%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU726^1 : 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.8363vLyFOd true
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:55:59 PM UTC 2025
% Result : Theorem 79.53s 10.80s
% Output : Refutation 79.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SEU726^1 : TPTP v9.2.0. Released v3.7.0.
% 0.06/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.8363vLyFOd true
% 0.14/0.36 % Computer : n001.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 1 16:08:53 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.39/0.62 % Total configuration time : 828
% 0.39/0.62 % Estimated wc time : 1656
% 0.39/0.62 % Estimated cpu time (8 cpus) : 207.0
% 0.51/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 79.53/10.80 % Solved by lams/40_c_ic.sh.
% 79.53/10.80 % done 3508 iterations in 9.953s
% 79.53/10.80 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 79.53/10.80 % SZS output start Refutation
% 79.53/10.80 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 79.53/10.80 thf(notdexE_type, type, notdexE: $o).
% 79.53/10.80 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 79.53/10.80 thf(setunionAx_type, type, setunionAx: $o).
% 79.53/10.80 thf(setminusELneg_type, type, setminusELneg: $o).
% 79.53/10.80 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 79.53/10.80 thf(ex1E1_type, type, ex1E1: $o).
% 79.53/10.80 thf(powersetE_type, type, powersetE: $o).
% 79.53/10.80 thf(omegaSAx_type, type, omegaSAx: $o).
% 79.53/10.80 thf(exuI1_type, type, exuI1: $o).
% 79.53/10.80 thf(exuI2_type, type, exuI2: $o).
% 79.53/10.80 thf(notequalI2_type, type, notequalI2: $o).
% 79.53/10.80 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 79.53/10.80 thf(sk__136_type, type, sk__136: $i).
% 79.53/10.80 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 79.53/10.80 thf(upairsubunion_type, type, upairsubunion: $o).
% 79.53/10.80 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 79.53/10.80 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 79.53/10.80 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 79.53/10.80 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 79.53/10.80 thf(sk__135_type, type, sk__135: $i).
% 79.53/10.80 thf(sk__134_type, type, sk__134: $i).
% 79.53/10.80 thf(setminusILneg_type, type, setminusILneg: $o).
% 79.53/10.80 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 79.53/10.80 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 79.53/10.80 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 79.53/10.80 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 79.53/10.80 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 79.53/10.80 thf(iftrue_type, type, iftrue: $o).
% 79.53/10.80 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 79.53/10.80 thf(ifSingleton_type, type, ifSingleton: $o).
% 79.53/10.80 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 79.53/10.80 thf(sk__130_type, type, sk__130: $i > $i > $i).
% 79.53/10.80 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 79.53/10.80 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 79.53/10.80 thf(lamProp_type, type, lamProp: $o).
% 79.53/10.80 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 79.53/10.80 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 79.53/10.80 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 79.53/10.80 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 79.53/10.80 thf(setukpairIR_type, type, setukpairIR: $o).
% 79.53/10.80 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 79.53/10.80 thf(lam2p_type, type, lam2p: $o).
% 79.53/10.80 thf(binunionE_type, type, binunionE: $o).
% 79.53/10.80 thf(setext_type, type, setext: $o).
% 79.53/10.80 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 79.53/10.80 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 79.53/10.80 thf(descr__Cong_type, type, descr__Cong: $o).
% 79.53/10.80 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 79.53/10.80 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 79.53/10.80 thf(eqbreln_type, type, eqbreln: $o).
% 79.53/10.80 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 79.53/10.80 thf(in_type, type, in: $i > $i > $o).
% 79.53/10.80 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 79.53/10.80 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 79.53/10.80 thf(complementT_lem_type, type, complementT_lem: $o).
% 79.53/10.80 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 79.53/10.80 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 79.53/10.80 thf(beta1_type, type, beta1: $o).
% 79.53/10.80 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 79.53/10.80 thf(powersetTE1_type, type, powersetTE1: $o).
% 79.53/10.80 thf(symdiffI2_type, type, symdiffI2: $o).
% 79.53/10.80 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 79.53/10.80 thf(upairset2IR_type, type, upairset2IR: $o).
% 79.53/10.80 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 79.53/10.80 thf(subsetE_type, type, subsetE: $o).
% 79.53/10.80 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 79.53/10.80 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 79.53/10.80 thf(setbeta_type, type, setbeta: $o).
% 79.53/10.80 thf(eqinunit_type, type, eqinunit: $o).
% 79.53/10.80 thf(upairsetIL_type, type, upairsetIL: $o).
% 79.53/10.80 thf(powersetI1_type, type, powersetI1: $o).
% 79.53/10.80 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 79.53/10.80 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 79.53/10.80 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 79.53/10.80 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 79.53/10.80 thf(powersetAx_type, type, powersetAx: $o).
% 79.53/10.80 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 79.53/10.80 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 79.53/10.80 thf(powersetI_type, type, powersetI: $o).
% 79.53/10.80 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 79.53/10.80 thf(upairsetIR_type, type, upairsetIR: $o).
% 79.53/10.80 thf(lamp_type, type, lamp: $o).
% 79.53/10.80 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 79.53/10.80 thf(inCongP_type, type, inCongP: $o).
% 79.53/10.80 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 79.53/10.80 thf(exuE3e_type, type, exuE3e: $o).
% 79.53/10.80 thf(emptysetE_type, type, emptysetE: $o).
% 79.53/10.80 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 79.53/10.80 thf(setunionI_type, type, setunionI: $o).
% 79.53/10.80 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 79.53/10.80 thf(prop2setI_type, type, prop2setI: $o).
% 79.53/10.80 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 79.53/10.80 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 79.53/10.80 thf(setminusER_type, type, setminusER: $o).
% 79.53/10.80 thf(exuE2_type, type, exuE2: $o).
% 79.53/10.80 thf(emptyset_type, type, emptyset: $i).
% 79.53/10.80 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 79.53/10.80 thf(ex1I_type, type, ex1I: $o).
% 79.53/10.80 thf(ex1E2_type, type, ex1E2: $o).
% 79.53/10.80 thf(setminus_type, type, setminus: $i > $i > $i).
% 79.53/10.80 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 79.53/10.80 thf(powersetsubset_type, type, powersetsubset: $o).
% 79.53/10.80 thf(subPowSU_type, type, subPowSU: $o).
% 79.53/10.80 thf(notequalI1_type, type, notequalI1: $o).
% 79.53/10.80 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 79.53/10.80 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 79.53/10.80 thf(notinemptyset_type, type, notinemptyset: $o).
% 79.53/10.80 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 79.53/10.80 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 79.53/10.80 thf(subsetTrans_type, type, subsetTrans: $o).
% 79.53/10.80 thf(kpairp_type, type, kpairp: $o).
% 79.53/10.80 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 79.53/10.80 thf(setminusI_type, type, setminusI: $o).
% 79.53/10.80 thf(binunionIL_type, type, binunionIL: $o).
% 79.53/10.80 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 79.53/10.80 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 79.53/10.80 thf(subsetE2_type, type, subsetE2: $o).
% 79.53/10.80 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 79.53/10.80 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 79.53/10.80 thf(beta2_type, type, beta2: $o).
% 79.53/10.80 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 79.53/10.80 thf(setextsub_type, type, setextsub: $o).
% 79.53/10.80 thf(binunionLsub_type, type, binunionLsub: $o).
% 79.53/10.80 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 79.53/10.80 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 79.53/10.80 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 79.53/10.80 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 79.53/10.80 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 79.53/10.80 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 79.53/10.80 thf(setunionE_type, type, setunionE: $o).
% 79.53/10.80 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 79.53/10.80 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 79.53/10.80 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 79.53/10.80 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 79.53/10.80 thf(binunionIR_type, type, binunionIR: $o).
% 79.53/10.80 thf(theeq_type, type, theeq: $o).
% 79.53/10.80 thf(setadjoinE_type, type, setadjoinE: $o).
% 79.53/10.80 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 79.53/10.80 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 79.53/10.80 thf(ap2p_type, type, ap2p: $o).
% 79.53/10.80 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 79.53/10.80 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 79.53/10.80 thf(exuE1_type, type, exuE1: $o).
% 79.53/10.80 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 79.53/10.80 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 79.53/10.80 thf(setminusLsub_type, type, setminusLsub: $o).
% 79.53/10.80 thf(funcextLem_type, type, funcextLem: $o).
% 79.53/10.80 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 79.53/10.80 thf(notinsingleton_type, type, notinsingleton: $o).
% 79.53/10.80 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 79.53/10.80 thf(exuEu_type, type, exuEu: $o).
% 79.53/10.80 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 79.53/10.80 thf(upairsetE_type, type, upairsetE: $o).
% 79.53/10.80 thf(omega0Ax_type, type, omega0Ax: $o).
% 79.53/10.80 thf(subsetTI_type, type, subsetTI: $o).
% 79.53/10.80 thf(notsubsetI_type, type, notsubsetI: $o).
% 79.53/10.80 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 79.53/10.80 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 79.53/10.80 thf(setextAx_type, type, setextAx: $o).
% 79.53/10.80 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 79.53/10.80 thf(powersetE1_type, type, powersetE1: $o).
% 79.53/10.80 thf(bs114d_type, type, bs114d: $o).
% 79.53/10.80 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 79.53/10.80 thf(ifp_type, type, ifp: $o).
% 79.53/10.80 thf(powersetTI1_type, type, powersetTI1: $o).
% 79.53/10.80 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 79.53/10.80 thf(subsetI1_type, type, subsetI1: $o).
% 79.53/10.80 thf(symdiffE_type, type, symdiffE: $o).
% 79.53/10.80 thf(descrp_type, type, descrp: $o).
% 79.53/10.80 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 79.53/10.80 thf(foundationAx_type, type, foundationAx: $o).
% 79.53/10.80 thf(emptysetAx_type, type, emptysetAx: $o).
% 79.53/10.80 thf(emptyI_type, type, emptyI: $o).
% 79.53/10.80 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 79.53/10.80 thf(eta2_type, type, eta2: $o).
% 79.53/10.80 thf(binintersectEL_type, type, binintersectEL: $o).
% 79.53/10.80 thf(emptyE1_type, type, emptyE1: $o).
% 79.53/10.80 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 79.53/10.80 thf(complementTI1_type, type, complementTI1: $o).
% 79.53/10.80 thf(vacuousDall_type, type, vacuousDall: $o).
% 79.53/10.80 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 79.53/10.80 thf(binintersectI_type, type, binintersectI: $o).
% 79.53/10.80 thf(funcext_type, type, funcext: $o).
% 79.53/10.80 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 79.53/10.80 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 79.53/10.80 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 79.53/10.80 thf(brelnall2_type, type, brelnall2: $o).
% 79.53/10.80 thf(setextT_type, type, setextT: $o).
% 79.53/10.80 thf(ex1I2_type, type, ex1I2: $o).
% 79.53/10.80 thf(symdiffI1_type, type, symdiffI1: $o).
% 79.53/10.80 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 79.53/10.80 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 79.53/10.80 thf(theprop_type, type, theprop: $o).
% 79.53/10.80 thf(subsetI2_type, type, subsetI2: $o).
% 79.53/10.80 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 79.53/10.80 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 79.53/10.80 thf(setminusERneg_type, type, setminusERneg: $o).
% 79.53/10.80 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 79.53/10.80 thf(omega__Cong_type, type, omega__Cong: $o).
% 79.53/10.80 thf(subsetRefl_type, type, subsetRefl: $o).
% 79.53/10.80 thf(uniqinunit_type, type, uniqinunit: $o).
% 79.53/10.80 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 79.53/10.80 thf(prop2setE_type, type, prop2setE: $o).
% 79.53/10.80 thf(binunionEcases_type, type, binunionEcases: $o).
% 79.53/10.80 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 79.53/10.80 thf(complementTE1_type, type, complementTE1: $o).
% 79.53/10.80 thf(nonemptyI_type, type, nonemptyI: $o).
% 79.53/10.80 thf(app_type, type, app: $o).
% 79.53/10.80 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 79.53/10.80 thf(exuE3u_type, type, exuE3u: $o).
% 79.53/10.80 thf(eta1_type, type, eta1: $o).
% 79.53/10.80 thf(setminusEL_type, type, setminusEL: $o).
% 79.53/10.80 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 79.53/10.80 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 79.53/10.80 thf(sepSubset_type, type, sepSubset: $o).
% 79.53/10.80 thf(upairset2E_type, type, upairset2E: $o).
% 79.53/10.80 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 79.53/10.80 thf(exuI3_type, type, exuI3: $o).
% 79.53/10.80 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 79.53/10.80 thf(apProp_type, type, apProp: $o).
% 79.53/10.80 thf(notdallE_type, type, notdallE: $o).
% 79.53/10.80 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 79.53/10.80 thf(binintersectER_type, type, binintersectER: $o).
% 79.53/10.80 thf(brelnall1_type, type, brelnall1: $o).
% 79.53/10.80 thf(powerset_type, type, powerset: $i > $i).
% 79.53/10.80 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 79.53/10.80 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 79.53/10.80 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 79.53/10.80 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 79.53/10.80 thf(exu__Cong_type, type, exu__Cong: $o).
% 79.53/10.80 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 79.53/10.80 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 79.53/10.80 thf(secondinupair_type, type, secondinupair: $o).
% 79.53/10.80 thf(singletonprop_type, type, singletonprop: $o).
% 79.53/10.80 thf(singletonsubset_type, type, singletonsubset: $o).
% 79.53/10.80 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 79.53/10.80 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 79.53/10.80 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 79.53/10.80 thf(replAx_type, type, replAx: $o).
% 79.53/10.80 thf(upairequniteq_type, type, upairequniteq: $o).
% 79.53/10.80 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 79.53/10.80 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 79.53/10.80 thf(setukpairIL_type, type, setukpairIL: $o).
% 79.53/10.80 thf(setunionE2_type, type, setunionE2: $o).
% 79.53/10.80 thf(inPowerset_type, type, inPowerset: $o).
% 79.53/10.80 thf(iffalse_type, type, iffalse: $o).
% 79.53/10.80 thf(funcext2_type, type, funcext2: $o).
% 79.53/10.80 thf(subset_type, type, subset: $i > $i > $o).
% 79.53/10.80 thf(subbreln_type, type, subbreln: $o).
% 79.53/10.80 thf(in__Cong_type, type, in__Cong: $o).
% 79.53/10.80 thf(binunionRsub_type, type, binunionRsub: $o).
% 79.53/10.80 thf(subset2powerset_type, type, subset2powerset: $o).
% 79.53/10.80 thf(contrasubsetT2, axiom, contrasubsetT2 =
% 79.53/10.80 (![A:$i,X:$i]:
% 79.53/10.80 ( ( in @ X @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ![Y:$i]:
% 79.53/10.80 ( ( in @ Y @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ( subset @ X @ Y ) =>
% 79.53/10.80 ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ))).
% 79.53/10.80 thf('0', plain,
% 79.53/10.80 (( contrasubsetT2 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ![X8:$i]:
% 79.53/10.80 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ( subset @ X6 @ X8 ) =>
% 79.53/10.80 ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(contrasubsetT1, axiom, contrasubsetT1 =
% 79.53/10.80 (![A:$i,X:$i]:
% 79.53/10.80 ( ( in @ X @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ![Y:$i]:
% 79.53/10.80 ( ( in @ Y @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ![Xx:$i]:
% 79.53/10.80 ( ( in @ Xx @ A ) =>
% 79.53/10.80 ( ( subset @ X @ Y ) =>
% 79.53/10.80 ( ( ~( in @ Xx @ Y ) ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 79.53/10.80 thf('1', plain,
% 79.53/10.80 (( contrasubsetT1 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ![X8:$i]:
% 79.53/10.80 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ![X10:$i]:
% 79.53/10.80 ( ( in @ X10 @ X4 ) =>
% 79.53/10.80 ( ( subset @ X6 @ X8 ) =>
% 79.53/10.80 ( ( ~( in @ X10 @ X8 ) ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(contrasubsetT, axiom, contrasubsetT =
% 79.53/10.80 (![A:$i,X:$i]:
% 79.53/10.80 ( ( in @ X @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ![Y:$i]:
% 79.53/10.80 ( ( in @ Y @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ![Xx:$i]:
% 79.53/10.80 ( ( in @ Xx @ A ) =>
% 79.53/10.80 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 79.53/10.80 ( ( in @ Xx @ Y ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 79.53/10.80 thf('2', plain,
% 79.53/10.80 (( contrasubsetT ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ![X8:$i]:
% 79.53/10.80 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ![X10:$i]:
% 79.53/10.80 ( ( in @ X10 @ X4 ) =>
% 79.53/10.80 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 79.53/10.80 ( ( in @ X10 @ X8 ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(complementTE1, axiom, complementTE1 =
% 79.53/10.80 (![A:$i,X:$i]:
% 79.53/10.80 ( ( in @ X @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ![Xx:$i]:
% 79.53/10.80 ( ( in @ Xx @ A ) =>
% 79.53/10.80 ( ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) => ( in @ Xx @ X ) ) ) ) ))).
% 79.53/10.80 thf('3', plain,
% 79.53/10.80 (( complementTE1 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ![X8:$i]:
% 79.53/10.80 ( ( in @ X8 @ X4 ) =>
% 79.53/10.80 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) => ( in @ X8 @ X6 ) ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(complementTI1, axiom, complementTI1 =
% 79.53/10.80 (![A:$i,X:$i]:
% 79.53/10.80 ( ( in @ X @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ![Xx:$i]:
% 79.53/10.80 ( ( in @ Xx @ A ) =>
% 79.53/10.80 ( ( in @ Xx @ X ) => ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 79.53/10.80 thf('4', plain,
% 79.53/10.80 (( complementTI1 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ![X8:$i]:
% 79.53/10.80 ( ( in @ X8 @ X4 ) =>
% 79.53/10.80 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(powersetTE1, axiom, powersetTE1 =
% 79.53/10.80 (![A:$i,X:$i]:
% 79.53/10.80 ( ( in @ X @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ![Y:$i]:
% 79.53/10.80 ( ( in @ Y @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ![Xx:$i]:
% 79.53/10.80 ( ( in @ Xx @ A ) =>
% 79.53/10.80 ( ( in @ X @ ( powerset @ Y ) ) =>
% 79.53/10.80 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 79.53/10.80 thf('5', plain,
% 79.53/10.80 (( powersetTE1 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ![X8:$i]:
% 79.53/10.80 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ![X10:$i]:
% 79.53/10.80 ( ( in @ X10 @ X4 ) =>
% 79.53/10.80 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 79.53/10.80 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(powersetTI1, axiom, powersetTI1 =
% 79.53/10.80 (![A:$i,X:$i]:
% 79.53/10.80 ( ( in @ X @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ![Y:$i]:
% 79.53/10.80 ( ( in @ Y @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ( ![Xx:$i]:
% 79.53/10.80 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 79.53/10.80 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 79.53/10.80 thf('6', plain,
% 79.53/10.80 (( powersetTI1 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ![X8:$i]:
% 79.53/10.80 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ( ![X10:$i]:
% 79.53/10.80 ( ( in @ X10 @ X4 ) =>
% 79.53/10.80 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 79.53/10.80 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(subsetTI, axiom, subsetTI =
% 79.53/10.80 (![A:$i,X:$i]:
% 79.53/10.80 ( ( in @ X @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ![Y:$i]:
% 79.53/10.80 ( ( in @ Y @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ( ![Xx:$i]:
% 79.53/10.80 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 79.53/10.80 ( subset @ X @ Y ) ) ) ) ))).
% 79.53/10.80 thf('7', plain,
% 79.53/10.80 (( subsetTI ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ![X8:$i]:
% 79.53/10.80 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ( ![X10:$i]:
% 79.53/10.80 ( ( in @ X10 @ X4 ) =>
% 79.53/10.80 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 79.53/10.80 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(setextT, axiom, setextT =
% 79.53/10.80 (![A:$i,X:$i]:
% 79.53/10.80 ( ( in @ X @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ![Y:$i]:
% 79.53/10.80 ( ( in @ Y @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ( ![Xx:$i]:
% 79.53/10.80 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 79.53/10.80 ( ( ![Xx:$i]:
% 79.53/10.80 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 79.53/10.80 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 79.53/10.80 thf('8', plain,
% 79.53/10.80 (( setextT ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ![X8:$i]:
% 79.53/10.80 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ( ![X10:$i]:
% 79.53/10.80 ( ( in @ X10 @ X4 ) =>
% 79.53/10.80 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 79.53/10.80 ( ( ![X12:$i]:
% 79.53/10.80 ( ( in @ X12 @ X4 ) =>
% 79.53/10.80 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 79.53/10.80 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(complementT_lem, axiom, complementT_lem =
% 79.53/10.80 (![A:$i,X:$i]:
% 79.53/10.80 ( ( in @ X @ ( powerset @ A ) ) =>
% 79.53/10.80 ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ))).
% 79.53/10.80 thf('9', plain,
% 79.53/10.80 (( complementT_lem ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( in @ ( setminus @ X4 @ X6 ) @ ( powerset @ X4 ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(setminusT_lem, axiom, setminusT_lem =
% 79.53/10.80 (![A:$i,X:$i]:
% 79.53/10.80 ( ( in @ X @ ( powerset @ A ) ) =>
% 79.53/10.80 ( ![Y:$i]:
% 79.53/10.80 ( ( in @ Y @ ( powerset @ A ) ) =>
% 79.53/10.80 ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 79.53/10.80 thf('10', plain,
% 79.53/10.80 (( setminusT_lem ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ![X8:$i]:
% 79.53/10.80 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( in @ ( setminus @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(powersetT_lem, axiom, powersetT_lem =
% 79.53/10.80 (![A:$i,X:$i]:
% 79.53/10.80 ( ( in @ X @ ( powerset @ A ) ) =>
% 79.53/10.80 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 79.53/10.80 thf('11', plain,
% 79.53/10.80 (( powersetT_lem ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(singletoninpowerset, axiom, singletoninpowerset =
% 79.53/10.80 (![A:$i,Xx:$i]:
% 79.53/10.80 ( ( in @ Xx @ A ) =>
% 79.53/10.80 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 79.53/10.80 thf('12', plain,
% 79.53/10.80 (( singletoninpowerset ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( in @ X6 @ X4 ) =>
% 79.53/10.80 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(singletonsubset, axiom, singletonsubset =
% 79.53/10.80 (![A:$i,Xx:$i]:
% 79.53/10.80 ( ( in @ Xx @ A ) => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ))).
% 79.53/10.80 thf('13', plain,
% 79.53/10.80 (( singletonsubset ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( in @ X6 @ X4 ) => ( subset @ ( setadjoin @ X6 @ emptyset ) @ X4 ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(setminusSubset1, axiom, setminusSubset1 =
% 79.53/10.80 (![A:$i,B:$i]:
% 79.53/10.80 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))).
% 79.53/10.80 thf('14', plain,
% 79.53/10.80 (( setminusSubset1 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(setminusLsub, axiom, setminusLsub =
% 79.53/10.80 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))).
% 79.53/10.80 thf('15', plain,
% 79.53/10.80 (( setminusLsub ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(setminusIRneg, axiom, setminusIRneg =
% 79.53/10.80 (![A:$i,B:$i,Xx:$i]:
% 79.53/10.80 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 79.53/10.80 thf('16', plain,
% 79.53/10.80 (( setminusIRneg ) =
% 79.53/10.80 ( ![X4:$i,X6:$i,X8:$i]:
% 79.53/10.80 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(setminusILneg, axiom, setminusILneg =
% 79.53/10.80 (![A:$i,B:$i,Xx:$i]:
% 79.53/10.80 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 79.53/10.80 thf('17', plain,
% 79.53/10.80 (( setminusILneg ) =
% 79.53/10.80 ( ![X4:$i,X6:$i,X8:$i]:
% 79.53/10.80 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(setminusELneg, axiom, setminusELneg =
% 79.53/10.80 (![A:$i,B:$i,Xx:$i]:
% 79.53/10.80 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 79.53/10.80 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 79.53/10.80 thf('18', plain,
% 79.53/10.80 (( setminusELneg ) =
% 79.53/10.80 ( ![X4:$i,X6:$i,X8:$i]:
% 79.53/10.80 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 79.53/10.80 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(setminusERneg, axiom, setminusERneg =
% 79.53/10.80 (![A:$i,B:$i,Xx:$i]:
% 79.53/10.80 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 79.53/10.80 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 79.53/10.80 thf('19', plain,
% 79.53/10.80 (( setminusERneg ) =
% 79.53/10.80 ( ![X4:$i,X6:$i,X8:$i]:
% 79.53/10.80 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 79.53/10.80 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(setminusSubset2, axiom, setminusSubset2 =
% 79.53/10.80 (![A:$i,B:$i]:
% 79.53/10.80 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))).
% 79.53/10.80 thf('20', plain,
% 79.53/10.80 (( setminusSubset2 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(setminusER, axiom, setminusER =
% 79.53/10.80 (![A:$i,B:$i,Xx:$i]:
% 79.53/10.80 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))).
% 79.53/10.80 thf('21', plain,
% 79.53/10.80 (( setminusER ) =
% 79.53/10.80 ( ![X4:$i,X6:$i,X8:$i]:
% 79.53/10.80 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(setminusEL, axiom, setminusEL =
% 79.53/10.80 (![A:$i,B:$i,Xx:$i]:
% 79.53/10.80 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 79.53/10.80 thf('22', plain,
% 79.53/10.80 (( setminusEL ) =
% 79.53/10.80 ( ![X4:$i,X6:$i,X8:$i]:
% 79.53/10.80 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(setminusI, axiom, setminusI =
% 79.53/10.80 (![A:$i,B:$i,Xx:$i]:
% 79.53/10.80 ( ( in @ Xx @ A ) =>
% 79.53/10.80 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 79.53/10.80 thf('23', plain,
% 79.53/10.80 (( setminusI ) =
% 79.53/10.80 ( ![X4:$i,X6:$i,X8:$i]:
% 79.53/10.80 ( ( in @ X8 @ X4 ) =>
% 79.53/10.80 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(powersetsubset, axiom, powersetsubset =
% 79.53/10.80 (![A:$i,B:$i]:
% 79.53/10.80 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 79.53/10.80 thf('24', plain,
% 79.53/10.80 (( powersetsubset ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( subset @ X4 @ X6 ) =>
% 79.53/10.80 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 79.53/10.80 thf('25', plain,
% 79.53/10.80 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(powersetE1, axiom, powersetE1 =
% 79.53/10.80 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 79.53/10.80 thf('26', plain,
% 79.53/10.80 (( powersetE1 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(powersetI1, axiom, powersetI1 =
% 79.53/10.80 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 79.53/10.80 thf('27', plain,
% 79.53/10.80 (( powersetI1 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq =
% 79.53/10.80 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))).
% 79.53/10.80 thf('28', plain,
% 79.53/10.80 (( subsetemptysetimpeq ) =
% 79.53/10.80 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(setextsub, axiom, setextsub =
% 79.53/10.80 (![A:$i,B:$i]:
% 79.53/10.80 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))).
% 79.53/10.80 thf('29', plain,
% 79.53/10.80 (( setextsub ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( subset @ X4 @ X6 ) =>
% 79.53/10.80 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(subset2powerset, axiom, subset2powerset =
% 79.53/10.80 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 79.53/10.80 thf('30', plain,
% 79.53/10.80 (( subset2powerset ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(setadjoinSub2, axiom, setadjoinSub2 =
% 79.53/10.80 (![A:$i,Xx:$i,B:$i]:
% 79.53/10.80 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))).
% 79.53/10.80 thf('31', plain,
% 79.53/10.80 (( setadjoinSub2 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i,X8:$i]:
% 79.53/10.80 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(setadjoinSub, axiom, setadjoinSub =
% 79.53/10.80 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))).
% 79.53/10.80 thf('32', plain,
% 79.53/10.80 (( setadjoinSub ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(subsetTrans, axiom, subsetTrans =
% 79.53/10.80 (![A:$i,B:$i,C:$i]:
% 79.53/10.80 ( ( subset @ A @ B ) => ( ( subset @ B @ C ) => ( subset @ A @ C ) ) ))).
% 79.53/10.80 thf('33', plain,
% 79.53/10.80 (( subsetTrans ) =
% 79.53/10.80 ( ![X4:$i,X6:$i,X8:$i]:
% 79.53/10.80 ( ( subset @ X4 @ X6 ) =>
% 79.53/10.80 ( ( subset @ X6 @ X8 ) => ( subset @ X4 @ X8 ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(subsetRefl, axiom, subsetRefl = (![A:$i]: ( subset @ A @ A ))).
% 79.53/10.80 thf('34', plain, (( subsetRefl ) = ( ![X4:$i]: ( subset @ X4 @ X4 ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(notequalI1, axiom, notequalI1 =
% 79.53/10.80 (![A:$i,B:$i]: ( ( ~( subset @ A @ B ) ) => ( ( A ) != ( B ) ) ))).
% 79.53/10.80 thf('35', plain,
% 79.53/10.80 (( notequalI1 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]: ( ( ~( subset @ X4 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(notsubsetI, axiom, notsubsetI =
% 79.53/10.80 (![A:$i,B:$i,Xx:$i]:
% 79.53/10.80 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ~( subset @ A @ B ) ) ) ))).
% 79.53/10.80 thf('36', plain,
% 79.53/10.80 (( notsubsetI ) =
% 79.53/10.80 ( ![X4:$i,X6:$i,X8:$i]:
% 79.53/10.80 ( ( in @ X8 @ X4 ) =>
% 79.53/10.80 ( ( ~( in @ X8 @ X6 ) ) => ( ~( subset @ X4 @ X6 ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(subsetE2, axiom, subsetE2 =
% 79.53/10.80 (![A:$i,B:$i,Xx:$i]:
% 79.53/10.80 ( ( subset @ A @ B ) => ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 79.53/10.80 thf('37', plain,
% 79.53/10.80 (( subsetE2 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i,X8:$i]:
% 79.53/10.80 ( ( subset @ X4 @ X6 ) =>
% 79.53/10.80 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(subsetE, axiom, subsetE =
% 79.53/10.80 (![A:$i,B:$i,Xx:$i]:
% 79.53/10.80 ( ( subset @ A @ B ) => ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 79.53/10.80 thf('38', plain,
% 79.53/10.80 (( subsetE ) =
% 79.53/10.80 ( ![X4:$i,X6:$i,X8:$i]:
% 79.53/10.80 ( ( subset @ X4 @ X6 ) => ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(emptysetsubset, axiom, emptysetsubset =
% 79.53/10.80 (![A:$i]: ( subset @ emptyset @ A ))).
% 79.53/10.80 thf('39', plain,
% 79.53/10.80 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(subsetI2, axiom, subsetI2 =
% 79.53/10.80 (![A:$i,B:$i]:
% 79.53/10.80 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 79.53/10.80 ( subset @ A @ B ) ))).
% 79.53/10.80 thf('40', plain,
% 79.53/10.80 (( subsetI2 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 79.53/10.80 ( subset @ X4 @ X6 ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(eqimpsubset1, axiom, eqimpsubset1 =
% 79.53/10.80 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ A @ B ) ))).
% 79.53/10.80 thf('41', plain,
% 79.53/10.80 (( eqimpsubset1 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X4 @ X6 ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(eqimpsubset2, axiom, eqimpsubset2 =
% 79.53/10.80 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ B @ A ) ))).
% 79.53/10.80 thf('42', plain,
% 79.53/10.80 (( eqimpsubset2 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(subsetI1, axiom, subsetI1 =
% 79.53/10.80 (![A:$i,B:$i]:
% 79.53/10.80 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 79.53/10.80 ( subset @ A @ B ) ))).
% 79.53/10.80 thf('43', plain,
% 79.53/10.80 (( subsetI1 ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 79.53/10.80 ( subset @ X4 @ X6 ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(powerset__Cong, axiom, powerset__Cong =
% 79.53/10.80 (![A:$i,B:$i]:
% 79.53/10.80 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 79.53/10.80 thf('44', plain,
% 79.53/10.80 (( powerset__Cong ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(powersetE, axiom, powersetE =
% 79.53/10.80 (![A:$i,B:$i,Xx:$i]:
% 79.53/10.80 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 79.53/10.80 thf('45', plain,
% 79.53/10.80 (( powersetE ) =
% 79.53/10.80 ( ![X4:$i,X6:$i,X8:$i]:
% 79.53/10.80 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 79.53/10.80 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(emptyInPowerset, axiom, emptyInPowerset =
% 79.53/10.80 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 79.53/10.80 thf('46', plain,
% 79.53/10.80 (( emptyInPowerset ) =
% 79.53/10.80 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(emptyinPowerset, axiom, emptyinPowerset =
% 79.53/10.80 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 79.53/10.80 thf('47', plain,
% 79.53/10.80 (( emptyinPowerset ) =
% 79.53/10.80 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(powersetI, axiom, powersetI =
% 79.53/10.80 (![A:$i,B:$i]:
% 79.53/10.80 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 79.53/10.80 ( in @ B @ ( powerset @ A ) ) ))).
% 79.53/10.80 thf('48', plain,
% 79.53/10.80 (( powersetI ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 79.53/10.80 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(powersetAx, axiom, powersetAx =
% 79.53/10.80 (![A:$i,B:$i]:
% 79.53/10.80 ( ( in @ B @ ( powerset @ A ) ) <=>
% 79.53/10.80 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 79.53/10.80 thf('49', plain,
% 79.53/10.80 (( powersetAx ) =
% 79.53/10.80 ( ![X4:$i,X6:$i]:
% 79.53/10.80 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 79.53/10.80 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 79.53/10.80 define([status(thm)])).
% 79.53/10.80 thf(contrasubsetT3, conjecture,
% 79.53/10.80 (( setextAx ) =>
% 79.53/10.80 ( ( emptysetAx ) =>
% 79.53/10.80 ( ( setadjoinAx ) =>
% 79.53/10.80 ( ( powersetAx ) =>
% 79.53/10.80 ( ( setunionAx ) =>
% 79.53/10.80 ( ( omega0Ax ) =>
% 79.53/10.80 ( ( omegaSAx ) =>
% 79.53/10.80 ( ( omegaIndAx ) =>
% 79.53/10.80 ( ( replAx ) =>
% 79.53/10.80 ( ( foundationAx ) =>
% 79.53/10.80 ( ( wellorderingAx ) =>
% 79.53/10.80 ( ( descrp ) =>
% 79.53/10.80 ( ( dsetconstrI ) =>
% 79.53/10.80 ( ( dsetconstrEL ) =>
% 79.53/10.80 ( ( dsetconstrER ) =>
% 79.53/10.80 ( ( exuE1 ) =>
% 79.53/10.80 ( ( prop2setE ) =>
% 79.53/10.80 ( ( emptysetE ) =>
% 79.53/10.80 ( ( emptysetimpfalse ) =>
% 79.53/10.80 ( ( notinemptyset ) =>
% 79.53/10.80 ( ( exuE3e ) =>
% 79.53/10.80 ( ( setext ) =>
% 79.53/10.80 ( ( emptyI ) =>
% 79.53/10.80 ( ( noeltsimpempty ) =>
% 79.53/10.80 ( ( setbeta ) =>
% 79.53/10.80 ( ( nonemptyE1 ) =>
% 79.53/10.80 ( ( nonemptyI ) =>
% 79.53/10.80 ( ( nonemptyI1 ) =>
% 79.53/10.80 ( ( setadjoinIL ) =>
% 79.53/10.80 ( ( emptyinunitempty ) =>
% 79.53/10.80 ( ( setadjoinIR ) =>
% 79.53/10.80 ( ( setadjoinE ) =>
% 79.53/10.80 ( (
% 79.53/10.80 setadjoinOr ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 setoftrueEq ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 powersetI ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 emptyinPowerset ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 emptyInPowerset ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 powersetE ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 setunionI ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 setunionE ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 subPowSU ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 exuE2 ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 nonemptyImpWitness ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 uniqinunit ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 notinsingleton ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 eqinunit ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 singletonsswitch ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 upairsetE ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 upairsetIL ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 upairsetIR ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 emptyE1 ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 vacuousDall ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 quantDeMorgan1 ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 quantDeMorgan2 ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 quantDeMorgan3 ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 quantDeMorgan4 ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 prop2setI ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 prop2set2propI ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 notdexE ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 notdallE ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 exuI1 ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 exuI3 ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 exuI2 ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 inCongP ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 in__Cong ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.80 exuE3u ) =>
% 79.53/10.80 (
% 79.53/10.80 (
% 79.53/10.81 exu__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 emptyset__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setadjoin__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 powerset__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setunion__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 omega__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 exuEu ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 descr__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 dsetconstr__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subsetI1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 eqimpsubset2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 eqimpsubset1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subsetI2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 emptysetsubset ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subsetE ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subsetE2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 notsubsetI ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 notequalI1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 notequalI2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subsetRefl ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subsetTrans ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setadjoinSub ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setadjoinSub2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subset2powerset ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setextsub ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subsetemptysetimpeq ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 powersetI1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 powersetE1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 inPowerset ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 powersetsubset ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 sepInPowerset ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 sepSubset ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binunionIL ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 upairset2IR ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binunionIR ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binunionEcases ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binunionE ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binunionLsub ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binunionRsub ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binintersectI ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binintersectSubset5 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binintersectEL ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binintersectLsub ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binintersectSubset2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binintersectSubset3 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binintersectER ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 disjointsetsI1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binintersectRsub ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binintersectSubset4 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binintersectSubset1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 bs114d ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setminusI ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setminusEL ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setminusER ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setminusSubset2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setminusERneg ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setminusELneg ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setminusILneg ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setminusIRneg ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setminusLsub ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setminusSubset1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 symdiffE ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 symdiffI1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 symdiffI2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 symdiffIneg1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 symdiffIneg2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 secondinupair ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setukpairIL ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setukpairIR ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 kpairiskpair ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 kpairp ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 singletonsubset ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 singletoninpowerset ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 singletoninpowunion ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 upairset2E ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 upairsubunion ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 upairinpowunion ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ubforcartprodlem1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ubforcartprodlem2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ubforcartprodlem3 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 cartprodpairin ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 cartprodmempair1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 cartprodmempair ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setunionE2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setunionsingleton1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setunionsingleton2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setunionsingleton ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 singletonprop ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ex1E1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ex1I ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ex1I2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 singletonsuniq ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setukpairinjL1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 kfstsingleton ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 theprop ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 kfstpairEq ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 cartprodfstin ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setukpairinjL2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setukpairinjL ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setukpairinjR11 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setukpairinjR12 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setukpairinjR1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 upairequniteq ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setukpairinjR2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setukpairinjR ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ksndsingleton ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ksndpairEq ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 kpairsurjEq ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 cartprodsndin ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 cartprodpairmemEL ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 cartprodpairmemER ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 cartprodmempaircEq ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 cartprodfstpairEq ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 cartprodsndpairEq ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 cartprodpairsurjEq ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 dpsetconstrI ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 dpsetconstrSub ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setOfPairsIsBReln ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 dpsetconstrERa ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 dpsetconstrEL1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 dpsetconstrEL2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 dpsetconstrER ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 funcImageSingleton ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 apProp ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 app ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 infuncsetfunc ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ap2p ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 funcinfuncset ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 lamProp ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 lamp ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 lam2p ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 brelnall1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 brelnall2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ex1E2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 funcGraphProp1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 funcGraphProp3 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 funcGraphProp2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 funcextLem ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 funcGraphProp4 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subbreln ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 eqbreln ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 funcext ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 funcext2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ap2apEq1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ap2apEq2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 beta1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 eta1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 lam2lamEq ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 beta2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 eta2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 iffalseProp1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 iffalseProp2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 iftrueProp1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 iftrueProp2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ifSingleton ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ifp ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 theeq ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 iftrue ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 iffalse ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 iftrueorfalse ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binintersectT_lem ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binunionT_lem ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 powersetT_lem ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setminusT_lem ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 complementT_lem ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setextT ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subsetTI ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 powersetTI1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 powersetTE1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 complementTI1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 complementTE1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binintersectTELcontra ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binintersectTERcontra ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 contrasubsetT ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 contrasubsetT1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 contrasubsetT2 ) =>
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 A:$i,X:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 A ) ) =>
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 Y:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 Y @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 A ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 (
% 79.53/10.81 setminus @
% 79.53/10.81 A @ Y ) @
% 79.53/10.81 (
% 79.53/10.81 setminus @
% 79.53/10.81 A @ X ) ) =>
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 79.53/10.81 thf(zf_stmt_0, conjecture,
% 79.53/10.81 (( setextAx ) =>
% 79.53/10.81 ( ( emptysetAx ) =>
% 79.53/10.81 ( ( setadjoinAx ) =>
% 79.53/10.81 ( ( ![X4:$i,X6:$i]:
% 79.53/10.81 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 79.53/10.81 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 79.53/10.81 ( ( setunionAx ) =>
% 79.53/10.81 ( ( omega0Ax ) =>
% 79.53/10.81 ( ( omegaSAx ) =>
% 79.53/10.81 ( ( omegaIndAx ) =>
% 79.53/10.81 ( ( replAx ) =>
% 79.53/10.81 ( ( foundationAx ) =>
% 79.53/10.81 ( ( wellorderingAx ) =>
% 79.53/10.81 ( ( descrp ) =>
% 79.53/10.81 ( ( dsetconstrI ) =>
% 79.53/10.81 ( ( dsetconstrEL ) =>
% 79.53/10.81 ( ( dsetconstrER ) =>
% 79.53/10.81 ( ( exuE1 ) =>
% 79.53/10.81 ( ( prop2setE ) =>
% 79.53/10.81 ( ( emptysetE ) =>
% 79.53/10.81 ( ( emptysetimpfalse ) =>
% 79.53/10.81 ( ( notinemptyset ) =>
% 79.53/10.81 ( ( exuE3e ) =>
% 79.53/10.81 ( ( setext ) =>
% 79.53/10.81 ( ( emptyI ) =>
% 79.53/10.81 ( ( noeltsimpempty ) =>
% 79.53/10.81 ( ( setbeta ) =>
% 79.53/10.81 ( ( nonemptyE1 ) =>
% 79.53/10.81 ( ( nonemptyI ) =>
% 79.53/10.81 ( ( nonemptyI1 ) =>
% 79.53/10.81 ( ( setadjoinIL ) =>
% 79.53/10.81 ( ( emptyinunitempty ) =>
% 79.53/10.81 ( ( setadjoinIR ) =>
% 79.53/10.81 ( ( setadjoinE ) =>
% 79.53/10.81 ( (
% 79.53/10.81 setadjoinOr ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setoftrueEq ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X10:$i,
% 79.53/10.81 X12:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X14:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X14 @ X12 ) =>
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X14 @ X10 ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X12 @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X10 ) ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X16:$i]:
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 emptyset @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X16 ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X18:$i]:
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 emptyset @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X18 ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X20:$i,
% 79.53/10.81 X22:$i,
% 79.53/10.81 X24:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X22 @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X20 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X24 @ X22 ) =>
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X24 @ X20 ) ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setunionI ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setunionE ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subPowSU ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 exuE2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 nonemptyImpWitness ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 uniqinunit ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 notinsingleton ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 eqinunit ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 singletonsswitch ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 upairsetE ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 upairsetIL ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 upairsetIR ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 emptyE1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 vacuousDall ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 quantDeMorgan1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 quantDeMorgan2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 quantDeMorgan3 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 quantDeMorgan4 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 prop2setI ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 prop2set2propI ) =>
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% 79.53/10.81 (
% 79.53/10.81 notdexE ) =>
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% 79.53/10.81 (
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% 79.53/10.81 (
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% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 emptyset__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
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% 79.53/10.81 (
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% 79.53/10.81 X26:$i,
% 79.53/10.81 X28:$i]:
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% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 X26 ) =
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% 79.53/10.81 X28 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X26 ) =
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X28 ) ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setunion__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 omega__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 exuEu ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 descr__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
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% 79.53/10.81 X34 @ X32 ) ) ) =>
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% 79.53/10.81 X38 @ X36 ) ) ) =>
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% 79.53/10.81 X56 @ X54 ) ) ) ) =>
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% 79.53/10.81 in @
% 79.53/10.81 X62 @ X58 ) ) ) ) ) =>
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% 79.53/10.81 subset @
% 79.53/10.81 X64 @ X66 ) ) ) ) ) =>
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% 79.53/10.81 subset @
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% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 X70 ) !=
% 79.53/10.81 (
% 79.53/10.81 X72 ) ) ) ) =>
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% 79.53/10.81 (
% 79.53/10.81 notequalI2 ) =>
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% 79.53/10.81 X76 @ X80 ) ) ) ) =>
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% 79.53/10.81 @
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% 79.53/10.81 setadjoin
% 79.53/10.81 @
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% 79.53/10.81 in @
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% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X94 ) ) ) ) =>
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% 79.53/10.81 (
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% 79.53/10.81 X96 ) =
% 79.53/10.81 (
% 79.53/10.81 X98 ) ) ) ) ) =>
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% 79.53/10.81 emptyset ) ) ) ) =>
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% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X102 ) ) ) ) =>
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% 79.53/10.81 X106 ) ) =>
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% 79.53/10.81 X108 @
% 79.53/10.81 X106 ) ) ) =>
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% 79.53/10.81 X110 ) ) ) =>
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% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X112 ) @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X114 ) ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 sepInPowerset ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 sepSubset ) =>
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% 79.53/10.81 binunionIL ) =>
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% 79.53/10.81 (
% 79.53/10.81 upairset2IR ) =>
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% 79.53/10.81 in @
% 79.53/10.81 X234 @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X232 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X236:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X236 @
% 79.53/10.81 X232 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ~(
% 79.53/10.81 in @
% 79.53/10.81 X236 @
% 79.53/10.81 (
% 79.53/10.81 setminus
% 79.53/10.81 @
% 79.53/10.81 X232 @
% 79.53/10.81 X234 ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X236 @
% 79.53/10.81 X234 ) ) ) ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binintersectTELcontra ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 binintersectTERcontra ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X238:$i,
% 79.53/10.81 X240:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X240 @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X238 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X242:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X242 @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X238 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X244:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X244 @
% 79.53/10.81 X238 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 X240 @
% 79.53/10.81 (
% 79.53/10.81 setminus @
% 79.53/10.81 X238 @
% 79.53/10.81 X242 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X244 @
% 79.53/10.81 X242 ) =>
% 79.53/10.81 (
% 79.53/10.81 ~(
% 79.53/10.81 in @
% 79.53/10.81 X244 @
% 79.53/10.81 X240 ) ) ) ) ) ) ) ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X246:$i,
% 79.53/10.81 X248:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X248 @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X246 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X250:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X250 @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X246 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X252:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X252 @
% 79.53/10.81 X246 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 X248 @
% 79.53/10.81 X250 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ~(
% 79.53/10.81 in @
% 79.53/10.81 X252 @
% 79.53/10.81 X250 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 ~(
% 79.53/10.81 in @
% 79.53/10.81 X252 @
% 79.53/10.81 X248 ) ) ) ) ) ) ) ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X254:$i,
% 79.53/10.81 X256:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X256 @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X254 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X258:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X258 @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X254 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 X256 @
% 79.53/10.81 X258 ) =>
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 (
% 79.53/10.81 setminus @
% 79.53/10.81 X254 @
% 79.53/10.81 X258 ) @
% 79.53/10.81 (
% 79.53/10.81 setminus @
% 79.53/10.81 X254 @
% 79.53/10.81 X256 ) ) ) ) ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X260:$i,
% 79.53/10.81 X262:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X262 @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X260 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X264:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X264 @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X260 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 (
% 79.53/10.81 setminus @
% 79.53/10.81 X260 @
% 79.53/10.81 X264 ) @
% 79.53/10.81 (
% 79.53/10.81 setminus @
% 79.53/10.81 X260 @
% 79.53/10.81 X262 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 X262 @
% 79.53/10.81 X264 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 79.53/10.81 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 79.53/10.81 thf(zf_stmt_2, axiom,
% 79.53/10.81 (![X8:$i,X6:$i,X4:$i]:
% 79.53/10.81 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 79.53/10.81 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 79.53/10.81 thf(zf_stmt_3, conjecture,
% 79.53/10.81 (( setextAx ) =>
% 79.53/10.81 ( ( emptysetAx ) =>
% 79.53/10.81 ( ( setadjoinAx ) =>
% 79.53/10.81 ( ( ![X4:$i,X6:$i]:
% 79.53/10.81 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 79.53/10.81 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 79.53/10.81 ( ( setunionAx ) =>
% 79.53/10.81 ( ( omega0Ax ) =>
% 79.53/10.81 ( ( omegaSAx ) =>
% 79.53/10.81 ( ( omegaIndAx ) =>
% 79.53/10.81 ( ( replAx ) =>
% 79.53/10.81 ( ( foundationAx ) =>
% 79.53/10.81 ( ( wellorderingAx ) =>
% 79.53/10.81 ( ( descrp ) =>
% 79.53/10.81 ( ( dsetconstrI ) =>
% 79.53/10.81 ( ( dsetconstrEL ) =>
% 79.53/10.81 ( ( dsetconstrER ) =>
% 79.53/10.81 ( ( exuE1 ) =>
% 79.53/10.81 ( ( prop2setE ) =>
% 79.53/10.81 ( ( emptysetE ) =>
% 79.53/10.81 ( ( emptysetimpfalse ) =>
% 79.53/10.81 ( ( notinemptyset ) =>
% 79.53/10.81 ( ( exuE3e ) =>
% 79.53/10.81 ( ( setext ) =>
% 79.53/10.81 ( ( emptyI ) =>
% 79.53/10.81 ( ( noeltsimpempty ) =>
% 79.53/10.81 ( ( setbeta ) =>
% 79.53/10.81 ( ( nonemptyE1 ) =>
% 79.53/10.81 ( ( nonemptyI ) =>
% 79.53/10.81 ( ( nonemptyI1 ) =>
% 79.53/10.81 ( ( setadjoinIL ) =>
% 79.53/10.81 ( ( emptyinunitempty ) =>
% 79.53/10.81 ( ( setadjoinIR ) =>
% 79.53/10.81 ( ( setadjoinE ) =>
% 79.53/10.81 ( (
% 79.53/10.81 setadjoinOr ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setoftrueEq ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X10:$i,
% 79.53/10.81 X12:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X14:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X14 @ X12 ) =>
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X14 @ X10 ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X12 @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X10 ) ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X16:$i]:
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 emptyset @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X16 ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X18:$i]:
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 emptyset @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X18 ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X20:$i,
% 79.53/10.81 X22:$i,
% 79.53/10.81 X24:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X22 @
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X20 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X24 @ X22 ) =>
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X24 @ X20 ) ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setunionI ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setunionE ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subPowSU ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 exuE2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 nonemptyImpWitness ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 uniqinunit ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 notinsingleton ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 eqinunit ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 singletonsswitch ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 upairsetE ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 upairsetIL ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 upairsetIR ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 emptyE1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 vacuousDall ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 quantDeMorgan1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 quantDeMorgan2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 quantDeMorgan3 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 quantDeMorgan4 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 prop2setI ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 prop2set2propI ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 notdexE ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 notdallE ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 exuI1 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 exuI3 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 exuI2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 inCongP ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 exuE3u ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 exu__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 emptyset__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setadjoin__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X26:$i,
% 79.53/10.81 X28:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 X26 ) =
% 79.53/10.81 (
% 79.53/10.81 X28 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X26 ) =
% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X28 ) ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 setunion__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 omega__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 exuEu ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 descr__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 dsetconstr__Cong ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X30:$i,
% 79.53/10.81 X32:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X34:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X34 @ X30 ) =>
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X34 @ X32 ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 X30 @ X32 ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X36:$i,
% 79.53/10.81 X38:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 X36 ) =
% 79.53/10.81 (
% 79.53/10.81 X38 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 X38 @ X36 ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X40:$i,
% 79.53/10.81 X42:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 X40 ) =
% 79.53/10.81 (
% 79.53/10.81 X42 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 X40 @ X42 ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X44:$i,
% 79.53/10.81 X46:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X48:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X48 @ X44 ) =>
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X48 @ X46 ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 X44 @ X46 ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X50:$i]:
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 emptyset @
% 79.53/10.81 X50 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X52:$i,
% 79.53/10.81 X54:$i,
% 79.53/10.81 X56:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 X52 @ X54 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X56 @ X52 ) =>
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X56 @ X54 ) ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X58:$i,
% 79.53/10.81 X60:$i,
% 79.53/10.81 X62:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 X58 @ X60 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ~(
% 79.53/10.81 in @
% 79.53/10.81 X62 @ X60 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 ~(
% 79.53/10.81 in @
% 79.53/10.81 X62 @ X58 ) ) ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X64:$i,
% 79.53/10.81 X66:$i,
% 79.53/10.81 X68:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 in @
% 79.53/10.81 X68 @ X64 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ~(
% 79.53/10.81 in @
% 79.53/10.81 X68 @ X66 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 ~(
% 79.53/10.81 subset @
% 79.53/10.81 X64 @ X66 ) ) ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X70:$i,
% 79.53/10.81 X72:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ~(
% 79.53/10.81 subset @
% 79.53/10.81 X70 @ X72 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 X70 ) !=
% 79.53/10.81 (
% 79.53/10.81 X72 ) ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 notequalI2 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X74:$i]:
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 X74 @ X74 ) ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 ![
% 79.53/10.81 X76:$i,
% 79.53/10.81 X78:$i,
% 79.53/10.81 X80:$i]:
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 X76 @ X78 ) =>
% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 X78 @ X80 ) =>
% 79.53/10.81 (
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% 79.53/10.81 (
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% 79.53/10.81 setminus @
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% 79.53/10.81 (
% 79.53/10.81 powerset @
% 79.53/10.81 X182 ) ) ) ) ) ) =>
% 79.53/10.81 (
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% 79.53/10.81 (
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% 79.53/10.81 powerset @
% 79.53/10.81 X188 ) ) ) ) =>
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% 79.53/10.81 (
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% 79.53/10.81 (
% 79.53/10.81 (
% 79.53/10.81 X194 ) =
% 79.53/10.81 (
% 79.53/10.81 X196 ) ) ) ) ) ) ) ) =>
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% 79.53/10.81 (
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% 79.53/10.81 X208 @
% 79.53/10.81 X206 ) ) ) ) =>
% 79.53/10.81 (
% 79.53/10.81 subset @
% 79.53/10.81 X204 @
% 79.53/10.81 X206 ) ) ) ) ) ) =>
% 79.53/10.81 (
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% 79.53/10.81 (
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% 79.53/10.82 (
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% 79.53/10.82 (
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% 79.53/10.82 (
% 79.53/10.82 powerset @
% 79.53/10.82 X214 ) ) ) ) ) ) ) =>
% 79.53/10.82 (
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% 79.53/10.82 (
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% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X224 @
% 79.53/10.82 X222 ) ) ) ) ) ) ) ) ) =>
% 79.53/10.82 (
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% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X230 @
% 79.53/10.82 X228 ) =>
% 79.53/10.82 (
% 79.53/10.82 ~(
% 79.53/10.82 in @
% 79.53/10.82 X230 @
% 79.53/10.82 (
% 79.53/10.82 setminus
% 79.53/10.82 @
% 79.53/10.82 X226 @
% 79.53/10.82 X228 ) ) ) ) ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 ![
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% 79.53/10.82 (
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% 79.53/10.82 X232 ) ) =>
% 79.53/10.82 (
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% 79.53/10.82 (
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% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 ~(
% 79.53/10.82 in @
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% 79.53/10.82 (
% 79.53/10.82 setminus
% 79.53/10.82 @
% 79.53/10.82 X232 @
% 79.53/10.82 X234 ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X236 @
% 79.53/10.82 X234 ) ) ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 binintersectTELcontra ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 binintersectTERcontra ) =>
% 79.53/10.82 (
% 79.53/10.82 (
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% 79.53/10.82 X238 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
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% 79.53/10.82 (
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% 79.53/10.82 in @
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% 79.53/10.82 X238 ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 subset @
% 79.53/10.82 X240 @
% 79.53/10.82 (
% 79.53/10.82 setminus @
% 79.53/10.82 X238 @
% 79.53/10.82 X242 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X244 @
% 79.53/10.82 X242 ) =>
% 79.53/10.82 (
% 79.53/10.82 ~(
% 79.53/10.82 in @
% 79.53/10.82 X244 @
% 79.53/10.82 X240 ) ) ) ) ) ) ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
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% 79.53/10.82 X246 ) ) =>
% 79.53/10.82 (
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% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 subset @
% 79.53/10.82 X248 @
% 79.53/10.82 X250 ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 ~(
% 79.53/10.82 in @
% 79.53/10.82 X252 @
% 79.53/10.82 X250 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ~(
% 79.53/10.82 in @
% 79.53/10.82 X252 @
% 79.53/10.82 X248 ) ) ) ) ) ) ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X254:$i,
% 79.53/10.82 X256:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
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% 79.53/10.82 powerset @
% 79.53/10.82 X254 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X258:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X258 @
% 79.53/10.82 (
% 79.53/10.82 powerset @
% 79.53/10.82 X254 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 subset @
% 79.53/10.82 X256 @
% 79.53/10.82 X258 ) =>
% 79.53/10.82 (
% 79.53/10.82 subset @
% 79.53/10.82 (
% 79.53/10.82 setminus @
% 79.53/10.82 X254 @
% 79.53/10.82 X258 ) @
% 79.53/10.82 (
% 79.53/10.82 setminus @
% 79.53/10.82 X254 @
% 79.53/10.82 X256 ) ) ) ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X260:$i,
% 79.53/10.82 X262:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X262 @
% 79.53/10.82 (
% 79.53/10.82 powerset @
% 79.53/10.82 X260 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X264:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X264 @
% 79.53/10.82 (
% 79.53/10.82 powerset @
% 79.53/10.82 X260 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 subset @
% 79.53/10.82 (
% 79.53/10.82 setminus @
% 79.53/10.82 X260 @
% 79.53/10.82 X264 ) @
% 79.53/10.82 (
% 79.53/10.82 setminus @
% 79.53/10.82 X260 @
% 79.53/10.82 X262 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 subset @
% 79.53/10.82 X262 @
% 79.53/10.82 X264 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 79.53/10.82 thf(zf_stmt_4, negated_conjecture,
% 79.53/10.82 (~( ( setextAx ) =>
% 79.53/10.82 ( ( emptysetAx ) =>
% 79.53/10.82 ( ( setadjoinAx ) =>
% 79.53/10.82 ( ( ![X4:$i,X6:$i]:
% 79.53/10.82 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 79.53/10.82 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 79.53/10.82 ( ( setunionAx ) =>
% 79.53/10.82 ( ( omega0Ax ) =>
% 79.53/10.82 ( ( omegaSAx ) =>
% 79.53/10.82 ( ( omegaIndAx ) =>
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% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X200:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X200 @
% 79.53/10.82 X192 ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X200 @
% 79.53/10.82 X196 ) =>
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X200 @
% 79.53/10.82 X194 ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 X194 ) =
% 79.53/10.82 (
% 79.53/10.82 X196 ) ) ) ) ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X202:$i,
% 79.53/10.82 X204:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X204 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X202 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X206:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X206 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X202 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X208:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X208 @
% 79.53/10.82 X202 ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X208 @
% 79.53/10.82 X204 ) =>
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X208 @
% 79.53/10.82 X206 ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 subset @
% 79.53/10.82 X204 @
% 79.53/10.82 X206 ) ) ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X210:$i,
% 79.53/10.82 X212:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X212 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X210 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X214:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X214 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X210 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X216:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X216 @
% 79.53/10.82 X210 ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X216 @
% 79.53/10.82 X212 ) =>
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X216 @
% 79.53/10.82 X214 ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X212 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X214 ) ) ) ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X218:$i,
% 79.53/10.82 X220:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X220 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X218 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X222:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X222 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X218 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X224:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X224 @
% 79.53/10.82 X218 ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X220 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X222 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X224 @
% 79.53/10.82 X220 ) =>
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X224 @
% 79.53/10.82 X222 ) ) ) ) ) ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X226:$i,
% 79.53/10.82 X228:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X228 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X226 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X230:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X230 @
% 79.53/10.82 X226 ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X230 @
% 79.53/10.82 X228 ) =>
% 79.53/10.82 (
% 79.53/10.82 ~
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X230 @
% 79.53/10.82 (
% 79.53/10.82 setminus
% 79.53/10.82 @
% 79.53/10.82 X226 @
% 79.53/10.82 X228 ) ) ) ) ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X232:$i,
% 79.53/10.82 X234:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X234 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X232 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X236:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X236 @
% 79.53/10.82 X232 ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 ~
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X236 @
% 79.53/10.82 (
% 79.53/10.82 setminus
% 79.53/10.82 @
% 79.53/10.82 X232 @
% 79.53/10.82 X234 ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X236 @
% 79.53/10.82 X234 ) ) ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 binintersectTELcontra ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 binintersectTERcontra ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X238:$i,
% 79.53/10.82 X240:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X240 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X238 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X242:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X242 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X238 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X244:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X244 @
% 79.53/10.82 X238 ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 subset @
% 79.53/10.82 X240 @
% 79.53/10.82 (
% 79.53/10.82 setminus
% 79.53/10.82 @
% 79.53/10.82 X238 @
% 79.53/10.82 X242 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X244 @
% 79.53/10.82 X242 ) =>
% 79.53/10.82 (
% 79.53/10.82 ~
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X244 @
% 79.53/10.82 X240 ) ) ) ) ) ) ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X246:$i,
% 79.53/10.82 X248:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X248 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X246 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X250:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X250 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X246 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X252:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X252 @
% 79.53/10.82 X246 ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 subset @
% 79.53/10.82 X248 @
% 79.53/10.82 X250 ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 ~
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X252 @
% 79.53/10.82 X250 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ~
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X252 @
% 79.53/10.82 X248 ) ) ) ) ) ) ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X254:$i,
% 79.53/10.82 X256:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X256 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X254 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X258:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X258 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X254 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 subset @
% 79.53/10.82 X256 @
% 79.53/10.82 X258 ) =>
% 79.53/10.82 (
% 79.53/10.82 subset @
% 79.53/10.82 (
% 79.53/10.82 setminus
% 79.53/10.82 @
% 79.53/10.82 X254 @
% 79.53/10.82 X258 ) @
% 79.53/10.82 (
% 79.53/10.82 setminus
% 79.53/10.82 @
% 79.53/10.82 X254 @
% 79.53/10.82 X256 ) ) ) ) ) ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X260:$i,
% 79.53/10.82 X262:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X262 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X260 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 ![
% 79.53/10.82 X264:$i]:
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 in @
% 79.53/10.82 X264 @
% 79.53/10.82 (
% 79.53/10.82 powerset
% 79.53/10.82 @
% 79.53/10.82 X260 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 (
% 79.53/10.82 subset @
% 79.53/10.82 (
% 79.53/10.82 setminus
% 79.53/10.82 @
% 79.53/10.82 X260 @
% 79.53/10.82 X264 ) @
% 79.53/10.82 (
% 79.53/10.82 setminus
% 79.53/10.82 @
% 79.53/10.82 X260 @
% 79.53/10.82 X262 ) ) =>
% 79.53/10.82 (
% 79.53/10.82 subset @
% 79.53/10.82 X262 @
% 79.53/10.82 X264 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 79.53/10.82 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 79.53/10.82 thf(zip_derived_cl225, plain,
% 79.53/10.82 (![X110 : $i, X111 : $i]:
% 79.53/10.82 ( (subset @ X110 @ X111) | ~ (in @ (sk__130 @ X111 @ X110) @ X111))),
% 79.53/10.82 inference('cnf', [status(esa)], [zf_stmt_4])).
% 79.53/10.82 thf(zip_derived_cl202, plain,
% 79.53/10.82 (![X83 : $i, X84 : $i, X85 : $i]:
% 79.53/10.82 (~ (in @ X83 @ X84)
% 79.53/10.82 | (in @ X83 @ X85)
% 79.53/10.82 | (in @ X83 @ (setminus @ X84 @ X85)))),
% 79.53/10.82 inference('cnf', [status(esa)], [zf_stmt_4])).
% 79.53/10.82 thf(zip_derived_cl130, plain,
% 79.53/10.82 ( (subset @ (setminus @ sk__134 @ sk__136) @
% 79.53/10.82 (setminus @ sk__134 @ sk__135))),
% 79.53/10.82 inference('cnf', [status(esa)], [zf_stmt_4])).
% 79.53/10.82 thf(zip_derived_cl133, plain,
% 79.53/10.82 (![X60 : $i, X61 : $i, X62 : $i, X63 : $i]:
% 79.53/10.82 (~ (in @ X60 @ (powerset @ X61))
% 79.53/10.82 | ~ (subset @ X62 @ (setminus @ X61 @ X60))
% 79.53/10.82 | ~ (in @ X63 @ X62)
% 79.53/10.82 | ~ (in @ X63 @ X60)
% 79.53/10.82 | ~ (in @ X63 @ X61)
% 79.53/10.82 | ~ (in @ X62 @ (powerset @ X61)))),
% 79.53/10.82 inference('cnf', [status(esa)], [zf_stmt_4])).
% 79.53/10.82 thf(zip_derived_cl245, plain,
% 79.53/10.82 (![X114 : $i, X115 : $i, X116 : $i]:
% 79.53/10.82 (~ (in @ X114 @ (powerset @ X115))
% 79.53/10.82 | (in @ X116 @ X115)
% 79.53/10.82 | ~ (in @ X116 @ X114))),
% 79.53/10.82 inference('cnf', [status(esa)], [zf_stmt_4])).
% 79.53/10.82 thf(zip_derived_cl1039, plain,
% 79.53/10.82 (![X60 : $i, X61 : $i, X62 : $i, X63 : $i]:
% 79.53/10.82 (~ (in @ X62 @ (powerset @ X61))
% 79.53/10.82 | ~ (in @ X63 @ X60)
% 79.53/10.82 | ~ (in @ X63 @ X62)
% 79.53/10.82 | ~ (subset @ X62 @ (setminus @ X61 @ X60))
% 79.53/10.82 | ~ (in @ X60 @ (powerset @ X61)))),
% 79.53/10.82 inference('clc', [status(thm)], [zip_derived_cl133, zip_derived_cl245])).
% 79.53/10.82 thf(zip_derived_cl1044, plain,
% 79.53/10.82 (![X0 : $i]:
% 79.53/10.82 (~ (in @ sk__135 @ (powerset @ sk__134))
% 79.53/10.82 | ~ (in @ X0 @ (setminus @ sk__134 @ sk__136))
% 79.53/10.82 | ~ (in @ X0 @ sk__135)
% 79.53/10.82 | ~ (in @ (setminus @ sk__134 @ sk__136) @ (powerset @ sk__134)))),
% 79.53/10.82 inference('sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl1039])).
% 79.53/10.82 thf(zip_derived_cl131, plain, ( (in @ sk__135 @ (powerset @ sk__134))),
% 79.53/10.82 inference('cnf', [status(esa)], [zf_stmt_4])).
% 79.53/10.82 thf(zip_derived_cl51, plain,
% 79.53/10.82 (![X21 : $i, X22 : $i]:
% 79.53/10.82 ( (in @ X21 @ (powerset @ X22)) | ~ (subset @ X21 @ X22))),
% 79.53/10.82 inference('cnf', [status(esa)], [zf_stmt_4])).
% 79.53/10.82 thf(zip_derived_cl200, plain,
% 79.53/10.82 (![X78 : $i, X79 : $i]: (subset @ (setminus @ X78 @ X79) @ X78)),
% 79.53/10.82 inference('cnf', [status(esa)], [zf_stmt_4])).
% 79.53/10.82 thf(zip_derived_cl338, plain,
% 79.53/10.82 (![X0 : $i, X1 : $i]: (in @ (setminus @ X0 @ X1) @ (powerset @ X0))),
% 79.53/10.82 inference('sup+', [status(thm)], [zip_derived_cl51, zip_derived_cl200])).
% 79.53/10.82 thf(zip_derived_cl1062, plain,
% 79.53/10.82 (![X0 : $i]:
% 79.53/10.82 (~ (in @ X0 @ (setminus @ sk__134 @ sk__136)) | ~ (in @ X0 @ sk__135))),
% 79.53/10.82 inference('demod', [status(thm)],
% 79.53/10.82 [zip_derived_cl1044, zip_derived_cl131, zip_derived_cl338])).
% 79.53/10.82 thf(zip_derived_cl226, plain,
% 79.53/10.82 (![X110 : $i, X111 : $i]:
% 79.53/10.82 ( (subset @ X110 @ X111) | (in @ (sk__130 @ X111 @ X110) @ X110))),
% 79.53/10.82 inference('cnf', [status(esa)], [zf_stmt_4])).
% 79.53/10.82 thf(zip_derived_cl129, plain, (~ (subset @ sk__135 @ sk__136)),
% 79.53/10.82 inference('cnf', [status(esa)], [zf_stmt_4])).
% 79.53/10.82 thf(zip_derived_cl131, plain, ( (in @ sk__135 @ (powerset @ sk__134))),
% 79.53/10.82 inference('cnf', [status(esa)], [zf_stmt_4])).
% 79.53/10.82 thf(zip_derived_cl245, plain,
% 79.53/10.82 (![X114 : $i, X115 : $i, X116 : $i]:
% 79.53/10.82 (~ (in @ X114 @ (powerset @ X115))
% 79.53/10.82 | (in @ X116 @ X115)
% 79.53/10.82 | ~ (in @ X116 @ X114))),
% 79.53/10.82 inference('cnf', [status(esa)], [zf_stmt_4])).
% 79.53/10.82 thf(zip_derived_cl637, plain,
% 79.53/10.82 (![X0 : $i]: (~ (in @ X0 @ sk__135) | (in @ X0 @ sk__134))),
% 79.53/10.82 inference('sup-', [status(thm)], [zip_derived_cl131, zip_derived_cl245])).
% 79.53/10.82 thf(zip_derived_cl17558, plain, ($false),
% 79.53/10.82 inference('eprover', [status(thm)],
% 79.53/10.82 [zip_derived_cl225, zip_derived_cl202, zip_derived_cl1062,
% 79.53/10.82 zip_derived_cl226, zip_derived_cl129, zip_derived_cl637])).
% 79.53/10.82
% 79.53/10.82 % SZS output end Refutation
% 79.53/10.82
% 79.53/10.82
% 79.53/10.82 % Terminating...
% 80.21/10.96 % Runner terminated.
% 80.21/10.96 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------