%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU557^1 : TPTP v9.2.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.uBmM66s48H true
% Computer : n023.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 04:55:03 PM UTC 2025
% Result : Theorem 8.68s 4.85s
% Output : Refutation 8.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.95 % Problem : SEU557^1 : TPTP v9.2.0. Bugfixed v4.0.0.
% 0.12/1.04 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.uBmM66s48H true
% 0.15/1.45 % Computer : n023.cluster.edu
% 0.15/1.45 % Model : x86_64 x86_64
% 0.15/1.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/1.45 % Memory : 8042.1875MB
% 0.15/1.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/1.45 % CPULimit : 300
% 0.15/1.45 % WCLimit : 300
% 0.15/1.45 % DateTime : Wed Oct 1 16:13:39 EDT 2025
% 0.19/1.46 % CPUTime :
% 0.19/1.46 % Running portfolio for 300 s
% 0.19/1.46 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/1.48 % Number of cores: 8
% 0.19/1.49 % Python version: Python 3.6.8
% 0.19/1.51 % Running in HO mode
% 0.31/2.20 % Total configuration time : 828
% 0.31/2.20 % Estimated wc time : 1656
% 0.31/2.20 % Estimated cpu time (8 cpus) : 207.0
% 1.42/2.53 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 1.42/2.55 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.42/2.56 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.42/2.59 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.53/2.68 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.54/2.70 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.55/2.71 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.55/2.73 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 8.68/4.85 % Solved by lams/40_noforms.sh.
% 8.68/4.85 % done 124 iterations in 1.898s
% 8.68/4.85 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 8.68/4.85 % SZS output start Refutation
% 8.68/4.85 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 8.68/4.85 thf(notdexE_type, type, notdexE: $o).
% 8.68/4.85 thf(setunionAx_type, type, setunionAx: $o).
% 8.68/4.85 thf(powersetE_type, type, powersetE: $o).
% 8.68/4.85 thf(omegaSAx_type, type, omegaSAx: $o).
% 8.68/4.85 thf(exuI1_type, type, exuI1: $o).
% 8.68/4.85 thf(exuI2_type, type, exuI2: $o).
% 8.68/4.85 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $i > $o).
% 8.68/4.85 thf(sk__231_type, type, sk__231: $i).
% 8.68/4.85 thf(zip_tseitin_3_type, type, zip_tseitin_3: $i > $i > $i > ($i > $i > $o) > $o).
% 8.68/4.85 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 8.68/4.85 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 8.68/4.85 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 8.68/4.85 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 8.68/4.85 thf(setext_type, type, setext: $o).
% 8.68/4.85 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 8.68/4.85 thf(in_type, type, in: $i > $i > $o).
% 8.68/4.85 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 8.68/4.85 thf(zip_tseitin_4_type, type, zip_tseitin_4: $i > $i > ($i > $o) > $o).
% 8.68/4.85 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 8.68/4.85 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 8.68/4.85 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 8.68/4.85 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 8.68/4.85 thf(setbeta_type, type, setbeta: $o).
% 8.68/4.85 thf(eqinunit_type, type, eqinunit: $o).
% 8.68/4.85 thf(upairsetIL_type, type, upairsetIL: $o).
% 8.68/4.85 thf(sk__229_type, type, sk__229: $i).
% 8.68/4.85 thf(powersetAx_type, type, powersetAx: $o).
% 8.68/4.85 thf(powersetI_type, type, powersetI: $o).
% 8.68/4.85 thf(upairsetIR_type, type, upairsetIR: $o).
% 8.68/4.85 thf(inCongP_type, type, inCongP: $o).
% 8.68/4.85 thf(sk__228_type, type, sk__228: $i > $o).
% 8.68/4.85 thf(exuE3e_type, type, exuE3e: $o).
% 8.68/4.85 thf(emptysetE_type, type, emptysetE: $o).
% 8.68/4.85 thf(setunionI_type, type, setunionI: $o).
% 8.68/4.85 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 8.68/4.85 thf(prop2setI_type, type, prop2setI: $o).
% 8.68/4.85 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 8.68/4.85 thf(exuE2_type, type, exuE2: $o).
% 8.68/4.85 thf(emptyset_type, type, emptyset: $i).
% 8.68/4.85 thf(subPowSU_type, type, subPowSU: $o).
% 8.68/4.85 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 8.68/4.85 thf(notinemptyset_type, type, notinemptyset: $o).
% 8.68/4.85 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 8.68/4.85 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 8.68/4.85 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 8.68/4.85 thf(setunionE_type, type, setunionE: $o).
% 8.68/4.85 thf(zip_tseitin_5_type, type, zip_tseitin_5: $i > ($i > $o) > $o).
% 8.68/4.85 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 8.68/4.85 thf(setadjoinE_type, type, setadjoinE: $o).
% 8.68/4.85 thf(descr_type, type, descr: ($i > $o) > $i).
% 8.68/4.85 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 8.68/4.85 thf(exuE1_type, type, exuE1: $o).
% 8.68/4.85 thf(prop2set_type, type, prop2set: $o > $i).
% 8.68/4.85 thf(notinsingleton_type, type, notinsingleton: $o).
% 8.68/4.85 thf(exuEu_type, type, exuEu: $o).
% 8.68/4.85 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 8.68/4.85 thf(upairsetE_type, type, upairsetE: $o).
% 8.68/4.85 thf(omega0Ax_type, type, omega0Ax: $o).
% 8.68/4.85 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 8.68/4.85 thf(setextAx_type, type, setextAx: $o).
% 8.68/4.85 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 8.68/4.85 thf(setunion_type, type, setunion: $i > $i).
% 8.68/4.85 thf(sk__230_type, type, sk__230: $i > $o).
% 8.68/4.85 thf(descrp_type, type, descrp: $o).
% 8.68/4.85 thf(foundationAx_type, type, foundationAx: $o).
% 8.68/4.85 thf(emptysetAx_type, type, emptysetAx: $o).
% 8.68/4.85 thf(emptyI_type, type, emptyI: $o).
% 8.68/4.85 thf(zip_tseitin_2_type, type, zip_tseitin_2: $i > $i > $i > $o).
% 8.68/4.85 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 8.68/4.85 thf(emptyE1_type, type, emptyE1: $o).
% 8.68/4.85 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 8.68/4.85 thf(vacuousDall_type, type, vacuousDall: $o).
% 8.68/4.85 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 8.68/4.85 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 8.68/4.85 thf(exu_type, type, exu: ($i > $o) > $o).
% 8.68/4.85 thf('#sk1_type', type, '#sk1': $i).
% 8.68/4.85 thf(omega__Cong_type, type, omega__Cong: $o).
% 8.68/4.85 thf(uniqinunit_type, type, uniqinunit: $o).
% 8.68/4.85 thf(prop2setE_type, type, prop2setE: $o).
% 8.68/4.85 thf(omega_type, type, omega: $i).
% 8.68/4.85 thf(nonemptyI_type, type, nonemptyI: $o).
% 8.68/4.85 thf(exuE3u_type, type, exuE3u: $o).
% 8.68/4.85 thf(exuI3_type, type, exuI3: $o).
% 8.68/4.85 thf(notdallE_type, type, notdallE: $o).
% 8.68/4.85 thf(powerset_type, type, powerset: $i > $i).
% 8.68/4.85 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 8.68/4.85 thf(nonempty_type, type, nonempty: $i > $o).
% 8.68/4.85 thf(set2prop_type, type, set2prop: $i > $o).
% 8.68/4.85 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 8.68/4.85 thf(exu__Cong_type, type, exu__Cong: $o).
% 8.68/4.85 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 8.68/4.85 thf(replAx_type, type, replAx: $o).
% 8.68/4.85 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 8.68/4.85 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 8.68/4.85 thf(in__Cong_type, type, in__Cong: $o).
% 8.68/4.85 thf(exuEu, axiom, exuEu =
% 8.68/4.85 (![Xphi:( $i > $o )]:
% 8.68/4.85 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 8.68/4.85 ( ![Xx:$i,Xy:$i]:
% 8.68/4.85 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ))).
% 8.68/4.85 thf('0', plain,
% 8.68/4.85 (( exuEu ) =
% 8.68/4.85 ( ![X4:( $i > $o )]:
% 8.68/4.85 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 8.68/4.85 ( ![X6:$i,X8:$i]:
% 8.68/4.85 ( ( X4 @ X6 ) => ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(omega__Cong, axiom, omega__Cong = (( omega ) = ( omega ))).
% 8.68/4.85 thf('1', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(setunion__Cong, axiom, setunion__Cong =
% 8.68/4.85 (![A:$i,B:$i]:
% 8.68/4.85 ( ( ( A ) = ( B ) ) => ( ( setunion @ A ) = ( setunion @ B ) ) ))).
% 8.68/4.85 thf('2', plain,
% 8.68/4.85 (( setunion__Cong ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( ( X4 ) = ( X6 ) ) => ( ( setunion @ X4 ) = ( setunion @ X6 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(powerset__Cong, axiom, powerset__Cong =
% 8.68/4.85 (![A:$i,B:$i]:
% 8.68/4.85 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 8.68/4.85 thf('3', plain,
% 8.68/4.85 (( powerset__Cong ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(setadjoin__Cong, axiom, setadjoin__Cong =
% 8.68/4.85 (![Xx:$i,Xy:$i]:
% 8.68/4.85 ( ( ( Xx ) = ( Xy ) ) =>
% 8.68/4.85 ( ![Xz:$i,Xu:$i]:
% 8.68/4.85 ( ( ( Xz ) = ( Xu ) ) =>
% 8.68/4.85 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))).
% 8.68/4.85 thf('4', plain,
% 8.68/4.85 (( setadjoin__Cong ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( ( X4 ) = ( X6 ) ) =>
% 8.68/4.85 ( ![X8:$i,X10:$i]:
% 8.68/4.85 ( ( ( X8 ) = ( X10 ) ) =>
% 8.68/4.85 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(emptyset__Cong, axiom, emptyset__Cong = (( emptyset ) = ( emptyset ))).
% 8.68/4.85 thf('5', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(exu__Cong, axiom, exu__Cong =
% 8.68/4.85 (![Xphi:( $i > $o ),Xpsi:( $i > $o )]:
% 8.68/4.85 ( ( ![Xx:$i,Xy:$i]:
% 8.68/4.85 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) =>
% 8.68/4.85 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) <=>
% 8.68/4.85 ( exu @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ))).
% 8.68/4.85 thf('6', plain,
% 8.68/4.85 (( exu__Cong ) =
% 8.68/4.85 ( ![X4:( $i > $o ),X6:( $i > $o )]:
% 8.68/4.85 ( ( ![X8:$i,X10:$i]:
% 8.68/4.85 ( ( ( X8 ) = ( X10 ) ) => ( ( X4 @ X8 ) <=> ( X6 @ X10 ) ) ) ) =>
% 8.68/4.85 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) <=>
% 8.68/4.85 ( exu @ ( ^[V_2:$i]: ( X6 @ V_2 ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(exuE3u, axiom, exuE3u =
% 8.68/4.85 (![Xphi:( $i > $o )]:
% 8.68/4.85 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 8.68/4.85 ( ![Xx:$i,Xy:$i]:
% 8.68/4.85 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ))).
% 8.68/4.85 thf('7', plain,
% 8.68/4.85 (( exuE3u ) =
% 8.68/4.85 ( ![X4:( $i > $o )]:
% 8.68/4.85 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 8.68/4.85 ( ![X6:$i,X8:$i]:
% 8.68/4.85 ( ( X4 @ X6 ) => ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(in__Cong, axiom, in__Cong =
% 8.68/4.85 (![A:$i,B:$i]:
% 8.68/4.85 ( ( ( A ) = ( B ) ) =>
% 8.68/4.85 ( ![Xx:$i,Xy:$i]:
% 8.68/4.85 ( ( ( Xx ) = ( Xy ) ) => ( ( in @ Xx @ A ) <=> ( in @ Xy @ B ) ) ) ) ))).
% 8.68/4.85 thf('8', plain,
% 8.68/4.85 (( in__Cong ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( ( X4 ) = ( X6 ) ) =>
% 8.68/4.85 ( ![X8:$i,X10:$i]:
% 8.68/4.85 ( ( ( X8 ) = ( X10 ) ) =>
% 8.68/4.85 ( ( in @ X8 @ X4 ) <=> ( in @ X10 @ X6 ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(inCongP, axiom, inCongP =
% 8.68/4.85 (![A:$i,B:$i]:
% 8.68/4.85 ( ( ( A ) = ( B ) ) =>
% 8.68/4.85 ( ![Xx:$i,Xy:$i]:
% 8.68/4.85 ( ( ( Xx ) = ( Xy ) ) => ( ( in @ Xx @ A ) => ( in @ Xy @ B ) ) ) ) ))).
% 8.68/4.85 thf('9', plain,
% 8.68/4.85 (( inCongP ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( ( X4 ) = ( X6 ) ) =>
% 8.68/4.85 ( ![X8:$i,X10:$i]:
% 8.68/4.85 ( ( ( X8 ) = ( X10 ) ) =>
% 8.68/4.85 ( ( in @ X8 @ X4 ) => ( in @ X10 @ X6 ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(exuI2, axiom, exuI2 =
% 8.68/4.85 (![Xphi:( $i > $o )]:
% 8.68/4.85 ( ( ?[Xx:$i]: ( ![Xy:$i]: ( ( Xphi @ Xy ) <=> ( ( Xy ) = ( Xx ) ) ) ) ) =>
% 8.68/4.85 ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ))).
% 8.68/4.85 thf('10', plain,
% 8.68/4.85 (( exuI2 ) =
% 8.68/4.85 ( ![X4:( $i > $o )]:
% 8.68/4.85 ( ( ?[X6:$i]: ( ![X8:$i]: ( ( X4 @ X8 ) <=> ( ( X8 ) = ( X6 ) ) ) ) ) =>
% 8.68/4.85 ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(exuI3, axiom, exuI3 =
% 8.68/4.85 (![Xphi:( $i > $o )]:
% 8.68/4.85 ( ( ?[Xx:$i]: ( Xphi @ Xx ) ) =>
% 8.68/4.85 ( ( ![Xx:$i,Xy:$i]:
% 8.68/4.85 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) =>
% 8.68/4.85 ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 8.68/4.85 thf('11', plain,
% 8.68/4.85 (( exuI3 ) =
% 8.68/4.85 ( ![X4:( $i > $o )]:
% 8.68/4.85 ( ( ?[X6:$i]: ( X4 @ X6 ) ) =>
% 8.68/4.85 ( ( ![X8:$i,X10:$i]:
% 8.68/4.85 ( ( X4 @ X8 ) => ( ( X4 @ X10 ) => ( ( X8 ) = ( X10 ) ) ) ) ) =>
% 8.68/4.85 ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(exuI1, axiom, exuI1 =
% 8.68/4.85 (![Xphi:( $i > $o )]:
% 8.68/4.85 ( ( ?[Xx:$i]:
% 8.68/4.85 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 8.68/4.85 ( Xphi @ Xx ) ) ) =>
% 8.68/4.85 ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ))).
% 8.68/4.85 thf('12', plain,
% 8.68/4.85 (( exuI1 ) =
% 8.68/4.85 ( ![X4:( $i > $o )]:
% 8.68/4.85 ( ( ?[X6:$i]:
% 8.68/4.85 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) &
% 8.68/4.85 ( X4 @ X6 ) ) ) =>
% 8.68/4.85 ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(notdallE, axiom, notdallE =
% 8.68/4.85 (![A:$i,Xphi:( $i > $o )]:
% 8.68/4.85 ( ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) =>
% 8.68/4.85 ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) ))).
% 8.68/4.85 thf('13', plain,
% 8.68/4.85 (( notdallE ) =
% 8.68/4.85 ( ![X4:$i,X6:( $i > $o )]:
% 8.68/4.85 ( ( ~( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( X6 @ X8 ) ) ) ) =>
% 8.68/4.85 ( ?[X10:$i]: ( ( ~( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(notdexE, axiom, notdexE =
% 8.68/4.85 (![A:$i,Xphi:( $i > $o )]:
% 8.68/4.85 ( ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) =>
% 8.68/4.85 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) ))).
% 8.68/4.85 thf('14', plain,
% 8.68/4.85 (( notdexE ) =
% 8.68/4.85 ( ![X4:$i,X6:( $i > $o )]:
% 8.68/4.85 ( ( ~( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 8.68/4.85 ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( ~( X6 @ X10 ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(prop2set2propI, axiom, prop2set2propI =
% 8.68/4.85 (![Xphi:$o]: ( ( Xphi ) => ( set2prop @ ( prop2set @ Xphi ) ) ))).
% 8.68/4.85 thf('15', plain,
% 8.68/4.85 (( prop2set2propI ) =
% 8.68/4.85 ( ![X4:$o]: ( ( X4 ) => ( set2prop @ ( prop2set @ X4 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(prop2setI, axiom, prop2setI =
% 8.68/4.85 (![Xphi:$o]: ( ( Xphi ) => ( in @ emptyset @ ( prop2set @ Xphi ) ) ))).
% 8.68/4.85 thf('16', plain,
% 8.68/4.85 (( prop2setI ) =
% 8.68/4.85 ( ![X4:$o]: ( ( X4 ) => ( in @ emptyset @ ( prop2set @ X4 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(quantDeMorgan4, axiom, quantDeMorgan4 =
% 8.68/4.85 (![A:$i,Xphi:( $i > $o )]:
% 8.68/4.85 ( ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) =>
% 8.68/4.85 ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) ))).
% 8.68/4.85 thf('17', plain,
% 8.68/4.85 (( quantDeMorgan4 ) =
% 8.68/4.85 ( ![X4:$i,X6:( $i > $o )]:
% 8.68/4.85 ( ( ?[X8:$i]: ( ( ~( X6 @ X8 ) ) & ( in @ X8 @ X4 ) ) ) =>
% 8.68/4.85 ( ~( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( X6 @ X10 ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(quantDeMorgan3, axiom, quantDeMorgan3 =
% 8.68/4.85 (![A:$i,Xphi:( $i > $o )]:
% 8.68/4.85 ( ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) =>
% 8.68/4.85 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) ))).
% 8.68/4.85 thf('18', plain,
% 8.68/4.85 (( quantDeMorgan3 ) =
% 8.68/4.85 ( ![X4:$i,X6:( $i > $o )]:
% 8.68/4.85 ( ( ~( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 8.68/4.85 ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( ~( X6 @ X10 ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(quantDeMorgan2, axiom, quantDeMorgan2 =
% 8.68/4.85 (![A:$i,Xphi:( $i > $o )]:
% 8.68/4.85 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) =>
% 8.68/4.85 ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) ))).
% 8.68/4.85 thf('19', plain,
% 8.68/4.85 (( quantDeMorgan2 ) =
% 8.68/4.85 ( ![X4:$i,X6:( $i > $o )]:
% 8.68/4.85 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( ~( X6 @ X8 ) ) ) ) =>
% 8.68/4.85 ( ~( ?[X10:$i]: ( ( X6 @ X10 ) & ( in @ X10 @ X4 ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(quantDeMorgan1, axiom, quantDeMorgan1 =
% 8.68/4.85 (![A:$i,Xphi:( $i > $o )]:
% 8.68/4.85 ( ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) =>
% 8.68/4.85 ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) ))).
% 8.68/4.85 thf('20', plain,
% 8.68/4.85 (( quantDeMorgan1 ) =
% 8.68/4.85 ( ![X4:$i,X6:( $i > $o )]:
% 8.68/4.85 ( ( ~( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( X6 @ X8 ) ) ) ) =>
% 8.68/4.85 ( ?[X10:$i]: ( ( ~( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(vacuousDall, axiom, vacuousDall =
% 8.68/4.85 (![Xphi:( $i > $o ),Xx:$i]: ( ( in @ Xx @ emptyset ) => ( Xphi @ Xx ) ))).
% 8.68/4.85 thf('21', plain,
% 8.68/4.85 (( vacuousDall ) =
% 8.68/4.85 ( ![X4:( $i > $o ),X6:$i]: ( ( in @ X6 @ emptyset ) => ( X4 @ X6 ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(emptyE1, axiom, emptyE1 =
% 8.68/4.85 (![A:$i,Xphi:( $i > $o )]:
% 8.68/4.85 ( ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) =>
% 8.68/4.85 ( ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) = ( emptyset ) ) =>
% 8.68/4.85 ( $false ) ) ))).
% 8.68/4.85 thf('22', plain,
% 8.68/4.85 (( emptyE1 ) =
% 8.68/4.85 ( ![X4:$i,X6:( $i > $o )]:
% 8.68/4.85 ( ( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) =>
% 8.68/4.85 ( ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) = ( emptyset ) ) =>
% 8.68/4.85 ( $false ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(upairsetIR, axiom, upairsetIR =
% 8.68/4.85 (![Xx:$i,Xy:$i]:
% 8.68/4.85 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 8.68/4.85 thf('23', plain,
% 8.68/4.85 (( upairsetIR ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(upairsetIL, axiom, upairsetIL =
% 8.68/4.85 (![Xx:$i,Xy:$i]:
% 8.68/4.85 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 8.68/4.85 thf('24', plain,
% 8.68/4.85 (( upairsetIL ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(upairsetE, axiom, upairsetE =
% 8.68/4.85 (![Xx:$i,Xy:$i,Xz:$i]:
% 8.68/4.85 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 8.68/4.85 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 8.68/4.85 thf('25', plain,
% 8.68/4.85 (( upairsetE ) =
% 8.68/4.85 ( ![X4:$i,X6:$i,X8:$i]:
% 8.68/4.85 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 8.68/4.85 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(singletonsswitch, axiom, singletonsswitch =
% 8.68/4.85 (![Xx:$i,Xy:$i]:
% 8.68/4.85 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 8.68/4.85 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 8.68/4.85 thf('26', plain,
% 8.68/4.85 (( singletonsswitch ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 8.68/4.85 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(eqinunit, axiom, eqinunit =
% 8.68/4.85 (![Xx:$i,Xy:$i]:
% 8.68/4.85 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 8.68/4.85 thf('27', plain,
% 8.68/4.85 (( eqinunit ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(notinsingleton, axiom, notinsingleton =
% 8.68/4.85 (![Xx:$i,Xy:$i]:
% 8.68/4.85 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 8.68/4.85 thf('28', plain,
% 8.68/4.85 (( notinsingleton ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( ( X4 ) != ( X6 ) ) =>
% 8.68/4.85 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(uniqinunit, axiom, uniqinunit =
% 8.68/4.85 (![Xx:$i,Xy:$i]:
% 8.68/4.85 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 8.68/4.85 thf('29', plain,
% 8.68/4.85 (( uniqinunit ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(nonemptyImpWitness, axiom, nonemptyImpWitness =
% 8.68/4.85 (![A:$i]: ( ( nonempty @ A ) => ( ?[Xx:$i]: ( in @ Xx @ A ) ) ))).
% 8.68/4.85 thf('30', plain,
% 8.68/4.85 (( nonemptyImpWitness ) =
% 8.68/4.85 ( ![X4:$i]: ( ( nonempty @ X4 ) => ( ?[X6:$i]: ( in @ X6 @ X4 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(exuE2, axiom, exuE2 =
% 8.68/4.85 (![Xphi:( $i > $o )]:
% 8.68/4.85 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 8.68/4.85 ( ?[Xx:$i]: ( ![Xy:$i]: ( ( Xphi @ Xy ) <=> ( ( Xy ) = ( Xx ) ) ) ) ) ))).
% 8.68/4.85 thf('31', plain,
% 8.68/4.85 (( exuE2 ) =
% 8.68/4.85 ( ![X4:( $i > $o )]:
% 8.68/4.85 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 8.68/4.85 ( ?[X6:$i]: ( ![X8:$i]: ( ( X4 @ X8 ) <=> ( ( X8 ) = ( X6 ) ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(subPowSU, axiom, subPowSU =
% 8.68/4.85 (![A:$i,Xx:$i]:
% 8.68/4.85 ( ( in @ Xx @ A ) => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ))).
% 8.68/4.85 thf('32', plain,
% 8.68/4.85 (( subPowSU ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( in @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ ( setunion @ X4 ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(setunionE, axiom, setunionE =
% 8.68/4.85 (![A:$i,Xx:$i]:
% 8.68/4.85 ( ( in @ Xx @ ( setunion @ A ) ) =>
% 8.68/4.85 ( ![Xphi:$o]:
% 8.68/4.85 ( ( ![B:$i]: ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( Xphi ) ) ) ) =>
% 8.68/4.85 ( Xphi ) ) ) ))).
% 8.68/4.85 thf('33', plain,
% 8.68/4.85 (( setunionE ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( in @ X6 @ ( setunion @ X4 ) ) =>
% 8.68/4.85 ( ![X8:$o]:
% 8.68/4.85 ( ( ![X10:$i]:
% 8.68/4.85 ( ( in @ X6 @ X10 ) => ( ( in @ X10 @ X4 ) => ( X8 ) ) ) ) =>
% 8.68/4.85 ( X8 ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(setunionI, axiom, setunionI =
% 8.68/4.85 (![A:$i,Xx:$i,B:$i]:
% 8.68/4.85 ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( in @ Xx @ ( setunion @ A ) ) ) ))).
% 8.68/4.85 thf('34', plain,
% 8.68/4.85 (( setunionI ) =
% 8.68/4.85 ( ![X4:$i,X6:$i,X8:$i]:
% 8.68/4.85 ( ( in @ X6 @ X8 ) =>
% 8.68/4.85 ( ( in @ X8 @ X4 ) => ( in @ X6 @ ( setunion @ X4 ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(powersetE, axiom, powersetE =
% 8.68/4.85 (![A:$i,B:$i,Xx:$i]:
% 8.68/4.85 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 8.68/4.85 thf('35', plain,
% 8.68/4.85 (( powersetE ) =
% 8.68/4.85 ( ![X4:$i,X6:$i,X8:$i]:
% 8.68/4.85 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 8.68/4.85 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(emptyInPowerset, axiom, emptyInPowerset =
% 8.68/4.85 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 8.68/4.85 thf('36', plain,
% 8.68/4.85 (( emptyInPowerset ) =
% 8.68/4.85 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(emptyinPowerset, axiom, emptyinPowerset =
% 8.68/4.85 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 8.68/4.85 thf('37', plain,
% 8.68/4.85 (( emptyinPowerset ) =
% 8.68/4.85 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(powersetI, axiom, powersetI =
% 8.68/4.85 (![A:$i,B:$i]:
% 8.68/4.85 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 8.68/4.85 ( in @ B @ ( powerset @ A ) ) ))).
% 8.68/4.85 thf('38', plain,
% 8.68/4.85 (( powersetI ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 8.68/4.85 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(setoftrueEq, axiom, setoftrueEq =
% 8.68/4.85 (![A:$i]: ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( $true ) ) ) = ( A ) ))).
% 8.68/4.85 thf('39', plain,
% 8.68/4.85 (( setoftrueEq ) =
% 8.68/4.85 ( ![X4:$i]: ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( $true ) ) ) = ( X4 ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(setadjoinOr, axiom, setadjoinOr =
% 8.68/4.85 (![Xx:$i,A:$i,Xy:$i]:
% 8.68/4.85 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 8.68/4.85 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 8.68/4.85 thf('40', plain,
% 8.68/4.85 (( setadjoinOr ) =
% 8.68/4.85 ( ![X4:$i,X6:$i,X8:$i]:
% 8.68/4.85 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 8.68/4.85 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(setadjoinE, axiom, setadjoinE =
% 8.68/4.85 (![Xx:$i,A:$i,Xy:$i]:
% 8.68/4.85 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 8.68/4.85 ( ![Xphi:$o]:
% 8.68/4.85 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 8.68/4.85 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 8.68/4.85 thf('41', plain,
% 8.68/4.85 (( setadjoinE ) =
% 8.68/4.85 ( ![X4:$i,X6:$i,X8:$i]:
% 8.68/4.85 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 8.68/4.85 ( ![X10:$o]:
% 8.68/4.85 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 8.68/4.85 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(setadjoinIR, axiom, setadjoinIR =
% 8.68/4.85 (![Xx:$i,A:$i,Xy:$i]:
% 8.68/4.85 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 8.68/4.85 thf('42', plain,
% 8.68/4.85 (( setadjoinIR ) =
% 8.68/4.85 ( ![X4:$i,X6:$i,X8:$i]:
% 8.68/4.85 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 8.68/4.85 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 8.68/4.85 thf('43', plain,
% 8.68/4.85 (( emptyinunitempty ) =
% 8.68/4.85 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 8.68/4.85 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 8.68/4.85 thf('44', plain,
% 8.68/4.85 (( emptyinunitempty ) =
% 8.68/4.85 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(setadjoinIL, axiom, setadjoinIL =
% 8.68/4.85 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 8.68/4.85 thf('45', plain,
% 8.68/4.85 (( setadjoinIL ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(nonemptyI1, axiom, nonemptyI1 =
% 8.68/4.85 (![A:$i]: ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) => ( nonempty @ A ) ))).
% 8.68/4.85 thf('46', plain,
% 8.68/4.85 (( nonemptyI1 ) =
% 8.68/4.85 ( ![X4:$i]: ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) => ( nonempty @ X4 ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(nonemptyI, axiom, nonemptyI =
% 8.68/4.85 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 8.68/4.85 ( ( in @ Xx @ A ) =>
% 8.68/4.85 ( ( Xphi @ Xx ) =>
% 8.68/4.85 ( nonempty @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 8.68/4.85 thf('47', plain,
% 8.68/4.85 (( nonemptyI ) =
% 8.68/4.85 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 8.68/4.85 ( ( in @ X8 @ X4 ) =>
% 8.68/4.85 ( ( X6 @ X8 ) =>
% 8.68/4.85 ( nonempty @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(nonemptyE1, axiom, nonemptyE1 =
% 8.68/4.85 (![A:$i]: ( ( nonempty @ A ) => ( ?[Xx:$i]: ( in @ Xx @ A ) ) ))).
% 8.68/4.85 thf('48', plain,
% 8.68/4.85 (( nonemptyE1 ) =
% 8.68/4.85 ( ![X4:$i]: ( ( nonempty @ X4 ) => ( ?[X6:$i]: ( in @ X6 @ X4 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(nonempty, axiom,(( nonempty ) = (^[Xx:$i]: ( ( Xx ) != ( emptyset ) )))).
% 8.68/4.85 thf('49', plain, (( nonempty ) = ( ^[Xx:$i]: ( ( Xx ) != ( emptyset ) ) )),
% 8.68/4.85 inference('simplify_rw_rule', [status(thm)], [nonempty])).
% 8.68/4.85 thf('50', plain, (( nonempty ) = ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(setbeta, axiom, setbeta =
% 8.68/4.85 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 8.68/4.85 ( ( in @ Xx @ A ) =>
% 8.68/4.85 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) <=>
% 8.68/4.85 ( Xphi @ Xx ) ) ))).
% 8.68/4.85 thf('51', plain,
% 8.68/4.85 (( setbeta ) =
% 8.68/4.85 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 8.68/4.85 ( ( in @ X8 @ X4 ) =>
% 8.68/4.85 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) <=>
% 8.68/4.85 ( X6 @ X8 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(noeltsimpempty, axiom, noeltsimpempty =
% 8.68/4.85 (![A:$i]:
% 8.68/4.85 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 8.68/4.85 thf('52', plain,
% 8.68/4.85 (( noeltsimpempty ) =
% 8.68/4.85 ( ![X4:$i]:
% 8.68/4.85 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(emptyI, axiom, emptyI =
% 8.68/4.85 (![A:$i]:
% 8.68/4.85 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 8.68/4.85 thf('53', plain,
% 8.68/4.85 (( emptyI ) =
% 8.68/4.85 ( ![X4:$i]:
% 8.68/4.85 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(setext, axiom, setext =
% 8.68/4.85 (![A:$i,B:$i]:
% 8.68/4.85 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 8.68/4.85 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 8.68/4.85 ( ( A ) = ( B ) ) ) ))).
% 8.68/4.85 thf('54', plain,
% 8.68/4.85 (( setext ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 8.68/4.85 ( ( ![X10:$i]: ( ( in @ X10 @ X6 ) => ( in @ X10 @ X4 ) ) ) =>
% 8.68/4.85 ( ( X4 ) = ( X6 ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(exuE3e, axiom, exuE3e =
% 8.68/4.85 (![Xphi:( $i > $o )]:
% 8.68/4.85 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) => ( ?[Xx:$i]: ( Xphi @ Xx ) ) ))).
% 8.68/4.85 thf('55', plain,
% 8.68/4.85 (( exuE3e ) =
% 8.68/4.85 ( ![X4:( $i > $o )]:
% 8.68/4.85 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) => ( ?[X6:$i]: ( X4 @ X6 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(notinemptyset, axiom, notinemptyset =
% 8.68/4.85 (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 8.68/4.85 thf('56', plain,
% 8.68/4.85 (( notinemptyset ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(emptysetimpfalse, axiom, emptysetimpfalse =
% 8.68/4.85 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( $false ) ))).
% 8.68/4.85 thf('57', plain,
% 8.68/4.85 (( emptysetimpfalse ) =
% 8.68/4.85 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( $false ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(emptysetE, axiom, emptysetE =
% 8.68/4.85 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( ![Xphi:$o]: ( Xphi ) ) ))).
% 8.68/4.85 thf('58', plain,
% 8.68/4.85 (( emptysetE ) =
% 8.68/4.85 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( ![X6:$o]: ( X6 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(prop2setE, axiom, prop2setE =
% 8.68/4.85 (![Xphi:$o,Xx:$i]: ( ( in @ Xx @ ( prop2set @ Xphi ) ) => ( Xphi ) ))).
% 8.68/4.85 thf('59', plain,
% 8.68/4.85 (( prop2setE ) =
% 8.68/4.85 ( ![X4:$o,X6:$i]: ( ( in @ X6 @ ( prop2set @ X4 ) ) => ( X4 ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(exuE1, axiom, exuE1 =
% 8.68/4.85 (![Xphi:( $i > $o )]:
% 8.68/4.85 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 8.68/4.85 ( ?[Xx:$i]:
% 8.68/4.85 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 8.68/4.85 ( Xphi @ Xx ) ) ) ))).
% 8.68/4.85 thf('60', plain,
% 8.68/4.85 (( exuE1 ) =
% 8.68/4.85 ( ![X4:( $i > $o )]:
% 8.68/4.85 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 8.68/4.85 ( ?[X6:$i]:
% 8.68/4.85 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) &
% 8.68/4.85 ( X4 @ X6 ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(dsetconstrER, axiom, dsetconstrER =
% 8.68/4.85 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 8.68/4.85 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 8.68/4.85 ( Xphi @ Xx ) ))).
% 8.68/4.85 thf('61', plain,
% 8.68/4.85 (( dsetconstrER ) =
% 8.68/4.85 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 8.68/4.85 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 8.68/4.85 ( X6 @ X8 ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(dsetconstrEL, axiom, dsetconstrEL =
% 8.68/4.85 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 8.68/4.85 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 8.68/4.85 ( in @ Xx @ A ) ))).
% 8.68/4.85 thf('62', plain,
% 8.68/4.85 (( dsetconstrEL ) =
% 8.68/4.85 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 8.68/4.85 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 8.68/4.85 ( in @ X8 @ X4 ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(dsetconstrI, axiom, dsetconstrI =
% 8.68/4.85 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 8.68/4.85 ( ( in @ Xx @ A ) =>
% 8.68/4.85 ( ( Xphi @ Xx ) =>
% 8.68/4.85 ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 8.68/4.85 thf('63', plain,
% 8.68/4.85 (( dsetconstrI ) =
% 8.68/4.85 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 8.68/4.85 ( ( in @ X8 @ X4 ) =>
% 8.68/4.85 ( ( X6 @ X8 ) =>
% 8.68/4.85 ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(descrp, axiom, descrp =
% 8.68/4.85 (![Xphi:( $i > $o )]:
% 8.68/4.85 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 8.68/4.85 ( Xphi @ ( descr @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 8.68/4.85 thf('64', plain,
% 8.68/4.85 (( descrp ) =
% 8.68/4.85 ( ![X4:( $i > $o )]:
% 8.68/4.85 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 8.68/4.85 ( X4 @ ( descr @ ( ^[V_2:$i]: ( X4 @ V_2 ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(wellorderingAx, axiom, wellorderingAx =
% 8.68/4.85 (![A:$i]:
% 8.68/4.85 ( ?[B:$i]:
% 8.68/4.85 ( ( ![C:$i]:
% 8.68/4.85 ( ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) &
% 8.68/4.85 ( ?[Xx:$i]: ( in @ Xx @ C ) ) ) =>
% 8.68/4.85 ( ?[D:$i,Xx:$i]:
% 8.68/4.85 ( ( ![E:$i]:
% 8.68/4.85 ( ( in @ E @ B ) =>
% 8.68/4.85 ( ( ![Xy:$i]: ( ( in @ Xy @ E ) => ( in @ Xy @ D ) ) ) |
% 8.68/4.85 ( in @ Xx @ E ) ) ) ) &
% 8.68/4.85 ( ~( ?[Xy:$i]: ( ( in @ Xy @ C ) & ( in @ Xy @ D ) ) ) ) &
% 8.68/4.85 ( in @ Xx @ C ) & ( in @ D @ B ) ) ) ) ) &
% 8.68/4.85 ( ![C:$i,D:$i]:
% 8.68/4.85 ( ( ( in @ C @ B ) & ( in @ D @ B ) ) =>
% 8.68/4.85 ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ D ) ) ) |
% 8.68/4.85 ( ![Xx:$i]: ( ( in @ Xx @ D ) => ( in @ Xx @ C ) ) ) ) ) ) &
% 8.68/4.85 ( ![Xx:$i,Xy:$i]:
% 8.68/4.85 ( ( ( in @ Xx @ A ) & ( in @ Xy @ A ) ) =>
% 8.68/4.85 ( ( ![C:$i]:
% 8.68/4.85 ( ( in @ C @ B ) => ( ( in @ Xx @ C ) <=> ( in @ Xy @ C ) ) ) ) =>
% 8.68/4.85 ( ( Xx ) = ( Xy ) ) ) ) ) &
% 8.68/4.85 ( ![C:$i]:
% 8.68/4.85 ( ( in @ C @ B ) =>
% 8.68/4.85 ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) ) ) ) ))).
% 8.68/4.85 thf('65', plain,
% 8.68/4.85 (( wellorderingAx ) =
% 8.68/4.85 ( ![X4:$i]:
% 8.68/4.85 ( ?[X6:$i]:
% 8.68/4.85 ( ( ![X8:$i]:
% 8.68/4.85 ( ( ( ![X10:$i]: ( ( in @ X10 @ X8 ) => ( in @ X10 @ X4 ) ) ) &
% 8.68/4.85 ( ?[X12:$i]: ( in @ X12 @ X8 ) ) ) =>
% 8.68/4.85 ( ?[X14:$i,X16:$i]:
% 8.68/4.85 ( ( ![X18:$i]:
% 8.68/4.85 ( ( in @ X18 @ X6 ) =>
% 8.68/4.85 ( ( ![X20:$i]:
% 8.68/4.85 ( ( in @ X20 @ X18 ) => ( in @ X20 @ X14 ) ) ) |
% 8.68/4.85 ( in @ X16 @ X18 ) ) ) ) &
% 8.68/4.85 ( ~( ?[X22:$i]: ( ( in @ X22 @ X8 ) & ( in @ X22 @ X14 ) ) ) ) &
% 8.68/4.85 ( in @ X16 @ X8 ) & ( in @ X14 @ X6 ) ) ) ) ) &
% 8.68/4.85 ( ![X24:$i,X26:$i]:
% 8.68/4.85 ( ( ( in @ X24 @ X6 ) & ( in @ X26 @ X6 ) ) =>
% 8.68/4.85 ( ( ![X28:$i]: ( ( in @ X28 @ X24 ) => ( in @ X28 @ X26 ) ) ) |
% 8.68/4.85 ( ![X30:$i]: ( ( in @ X30 @ X26 ) => ( in @ X30 @ X24 ) ) ) ) ) ) &
% 8.68/4.85 ( ![X32:$i,X34:$i]:
% 8.68/4.85 ( ( ( in @ X32 @ X4 ) & ( in @ X34 @ X4 ) ) =>
% 8.68/4.85 ( ( ![X36:$i]:
% 8.68/4.85 ( ( in @ X36 @ X6 ) =>
% 8.68/4.85 ( ( in @ X32 @ X36 ) <=> ( in @ X34 @ X36 ) ) ) ) =>
% 8.68/4.85 ( ( X32 ) = ( X34 ) ) ) ) ) &
% 8.68/4.85 ( ![X38:$i]:
% 8.68/4.85 ( ( in @ X38 @ X6 ) =>
% 8.68/4.85 ( ![X40:$i]: ( ( in @ X40 @ X38 ) => ( in @ X40 @ X4 ) ) ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(foundationAx, axiom, foundationAx =
% 8.68/4.85 (![A:$i]:
% 8.68/4.85 ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) =>
% 8.68/4.85 ( ?[B:$i]:
% 8.68/4.85 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ A ) & ( in @ Xx @ B ) ) ) ) &
% 8.68/4.85 ( in @ B @ A ) ) ) ))).
% 8.68/4.85 thf('66', plain,
% 8.68/4.85 (( foundationAx ) =
% 8.68/4.85 ( ![X4:$i]:
% 8.68/4.85 ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) =>
% 8.68/4.85 ( ?[X8:$i]:
% 8.68/4.85 ( ( ~( ?[X10:$i]: ( ( in @ X10 @ X4 ) & ( in @ X10 @ X8 ) ) ) ) &
% 8.68/4.85 ( in @ X8 @ X4 ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(replAx, axiom, replAx =
% 8.68/4.85 (![Xphi:( $i > $i > $o ),A:$i]:
% 8.68/4.85 ( ( ![Xx:$i]:
% 8.68/4.85 ( ( in @ Xx @ A ) => ( exu @ ( ^[Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) ) ) =>
% 8.68/4.85 ( ?[B:$i]:
% 8.68/4.85 ( ![Xx:$i]:
% 8.68/4.85 ( ( in @ Xx @ B ) <=>
% 8.68/4.85 ( ?[Xy:$i]: ( ( Xphi @ Xy @ Xx ) & ( in @ Xy @ A ) ) ) ) ) ) ))).
% 8.68/4.85 thf('67', plain,
% 8.68/4.85 (( replAx ) =
% 8.68/4.85 ( ![X4:( $i > $i > $o ),X6:$i]:
% 8.68/4.85 ( ( ![X8:$i]:
% 8.68/4.85 ( ( in @ X8 @ X6 ) => ( exu @ ( ^[V_1:$i]: ( X4 @ X8 @ V_1 ) ) ) ) ) =>
% 8.68/4.85 ( ?[X10:$i]:
% 8.68/4.85 ( ![X12:$i]:
% 8.68/4.85 ( ( in @ X12 @ X10 ) <=>
% 8.68/4.85 ( ?[X14:$i]: ( ( X4 @ X14 @ X12 ) & ( in @ X14 @ X6 ) ) ) ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(omegaIndAx, axiom, omegaIndAx =
% 8.68/4.85 (![A:$i]:
% 8.68/4.85 ( ( ( in @ emptyset @ A ) &
% 8.68/4.85 ( ![Xx:$i]:
% 8.68/4.85 ( ( ( in @ Xx @ omega ) & ( in @ Xx @ A ) ) =>
% 8.68/4.85 ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) ) =>
% 8.68/4.85 ( ![Xx:$i]: ( ( in @ Xx @ omega ) => ( in @ Xx @ A ) ) ) ))).
% 8.68/4.85 thf('68', plain,
% 8.68/4.85 (( omegaIndAx ) =
% 8.68/4.85 ( ![X4:$i]:
% 8.68/4.85 ( ( ( in @ emptyset @ X4 ) &
% 8.68/4.85 ( ![X6:$i]:
% 8.68/4.85 ( ( ( in @ X6 @ omega ) & ( in @ X6 @ X4 ) ) =>
% 8.68/4.85 ( in @ ( setadjoin @ X6 @ X6 ) @ X4 ) ) ) ) =>
% 8.68/4.85 ( ![X8:$i]: ( ( in @ X8 @ omega ) => ( in @ X8 @ X4 ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(omegaSAx, axiom, omegaSAx =
% 8.68/4.85 (![Xx:$i]:
% 8.68/4.85 ( ( in @ Xx @ omega ) => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ))).
% 8.68/4.85 thf('69', plain,
% 8.68/4.85 (( omegaSAx ) =
% 8.68/4.85 ( ![X4:$i]:
% 8.68/4.85 ( ( in @ X4 @ omega ) => ( in @ ( setadjoin @ X4 @ X4 ) @ omega ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(omega0Ax, axiom,(( omega0Ax ) = (in @ emptyset @ omega))).
% 8.68/4.85 thf('70', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 8.68/4.85 inference('simplify_rw_rule', [status(thm)], [omega0Ax])).
% 8.68/4.85 thf('71', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(setunionAx, axiom, setunionAx =
% 8.68/4.85 (![A:$i,Xx:$i]:
% 8.68/4.85 ( ( in @ Xx @ ( setunion @ A ) ) <=>
% 8.68/4.85 ( ?[B:$i]: ( ( in @ B @ A ) & ( in @ Xx @ B ) ) ) ))).
% 8.68/4.85 thf('72', plain,
% 8.68/4.85 (( setunionAx ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( in @ X6 @ ( setunion @ X4 ) ) <=>
% 8.68/4.85 ( ?[X8:$i]: ( ( in @ X8 @ X4 ) & ( in @ X6 @ X8 ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(powersetAx, axiom, powersetAx =
% 8.68/4.85 (![A:$i,B:$i]:
% 8.68/4.85 ( ( in @ B @ ( powerset @ A ) ) <=>
% 8.68/4.85 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 8.68/4.85 thf('73', plain,
% 8.68/4.85 (( powersetAx ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 8.68/4.85 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(setadjoinAx, axiom, setadjoinAx =
% 8.68/4.85 (![Xx:$i,A:$i,Xy:$i]:
% 8.68/4.85 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 8.68/4.85 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 8.68/4.85 thf('74', plain,
% 8.68/4.85 (( setadjoinAx ) =
% 8.68/4.85 ( ![X4:$i,X6:$i,X8:$i]:
% 8.68/4.85 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 8.68/4.85 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(emptysetAx, axiom, emptysetAx = (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 8.68/4.85 thf('75', plain,
% 8.68/4.85 (( emptysetAx ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(setextAx, axiom, setextAx =
% 8.68/4.85 (![A:$i,B:$i]:
% 8.68/4.85 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) <=> ( in @ Xx @ B ) ) ) =>
% 8.68/4.85 ( ( A ) = ( B ) ) ))).
% 8.68/4.85 thf('76', plain,
% 8.68/4.85 (( setextAx ) =
% 8.68/4.85 ( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 8.68/4.85 ( ( X4 ) = ( X6 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(exu, axiom,(( exu ) =
% 8.68/4.85 (^[Xphi:( $i > $o )]:
% 8.68/4.85 ( ?[Xx:$i]:
% 8.68/4.85 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) & ( Xphi @ Xx ) ) )))).
% 8.68/4.85 thf('77', plain,
% 8.68/4.85 (( exu ) =
% 8.68/4.85 ( ^[Xphi:( $i > $o )]:
% 8.68/4.85 ( ?[Xx:$i]:
% 8.68/4.85 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 8.68/4.85 ( Xphi @ Xx ) ) ) )),
% 8.68/4.85 inference('simplify_rw_rule', [status(thm)], [exu])).
% 8.68/4.85 thf('78', plain,
% 8.68/4.85 (( exu ) =
% 8.68/4.85 ( ^[V_1:( $i > $o )]:
% 8.68/4.85 ( ?[X4:$i]:
% 8.68/4.85 ( ( ![X6:$i]: ( ( V_1 @ X6 ) => ( ( X4 ) = ( X6 ) ) ) ) &
% 8.68/4.85 ( V_1 @ X4 ) ) ) )),
% 8.68/4.85 define([status(thm)])).
% 8.68/4.85 thf(descr__Cong, conjecture,
% 8.68/4.85 (( setextAx ) =>
% 8.68/4.85 ( ( emptysetAx ) =>
% 8.68/4.85 ( ( setadjoinAx ) =>
% 8.68/4.85 ( ( powersetAx ) =>
% 8.68/4.85 ( ( setunionAx ) =>
% 8.68/4.85 ( ( omega0Ax ) =>
% 8.68/4.85 ( ( omegaSAx ) =>
% 8.68/4.85 ( ( omegaIndAx ) =>
% 8.68/4.85 ( ( replAx ) =>
% 8.68/4.85 ( ( foundationAx ) =>
% 8.68/4.85 ( ( wellorderingAx ) =>
% 8.68/4.85 ( ( descrp ) =>
% 8.68/4.85 ( ( dsetconstrI ) =>
% 8.68/4.85 ( ( dsetconstrEL ) =>
% 8.68/4.85 ( ( dsetconstrER ) =>
% 8.68/4.85 ( ( exuE1 ) =>
% 8.68/4.85 ( ( prop2setE ) =>
% 8.68/4.85 ( ( emptysetE ) =>
% 8.68/4.85 ( ( emptysetimpfalse ) =>
% 8.68/4.85 ( ( notinemptyset ) =>
% 8.68/4.85 ( ( exuE3e ) =>
% 8.68/4.85 ( ( setext ) =>
% 8.68/4.85 ( ( emptyI ) =>
% 8.68/4.85 ( ( noeltsimpempty ) =>
% 8.68/4.85 ( ( setbeta ) =>
% 8.68/4.85 ( ( nonemptyE1 ) =>
% 8.68/4.85 ( ( nonemptyI ) =>
% 8.68/4.85 ( ( nonemptyI1 ) =>
% 8.68/4.85 ( ( setadjoinIL ) =>
% 8.68/4.85 ( ( emptyinunitempty ) =>
% 8.68/4.85 ( ( setadjoinIR ) =>
% 8.68/4.85 ( ( setadjoinE ) =>
% 8.68/4.85 ( (
% 8.68/4.85 setadjoinOr ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 setoftrueEq ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 powersetI ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 emptyinPowerset ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 emptyInPowerset ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 powersetE ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 setunionI ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 setunionE ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 subPowSU ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 exuE2 ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 nonemptyImpWitness ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 uniqinunit ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 notinsingleton ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 eqinunit ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 singletonsswitch ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 upairsetE ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 upairsetIL ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 upairsetIR ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 emptyE1 ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 vacuousDall ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 quantDeMorgan1 ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 quantDeMorgan2 ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 quantDeMorgan3 ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 quantDeMorgan4 ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 prop2setI ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 prop2set2propI ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 notdexE ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 notdallE ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 exuI1 ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 exuI3 ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 exuI2 ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 inCongP ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 in__Cong ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 exuE3u ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 exu__Cong ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 emptyset__Cong ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 setadjoin__Cong ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 powerset__Cong ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 setunion__Cong ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 omega__Cong ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 exuEu ) =>
% 8.68/4.85 (
% 8.68/4.85 ![
% 8.68/4.85 Xphi:(
% 8.68/4.85 $i > $o ),
% 8.68/4.85 Xpsi:(
% 8.68/4.85 $i > $o )]:
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 ![
% 8.68/4.85 Xx:$i,
% 8.68/4.85 Xy:$i]:
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 Xx ) =
% 8.68/4.85 (
% 8.68/4.85 Xy ) ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 Xphi @ Xx ) <=>
% 8.68/4.85 (
% 8.68/4.85 Xpsi @ Xy ) ) ) ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 exu @
% 8.68/4.85 (
% 8.68/4.85 ^[
% 8.68/4.85 Xx:$i]:
% 8.68/4.85 (
% 8.68/4.85 Xphi @ Xx ) ) ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 exu @
% 8.68/4.85 (
% 8.68/4.85 ^[
% 8.68/4.85 Xx:$i]:
% 8.68/4.85 (
% 8.68/4.85 Xpsi @ Xx ) ) ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 descr @
% 8.68/4.85 (
% 8.68/4.85 ^[
% 8.68/4.85 Xx:$i]:
% 8.68/4.85 (
% 8.68/4.85 Xphi @ Xx ) ) ) =
% 8.68/4.85 (
% 8.68/4.85 descr @
% 8.68/4.85 (
% 8.68/4.85 ^[
% 8.68/4.85 Xx:$i]:
% 8.68/4.85 (
% 8.68/4.85 Xpsi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 8.68/4.85 thf(zf_stmt_0, conjecture,
% 8.68/4.85 (( ![X4:$i,X6:$i]:
% 8.68/4.85 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 8.68/4.85 ( ( X4 ) = ( X6 ) ) ) ) =>
% 8.68/4.85 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 8.68/4.85 ( ( ![X12:$i,X14:$i,X16:$i]:
% 8.68/4.85 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 8.68/4.85 ( ( in @ X16 @ X14 ) | ( ( X16 ) = ( X12 ) ) ) ) ) =>
% 8.68/4.85 ( ( ![X18:$i,X20:$i]:
% 8.68/4.85 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 8.68/4.85 ( ![X22:$i]: ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ) ) ) =>
% 8.68/4.85 ( ( ![X24:$i,X26:$i]:
% 8.68/4.85 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 8.68/4.85 ( ?[X28:$i]: ( ( in @ X26 @ X28 ) & ( in @ X28 @ X24 ) ) ) ) ) =>
% 8.68/4.85 ( ( in @ emptyset @ omega ) =>
% 8.68/4.85 ( ( ![X30:$i]:
% 8.68/4.85 ( ( in @ X30 @ omega ) =>
% 8.68/4.85 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 8.68/4.85 ( ( ![X32:$i]:
% 8.68/4.85 ( ( ( ![X34:$i]:
% 8.68/4.85 ( ( ( in @ X34 @ X32 ) & ( in @ X34 @ omega ) ) =>
% 8.68/4.85 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) &
% 8.68/4.85 ( in @ emptyset @ X32 ) ) =>
% 8.68/4.85 ( ![X36:$i]:
% 8.68/4.85 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 8.68/4.85 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 8.68/4.85 ( ( ![X42:$i]:
% 8.68/4.85 ( ( in @ X42 @ X40 ) =>
% 8.68/4.85 ( ?[X44:$i]:
% 8.68/4.85 ( ( X38 @ X42 @ X44 ) &
% 8.68/4.85 ( ![X46:$i]:
% 8.68/4.85 ( ( X38 @ X42 @ X46 ) =>
% 8.68/4.85 ( ( X44 ) = ( X46 ) ) ) ) ) ) ) ) =>
% 8.68/4.85 ( ?[X48:$i]:
% 8.68/4.85 ( ![X50:$i]:
% 8.68/4.85 ( ( in @ X50 @ X48 ) <=>
% 8.68/4.85 ( ?[X52:$i]:
% 8.68/4.85 ( ( in @ X52 @ X40 ) & ( X38 @ X52 @ X50 ) ) ) ) ) ) ) ) =>
% 8.68/4.85 ( ( ![X54:$i]:
% 8.68/4.85 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 8.68/4.85 ( ?[X58:$i]:
% 8.68/4.85 ( ( in @ X58 @ X54 ) &
% 8.68/4.85 ( ~( ?[X60:$i]:
% 8.68/4.85 ( ( in @ X60 @ X58 ) & ( in @ X60 @ X54 ) ) ) ) ) ) ) ) =>
% 8.68/4.85 ( ( ![X62:$i]:
% 8.68/4.85 ( ?[X64:$i]:
% 8.68/4.85 ( ( ![X96:$i]:
% 8.68/4.85 ( ( in @ X96 @ X64 ) =>
% 8.68/4.85 ( ![X98:$i]:
% 8.68/4.85 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) &
% 8.68/4.85 ( ![X90:$i,X92:$i]:
% 8.68/4.85 ( ( ( in @ X92 @ X62 ) & ( in @ X90 @ X62 ) ) =>
% 8.68/4.85 ( ( ![X94:$i]:
% 8.68/4.85 ( ( in @ X94 @ X64 ) =>
% 8.68/4.85 ( ( in @ X90 @ X94 ) <=>
% 8.68/4.85 ( in @ X92 @ X94 ) ) ) ) =>
% 8.68/4.85 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 8.68/4.85 ( ![X82:$i,X84:$i]:
% 8.68/4.85 ( ( ( in @ X84 @ X64 ) & ( in @ X82 @ X64 ) ) =>
% 8.68/4.85 ( ( ![X88:$i]:
% 8.68/4.85 ( ( in @ X88 @ X84 ) =>
% 8.68/4.85 ( in @ X88 @ X82 ) ) ) |
% 8.68/4.85 ( ![X86:$i]:
% 8.68/4.85 ( ( in @ X86 @ X82 ) =>
% 8.68/4.85 ( in @ X86 @ X84 ) ) ) ) ) ) &
% 8.68/4.85 ( ![X66:$i]:
% 8.68/4.85 ( ( ( ?[X70:$i]: ( in @ X70 @ X66 ) ) &
% 8.68/4.85 ( ![X68:$i]:
% 8.68/4.85 ( ( in @ X68 @ X66 ) =>
% 8.68/4.85 ( in @ X68 @ X62 ) ) ) ) =>
% 8.68/4.85 ( ?[X72:$i,X74:$i]:
% 8.68/4.85 ( ( in @ X72 @ X64 ) &
% 8.68/4.85 ( in @ X74 @ X66 ) &
% 8.68/4.85 ( ~( ?[X80:$i]:
% 8.68/4.85 ( ( in @ X80 @ X72 ) &
% 8.68/4.85 ( in @ X80 @ X66 ) ) ) ) &
% 8.68/4.85 ( ![X76:$i]:
% 8.68/4.85 ( ( in @ X76 @ X64 ) =>
% 8.68/4.85 ( ( in @ X74 @ X76 ) |
% 8.68/4.85 ( ![X78:$i]:
% 8.68/4.85 ( ( in @ X78 @ X76 ) =>
% 8.68/4.85 ( in @ X78 @ X72 ) ) ) ) ) ) ) ) ) ) ) ) ) =>
% 8.68/4.85 ( ( ![X100:( $i > $o )]:
% 8.68/4.85 ( ( ?[X102:$i]:
% 8.68/4.85 ( ( X100 @ X102 ) &
% 8.68/4.85 ( ![X104:$i]:
% 8.68/4.85 ( ( X100 @ X104 ) =>
% 8.68/4.85 ( ( X102 ) = ( X104 ) ) ) ) ) ) =>
% 8.68/4.85 ( X100 @
% 8.68/4.85 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 8.68/4.85 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 8.68/4.85 ( ( in @ X110 @ X106 ) =>
% 8.68/4.85 ( ( X108 @ X110 ) =>
% 8.68/4.85 ( in @
% 8.68/4.85 X110 @
% 8.68/4.85 ( dsetconstr @
% 8.68/4.85 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 8.68/4.85 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 8.68/4.85 ( ( in @
% 8.68/4.85 X116 @
% 8.68/4.85 ( dsetconstr @
% 8.68/4.85 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 8.68/4.85 ( in @ X116 @ X112 ) ) ) =>
% 8.68/4.85 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 8.68/4.85 ( ( in @
% 8.68/4.85 X122 @
% 8.68/4.85 ( dsetconstr @
% 8.68/4.85 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 8.68/4.85 ( X120 @ X122 ) ) ) =>
% 8.68/4.85 ( ( ![X124:( $i > $o )]:
% 8.68/4.85 ( ( ?[X126:$i]:
% 8.68/4.85 ( ( X124 @ X126 ) &
% 8.68/4.85 ( ![X128:$i]:
% 8.68/4.85 ( ( X124 @ X128 ) =>
% 8.68/4.85 ( ( X126 ) = ( X128 ) ) ) ) ) ) =>
% 8.68/4.85 ( ?[X130:$i]:
% 8.68/4.85 ( ( X124 @ X130 ) &
% 8.68/4.85 ( ![X132:$i]:
% 8.68/4.85 ( ( X124 @ X132 ) =>
% 8.68/4.85 ( ( X130 ) = ( X132 ) ) ) ) ) ) ) ) =>
% 8.68/4.85 ( ( ![X134:$o,X136:$i]:
% 8.68/4.85 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 8.68/4.85 ( X134 ) ) ) =>
% 8.68/4.85 ( ( ![X138:$i]:
% 8.68/4.85 ( ( in @ X138 @ emptyset ) =>
% 8.68/4.85 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 8.68/4.85 ( ( ![X142:$i]:
% 8.68/4.85 ( ( in @ X142 @ emptyset ) =>
% 8.68/4.85 ( $false ) ) ) =>
% 8.68/4.85 ( ( ![X144:$i]:
% 8.68/4.85 ( ~( in @ X144 @ emptyset ) ) ) =>
% 8.68/4.85 ( ( ![X146:( $i > $o )]:
% 8.68/4.85 ( ( ?[X148:$i]:
% 8.68/4.85 ( ( X146 @ X148 ) &
% 8.68/4.85 ( ![X150:$i]:
% 8.68/4.85 ( ( X146 @ X150 ) =>
% 8.68/4.85 ( ( X148 ) = ( X150 ) ) ) ) ) ) =>
% 8.68/4.85 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) =>
% 8.68/4.85 ( ( ![X154:$i,X156:$i]:
% 8.68/4.85 ( ( ![X158:$i]:
% 8.68/4.85 ( ( in @ X158 @ X154 ) =>
% 8.68/4.85 ( in @ X158 @ X156 ) ) ) =>
% 8.68/4.85 ( ( ![X160:$i]:
% 8.68/4.85 ( ( in @ X160 @ X156 ) =>
% 8.68/4.85 ( in @ X160 @ X154 ) ) ) =>
% 8.68/4.85 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 8.68/4.85 ( ( ![X162:$i]:
% 8.68/4.85 ( ( ![X164:$i]:
% 8.68/4.85 ( ~( in @ X164 @ X162 ) ) ) =>
% 8.68/4.85 ( ( X162 ) = ( emptyset ) ) ) ) =>
% 8.68/4.85 ( ( ![X166:$i]:
% 8.68/4.85 ( ( ![X168:$i]:
% 8.68/4.85 ( ~( in @ X168 @ X166 ) ) ) =>
% 8.68/4.85 ( ( X166 ) =
% 8.68/4.85 ( emptyset ) ) ) ) =>
% 8.68/4.85 ( ( ![X170:$i,
% 8.68/4.85 X172:( $i > $o ),
% 8.68/4.85 X174:$i]:
% 8.68/4.85 ( ( in @ X174 @ X170 ) =>
% 8.68/4.85 ( ( in @
% 8.68/4.85 X174 @
% 8.68/4.85 ( dsetconstr @
% 8.68/4.85 X170 @
% 8.68/4.85 ( ^[V_5:$i]:
% 8.68/4.85 ( X172 @ V_5 ) ) ) ) <=>
% 8.68/4.85 ( X172 @ X174 ) ) ) ) =>
% 8.68/4.85 ( ( ![X176:$i]:
% 8.68/4.85 ( ( ( X176 ) !=
% 8.68/4.85 ( emptyset ) ) =>
% 8.68/4.85 ( ?[X178:$i]:
% 8.68/4.85 ( in @ X178 @ X176 ) ) ) ) =>
% 8.68/4.85 ( ( ![X180:$i,
% 8.68/4.85 X182:( $i > $o ),
% 8.68/4.85 X184:$i]:
% 8.68/4.85 ( ( in @ X184 @ X180 ) =>
% 8.68/4.85 ( ( X182 @ X184 ) =>
% 8.68/4.85 ( ( dsetconstr @
% 8.68/4.85 X180 @
% 8.68/4.85 ( ^[
% 8.68/4.85 V_6:$i]:
% 8.68/4.85 (
% 8.68/4.85 X182 @ V_6 ) ) ) !=
% 8.68/4.85 ( emptyset ) ) ) ) ) =>
% 8.68/4.85 ( ( ![X186:$i]:
% 8.68/4.85 ( ( ?[X188:$i]:
% 8.68/4.85 ( in @
% 8.68/4.85 X188 @ X186 ) ) =>
% 8.68/4.85 ( ( X186 ) !=
% 8.68/4.85 ( emptyset ) ) ) ) =>
% 8.68/4.85 ( ( ![X190:$i,
% 8.68/4.85 X192:$i]:
% 8.68/4.85 ( in @
% 8.68/4.85 X190 @
% 8.68/4.85 ( setadjoin @
% 8.68/4.85 X190 @ X192 ) ) ) =>
% 8.68/4.85 ( ( in @
% 8.68/4.85 emptyset @
% 8.68/4.85 ( setadjoin @
% 8.68/4.85 emptyset @
% 8.68/4.85 emptyset ) ) =>
% 8.68/4.85 ( ( ![X194:$i,
% 8.68/4.85 X196:$i,
% 8.68/4.85 X198:$i]:
% 8.68/4.85 ( (
% 8.68/4.85 in @
% 8.68/4.85 X198 @
% 8.68/4.85 X196 ) =>
% 8.68/4.85 (
% 8.68/4.85 in @
% 8.68/4.85 X198 @
% 8.68/4.85 (
% 8.68/4.85 setadjoin
% 8.68/4.85 @
% 8.68/4.85 X194 @
% 8.68/4.85 X196 ) ) ) ) =>
% 8.68/4.85 ( ( ![
% 8.68/4.85 X200:$i,
% 8.68/4.85 X202:$i,
% 8.68/4.85 X204:$i]:
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 in @
% 8.68/4.85 X204 @
% 8.68/4.85 (
% 8.68/4.85 setadjoin
% 8.68/4.85 @
% 8.68/4.85 X200 @
% 8.68/4.85 X202 ) ) =>
% 8.68/4.85 (
% 8.68/4.85 ![
% 8.68/4.85 X206:$o]:
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 X204 ) =
% 8.68/4.85 (
% 8.68/4.85 X200 ) ) =>
% 8.68/4.85 (
% 8.68/4.85 X206 ) ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 in @
% 8.68/4.85 X204 @
% 8.68/4.85 X202 ) =>
% 8.68/4.85 (
% 8.68/4.85 X206 ) ) =>
% 8.68/4.85 (
% 8.68/4.85 X206 ) ) ) ) ) ) =>
% 8.68/4.85 ( (
% 8.68/4.85 ![
% 8.68/4.85 X208:$i,
% 8.68/4.85 X210:$i,
% 8.68/4.85 X212:$i]:
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 in @
% 8.68/4.85 X212 @
% 8.68/4.85 (
% 8.68/4.85 setadjoin
% 8.68/4.85 @
% 8.68/4.85 X208 @
% 8.68/4.85 X210 ) ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 in @
% 8.68/4.85 X212 @
% 8.68/4.85 X210 ) |
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 X212 ) =
% 8.68/4.85 (
% 8.68/4.85 X208 ) ) ) ) ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 ![
% 8.68/4.85 X214:$i]:
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 dsetconstr
% 8.68/4.85 @
% 8.68/4.85 X214 @
% 8.68/4.85 (
% 8.68/4.85 ^[
% 8.68/4.85 V_7:$i]:
% 8.68/4.85 (
% 8.68/4.85 $true ) ) ) =
% 8.68/4.85 (
% 8.68/4.85 X214 ) ) ) =>
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 ![
% 8.68/4.85 X216:$i,
% 8.68/4.85 X218:$i]:
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 ![
% 8.68/4.85 X220:$i]:
% 8.68/4.85 (
% 8.68/4.85 (
% 8.68/4.85 in @
% 8.68/4.85 X220 @
% 8.68/4.85 X218 ) =>
% 8.68/4.85 (
% 8.68/4.85 in @
% 8.68/4.85 X220 @
% 8.68/4.85 X216 ) ) ) =>
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% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X366 @
% 8.99/4.86 X372 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X370 ) =
% 8.99/4.86 (
% 8.99/4.86 X372 ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 ?[
% 8.99/4.86 X374:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X366 @
% 8.99/4.86 X374 ) &
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X376:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X366 @
% 8.99/4.86 X376 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X374 ) =
% 8.99/4.86 (
% 8.99/4.86 X376 ) ) ) ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X378:(
% 8.99/4.86 $i > $o )]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ?[
% 8.99/4.86 X380:$i]:
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X382:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X378 @
% 8.99/4.86 X382 ) <=>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X382 ) =
% 8.99/4.86 (
% 8.99/4.86 X380 ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 ?[
% 8.99/4.86 X384:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X378 @
% 8.99/4.86 X384 ) &
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X386:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X378 @
% 8.99/4.86 X386 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X384 ) =
% 8.99/4.86 (
% 8.99/4.86 X386 ) ) ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X388:$i,
% 8.99/4.86 X390:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X388 ) =
% 8.99/4.86 (
% 8.99/4.86 X390 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X392:$i,
% 8.99/4.86 X394:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X392 ) =
% 8.99/4.86 (
% 8.99/4.86 X394 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 in @
% 8.99/4.86 X392 @
% 8.99/4.86 X388 ) =>
% 8.99/4.86 (
% 8.99/4.86 in @
% 8.99/4.86 X394 @
% 8.99/4.86 X390 ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X396:$i,
% 8.99/4.86 X398:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X396 ) =
% 8.99/4.86 (
% 8.99/4.86 X398 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X400:$i,
% 8.99/4.86 X402:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X400 ) =
% 8.99/4.86 (
% 8.99/4.86 X402 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 in @
% 8.99/4.86 X400 @
% 8.99/4.86 X396 ) <=>
% 8.99/4.86 (
% 8.99/4.86 in @
% 8.99/4.86 X402 @
% 8.99/4.86 X398 ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X404:(
% 8.99/4.86 $i > $o )]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ?[
% 8.99/4.86 X406:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X404 @
% 8.99/4.86 X406 ) &
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X408:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X404 @
% 8.99/4.86 X408 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X406 ) =
% 8.99/4.86 (
% 8.99/4.86 X408 ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X410:$i,
% 8.99/4.86 X412:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X404 @
% 8.99/4.86 X410 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X404 @
% 8.99/4.86 X412 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X410 ) =
% 8.99/4.86 (
% 8.99/4.86 X412 ) ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X414:(
% 8.99/4.86 $i > $o ),
% 8.99/4.86 X416:(
% 8.99/4.86 $i > $o )]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X418:$i,
% 8.99/4.86 X420:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X418 ) =
% 8.99/4.86 (
% 8.99/4.86 X420 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X414 @
% 8.99/4.86 X418 ) <=>
% 8.99/4.86 (
% 8.99/4.86 X416 @
% 8.99/4.86 X420 ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ?[
% 8.99/4.86 X422:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X414 @
% 8.99/4.86 X422 ) &
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X424:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X414 @
% 8.99/4.86 X424 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X422 ) =
% 8.99/4.86 (
% 8.99/4.86 X424 ) ) ) ) ) ) <=>
% 8.99/4.86 (
% 8.99/4.86 ?[
% 8.99/4.86 X426:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X416 @
% 8.99/4.86 X426 ) &
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X428:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X416 @
% 8.99/4.86 X428 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X426 ) =
% 8.99/4.86 (
% 8.99/4.86 X428 ) ) ) ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 emptyset ) =
% 8.99/4.86 (
% 8.99/4.86 emptyset ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X430:$i,
% 8.99/4.86 X432:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X430 ) =
% 8.99/4.86 (
% 8.99/4.86 X432 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X434:$i,
% 8.99/4.86 X436:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X434 ) =
% 8.99/4.86 (
% 8.99/4.86 X436 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 setadjoin
% 8.99/4.86 @
% 8.99/4.86 X430 @
% 8.99/4.86 X434 ) =
% 8.99/4.86 (
% 8.99/4.86 setadjoin
% 8.99/4.86 @
% 8.99/4.86 X432 @
% 8.99/4.86 X436 ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X438:$i,
% 8.99/4.86 X440:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X438 ) =
% 8.99/4.86 (
% 8.99/4.86 X440 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 powerset @
% 8.99/4.86 X438 ) =
% 8.99/4.86 (
% 8.99/4.86 powerset @
% 8.99/4.86 X440 ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X442:$i,
% 8.99/4.86 X444:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X442 ) =
% 8.99/4.86 (
% 8.99/4.86 X444 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 setunion @
% 8.99/4.86 X442 ) =
% 8.99/4.86 (
% 8.99/4.86 setunion @
% 8.99/4.86 X444 ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 omega ) =
% 8.99/4.86 (
% 8.99/4.86 omega ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X446:(
% 8.99/4.86 $i > $o )]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ?[
% 8.99/4.86 X448:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X446 @
% 8.99/4.86 X448 ) &
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X450:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X446 @
% 8.99/4.86 X450 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X448 ) =
% 8.99/4.86 (
% 8.99/4.86 X450 ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X452:$i,
% 8.99/4.86 X454:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X446 @
% 8.99/4.86 X452 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X446 @
% 8.99/4.86 X454 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X452 ) =
% 8.99/4.86 (
% 8.99/4.86 X454 ) ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X456:(
% 8.99/4.86 $i > $o ),
% 8.99/4.86 X458:(
% 8.99/4.86 $i > $o )]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X460:$i,
% 8.99/4.86 X462:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X460 ) =
% 8.99/4.86 (
% 8.99/4.86 X462 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X456 @
% 8.99/4.86 X460 ) <=>
% 8.99/4.86 (
% 8.99/4.86 X458 @
% 8.99/4.86 X462 ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ?[
% 8.99/4.86 X464:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X456 @
% 8.99/4.86 X464 ) &
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X466:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X456 @
% 8.99/4.86 X466 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X464 ) =
% 8.99/4.86 (
% 8.99/4.86 X466 ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ?[
% 8.99/4.86 X468:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X458 @
% 8.99/4.86 X468 ) &
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X470:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X458 @
% 8.99/4.86 X470 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X468 ) =
% 8.99/4.86 (
% 8.99/4.86 X470 ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 descr @
% 8.99/4.86 (
% 8.99/4.86 ^[
% 8.99/4.86 V_9:$i]:
% 8.99/4.86 (
% 8.99/4.86 X456 @ V_9 ) ) ) =
% 8.99/4.86 (
% 8.99/4.86 descr @
% 8.99/4.86 (
% 8.99/4.86 ^[
% 8.99/4.86 V_10:$i]:
% 8.99/4.86 (
% 8.99/4.86 X458 @
% 8.99/4.86 V_10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 8.99/4.86 thf(zf_stmt_1, type, zip_tseitin_5 : $i > ( $i > $o ) > $o).
% 8.99/4.86 thf(zf_stmt_2, axiom,
% 8.99/4.86 (![X422:$i,X414:( $i > $o )]:
% 8.99/4.86 ( ( zip_tseitin_5 @ X422 @ X414 ) <=>
% 8.99/4.86 ( ( ![X424:$i]: ( zip_tseitin_4 @ X424 @ X422 @ X414 ) ) &
% 8.99/4.86 ( X414 @ X422 ) ) ))).
% 8.99/4.86 thf(zf_stmt_3, type, zip_tseitin_4 : $i > $i > ( $i > $o ) > $o).
% 8.99/4.86 thf(zf_stmt_4, axiom,
% 8.99/4.86 (![X424:$i,X422:$i,X414:( $i > $o )]:
% 8.99/4.86 ( ( zip_tseitin_4 @ X424 @ X422 @ X414 ) <=>
% 8.99/4.86 ( ( X414 @ X424 ) => ( ( X422 ) = ( X424 ) ) ) ))).
% 8.99/4.86 thf(zf_stmt_5, type, zip_tseitin_3 : $i > $i > $i > ( $i > $i > $o ) > $o).
% 8.99/4.86 thf(zf_stmt_6, axiom,
% 8.99/4.86 (![X52:$i,X50:$i,X40:$i,X38:( $i > $i > $o )]:
% 8.99/4.86 ( ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) <=>
% 8.99/4.86 ( ( X38 @ X52 @ X50 ) & ( in @ X52 @ X40 ) ) ))).
% 8.99/4.86 thf(zf_stmt_7, type, zip_tseitin_2 : $i > $i > $i > $o).
% 8.99/4.86 thf(zf_stmt_8, axiom,
% 8.99/4.86 (![X28:$i,X26:$i,X24:$i]:
% 8.99/4.86 ( ( zip_tseitin_2 @ X28 @ X26 @ X24 ) <=>
% 8.99/4.86 ( ( in @ X28 @ X24 ) & ( in @ X26 @ X28 ) ) ))).
% 8.99/4.86 thf(zf_stmt_9, type, zip_tseitin_1 : $i > $i > $i > $o).
% 8.99/4.86 thf(zf_stmt_10, axiom,
% 8.99/4.86 (![X22:$i,X20:$i,X18:$i]:
% 8.99/4.86 ( ( zip_tseitin_1 @ X22 @ X20 @ X18 ) <=>
% 8.99/4.86 ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ))).
% 8.99/4.86 thf(zf_stmt_11, type, zip_tseitin_0 : $i > $i > $i > $o).
% 8.99/4.86 thf(zf_stmt_12, axiom,
% 8.99/4.86 (![X16:$i,X14:$i,X12:$i]:
% 8.99/4.86 ( ( zip_tseitin_0 @ X16 @ X14 @ X12 ) <=>
% 8.99/4.86 ( ( ( X16 ) = ( X12 ) ) | ( in @ X16 @ X14 ) ) ))).
% 8.99/4.86 thf(zf_stmt_13, conjecture,
% 8.99/4.86 (( ![X4:$i,X6:$i]:
% 8.99/4.86 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 8.99/4.86 ( ( X4 ) = ( X6 ) ) ) ) =>
% 8.99/4.86 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 8.99/4.86 ( ( ![X12:$i,X14:$i,X16:$i]:
% 8.99/4.86 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 8.99/4.86 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 8.99/4.86 ( ( ![X18:$i,X20:$i]:
% 8.99/4.86 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 8.99/4.86 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 8.99/4.86 ( ( ![X24:$i,X26:$i]:
% 8.99/4.86 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 8.99/4.86 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 8.99/4.86 ( ( in @ emptyset @ omega ) =>
% 8.99/4.86 ( ( ![X30:$i]:
% 8.99/4.86 ( ( in @ X30 @ omega ) =>
% 8.99/4.86 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 8.99/4.86 ( ( ![X32:$i]:
% 8.99/4.86 ( ( ( in @ emptyset @ X32 ) &
% 8.99/4.86 ( ![X34:$i]:
% 8.99/4.86 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 8.99/4.86 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 8.99/4.86 ( ![X36:$i]:
% 8.99/4.86 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 8.99/4.86 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 8.99/4.86 ( ( ![X42:$i]:
% 8.99/4.86 ( ( in @ X42 @ X40 ) =>
% 8.99/4.86 ( ?[X44:$i]:
% 8.99/4.86 ( ( ![X46:$i]:
% 8.99/4.86 ( ( X38 @ X42 @ X46 ) =>
% 8.99/4.86 ( ( X44 ) = ( X46 ) ) ) ) &
% 8.99/4.86 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 8.99/4.86 ( ?[X48:$i]:
% 8.99/4.86 ( ![X50:$i]:
% 8.99/4.86 ( ( in @ X50 @ X48 ) <=>
% 8.99/4.86 ( ?[X52:$i]:
% 8.99/4.86 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 8.99/4.86 ( ( ![X54:$i]:
% 8.99/4.86 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 8.99/4.86 ( ?[X58:$i]:
% 8.99/4.86 ( ( ~( ?[X60:$i]:
% 8.99/4.86 ( ( in @ X60 @ X54 ) & ( in @ X60 @ X58 ) ) ) ) &
% 8.99/4.86 ( in @ X58 @ X54 ) ) ) ) ) =>
% 8.99/4.86 ( ( ![X62:$i]:
% 8.99/4.86 ( ?[X64:$i]:
% 8.99/4.86 ( ( ![X66:$i]:
% 8.99/4.86 ( ( ( ![X68:$i]:
% 8.99/4.86 ( ( in @ X68 @ X66 ) =>
% 8.99/4.86 ( in @ X68 @ X62 ) ) ) &
% 8.99/4.86 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 8.99/4.86 ( ?[X72:$i,X74:$i]:
% 8.99/4.86 ( ( ![X76:$i]:
% 8.99/4.86 ( ( in @ X76 @ X64 ) =>
% 8.99/4.86 ( ( ![X78:$i]:
% 8.99/4.86 ( ( in @ X78 @ X76 ) =>
% 8.99/4.86 ( in @ X78 @ X72 ) ) ) |
% 8.99/4.86 ( in @ X74 @ X76 ) ) ) ) &
% 8.99/4.86 ( ~( ?[X80:$i]:
% 8.99/4.86 ( ( in @ X80 @ X66 ) &
% 8.99/4.86 ( in @ X80 @ X72 ) ) ) ) &
% 8.99/4.86 ( in @ X74 @ X66 ) & ( in @ X72 @ X64 ) ) ) ) ) &
% 8.99/4.86 ( ![X82:$i,X84:$i]:
% 8.99/4.86 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 8.99/4.86 ( ( ![X86:$i]:
% 8.99/4.86 ( ( in @ X86 @ X82 ) =>
% 8.99/4.86 ( in @ X86 @ X84 ) ) ) |
% 8.99/4.86 ( ![X88:$i]:
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% 8.99/4.86 ( ![X90:$i,X92:$i]:
% 8.99/4.86 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 8.99/4.86 ( ( ![X94:$i]:
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% 8.99/4.86 ( ![X98:$i]:
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% 8.99/4.86 ( ( ![X100:( $i > $o )]:
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% 8.99/4.86 ( ( ![X104:$i]:
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% 8.99/4.86 ( X100 @
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% 8.99/4.86 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
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% 8.99/4.86 ( ( X108 @ X110 ) =>
% 8.99/4.86 ( in @
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% 8.99/4.86 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
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% 8.99/4.86 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
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% 8.99/4.86 ( X120 @ X122 ) ) ) =>
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% 8.99/4.86 ( ( ![X128:$i]:
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% 8.99/4.86 ( ?[X130:$i]:
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% 8.99/4.86 ( ( ![X134:$o,X136:$i]:
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% 8.99/4.86 ( ( ![X138:$i]:
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% 8.99/4.86 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 8.99/4.86 ( ( ![X142:$i]:
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% 8.99/4.86 ( ( ![X144:$i]:
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% 8.99/4.86 ( ( ![X146:( $i > $o )]:
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% 8.99/4.86 ( ( ![X150:$i]:
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% 8.99/4.86 ( ( ![X154:$i,X156:$i]:
% 8.99/4.86 ( ( ![X158:$i]:
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% 8.99/4.86 ( ( ![X160:$i]:
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% 8.99/4.86 ( ( ![X164:$i]:
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% 8.99/4.86 ( ( ![X166:$i]:
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% 8.99/4.86 ( ( ![X170:$i,
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% 8.99/4.86 X174:$i]:
% 8.99/4.86 ( ( in @ X174 @ X170 ) =>
% 8.99/4.86 ( ( in @
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% 8.99/4.86 ( ( ![X180:$i,
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% 8.99/4.86 X184:$i]:
% 8.99/4.86 ( ( in @ X184 @ X180 ) =>
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% 8.99/4.86 ( ( in @
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% 8.99/4.86 X456:(
% 8.99/4.86 $i > $o ),
% 8.99/4.86 X458:(
% 8.99/4.86 $i > $o )]:
% 8.99/4.86 (
% 8.99/4.86 (
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% 8.99/4.86 X460:$i,
% 8.99/4.86 X462:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
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% 8.99/4.86 X460 ) =
% 8.99/4.86 (
% 8.99/4.86 X462 ) ) =>
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% 8.99/4.86 (
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% 8.99/4.86 X466 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
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% 8.99/4.86 (
% 8.99/4.86 X466 ) ) ) ) &
% 8.99/4.86 (
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% 8.99/4.86 X464 ) ) ) =>
% 8.99/4.86 (
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% 8.99/4.86 (
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% 8.99/4.86 X470:$i]:
% 8.99/4.86 (
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% 8.99/4.86 X470 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
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% 8.99/4.86 X470 ) ) ) ) &
% 8.99/4.86 (
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% 8.99/4.86 X468 ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 descr @
% 8.99/4.86 (
% 8.99/4.86 ^[
% 8.99/4.86 V_9:$i]:
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% 8.99/4.86 (
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% 8.99/4.86 (
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% 8.99/4.86 thf(zf_stmt_14, negated_conjecture,
% 8.99/4.86 (~( ( ![X4:$i,X6:$i]:
% 8.99/4.86 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 8.99/4.86 ( ( X4 ) = ( X6 ) ) ) ) =>
% 8.99/4.86 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 8.99/4.86 ( ( ![X12:$i,X14:$i,X16:$i]:
% 8.99/4.86 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 8.99/4.86 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 8.99/4.86 ( ( ![X18:$i,X20:$i]:
% 8.99/4.86 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 8.99/4.86 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 8.99/4.86 ( ( ![X24:$i,X26:$i]:
% 8.99/4.86 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 8.99/4.86 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 8.99/4.86 ( ( in @ emptyset @ omega ) =>
% 8.99/4.86 ( ( ![X30:$i]:
% 8.99/4.86 ( ( in @ X30 @ omega ) =>
% 8.99/4.86 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 8.99/4.86 ( ( ![X32:$i]:
% 8.99/4.86 ( ( ( in @ emptyset @ X32 ) &
% 8.99/4.86 ( ![X34:$i]:
% 8.99/4.86 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 8.99/4.86 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 8.99/4.86 ( ![X36:$i]:
% 8.99/4.86 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 8.99/4.86 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 8.99/4.86 ( ( ![X42:$i]:
% 8.99/4.86 ( ( in @ X42 @ X40 ) =>
% 8.99/4.86 ( ?[X44:$i]:
% 8.99/4.86 ( ( ![X46:$i]:
% 8.99/4.86 ( ( X38 @ X42 @ X46 ) =>
% 8.99/4.86 ( ( X44 ) = ( X46 ) ) ) ) &
% 8.99/4.86 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 8.99/4.86 ( ?[X48:$i]:
% 8.99/4.86 ( ![X50:$i]:
% 8.99/4.86 ( ( in @ X50 @ X48 ) <=>
% 8.99/4.86 ( ?[X52:$i]:
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% 8.99/4.86 ( ( ![X54:$i]:
% 8.99/4.86 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 8.99/4.86 ( ?[X58:$i]:
% 8.99/4.86 ( ( ~( ?[X60:$i]:
% 8.99/4.86 ( ( in @ X60 @ X54 ) &
% 8.99/4.86 ( in @ X60 @ X58 ) ) ) ) &
% 8.99/4.86 ( in @ X58 @ X54 ) ) ) ) ) =>
% 8.99/4.86 ( ( ![X62:$i]:
% 8.99/4.86 ( ?[X64:$i]:
% 8.99/4.86 ( ( ![X66:$i]:
% 8.99/4.86 ( ( ( ![X68:$i]:
% 8.99/4.86 ( ( in @ X68 @ X66 ) =>
% 8.99/4.86 ( in @ X68 @ X62 ) ) ) &
% 8.99/4.86 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 8.99/4.86 ( ?[X72:$i,X74:$i]:
% 8.99/4.86 ( ( ![X76:$i]:
% 8.99/4.86 ( ( in @ X76 @ X64 ) =>
% 8.99/4.86 ( ( ![X78:$i]:
% 8.99/4.86 ( ( in @ X78 @ X76 ) =>
% 8.99/4.86 ( in @ X78 @ X72 ) ) ) |
% 8.99/4.86 ( in @ X74 @ X76 ) ) ) ) &
% 8.99/4.86 ( ~( ?[X80:$i]:
% 8.99/4.86 ( ( in @ X80 @ X66 ) &
% 8.99/4.86 ( in @ X80 @ X72 ) ) ) ) &
% 8.99/4.86 ( in @ X74 @ X66 ) &
% 8.99/4.86 ( in @ X72 @ X64 ) ) ) ) ) &
% 8.99/4.86 ( ![X82:$i,X84:$i]:
% 8.99/4.86 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 8.99/4.86 ( ( ![X86:$i]:
% 8.99/4.86 ( ( in @ X86 @ X82 ) =>
% 8.99/4.86 ( in @ X86 @ X84 ) ) ) |
% 8.99/4.86 ( ![X88:$i]:
% 8.99/4.86 ( ( in @ X88 @ X84 ) =>
% 8.99/4.86 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 8.99/4.86 ( ![X90:$i,X92:$i]:
% 8.99/4.86 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 8.99/4.86 ( ( ![X94:$i]:
% 8.99/4.86 ( ( in @ X94 @ X64 ) =>
% 8.99/4.86 ( ( in @ X90 @ X94 ) <=>
% 8.99/4.86 ( in @ X92 @ X94 ) ) ) ) =>
% 8.99/4.86 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 8.99/4.86 ( ![X96:$i]:
% 8.99/4.86 ( ( in @ X96 @ X64 ) =>
% 8.99/4.86 ( ![X98:$i]:
% 8.99/4.86 ( ( in @ X98 @ X96 ) =>
% 8.99/4.86 ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 8.99/4.86 ( ( ![X100:( $i > $o )]:
% 8.99/4.86 ( ( ?[X102:$i]:
% 8.99/4.86 ( ( ![X104:$i]:
% 8.99/4.86 ( ( X100 @ X104 ) =>
% 8.99/4.86 ( ( X102 ) = ( X104 ) ) ) ) &
% 8.99/4.86 ( X100 @ X102 ) ) ) =>
% 8.99/4.86 ( X100 @
% 8.99/4.86 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 8.99/4.86 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 8.99/4.86 ( ( in @ X110 @ X106 ) =>
% 8.99/4.86 ( ( X108 @ X110 ) =>
% 8.99/4.86 ( in @
% 8.99/4.86 X110 @
% 8.99/4.86 ( dsetconstr @
% 8.99/4.86 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 8.99/4.86 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 8.99/4.86 ( ( in @
% 8.99/4.86 X116 @
% 8.99/4.86 ( dsetconstr @
% 8.99/4.86 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 8.99/4.86 ( in @ X116 @ X112 ) ) ) =>
% 8.99/4.86 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 8.99/4.86 ( ( in @
% 8.99/4.86 X122 @
% 8.99/4.86 ( dsetconstr @
% 8.99/4.86 X118 @
% 8.99/4.86 ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 8.99/4.86 ( X120 @ X122 ) ) ) =>
% 8.99/4.86 ( ( ![X124:( $i > $o )]:
% 8.99/4.86 ( ( ?[X126:$i]:
% 8.99/4.86 ( ( ![X128:$i]:
% 8.99/4.86 ( ( X124 @ X128 ) =>
% 8.99/4.86 ( ( X126 ) = ( X128 ) ) ) ) &
% 8.99/4.86 ( X124 @ X126 ) ) ) =>
% 8.99/4.86 ( ?[X130:$i]:
% 8.99/4.86 ( ( ![X132:$i]:
% 8.99/4.86 ( ( X124 @ X132 ) =>
% 8.99/4.86 ( ( X130 ) = ( X132 ) ) ) ) &
% 8.99/4.86 ( X124 @ X130 ) ) ) ) ) =>
% 8.99/4.86 ( ( ![X134:$o,X136:$i]:
% 8.99/4.86 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 8.99/4.86 ( X134 ) ) ) =>
% 8.99/4.86 ( ( ![X138:$i]:
% 8.99/4.86 ( ( in @ X138 @ emptyset ) =>
% 8.99/4.86 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 8.99/4.86 ( ( ![X142:$i]:
% 8.99/4.86 ( ~( in @ X142 @ emptyset ) ) ) =>
% 8.99/4.86 ( ( ![X144:$i]:
% 8.99/4.86 ( ~( in @ X144 @ emptyset ) ) ) =>
% 8.99/4.86 ( ( ![X146:( $i > $o )]:
% 8.99/4.86 ( ( ?[X148:$i]:
% 8.99/4.86 ( ( ![X150:$i]:
% 8.99/4.86 ( ( X146 @ X150 ) =>
% 8.99/4.86 ( ( X148 ) =
% 8.99/4.86 ( X150 ) ) ) ) &
% 8.99/4.86 ( X146 @ X148 ) ) ) =>
% 8.99/4.86 ( ?[X152:$i]:
% 8.99/4.86 ( X146 @ X152 ) ) ) ) =>
% 8.99/4.86 ( ( ![X154:$i,X156:$i]:
% 8.99/4.86 ( ( ![X158:$i]:
% 8.99/4.86 ( ( in @ X158 @ X154 ) =>
% 8.99/4.86 ( in @ X158 @ X156 ) ) ) =>
% 8.99/4.86 ( ( ![X160:$i]:
% 8.99/4.86 ( ( in @ X160 @ X156 ) =>
% 8.99/4.86 ( in @ X160 @ X154 ) ) ) =>
% 8.99/4.86 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 8.99/4.86 ( ( ![X162:$i]:
% 8.99/4.86 ( ( ![X164:$i]:
% 8.99/4.86 ( ~( in @ X164 @ X162 ) ) ) =>
% 8.99/4.86 ( ( X162 ) =
% 8.99/4.86 ( emptyset ) ) ) ) =>
% 8.99/4.86 ( ( ![X166:$i]:
% 8.99/4.86 ( ( ![X168:$i]:
% 8.99/4.86 ( ~( in @
% 8.99/4.86 X168 @ X166 ) ) ) =>
% 8.99/4.86 ( ( X166 ) =
% 8.99/4.86 ( emptyset ) ) ) ) =>
% 8.99/4.86 ( ( ![X170:$i,
% 8.99/4.86 X172:( $i > $o ),
% 8.99/4.86 X174:$i]:
% 8.99/4.86 ( ( in @ X174 @ X170 ) =>
% 8.99/4.86 ( ( in @
% 8.99/4.86 X174 @
% 8.99/4.86 ( dsetconstr @
% 8.99/4.86 X170 @
% 8.99/4.86 ( ^[V_5:$i]:
% 8.99/4.86 ( X172 @
% 8.99/4.86 V_5 ) ) ) ) <=>
% 8.99/4.86 ( X172 @ X174 ) ) ) ) =>
% 8.99/4.86 ( ( ![X176:$i]:
% 8.99/4.86 ( ( ( X176 ) !=
% 8.99/4.86 ( emptyset ) ) =>
% 8.99/4.86 ( ?[X178:$i]:
% 8.99/4.86 ( in @
% 8.99/4.86 X178 @ X176 ) ) ) ) =>
% 8.99/4.86 ( ( ![X180:$i,
% 8.99/4.86 X182:(
% 8.99/4.86 $i > $o ),
% 8.99/4.86 X184:$i]:
% 8.99/4.86 ( ( in @
% 8.99/4.86 X184 @ X180 ) =>
% 8.99/4.86 ( ( X182 @ X184 ) =>
% 8.99/4.86 ( ( dsetconstr
% 8.99/4.86 @
% 8.99/4.86 X180 @
% 8.99/4.86 (
% 8.99/4.86 ^[
% 8.99/4.86 V_6:$i]:
% 8.99/4.86 (
% 8.99/4.86 X182 @
% 8.99/4.86 V_6 ) ) ) !=
% 8.99/4.86 ( emptyset ) ) ) ) ) =>
% 8.99/4.86 ( ( ![X186:$i]:
% 8.99/4.86 ( ( ?[X188:$i]:
% 8.99/4.86 ( in @
% 8.99/4.86 X188 @
% 8.99/4.86 X186 ) ) =>
% 8.99/4.86 ( ( X186 ) !=
% 8.99/4.86 ( emptyset ) ) ) ) =>
% 8.99/4.86 ( ( ![X190:$i,
% 8.99/4.86 X192:$i]:
% 8.99/4.86 ( in @
% 8.99/4.86 X190 @
% 8.99/4.86 ( setadjoin
% 8.99/4.86 @
% 8.99/4.86 X190 @
% 8.99/4.86 X192 ) ) ) =>
% 8.99/4.86 ( ( in @
% 8.99/4.86 emptyset @
% 8.99/4.86 ( setadjoin
% 8.99/4.86 @
% 8.99/4.86 emptyset @
% 8.99/4.86 emptyset ) ) =>
% 8.99/4.86 ( ( ![
% 8.99/4.86 X194:$i,
% 8.99/4.86 X196:$i,
% 8.99/4.86 X198:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 in @
% 8.99/4.86 X198 @
% 8.99/4.86 X196 ) =>
% 8.99/4.86 (
% 8.99/4.86 in @
% 8.99/4.86 X198 @
% 8.99/4.86 (
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% 8.99/4.86 @
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% 8.99/4.86 X196 ) ) ) ) =>
% 8.99/4.86 ( (
% 8.99/4.86 ![
% 8.99/4.86 X200:$i,
% 8.99/4.86 X202:$i,
% 8.99/4.86 X204:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 in @
% 8.99/4.86 X204 @
% 8.99/4.86 (
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% 8.99/4.86 (
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% 8.99/4.86 X206:$o]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X204 ) =
% 8.99/4.86 (
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% 8.99/4.86 (
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% 8.99/4.86 (
% 8.99/4.86 (
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% 8.99/4.86 (
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% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X208:$i,
% 8.99/4.86 X210:$i,
% 8.99/4.86 X212:$i]:
% 8.99/4.86 (
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% 8.99/4.86 in @
% 8.99/4.86 X212 @
% 8.99/4.86 (
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% 8.99/4.86 X208 @
% 8.99/4.86 X210 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
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% 8.99/4.86 (
% 8.99/4.86 X208 ) ) |
% 8.99/4.86 (
% 8.99/4.86 in @
% 8.99/4.86 X212 @
% 8.99/4.86 X210 ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X214:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
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% 8.99/4.86 (
% 8.99/4.86 ^[
% 8.99/4.86 V_7:$i]:
% 8.99/4.86 (
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% 8.99/4.86 (
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% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X216:$i,
% 8.99/4.86 X218:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X220:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
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% 8.99/4.86 X220 @
% 8.99/4.86 X218 ) =>
% 8.99/4.86 (
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% 8.99/4.86 (
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% 8.99/4.86 (
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% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X222:$i]:
% 8.99/4.86 (
% 8.99/4.86 in @
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% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
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% 8.99/4.86 (
% 8.99/4.86 in @
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% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X226:$i,
% 8.99/4.86 X228:$i,
% 8.99/4.86 X230:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 in @
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% 8.99/4.86 X230 @
% 8.99/4.86 X228 ) =>
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% 8.99/4.86 (
% 8.99/4.86 (
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% 8.99/4.86 X232:$i,
% 8.99/4.86 X234:$i,
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% 8.99/4.86 X236 ) =>
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% 8.99/4.86 (
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% 8.99/4.86 (
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% 8.99/4.86 X240:$i]:
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% 8.99/4.86 (
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% 8.99/4.86 (
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% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X392 ) =
% 8.99/4.86 (
% 8.99/4.86 X394 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 in @
% 8.99/4.86 X392 @
% 8.99/4.86 X388 ) =>
% 8.99/4.86 (
% 8.99/4.86 in @
% 8.99/4.86 X394 @
% 8.99/4.86 X390 ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X396:$i,
% 8.99/4.86 X398:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X396 ) =
% 8.99/4.86 (
% 8.99/4.86 X398 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X400:$i,
% 8.99/4.86 X402:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X400 ) =
% 8.99/4.86 (
% 8.99/4.86 X402 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 in @
% 8.99/4.86 X400 @
% 8.99/4.86 X396 ) <=>
% 8.99/4.86 (
% 8.99/4.86 in @
% 8.99/4.86 X402 @
% 8.99/4.86 X398 ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X404:(
% 8.99/4.86 $i > $o )]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ?[
% 8.99/4.86 X406:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X408:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X404 @
% 8.99/4.86 X408 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X406 ) =
% 8.99/4.86 (
% 8.99/4.86 X408 ) ) ) ) &
% 8.99/4.86 (
% 8.99/4.86 X404 @
% 8.99/4.86 X406 ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X410:$i,
% 8.99/4.86 X412:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X404 @
% 8.99/4.86 X410 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X404 @
% 8.99/4.86 X412 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X410 ) =
% 8.99/4.86 (
% 8.99/4.86 X412 ) ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X414:(
% 8.99/4.86 $i > $o ),
% 8.99/4.86 X416:(
% 8.99/4.86 $i > $o )]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X418:$i,
% 8.99/4.86 X420:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X418 ) =
% 8.99/4.86 (
% 8.99/4.86 X420 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X414 @
% 8.99/4.86 X418 ) <=>
% 8.99/4.86 (
% 8.99/4.86 X416 @
% 8.99/4.86 X420 ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ?[
% 8.99/4.86 X422:$i]:
% 8.99/4.86 (
% 8.99/4.86 zip_tseitin_5
% 8.99/4.86 @
% 8.99/4.86 X422 @
% 8.99/4.86 X414 ) ) <=>
% 8.99/4.86 (
% 8.99/4.86 ?[
% 8.99/4.86 X426:$i]:
% 8.99/4.86 (
% 8.99/4.86 zip_tseitin_5
% 8.99/4.86 @
% 8.99/4.86 X426 @
% 8.99/4.86 X416 ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 emptyset ) =
% 8.99/4.86 (
% 8.99/4.86 emptyset ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X430:$i,
% 8.99/4.86 X432:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X430 ) =
% 8.99/4.86 (
% 8.99/4.86 X432 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X434:$i,
% 8.99/4.86 X436:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X434 ) =
% 8.99/4.86 (
% 8.99/4.86 X436 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 setadjoin
% 8.99/4.86 @
% 8.99/4.86 X430 @
% 8.99/4.86 X434 ) =
% 8.99/4.86 (
% 8.99/4.86 setadjoin
% 8.99/4.86 @
% 8.99/4.86 X432 @
% 8.99/4.86 X436 ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X438:$i,
% 8.99/4.86 X440:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X438 ) =
% 8.99/4.86 (
% 8.99/4.86 X440 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 powerset
% 8.99/4.86 @
% 8.99/4.86 X438 ) =
% 8.99/4.86 (
% 8.99/4.86 powerset
% 8.99/4.86 @
% 8.99/4.86 X440 ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X442:$i,
% 8.99/4.86 X444:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X442 ) =
% 8.99/4.86 (
% 8.99/4.86 X444 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 setunion
% 8.99/4.86 @
% 8.99/4.86 X442 ) =
% 8.99/4.86 (
% 8.99/4.86 setunion
% 8.99/4.86 @
% 8.99/4.86 X444 ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 omega ) =
% 8.99/4.86 (
% 8.99/4.86 omega ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X446:(
% 8.99/4.86 $i > $o )]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ?[
% 8.99/4.86 X448:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X450:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X446 @
% 8.99/4.86 X450 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X448 ) =
% 8.99/4.86 (
% 8.99/4.86 X450 ) ) ) ) &
% 8.99/4.86 (
% 8.99/4.86 X446 @
% 8.99/4.86 X448 ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X452:$i,
% 8.99/4.86 X454:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X446 @
% 8.99/4.86 X452 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X446 @
% 8.99/4.86 X454 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X452 ) =
% 8.99/4.86 (
% 8.99/4.86 X454 ) ) ) ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X456:(
% 8.99/4.86 $i > $o ),
% 8.99/4.86 X458:(
% 8.99/4.86 $i > $o )]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X460:$i,
% 8.99/4.86 X462:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X460 ) =
% 8.99/4.86 (
% 8.99/4.86 X462 ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X456 @
% 8.99/4.86 X460 ) <=>
% 8.99/4.86 (
% 8.99/4.86 X458 @
% 8.99/4.86 X462 ) ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ?[
% 8.99/4.86 X464:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X466:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X456 @
% 8.99/4.86 X466 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X464 ) =
% 8.99/4.86 (
% 8.99/4.86 X466 ) ) ) ) &
% 8.99/4.86 (
% 8.99/4.86 X456 @
% 8.99/4.86 X464 ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ?[
% 8.99/4.86 X468:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 ![
% 8.99/4.86 X470:$i]:
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X458 @
% 8.99/4.86 X470 ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 X468 ) =
% 8.99/4.86 (
% 8.99/4.86 X470 ) ) ) ) &
% 8.99/4.86 (
% 8.99/4.86 X458 @
% 8.99/4.86 X468 ) ) ) =>
% 8.99/4.86 (
% 8.99/4.86 (
% 8.99/4.86 descr @
% 8.99/4.86 (
% 8.99/4.86 ^[
% 8.99/4.86 V_9:$i]:
% 8.99/4.86 (
% 8.99/4.86 X456 @
% 8.99/4.86 V_9 ) ) ) =
% 8.99/4.86 (
% 8.99/4.86 descr @
% 8.99/4.86 (
% 8.99/4.86 ^[
% 8.99/4.86 V_10:$i]:
% 8.99/4.86 (
% 8.99/4.86 X458 @
% 8.99/4.86 V_10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 8.99/4.86 inference('cnf.neg', [status(esa)], [zf_stmt_13])).
% 8.99/4.86 thf(zip_derived_cl95, plain,
% 8.99/4.86 (![X109 : $i]: (((sk__229) = (X109)) | ~ (sk__228 @ X109))),
% 8.99/4.86 inference('cnf', [status(esa)], [zf_stmt_14])).
% 8.99/4.86 thf(zip_derived_cl99, plain, ( (sk__230 @ sk__231)),
% 8.99/4.86 inference('cnf', [status(esa)], [zf_stmt_14])).
% 8.99/4.86 thf(zip_derived_cl96, plain,
% 8.99/4.86 (![X110 : $i, X111 : $i]:
% 8.99/4.86 (~ (sk__230 @ X110) | (sk__228 @ X111) | ((X111) != (X110)))),
% 8.99/4.86 inference('cnf', [status(esa)], [zf_stmt_14])).
% 8.99/4.86 thf(zip_derived_cl598, plain,
% 8.99/4.86 (![X110 : $i]: ( (sk__228 @ X110) | ~ (sk__230 @ X110))),
% 8.99/4.86 inference('simplify', [status(thm)], [zip_derived_cl96])).
% 8.99/4.86 thf(zip_derived_cl99, plain, ( (sk__230 @ sk__231)),
% 8.99/4.86 inference('cnf', [status(esa)], [zf_stmt_14])).
% 8.99/4.86 thf(zip_derived_cl600, plain, ( (sk__228 @ sk__231)),
% 8.99/4.86 inference('sup+', [status(thm)], [zip_derived_cl598, zip_derived_cl99])).
% 8.99/4.86 thf(zip_derived_cl95, plain,
% 8.99/4.86 (![X109 : $i]: (((sk__229) = (X109)) | ~ (sk__228 @ X109))),
% 8.99/4.86 inference('cnf', [status(esa)], [zf_stmt_14])).
% 8.99/4.86 thf(zip_derived_cl719, plain, (((sk__229) = (sk__231))),
% 8.99/4.86 inference('sup-', [status(thm)], [zip_derived_cl600, zip_derived_cl95])).
% 8.99/4.86 thf(zip_derived_cl767, plain, ( (sk__230 @ sk__229)),
% 8.99/4.86 inference('demod', [status(thm)], [zip_derived_cl99, zip_derived_cl719])).
% 8.99/4.86 thf(zip_derived_cl987, plain,
% 8.99/4.86 (![X0 : $i]: ( (sk__230 @ X0) | ~ (sk__228 @ X0))),
% 8.99/4.86 inference('sup+', [status(thm)], [zip_derived_cl95, zip_derived_cl767])).
% 8.99/4.86 thf(zip_derived_cl100, plain,
% 8.99/4.86 (((descr @ (^[Y0 : $i]: (sk__228 @ Y0)))
% 8.99/4.86 != (descr @ (^[Y0 : $i]: (sk__230 @ Y0))))),
% 8.99/4.86 inference('cnf', [status(esa)], [zf_stmt_14])).
% 8.99/4.86 thf(zip_derived_cl170, plain, (((descr @ sk__228) != (descr @ sk__230))),
% 8.99/4.86 inference('ho_norm', [status(thm)], [zip_derived_cl100])).
% 8.99/4.86 thf(zip_derived_cl171, plain,
% 8.99/4.86 ((((^[Y0 : $i]: (sk__230 @ Y0))) != ((^[Y0 : $i]: (sk__228 @ Y0))))),
% 8.99/4.86 inference('ext_eqres', [status(thm)], [zip_derived_cl170])).
% 8.99/4.86 thf(zip_derived_cl172, plain, (((sk__230) != (sk__228))),
% 8.99/4.86 inference('ho_norm', [status(thm)], [zip_derived_cl171])).
% 8.99/4.86 thf(zip_derived_cl173, plain, (((sk__230 @ '#sk1') != (sk__228 @ '#sk1'))),
% 8.99/4.86 inference('neg_ext', [status(thm)], [zip_derived_cl172])).
% 8.99/4.86 thf(zip_derived_cl177, plain,
% 8.99/4.86 ((~ (sk__228 @ '#sk1') | ~ (sk__230 @ '#sk1'))),
% 8.99/4.86 inference('cnf_otf', [status(thm)], [zip_derived_cl173])).
% 8.99/4.86 thf(zip_derived_cl176, plain, (( (sk__228 @ '#sk1') | (sk__230 @ '#sk1'))),
% 8.99/4.86 inference('cnf_otf', [status(thm)], [zip_derived_cl173])).
% 8.99/4.86 thf(zip_derived_cl598, plain,
% 8.99/4.86 (![X110 : $i]: ( (sk__228 @ X110) | ~ (sk__230 @ X110))),
% 8.99/4.86 inference('simplify', [status(thm)], [zip_derived_cl96])).
% 8.99/4.86 thf(zip_derived_cl601, plain, (( (sk__228 @ '#sk1') | (sk__228 @ '#sk1'))),
% 8.99/4.86 inference('sup-', [status(thm)], [zip_derived_cl176, zip_derived_cl598])).
% 8.99/4.86 thf(zip_derived_cl651, plain, ( (sk__228 @ '#sk1')),
% 8.99/4.86 inference('simplify', [status(thm)], [zip_derived_cl601])).
% 8.99/4.86 thf(zip_derived_cl771, plain, (~ (sk__230 @ '#sk1')),
% 8.99/4.86 inference('demod', [status(thm)], [zip_derived_cl177, zip_derived_cl651])).
% 8.99/4.86 thf(zip_derived_cl1045, plain, (~ (sk__228 @ '#sk1')),
% 8.99/4.86 inference('sup-', [status(thm)], [zip_derived_cl987, zip_derived_cl771])).
% 8.99/4.86 thf(zip_derived_cl651, plain, ( (sk__228 @ '#sk1')),
% 8.99/4.86 inference('simplify', [status(thm)], [zip_derived_cl601])).
% 8.99/4.86 thf(zip_derived_cl1059, plain, ($false),
% 8.99/4.86 inference('demod', [status(thm)], [zip_derived_cl1045, zip_derived_cl651])).
% 8.99/4.86
% 8.99/4.86 % SZS output end Refutation
% 8.99/4.86
% 8.99/4.86
% 8.99/4.86 % Terminating...
% 9.08/5.02 % Runner terminated.
% 9.13/5.06 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------