%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU650^1 : 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.wK0QhEin4n true
% Computer : n019.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 04:55:33 PM UTC 2025
% Result : Theorem 0.60s 1.02s
% Output : Refutation 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU650^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.wK0QhEin4n true
% 0.14/0.36 % Computer : n019.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 16:03:53 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
% 0.14/0.37 % Python version: Python 3.6.8
% 0.14/0.37 % Running in HO mode
% 0.54/0.69 % Total configuration time : 828
% 0.54/0.69 % Estimated wc time : 1656
% 0.54/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.59/0.78 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.59/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.59/0.78 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.59/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.59/0.80 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.59/0.85 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.60/1.02 % Solved by lams/40_c_ic.sh.
% 0.60/1.02 % done 223 iterations in 0.135s
% 0.60/1.02 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.60/1.02 % SZS output start Refutation
% 0.60/1.02 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 0.60/1.02 thf(notdexE_type, type, notdexE: $o).
% 0.60/1.02 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 0.60/1.02 thf(setunionAx_type, type, setunionAx: $o).
% 0.60/1.02 thf(setminusELneg_type, type, setminusELneg: $o).
% 0.60/1.02 thf(sk__53_type, type, sk__53: $i).
% 0.60/1.02 thf(powersetE_type, type, powersetE: $o).
% 0.60/1.02 thf(omegaSAx_type, type, omegaSAx: $o).
% 0.60/1.02 thf(exuI1_type, type, exuI1: $o).
% 0.60/1.02 thf(exuI2_type, type, exuI2: $o).
% 0.60/1.02 thf(notequalI2_type, type, notequalI2: $o).
% 0.60/1.02 thf(setukpairIR_type, type, setukpairIR: $o).
% 0.60/1.02 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 0.60/1.02 thf(setminusILneg_type, type, setminusILneg: $o).
% 0.60/1.02 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 0.60/1.02 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 0.60/1.02 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 0.60/1.02 thf(upairsubunion_type, type, upairsubunion: $o).
% 0.60/1.02 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 0.60/1.02 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 0.60/1.02 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 0.60/1.02 thf(setukpairIL_type, type, setukpairIL: $o).
% 0.60/1.02 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 0.60/1.02 thf(binunionE_type, type, binunionE: $o).
% 0.60/1.02 thf(setext_type, type, setext: $o).
% 0.60/1.02 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 0.60/1.02 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 0.60/1.02 thf(descr__Cong_type, type, descr__Cong: $o).
% 0.60/1.02 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 0.60/1.02 thf(in_type, type, in: $i > $i > $o).
% 0.60/1.02 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 0.60/1.02 thf(theprop_type, type, theprop: $o).
% 0.60/1.02 thf(upairset2E_type, type, upairset2E: $o).
% 0.60/1.02 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 0.60/1.02 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 0.60/1.02 thf(symdiffI2_type, type, symdiffI2: $o).
% 0.60/1.02 thf(upairset2IR_type, type, upairset2IR: $o).
% 0.60/1.02 thf(subsetE_type, type, subsetE: $o).
% 0.60/1.02 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 0.60/1.02 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 0.60/1.02 thf(setbeta_type, type, setbeta: $o).
% 0.60/1.02 thf(eqinunit_type, type, eqinunit: $o).
% 0.60/1.02 thf(upairsetIL_type, type, upairsetIL: $o).
% 0.60/1.02 thf(powersetI1_type, type, powersetI1: $o).
% 0.60/1.02 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 0.60/1.02 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 0.60/1.02 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 0.60/1.02 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 0.60/1.02 thf(powersetAx_type, type, powersetAx: $o).
% 0.60/1.02 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 0.60/1.02 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 0.60/1.02 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 0.60/1.02 thf(powersetI_type, type, powersetI: $o).
% 0.60/1.02 thf(upairsetIR_type, type, upairsetIR: $o).
% 0.60/1.02 thf(inCongP_type, type, inCongP: $o).
% 0.60/1.02 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 0.60/1.02 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 0.60/1.02 thf(exuE3e_type, type, exuE3e: $o).
% 0.60/1.02 thf(emptysetE_type, type, emptysetE: $o).
% 0.60/1.02 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 0.60/1.02 thf(setunionI_type, type, setunionI: $o).
% 0.60/1.02 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 0.60/1.02 thf(prop2setI_type, type, prop2setI: $o).
% 0.60/1.02 thf(ex1I2_type, type, ex1I2: $o).
% 0.60/1.02 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 0.60/1.02 thf(setminusER_type, type, setminusER: $o).
% 0.60/1.02 thf(exuE2_type, type, exuE2: $o).
% 0.60/1.02 thf(emptyset_type, type, emptyset: $i).
% 0.60/1.02 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 0.60/1.02 thf(powersetsubset_type, type, powersetsubset: $o).
% 0.60/1.02 thf(subPowSU_type, type, subPowSU: $o).
% 0.60/1.02 thf(notequalI1_type, type, notequalI1: $o).
% 0.60/1.02 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 0.60/1.02 thf(notinemptyset_type, type, notinemptyset: $o).
% 0.60/1.02 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 0.60/1.02 thf(subsetTrans_type, type, subsetTrans: $o).
% 0.60/1.02 thf(setminusI_type, type, setminusI: $o).
% 0.60/1.02 thf(binunionIL_type, type, binunionIL: $o).
% 0.60/1.02 thf(subsetE2_type, type, subsetE2: $o).
% 0.60/1.02 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 0.60/1.02 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 0.60/1.02 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 0.60/1.02 thf(setextsub_type, type, setextsub: $o).
% 0.60/1.02 thf(binunionLsub_type, type, binunionLsub: $o).
% 0.60/1.02 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 0.60/1.02 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 0.60/1.02 thf(setunionE_type, type, setunionE: $o).
% 0.60/1.02 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 0.60/1.02 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 0.60/1.02 thf(binunionIR_type, type, binunionIR: $o).
% 0.60/1.02 thf(setadjoinE_type, type, setadjoinE: $o).
% 0.60/1.02 thf(singletonprop_type, type, singletonprop: $o).
% 0.60/1.02 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 0.60/1.02 thf(exuE1_type, type, exuE1: $o).
% 0.60/1.02 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 0.60/1.02 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 0.60/1.02 thf(setminusLsub_type, type, setminusLsub: $o).
% 0.60/1.02 thf(notinsingleton_type, type, notinsingleton: $o).
% 0.60/1.02 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 0.60/1.02 thf(exuEu_type, type, exuEu: $o).
% 0.60/1.02 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 0.60/1.02 thf(upairsetE_type, type, upairsetE: $o).
% 0.60/1.02 thf(omega0Ax_type, type, omega0Ax: $o).
% 0.60/1.02 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 0.60/1.02 thf(notsubsetI_type, type, notsubsetI: $o).
% 0.60/1.02 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 0.60/1.02 thf(setextAx_type, type, setextAx: $o).
% 0.60/1.02 thf(powersetE1_type, type, powersetE1: $o).
% 0.60/1.02 thf(bs114d_type, type, bs114d: $o).
% 0.60/1.02 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 0.60/1.02 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 0.60/1.02 thf(subsetI1_type, type, subsetI1: $o).
% 0.60/1.02 thf(symdiffE_type, type, symdiffE: $o).
% 0.60/1.02 thf(descrp_type, type, descrp: $o).
% 0.60/1.02 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 0.60/1.02 thf(foundationAx_type, type, foundationAx: $o).
% 0.60/1.02 thf(emptysetAx_type, type, emptysetAx: $o).
% 0.60/1.02 thf(emptyI_type, type, emptyI: $o).
% 0.60/1.02 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 0.60/1.02 thf(binintersectEL_type, type, binintersectEL: $o).
% 0.60/1.02 thf(emptyE1_type, type, emptyE1: $o).
% 0.60/1.02 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 0.60/1.02 thf(vacuousDall_type, type, vacuousDall: $o).
% 0.60/1.02 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 0.60/1.02 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 0.60/1.02 thf(binintersectI_type, type, binintersectI: $o).
% 0.60/1.02 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 0.60/1.02 thf(ex1E1_type, type, ex1E1: $o).
% 0.60/1.02 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 0.60/1.02 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 0.60/1.02 thf(symdiffI1_type, type, symdiffI1: $o).
% 0.60/1.02 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 0.60/1.02 thf(subsetI2_type, type, subsetI2: $o).
% 0.60/1.02 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 0.60/1.02 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 0.60/1.02 thf(setminusERneg_type, type, setminusERneg: $o).
% 0.60/1.02 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 0.60/1.02 thf(omega__Cong_type, type, omega__Cong: $o).
% 0.60/1.02 thf(subsetRefl_type, type, subsetRefl: $o).
% 0.60/1.02 thf(uniqinunit_type, type, uniqinunit: $o).
% 0.60/1.02 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 0.60/1.02 thf(prop2setE_type, type, prop2setE: $o).
% 0.60/1.02 thf(binunionEcases_type, type, binunionEcases: $o).
% 0.60/1.02 thf(nonemptyI_type, type, nonemptyI: $o).
% 0.60/1.02 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 0.60/1.02 thf(exuE3u_type, type, exuE3u: $o).
% 0.60/1.02 thf(setminusEL_type, type, setminusEL: $o).
% 0.60/1.02 thf(singletonsubset_type, type, singletonsubset: $o).
% 0.60/1.02 thf(sepSubset_type, type, sepSubset: $o).
% 0.60/1.02 thf(setunionE2_type, type, setunionE2: $o).
% 0.60/1.02 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 0.60/1.02 thf(ex1I_type, type, ex1I: $o).
% 0.60/1.02 thf(exuI3_type, type, exuI3: $o).
% 0.60/1.02 thf(notdallE_type, type, notdallE: $o).
% 0.60/1.02 thf(binintersectER_type, type, binintersectER: $o).
% 0.60/1.02 thf(kpairp_type, type, kpairp: $o).
% 0.60/1.02 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 0.60/1.02 thf(sk__52_type, type, sk__52: $i).
% 0.60/1.02 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 0.60/1.02 thf(exu__Cong_type, type, exu__Cong: $o).
% 0.60/1.02 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 0.60/1.02 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 0.60/1.02 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 0.60/1.02 thf(replAx_type, type, replAx: $o).
% 0.60/1.02 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 0.60/1.02 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 0.60/1.02 thf(secondinupair_type, type, secondinupair: $o).
% 0.60/1.02 thf(inPowerset_type, type, inPowerset: $o).
% 0.60/1.02 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 0.60/1.02 thf(in__Cong_type, type, in__Cong: $o).
% 0.60/1.02 thf(binunionRsub_type, type, binunionRsub: $o).
% 0.60/1.02 thf(subset2powerset_type, type, subset2powerset: $o).
% 0.60/1.02 thf(setukpairinjR11, axiom, setukpairinjR11 =
% 0.60/1.02 (![Xx:$i,Xy:$i]:
% 0.60/1.02 ( ( ( Xx ) = ( Xy ) ) =>
% 0.60/1.02 ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =
% 0.60/1.02 ( setadjoin @ Xx @ emptyset ) ) ))).
% 0.60/1.02 thf('0', plain,
% 0.60/1.02 (( setukpairinjR11 ) =
% 0.60/1.02 ( ![X4:$i,X6:$i]:
% 0.60/1.02 ( ( ( X4 ) = ( X6 ) ) =>
% 0.60/1.02 ( ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =
% 0.60/1.02 ( setadjoin @ X4 @ emptyset ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(setukpairinjL2, axiom, setukpairinjL2 =
% 0.60/1.02 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]:
% 0.60/1.02 ( ( ( setadjoin @
% 0.60/1.02 ( setadjoin @ Xx @ emptyset ) @
% 0.60/1.02 ( setadjoin @
% 0.60/1.02 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 0.60/1.02 ( setadjoin @
% 0.60/1.02 ( setadjoin @ Xz @ emptyset ) @
% 0.60/1.02 ( setadjoin @
% 0.60/1.02 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) =>
% 0.60/1.02 ( ( Xx ) = ( Xz ) ) ))).
% 0.60/1.02 thf('1', plain,
% 0.60/1.02 (( setukpairinjL2 ) =
% 0.60/1.02 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 0.60/1.02 ( ( ( setadjoin @
% 0.60/1.02 ( setadjoin @ X4 @ emptyset ) @
% 0.60/1.02 ( setadjoin @
% 0.60/1.02 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 0.60/1.02 ( setadjoin @
% 0.60/1.02 ( setadjoin @ X8 @ emptyset ) @
% 0.60/1.02 ( setadjoin @
% 0.60/1.02 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) =>
% 0.60/1.02 ( ( X4 ) = ( X8 ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(setukpairinjL1, axiom, setukpairinjL1 =
% 0.60/1.02 (![Xx:$i,Xy:$i,Xz:$i]:
% 0.60/1.02 ( ( in @
% 0.60/1.02 ( setadjoin @ Xz @ emptyset ) @
% 0.60/1.02 ( setadjoin @
% 0.60/1.02 ( setadjoin @ Xx @ emptyset ) @
% 0.60/1.02 ( setadjoin @
% 0.60/1.02 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) =>
% 0.60/1.02 ( ( Xx ) = ( Xz ) ) ))).
% 0.60/1.02 thf('2', plain,
% 0.60/1.02 (( setukpairinjL1 ) =
% 0.60/1.02 ( ![X4:$i,X6:$i,X8:$i]:
% 0.60/1.02 ( ( in @
% 0.60/1.02 ( setadjoin @ X8 @ emptyset ) @
% 0.60/1.02 ( setadjoin @
% 0.60/1.02 ( setadjoin @ X4 @ emptyset ) @
% 0.60/1.02 ( setadjoin @
% 0.60/1.02 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) =>
% 0.60/1.02 ( ( X4 ) = ( X8 ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(singletonsuniq, axiom, singletonsuniq =
% 0.60/1.02 (![Xx:$i,Xy:$i]:
% 0.60/1.02 ( ( ( setadjoin @ Xx @ emptyset ) = ( setadjoin @ Xy @ emptyset ) ) =>
% 0.60/1.02 ( ( Xx ) = ( Xy ) ) ))).
% 0.60/1.02 thf('3', plain,
% 0.60/1.02 (( singletonsuniq ) =
% 0.60/1.02 ( ![X4:$i,X6:$i]:
% 0.60/1.02 ( ( ( setadjoin @ X4 @ emptyset ) = ( setadjoin @ X6 @ emptyset ) ) =>
% 0.60/1.02 ( ( X4 ) = ( X6 ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(upairset2E, axiom, upairset2E =
% 0.60/1.02 (![Xx:$i,Xy:$i,Xz:$i]:
% 0.60/1.02 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 0.60/1.02 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 0.60/1.02 thf('4', plain,
% 0.60/1.02 (( upairset2E ) =
% 0.60/1.02 ( ![X4:$i,X6:$i,X8:$i]:
% 0.60/1.02 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 0.60/1.02 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(secondinupair, axiom, secondinupair =
% 0.60/1.02 (![Xx:$i,Xy:$i]:
% 0.60/1.02 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.60/1.02 thf('5', plain,
% 0.60/1.02 (( secondinupair ) =
% 0.60/1.02 ( ![X4:$i,X6:$i]:
% 0.60/1.02 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(upairset2IR, axiom, upairset2IR =
% 0.60/1.02 (![Xx:$i,Xy:$i]:
% 0.60/1.02 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.60/1.02 thf('6', plain,
% 0.60/1.02 (( upairset2IR ) =
% 0.60/1.02 ( ![X4:$i,X6:$i]:
% 0.60/1.02 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(setadjoin__Cong, axiom, setadjoin__Cong =
% 0.60/1.02 (![Xx:$i,Xy:$i]:
% 0.60/1.02 ( ( ( Xx ) = ( Xy ) ) =>
% 0.60/1.02 ( ![Xz:$i,Xu:$i]:
% 0.60/1.02 ( ( ( Xz ) = ( Xu ) ) =>
% 0.60/1.02 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))).
% 0.60/1.02 thf('7', plain,
% 0.60/1.02 (( setadjoin__Cong ) =
% 0.60/1.02 ( ![X4:$i,X6:$i]:
% 0.60/1.02 ( ( ( X4 ) = ( X6 ) ) =>
% 0.60/1.02 ( ![X8:$i,X10:$i]:
% 0.60/1.02 ( ( ( X8 ) = ( X10 ) ) =>
% 0.60/1.02 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(upairsetIR, axiom, upairsetIR =
% 0.60/1.02 (![Xx:$i,Xy:$i]:
% 0.60/1.02 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.60/1.02 thf('8', plain,
% 0.60/1.02 (( upairsetIR ) =
% 0.60/1.02 ( ![X4:$i,X6:$i]:
% 0.60/1.02 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(upairsetIL, axiom, upairsetIL =
% 0.60/1.02 (![Xx:$i,Xy:$i]:
% 0.60/1.02 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.60/1.02 thf('9', plain,
% 0.60/1.02 (( upairsetIL ) =
% 0.60/1.02 ( ![X4:$i,X6:$i]:
% 0.60/1.02 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(upairsetE, axiom, upairsetE =
% 0.60/1.02 (![Xx:$i,Xy:$i,Xz:$i]:
% 0.60/1.02 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 0.60/1.02 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 0.60/1.02 thf('10', plain,
% 0.60/1.02 (( upairsetE ) =
% 0.60/1.02 ( ![X4:$i,X6:$i,X8:$i]:
% 0.60/1.02 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 0.60/1.02 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(singletonsswitch, axiom, singletonsswitch =
% 0.60/1.02 (![Xx:$i,Xy:$i]:
% 0.60/1.02 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 0.60/1.02 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 0.60/1.02 thf('11', plain,
% 0.60/1.02 (( singletonsswitch ) =
% 0.60/1.02 ( ![X4:$i,X6:$i]:
% 0.60/1.02 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 0.60/1.02 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(eqinunit, axiom, eqinunit =
% 0.60/1.02 (![Xx:$i,Xy:$i]:
% 0.60/1.02 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.60/1.02 thf('12', plain,
% 0.60/1.02 (( eqinunit ) =
% 0.60/1.02 ( ![X4:$i,X6:$i]:
% 0.60/1.02 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(notinsingleton, axiom, notinsingleton =
% 0.60/1.02 (![Xx:$i,Xy:$i]:
% 0.60/1.02 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 0.60/1.02 thf('13', plain,
% 0.60/1.02 (( notinsingleton ) =
% 0.60/1.02 ( ![X4:$i,X6:$i]:
% 0.60/1.02 ( ( ( X4 ) != ( X6 ) ) =>
% 0.60/1.02 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(uniqinunit, axiom, uniqinunit =
% 0.60/1.02 (![Xx:$i,Xy:$i]:
% 0.60/1.02 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 0.60/1.02 thf('14', plain,
% 0.60/1.02 (( uniqinunit ) =
% 0.60/1.02 ( ![X4:$i,X6:$i]:
% 0.60/1.02 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(setadjoinOr, axiom, setadjoinOr =
% 0.60/1.02 (![Xx:$i,A:$i,Xy:$i]:
% 0.60/1.02 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 0.60/1.02 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 0.60/1.02 thf('15', plain,
% 0.60/1.02 (( setadjoinOr ) =
% 0.60/1.02 ( ![X4:$i,X6:$i,X8:$i]:
% 0.60/1.02 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 0.60/1.02 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(setadjoinE, axiom, setadjoinE =
% 0.60/1.02 (![Xx:$i,A:$i,Xy:$i]:
% 0.60/1.02 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 0.60/1.02 ( ![Xphi:$o]:
% 0.60/1.02 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 0.60/1.02 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 0.60/1.02 thf('16', plain,
% 0.60/1.02 (( setadjoinE ) =
% 0.60/1.02 ( ![X4:$i,X6:$i,X8:$i]:
% 0.60/1.02 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 0.60/1.02 ( ![X10:$o]:
% 0.60/1.02 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 0.60/1.02 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(setadjoinIR, axiom, setadjoinIR =
% 0.60/1.02 (![Xx:$i,A:$i,Xy:$i]:
% 0.60/1.02 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 0.60/1.02 thf('17', plain,
% 0.60/1.02 (( setadjoinIR ) =
% 0.60/1.02 ( ![X4:$i,X6:$i,X8:$i]:
% 0.60/1.02 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 0.60/1.02 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 0.60/1.02 thf('18', plain,
% 0.60/1.02 (( emptyinunitempty ) =
% 0.60/1.02 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 0.60/1.02 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 0.60/1.02 thf('19', plain,
% 0.60/1.02 (( emptyinunitempty ) =
% 0.60/1.02 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(setadjoinIL, axiom, setadjoinIL =
% 0.60/1.02 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 0.60/1.02 thf('20', plain,
% 0.60/1.02 (( setadjoinIL ) =
% 0.60/1.02 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(setadjoinAx, axiom, setadjoinAx =
% 0.60/1.02 (![Xx:$i,A:$i,Xy:$i]:
% 0.60/1.02 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 0.60/1.02 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 0.60/1.02 thf('21', plain,
% 0.60/1.02 (( setadjoinAx ) =
% 0.60/1.02 ( ![X4:$i,X6:$i,X8:$i]:
% 0.60/1.02 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.60/1.02 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 0.60/1.02 define([status(thm)])).
% 0.60/1.02 thf(setukpairinjR12, conjecture,
% 0.60/1.02 (( setextAx ) =>
% 0.60/1.02 ( ( emptysetAx ) =>
% 0.60/1.02 ( ( setadjoinAx ) =>
% 0.60/1.02 ( ( powersetAx ) =>
% 0.60/1.02 ( ( setunionAx ) =>
% 0.60/1.02 ( ( omega0Ax ) =>
% 0.60/1.02 ( ( omegaSAx ) =>
% 0.60/1.02 ( ( omegaIndAx ) =>
% 0.60/1.02 ( ( replAx ) =>
% 0.60/1.02 ( ( foundationAx ) =>
% 0.60/1.02 ( ( wellorderingAx ) =>
% 0.60/1.02 ( ( descrp ) =>
% 0.60/1.02 ( ( dsetconstrI ) =>
% 0.60/1.02 ( ( dsetconstrEL ) =>
% 0.60/1.02 ( ( dsetconstrER ) =>
% 0.60/1.02 ( ( exuE1 ) =>
% 0.60/1.02 ( ( prop2setE ) =>
% 0.60/1.02 ( ( emptysetE ) =>
% 0.60/1.02 ( ( emptysetimpfalse ) =>
% 0.60/1.02 ( ( notinemptyset ) =>
% 0.60/1.02 ( ( exuE3e ) =>
% 0.60/1.02 ( ( setext ) =>
% 0.60/1.02 ( ( emptyI ) =>
% 0.60/1.02 ( ( noeltsimpempty ) =>
% 0.60/1.02 ( ( setbeta ) =>
% 0.60/1.02 ( ( nonemptyE1 ) =>
% 0.60/1.02 ( ( nonemptyI ) =>
% 0.60/1.02 ( ( nonemptyI1 ) =>
% 0.60/1.02 ( ( setadjoinIL ) =>
% 0.60/1.02 ( ( emptyinunitempty ) =>
% 0.60/1.02 ( ( setadjoinIR ) =>
% 0.60/1.02 ( ( setadjoinE ) =>
% 0.60/1.02 ( (
% 0.60/1.02 setadjoinOr ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setoftrueEq ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptyinPowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptyInPowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subPowSU ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuE2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 nonemptyImpWitness ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 uniqinunit ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notinsingleton ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 eqinunit ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletonsswitch ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 upairsetE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 upairsetIL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 upairsetIR ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptyE1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 vacuousDall ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 quantDeMorgan1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 quantDeMorgan2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 quantDeMorgan3 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 quantDeMorgan4 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 prop2setI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 prop2set2propI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notdexE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notdallE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuI3 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuI2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 inCongP ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuE3u ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exu__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptyset__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powerset__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunion__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 omega__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuEu ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 descr__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 dsetconstr__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 eqimpsubset2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 eqimpsubset1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetI2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptysetsubset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetE2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notsubsetI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notequalI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notequalI2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetRefl ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetTrans ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoinSub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoinSub2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subset2powerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setextsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetemptysetimpeq ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetE1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 inPowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetsubset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 sepInPowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 sepSubset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionIL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 upairset2IR ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionIR ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionEcases ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionLsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionRsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset5 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectEL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectLsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset3 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectER ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 disjointsetsI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectRsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset4 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 bs114d ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusEL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusER ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusSubset2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusERneg ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusELneg ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusILneg ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusIRneg ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusLsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusSubset1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffI2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffIneg1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffIneg2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 secondinupair ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setukpairIL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setukpairIR ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 kpairiskpair ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 kpairp ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletonsubset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletoninpowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletoninpowunion ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 upairset2E ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 upairsubunion ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 upairinpowunion ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ubforcartprodlem1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ubforcartprodlem2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ubforcartprodlem3 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 cartprodpairin ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 cartprodmempair1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 cartprodmempair ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionE2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionsingleton1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionsingleton2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionsingleton ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletonprop ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ex1E1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ex1I ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ex1I2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletonsuniq ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setukpairinjL1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 kfstsingleton ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 theprop ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 kfstpairEq ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 cartprodfstin ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setukpairinjL2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setukpairinjL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setukpairinjR11 ) =>
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 Xx:$i,
% 0.60/1.02 Xy:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 Xx ) =
% 0.60/1.02 (
% 0.60/1.02 Xy ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 Xx @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 Xx @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 Xy @
% 0.60/1.02 emptyset ) ) @
% 0.60/1.02 emptyset ) ) =
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 Xx @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.60/1.02 thf(zf_stmt_0, conjecture,
% 0.60/1.02 (( setextAx ) =>
% 0.60/1.02 ( ( emptysetAx ) =>
% 0.60/1.02 ( ( ![X4:$i,X6:$i,X8:$i]:
% 0.60/1.02 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.60/1.02 ( ( in @ X8 @ X6 ) | ( ( X8 ) = ( X4 ) ) ) ) ) =>
% 0.60/1.02 ( ( powersetAx ) =>
% 0.60/1.02 ( ( setunionAx ) =>
% 0.60/1.02 ( ( omega0Ax ) =>
% 0.60/1.02 ( ( omegaSAx ) =>
% 0.60/1.02 ( ( omegaIndAx ) =>
% 0.60/1.02 ( ( replAx ) =>
% 0.60/1.02 ( ( foundationAx ) =>
% 0.60/1.02 ( ( wellorderingAx ) =>
% 0.60/1.02 ( ( descrp ) =>
% 0.60/1.02 ( ( dsetconstrI ) =>
% 0.60/1.02 ( ( dsetconstrEL ) =>
% 0.60/1.02 ( ( dsetconstrER ) =>
% 0.60/1.02 ( ( exuE1 ) =>
% 0.60/1.02 ( ( prop2setE ) =>
% 0.60/1.02 ( ( emptysetE ) =>
% 0.60/1.02 ( ( emptysetimpfalse ) =>
% 0.60/1.02 ( ( notinemptyset ) =>
% 0.60/1.02 ( ( exuE3e ) =>
% 0.60/1.02 ( ( setext ) =>
% 0.60/1.02 ( ( emptyI ) =>
% 0.60/1.02 ( ( noeltsimpempty ) =>
% 0.60/1.02 ( ( setbeta ) =>
% 0.60/1.02 ( ( nonemptyE1 ) =>
% 0.60/1.02 ( ( nonemptyI ) =>
% 0.60/1.02 ( ( nonemptyI1 ) =>
% 0.60/1.02 ( ( ![X10:$i,X12:$i]:
% 0.60/1.02 ( in @
% 0.60/1.02 X10 @
% 0.60/1.02 ( setadjoin @
% 0.60/1.02 X10 @ X12 ) ) ) =>
% 0.60/1.02 ( ( in @
% 0.60/1.02 emptyset @
% 0.60/1.02 ( setadjoin @
% 0.60/1.02 emptyset @
% 0.60/1.02 emptyset ) ) =>
% 0.60/1.02 ( ( ![X14:$i,
% 0.60/1.02 X16:$i,
% 0.60/1.02 X18:$i]:
% 0.60/1.02 ( (
% 0.60/1.02 in @
% 0.60/1.02 X18 @ X16 ) =>
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X18 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X14 @ X16 ) ) ) ) =>
% 0.60/1.02 ( ( ![
% 0.60/1.02 X20:$i,
% 0.60/1.02 X22:$i,
% 0.60/1.02 X24:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X24 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X20 @ X22 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X26:$o]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X24 ) =
% 0.60/1.02 (
% 0.60/1.02 X20 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 X26 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X24 @ X22 ) =>
% 0.60/1.02 (
% 0.60/1.02 X26 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 X26 ) ) ) ) ) ) =>
% 0.60/1.02 ( (
% 0.60/1.02 ![
% 0.60/1.02 X28:$i,
% 0.60/1.02 X30:$i,
% 0.60/1.02 X32:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X32 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X28 @ X30 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X32 @ X30 ) |
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X32 ) =
% 0.60/1.02 (
% 0.60/1.02 X28 ) ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setoftrueEq ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptyinPowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptyInPowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subPowSU ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuE2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 nonemptyImpWitness ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X34:$i,
% 0.60/1.02 X36:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X34 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X36 @
% 0.60/1.02 emptyset ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X34 ) =
% 0.60/1.02 (
% 0.60/1.02 X36 ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X38:$i,
% 0.60/1.02 X40:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X38 ) !=
% 0.60/1.02 (
% 0.60/1.02 X40 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 ~(
% 0.60/1.02 in @
% 0.60/1.02 X40 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X38 @
% 0.60/1.02 emptyset ) ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X42:$i,
% 0.60/1.02 X44:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X42 ) =
% 0.60/1.02 (
% 0.60/1.02 X44 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X42 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X44 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X46:$i,
% 0.60/1.02 X48:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X46 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X48 @
% 0.60/1.02 emptyset ) ) =>
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X48 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X46 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X50:$i,
% 0.60/1.02 X52:$i,
% 0.60/1.02 X54:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X54 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X50 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X52 @
% 0.60/1.02 emptyset ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X54 ) =
% 0.60/1.02 (
% 0.60/1.02 X52 ) ) |
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X54 ) =
% 0.60/1.02 (
% 0.60/1.02 X50 ) ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X56:$i,
% 0.60/1.02 X58:$i]:
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X56 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X56 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X58 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X60:$i,
% 0.60/1.02 X62:$i]:
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X62 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X60 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X62 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptyE1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 vacuousDall ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 quantDeMorgan1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 quantDeMorgan2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 quantDeMorgan3 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 quantDeMorgan4 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 prop2setI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 prop2set2propI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notdexE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notdallE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuI3 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuI2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 inCongP ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuE3u ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exu__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptyset__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X64:$i,
% 0.60/1.02 X66:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X64 ) =
% 0.60/1.02 (
% 0.60/1.02 X66 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X68:$i,
% 0.60/1.02 X70:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X68 ) =
% 0.60/1.02 (
% 0.60/1.02 X70 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X64 @ X68 ) =
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X66 @ X70 ) ) ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powerset__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunion__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 omega__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuEu ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 descr__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 dsetconstr__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 eqimpsubset2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 eqimpsubset1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetI2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptysetsubset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetE2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notsubsetI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notequalI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notequalI2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetRefl ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetTrans ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoinSub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoinSub2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subset2powerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setextsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetemptysetimpeq ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetE1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 inPowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetsubset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 sepInPowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 sepSubset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionIL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X72:$i,
% 0.60/1.02 X74:$i]:
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X74 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X72 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X74 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionIR ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionEcases ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionLsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionRsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset5 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectEL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectLsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset3 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectER ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 disjointsetsI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectRsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset4 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 bs114d ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusEL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusER ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusSubset2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusERneg ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusELneg ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusILneg ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusIRneg ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusLsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusSubset1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffI2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffIneg1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffIneg2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X76:$i,
% 0.60/1.02 X78:$i]:
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X78 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X76 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X78 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setukpairIL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setukpairIR ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 kpairiskpair ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 kpairp ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletonsubset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletoninpowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletoninpowunion ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X80:$i,
% 0.60/1.02 X82:$i,
% 0.60/1.02 X84:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X84 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X80 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X82 @
% 0.60/1.02 emptyset ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X84 ) =
% 0.60/1.02 (
% 0.60/1.02 X82 ) ) |
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X84 ) =
% 0.60/1.02 (
% 0.60/1.02 X80 ) ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 upairsubunion ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 upairinpowunion ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ubforcartprodlem1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ubforcartprodlem2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ubforcartprodlem3 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 cartprodpairin ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 cartprodmempair1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 cartprodmempair ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionE2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionsingleton1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionsingleton2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionsingleton ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletonprop ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ex1E1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ex1I ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ex1I2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X86:$i,
% 0.60/1.02 X88:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X86 @
% 0.60/1.02 emptyset ) =
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X88 @
% 0.60/1.02 emptyset ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X86 ) =
% 0.60/1.02 (
% 0.60/1.02 X88 ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X90:$i,
% 0.60/1.02 X92:$i,
% 0.60/1.02 X94:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X94 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X90 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X90 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X92 @
% 0.60/1.02 emptyset ) ) @
% 0.60/1.02 emptyset ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X90 ) =
% 0.60/1.02 (
% 0.60/1.02 X94 ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 kfstsingleton ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 theprop ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 kfstpairEq ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 cartprodfstin ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X96:$i,
% 0.60/1.02 X98:$i,
% 0.60/1.02 X100:$i,
% 0.60/1.02 X102:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X96 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X96 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X98 @
% 0.60/1.02 emptyset ) ) @
% 0.60/1.02 emptyset ) ) =
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X100 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X100 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X102 @
% 0.60/1.02 emptyset ) ) @
% 0.60/1.02 emptyset ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X96 ) =
% 0.60/1.02 (
% 0.60/1.02 X100 ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setukpairinjL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X104:$i,
% 0.60/1.02 X106:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X104 ) =
% 0.60/1.02 (
% 0.60/1.02 X106 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X104 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X106 @
% 0.60/1.02 emptyset ) ) =
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X104 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X108:$i,
% 0.60/1.02 X110:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X108 ) =
% 0.60/1.02 (
% 0.60/1.02 X110 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X108 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X108 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X110 @
% 0.60/1.02 emptyset ) ) @
% 0.60/1.02 emptyset ) ) =
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X108 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.60/1.02 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 0.60/1.02 thf(zf_stmt_2, axiom,
% 0.60/1.02 (![X8:$i,X6:$i,X4:$i]:
% 0.60/1.02 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 0.60/1.02 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ))).
% 0.60/1.02 thf(zf_stmt_3, conjecture,
% 0.60/1.02 (( setextAx ) =>
% 0.60/1.02 ( ( emptysetAx ) =>
% 0.60/1.02 ( ( ![X4:$i,X6:$i,X8:$i]:
% 0.60/1.02 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.60/1.02 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 0.60/1.02 ( ( powersetAx ) =>
% 0.60/1.02 ( ( setunionAx ) =>
% 0.60/1.02 ( ( omega0Ax ) =>
% 0.60/1.02 ( ( omegaSAx ) =>
% 0.60/1.02 ( ( omegaIndAx ) =>
% 0.60/1.02 ( ( replAx ) =>
% 0.60/1.02 ( ( foundationAx ) =>
% 0.60/1.02 ( ( wellorderingAx ) =>
% 0.60/1.02 ( ( descrp ) =>
% 0.60/1.02 ( ( dsetconstrI ) =>
% 0.60/1.02 ( ( dsetconstrEL ) =>
% 0.60/1.02 ( ( dsetconstrER ) =>
% 0.60/1.02 ( ( exuE1 ) =>
% 0.60/1.02 ( ( prop2setE ) =>
% 0.60/1.02 ( ( emptysetE ) =>
% 0.60/1.02 ( ( emptysetimpfalse ) =>
% 0.60/1.02 ( ( notinemptyset ) =>
% 0.60/1.02 ( ( exuE3e ) =>
% 0.60/1.02 ( ( setext ) =>
% 0.60/1.02 ( ( emptyI ) =>
% 0.60/1.02 ( ( noeltsimpempty ) =>
% 0.60/1.02 ( ( setbeta ) =>
% 0.60/1.02 ( ( nonemptyE1 ) =>
% 0.60/1.02 ( ( nonemptyI ) =>
% 0.60/1.02 ( ( nonemptyI1 ) =>
% 0.60/1.02 ( ( ![X10:$i,X12:$i]:
% 0.60/1.02 ( in @
% 0.60/1.02 X10 @
% 0.60/1.02 ( setadjoin @
% 0.60/1.02 X10 @ X12 ) ) ) =>
% 0.60/1.02 ( ( in @
% 0.60/1.02 emptyset @
% 0.60/1.02 ( setadjoin @
% 0.60/1.02 emptyset @
% 0.60/1.02 emptyset ) ) =>
% 0.60/1.02 ( ( ![X14:$i,
% 0.60/1.02 X16:$i,
% 0.60/1.02 X18:$i]:
% 0.60/1.02 ( (
% 0.60/1.02 in @
% 0.60/1.02 X18 @ X16 ) =>
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X18 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X14 @ X16 ) ) ) ) =>
% 0.60/1.02 ( ( ![
% 0.60/1.02 X20:$i,
% 0.60/1.02 X22:$i,
% 0.60/1.02 X24:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X24 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X20 @ X22 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X26:$o]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X24 ) =
% 0.60/1.02 (
% 0.60/1.02 X20 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 X26 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X24 @ X22 ) =>
% 0.60/1.02 (
% 0.60/1.02 X26 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 X26 ) ) ) ) ) ) =>
% 0.60/1.02 ( (
% 0.60/1.02 ![
% 0.60/1.02 X28:$i,
% 0.60/1.02 X30:$i,
% 0.60/1.02 X32:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X32 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X28 @ X30 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X32 ) =
% 0.60/1.02 (
% 0.60/1.02 X28 ) ) |
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X32 @ X30 ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setoftrueEq ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptyinPowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptyInPowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subPowSU ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuE2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 nonemptyImpWitness ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X34:$i,
% 0.60/1.02 X36:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X34 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X36 @
% 0.60/1.02 emptyset ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X34 ) =
% 0.60/1.02 (
% 0.60/1.02 X36 ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X38:$i,
% 0.60/1.02 X40:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X38 ) !=
% 0.60/1.02 (
% 0.60/1.02 X40 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 ~(
% 0.60/1.02 in @
% 0.60/1.02 X40 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X38 @
% 0.60/1.02 emptyset ) ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X42:$i,
% 0.60/1.02 X44:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X42 ) =
% 0.60/1.02 (
% 0.60/1.02 X44 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X42 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X44 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X46:$i,
% 0.60/1.02 X48:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X46 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X48 @
% 0.60/1.02 emptyset ) ) =>
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X48 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X46 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X50:$i,
% 0.60/1.02 X52:$i,
% 0.60/1.02 X54:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X54 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X50 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X52 @
% 0.60/1.02 emptyset ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X54 ) =
% 0.60/1.02 (
% 0.60/1.02 X50 ) ) |
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X54 ) =
% 0.60/1.02 (
% 0.60/1.02 X52 ) ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X56:$i,
% 0.60/1.02 X58:$i]:
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X56 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X56 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X58 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X60:$i,
% 0.60/1.02 X62:$i]:
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X62 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X60 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X62 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptyE1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 vacuousDall ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 quantDeMorgan1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 quantDeMorgan2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 quantDeMorgan3 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 quantDeMorgan4 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 prop2setI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 prop2set2propI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notdexE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notdallE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuI3 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuI2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 inCongP ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuE3u ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exu__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptyset__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X64:$i,
% 0.60/1.02 X66:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X64 ) =
% 0.60/1.02 (
% 0.60/1.02 X66 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X68:$i,
% 0.60/1.02 X70:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X68 ) =
% 0.60/1.02 (
% 0.60/1.02 X70 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X64 @ X68 ) =
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X66 @ X70 ) ) ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powerset__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunion__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 omega__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuEu ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 descr__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 dsetconstr__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 eqimpsubset2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 eqimpsubset1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetI2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptysetsubset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetE2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notsubsetI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notequalI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notequalI2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetRefl ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetTrans ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoinSub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoinSub2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subset2powerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setextsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetemptysetimpeq ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetE1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 inPowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetsubset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 sepInPowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 sepSubset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionIL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X72:$i,
% 0.60/1.02 X74:$i]:
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X74 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X72 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X74 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionIR ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionEcases ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionLsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionRsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset5 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectEL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectLsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset3 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectER ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 disjointsetsI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectRsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset4 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 bs114d ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusEL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusER ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusSubset2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusERneg ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusELneg ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusILneg ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusIRneg ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusLsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusSubset1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffI2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffIneg1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffIneg2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X76:$i,
% 0.60/1.02 X78:$i]:
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X78 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X76 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X78 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setukpairIL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setukpairIR ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 kpairiskpair ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 kpairp ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletonsubset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletoninpowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletoninpowunion ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X80:$i,
% 0.60/1.02 X82:$i,
% 0.60/1.02 X84:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X84 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X80 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X82 @
% 0.60/1.02 emptyset ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X84 ) =
% 0.60/1.02 (
% 0.60/1.02 X80 ) ) |
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X84 ) =
% 0.60/1.02 (
% 0.60/1.02 X82 ) ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 upairsubunion ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 upairinpowunion ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ubforcartprodlem1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ubforcartprodlem2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ubforcartprodlem3 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 cartprodpairin ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 cartprodmempair1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 cartprodmempair ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionE2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionsingleton1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionsingleton2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionsingleton ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletonprop ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ex1E1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ex1I ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ex1I2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X86:$i,
% 0.60/1.02 X88:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X86 @
% 0.60/1.02 emptyset ) =
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X88 @
% 0.60/1.02 emptyset ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X86 ) =
% 0.60/1.02 (
% 0.60/1.02 X88 ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X90:$i,
% 0.60/1.02 X92:$i,
% 0.60/1.02 X94:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X94 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X90 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X90 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X92 @
% 0.60/1.02 emptyset ) ) @
% 0.60/1.02 emptyset ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X90 ) =
% 0.60/1.02 (
% 0.60/1.02 X94 ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 kfstsingleton ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 theprop ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 kfstpairEq ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 cartprodfstin ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X96:$i,
% 0.60/1.02 X98:$i,
% 0.60/1.02 X100:$i,
% 0.60/1.02 X102:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X96 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X96 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X98 @
% 0.60/1.02 emptyset ) ) @
% 0.60/1.02 emptyset ) ) =
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X100 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X100 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X102 @
% 0.60/1.02 emptyset ) ) @
% 0.60/1.02 emptyset ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X96 ) =
% 0.60/1.02 (
% 0.60/1.02 X100 ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setukpairinjL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X104:$i,
% 0.60/1.02 X106:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X104 ) =
% 0.60/1.02 (
% 0.60/1.02 X106 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X104 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X106 @
% 0.60/1.02 emptyset ) ) =
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X104 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X108:$i,
% 0.60/1.02 X110:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X108 ) =
% 0.60/1.02 (
% 0.60/1.02 X110 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X108 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X108 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X110 @
% 0.60/1.02 emptyset ) ) @
% 0.60/1.02 emptyset ) ) =
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X108 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.60/1.02 thf(zf_stmt_4, negated_conjecture,
% 0.60/1.02 (~( ( setextAx ) =>
% 0.60/1.02 ( ( emptysetAx ) =>
% 0.60/1.02 ( ( ![X4:$i,X6:$i,X8:$i]:
% 0.60/1.02 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.60/1.02 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 0.60/1.02 ( ( powersetAx ) =>
% 0.60/1.02 ( ( setunionAx ) =>
% 0.60/1.02 ( ( omega0Ax ) =>
% 0.60/1.02 ( ( omegaSAx ) =>
% 0.60/1.02 ( ( omegaIndAx ) =>
% 0.60/1.02 ( ( replAx ) =>
% 0.60/1.02 ( ( foundationAx ) =>
% 0.60/1.02 ( ( wellorderingAx ) =>
% 0.60/1.02 ( ( descrp ) =>
% 0.60/1.02 ( ( dsetconstrI ) =>
% 0.60/1.02 ( ( dsetconstrEL ) =>
% 0.60/1.02 ( ( dsetconstrER ) =>
% 0.60/1.02 ( ( exuE1 ) =>
% 0.60/1.02 ( ( prop2setE ) =>
% 0.60/1.02 ( ( emptysetE ) =>
% 0.60/1.02 ( ( emptysetimpfalse ) =>
% 0.60/1.02 ( ( notinemptyset ) =>
% 0.60/1.02 ( ( exuE3e ) =>
% 0.60/1.02 ( ( setext ) =>
% 0.60/1.02 ( ( emptyI ) =>
% 0.60/1.02 ( ( noeltsimpempty ) =>
% 0.60/1.02 ( ( setbeta ) =>
% 0.60/1.02 ( ( nonemptyE1 ) =>
% 0.60/1.02 ( ( nonemptyI ) =>
% 0.60/1.02 ( ( nonemptyI1 ) =>
% 0.60/1.02 ( ( ![X10:$i,
% 0.60/1.02 X12:$i]:
% 0.60/1.02 ( in @
% 0.60/1.02 X10 @
% 0.60/1.02 ( setadjoin
% 0.60/1.02 @
% 0.60/1.02 X10 @ X12 ) ) ) =>
% 0.60/1.02 ( ( in @
% 0.60/1.02 emptyset @
% 0.60/1.02 ( setadjoin
% 0.60/1.02 @
% 0.60/1.02 emptyset @
% 0.60/1.02 emptyset ) ) =>
% 0.60/1.02 ( ( ![
% 0.60/1.02 X14:$i,
% 0.60/1.02 X16:$i,
% 0.60/1.02 X18:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X18 @ X16 ) =>
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X18 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X14 @ X16 ) ) ) ) =>
% 0.60/1.02 ( (
% 0.60/1.02 ![
% 0.60/1.02 X20:$i,
% 0.60/1.02 X22:$i,
% 0.60/1.02 X24:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X24 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X20 @ X22 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X26:$o]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X24 ) =
% 0.60/1.02 (
% 0.60/1.02 X20 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 X26 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X24 @ X22 ) =>
% 0.60/1.02 (
% 0.60/1.02 X26 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 X26 ) ) ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X28:$i,
% 0.60/1.02 X30:$i,
% 0.60/1.02 X32:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X32 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X28 @ X30 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X32 ) =
% 0.60/1.02 (
% 0.60/1.02 X28 ) ) |
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X32 @ X30 ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setoftrueEq ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptyinPowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptyInPowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subPowSU ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuE2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 nonemptyImpWitness ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X34:$i,
% 0.60/1.02 X36:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X34 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X36 @
% 0.60/1.02 emptyset ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X34 ) =
% 0.60/1.02 (
% 0.60/1.02 X36 ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X38:$i,
% 0.60/1.02 X40:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X38 ) !=
% 0.60/1.02 (
% 0.60/1.02 X40 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 ~
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X40 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X38 @
% 0.60/1.02 emptyset ) ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X42:$i,
% 0.60/1.02 X44:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X42 ) =
% 0.60/1.02 (
% 0.60/1.02 X44 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X42 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X44 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X46:$i,
% 0.60/1.02 X48:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X46 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X48 @
% 0.60/1.02 emptyset ) ) =>
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X48 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X46 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X50:$i,
% 0.60/1.02 X52:$i,
% 0.60/1.02 X54:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X54 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X50 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X52 @
% 0.60/1.02 emptyset ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X54 ) =
% 0.60/1.02 (
% 0.60/1.02 X50 ) ) |
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X54 ) =
% 0.60/1.02 (
% 0.60/1.02 X52 ) ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X56:$i,
% 0.60/1.02 X58:$i]:
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X56 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X56 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X58 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X60:$i,
% 0.60/1.02 X62:$i]:
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X62 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X60 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X62 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptyE1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 vacuousDall ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 quantDeMorgan1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 quantDeMorgan2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 quantDeMorgan3 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 quantDeMorgan4 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 prop2setI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 prop2set2propI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notdexE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notdallE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuI3 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuI2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 inCongP ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuE3u ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exu__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptyset__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X64:$i,
% 0.60/1.02 X66:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X64 ) =
% 0.60/1.02 (
% 0.60/1.02 X66 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X68:$i,
% 0.60/1.02 X70:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X68 ) =
% 0.60/1.02 (
% 0.60/1.02 X70 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X64 @ X68 ) =
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X66 @ X70 ) ) ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powerset__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunion__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 omega__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 exuEu ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 descr__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 dsetconstr__Cong ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 eqimpsubset2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 eqimpsubset1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetI2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 emptysetsubset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetE2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notsubsetI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notequalI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 notequalI2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetRefl ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetTrans ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoinSub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoinSub2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subset2powerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setextsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 subsetemptysetimpeq ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetE1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 inPowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 powersetsubset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 sepInPowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 sepSubset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionIL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X72:$i,
% 0.60/1.02 X74:$i]:
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X74 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X72 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X74 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionIR ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionEcases ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionLsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binunionRsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset5 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectEL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectLsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset3 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectER ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 disjointsetsI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectRsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset4 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 binintersectSubset1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 bs114d ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusI ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusEL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusER ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusSubset2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusERneg ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusELneg ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusILneg ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusIRneg ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusLsub ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setminusSubset1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffE ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffI1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffI2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffIneg1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 symdiffIneg2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X76:$i,
% 0.60/1.02 X78:$i]:
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X78 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X76 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X78 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setukpairIL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setukpairIR ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 kpairiskpair ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 kpairp ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletonsubset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletoninpowerset ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletoninpowunion ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X80:$i,
% 0.60/1.02 X82:$i,
% 0.60/1.02 X84:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 X84 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X80 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X82 @
% 0.60/1.02 emptyset ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X84 ) =
% 0.60/1.02 (
% 0.60/1.02 X80 ) ) |
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X84 ) =
% 0.60/1.02 (
% 0.60/1.02 X82 ) ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 upairsubunion ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 upairinpowunion ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ubforcartprodlem1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ubforcartprodlem2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ubforcartprodlem3 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 cartprodpairin ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 cartprodmempair1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 cartprodmempair ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionE2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionsingleton1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionsingleton2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setunionsingleton ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 singletonprop ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ex1E1 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ex1I ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ex1I2 ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X86:$i,
% 0.60/1.02 X88:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X86 @
% 0.60/1.02 emptyset ) =
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X88 @
% 0.60/1.02 emptyset ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X86 ) =
% 0.60/1.02 (
% 0.60/1.02 X88 ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X90:$i,
% 0.60/1.02 X92:$i,
% 0.60/1.02 X94:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 in @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X94 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X90 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X90 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X92 @
% 0.60/1.02 emptyset ) ) @
% 0.60/1.02 emptyset ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X90 ) =
% 0.60/1.02 (
% 0.60/1.02 X94 ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 kfstsingleton ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 theprop ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 kfstpairEq ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 cartprodfstin ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X96:$i,
% 0.60/1.02 X98:$i,
% 0.60/1.02 X100:$i,
% 0.60/1.02 X102:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X96 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X96 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X98 @
% 0.60/1.02 emptyset ) ) @
% 0.60/1.02 emptyset ) ) =
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X100 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X100 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X102 @
% 0.60/1.02 emptyset ) ) @
% 0.60/1.02 emptyset ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X96 ) =
% 0.60/1.02 (
% 0.60/1.02 X100 ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setukpairinjL ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X104:$i,
% 0.60/1.02 X106:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X104 ) =
% 0.60/1.02 (
% 0.60/1.02 X106 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X104 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X106 @
% 0.60/1.02 emptyset ) ) =
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X104 @
% 0.60/1.02 emptyset ) ) ) ) =>
% 0.60/1.02 (
% 0.60/1.02 ![
% 0.60/1.02 X108:$i,
% 0.60/1.02 X110:$i]:
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 X108 ) =
% 0.60/1.02 (
% 0.60/1.02 X110 ) ) =>
% 0.60/1.02 (
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X108 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X108 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X110 @
% 0.60/1.02 emptyset ) ) @
% 0.60/1.02 emptyset ) ) =
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 (
% 0.60/1.02 setadjoin
% 0.60/1.02 @
% 0.60/1.02 X108 @
% 0.60/1.02 emptyset ) @
% 0.60/1.02 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 0.60/1.02 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 0.60/1.02 thf(zip_derived_cl87, plain,
% 0.60/1.02 (((setadjoin @ (setadjoin @ sk__52 @ emptyset) @
% 0.60/1.02 (setadjoin @ (setadjoin @ sk__52 @ (setadjoin @ sk__53 @ emptyset)) @
% 0.60/1.02 emptyset))
% 0.60/1.02 != (setadjoin @ (setadjoin @ sk__52 @ emptyset) @ emptyset))),
% 0.60/1.02 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.60/1.02 thf(zip_derived_cl88, plain, (((sk__52) = (sk__53))),
% 0.60/1.02 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.60/1.02 thf(zip_derived_cl89, plain,
% 0.60/1.02 (![X30 : $i, X31 : $i]:
% 0.60/1.02 (((setadjoin @ X30 @ (setadjoin @ X31 @ emptyset))
% 0.60/1.02 = (setadjoin @ X30 @ emptyset))
% 0.60/1.02 | ((X30) != (X31)))),
% 0.60/1.02 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.60/1.02 thf(zip_derived_cl326, plain,
% 0.60/1.02 (![X31 : $i]:
% 0.60/1.02 ((setadjoin @ X31 @ (setadjoin @ X31 @ emptyset))
% 0.60/1.02 = (setadjoin @ X31 @ emptyset))),
% 0.60/1.02 inference('simplify', [status(thm)], [zip_derived_cl89])).
% 0.60/1.02 thf(zip_derived_cl326, plain,
% 0.60/1.02 (![X31 : $i]:
% 0.60/1.02 ((setadjoin @ X31 @ (setadjoin @ X31 @ emptyset))
% 0.60/1.02 = (setadjoin @ X31 @ emptyset))),
% 0.60/1.02 inference('simplify', [status(thm)], [zip_derived_cl89])).
% 0.60/1.02 thf(zip_derived_cl399, plain,
% 0.60/1.02 (((setadjoin @ (setadjoin @ sk__52 @ emptyset) @ emptyset)
% 0.60/1.02 != (setadjoin @ (setadjoin @ sk__52 @ emptyset) @ emptyset))),
% 0.60/1.02 inference('demod', [status(thm)],
% 0.60/1.02 [zip_derived_cl87, zip_derived_cl88, zip_derived_cl326,
% 0.60/1.02 zip_derived_cl326])).
% 0.60/1.02 thf(zip_derived_cl400, plain, ($false),
% 0.60/1.02 inference('simplify', [status(thm)], [zip_derived_cl399])).
% 0.60/1.02
% 0.60/1.02 % SZS output end Refutation
% 0.60/1.02
% 0.60/1.02
% 0.60/1.02 % Terminating...
% 2.75/1.21 % Runner terminated.
% 2.75/1.22 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------