.98/9.18 (
% 45.98/9.18 subset @
% 45.98/9.18 (
% 45.98/9.18 setminus
% 45.98/9.18 @
% 45.98/9.18 X282 @
% 45.98/9.18 (
% 45.98/9.18 setminus
% 45.98/9.18 @
% 45.98/9.18 X282 @
% 45.98/9.18 X284 ) ) @
% 45.98/9.18 X284 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 45.98/9.18 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 45.98/9.18 thf(zip_derived_cl131, plain, ( (in @ sk__146 @ (powerset @ sk__145))),
% 45.98/9.18 inference('cnf', [status(esa)], [zf_stmt_4])).
% 45.98/9.18 thf(zip_derived_cl130, plain,
% 45.98/9.18 (~ (subset @ (setminus @ sk__145 @ (setminus @ sk__145 @ sk__146)) @
% 45.98/9.18 sk__146)),
% 45.98/9.18 inference('cnf', [status(esa)], [zf_stmt_4])).
% 45.98/9.18 thf(zip_derived_cl132, plain,
% 45.98/9.18 (![X63 : $i, X64 : $i]:
% 45.98/9.18 ( (subset @ X63 @ (setminus @ X64 @ (setminus @ X64 @ X63)))
% 45.98/9.18 | ~ (in @ X63 @ (powerset @ X64)))),
% 45.98/9.18 inference('cnf', [status(esa)], [zf_stmt_4])).
% 45.98/9.18 thf(zip_derived_cl128, plain,
% 45.98/9.18 (![X57 : $i, X58 : $i, X59 : $i]:
% 45.98/9.18 (~ (in @ X57 @ (powerset @ X58))
% 45.98/9.18 | (subset @ X59 @ X57)
% 45.98/9.18 | ~ (subset @ (setminus @ X58 @ X57) @ (setminus @ X58 @ X59))
% 45.98/9.18 | ~ (in @ X59 @ (powerset @ X58)))),
% 45.98/9.18 inference('cnf', [status(esa)], [zf_stmt_4])).
% 45.98/9.18 thf(zip_derived_cl1001, plain,
% 45.98/9.18 (![X0 : $i, X1 : $i]:
% 45.98/9.18 (~ (in @ (setminus @ X1 @ X0) @ (powerset @ X1))
% 45.98/9.18 | ~ (in @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ (powerset @ X1))
% 45.98/9.18 | (subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0)
% 45.98/9.18 | ~ (in @ X0 @ (powerset @ X1)))),
% 45.98/9.18 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl128])).
% 45.98/9.18 thf(zip_derived_cl51, plain,
% 45.98/9.18 (![X21 : $i, X22 : $i]:
% 45.98/9.18 ( (in @ X21 @ (powerset @ X22)) | ~ (subset @ X21 @ X22))),
% 45.98/9.18 inference('cnf', [status(esa)], [zf_stmt_4])).
% 45.98/9.18 thf(zip_derived_cl202, plain,
% 45.98/9.18 (![X89 : $i, X90 : $i]: (subset @ (setminus @ X89 @ X90) @ X89)),
% 45.98/9.18 inference('cnf', [status(esa)], [zf_stmt_4])).
% 45.98/9.18 thf(zip_derived_cl348, plain,
% 45.98/9.18 (![X0 : $i, X1 : $i]: (in @ (setminus @ X0 @ X1) @ (powerset @ X0))),
% 45.98/9.18 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl202])).
% 45.98/9.18 thf(zip_derived_cl348, plain,
% 45.98/9.18 (![X0 : $i, X1 : $i]: (in @ (setminus @ X0 @ X1) @ (powerset @ X0))),
% 45.98/9.18 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl202])).
% 45.98/9.18 thf(zip_derived_cl1035, plain,
% 45.98/9.18 (![X0 : $i, X1 : $i]:
% 45.98/9.18 ( (subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0)
% 45.98/9.18 | ~ (in @ X0 @ (powerset @ X1)))),
% 45.98/9.18 inference('demod', [status(thm)],
% 45.98/9.18 [zip_derived_cl1001, zip_derived_cl348, zip_derived_cl348])).
% 45.98/9.18 thf(zip_derived_cl20683, plain, ($false),
% 45.98/9.18 inference('eprover', [status(thm)],
% 45.98/9.18 [zip_derived_cl131, zip_derived_cl130, zip_derived_cl1035])).
% 45.98/9.18
% 45.98/9.18 % SZS output end Refutation
% 45.98/9.18
% 45.98/9.18
% 45.98/9.18 % Terminating...
% 46.96/9.41 % Runner terminated.
% 46.99/9.42 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------