%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU511^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.yhs8glxcfN true
% Computer : n020.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 04:54:51 PM UTC 2025
% Result : Theorem 0.57s 0.81s
% Output : Refutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU511^1 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.yhs8glxcfN true
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 16:08:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.55/0.67 % Total configuration time : 828
% 0.55/0.67 % Estimated wc time : 1656
% 0.55/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.55/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.56/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.73 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.56/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.56/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.56/0.75 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.57/0.76 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.57/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 0.57/0.81 % Solved by lams/40_c.s.sh.
% 0.57/0.81 % done 6 iterations in 0.077s
% 0.57/0.81 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.57/0.81 % SZS output start Refutation
% 0.57/0.81 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 0.57/0.81 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 0.57/0.81 thf(setunionAx_type, type, setunionAx: $o).
% 0.57/0.81 thf(omegaSAx_type, type, omegaSAx: $o).
% 0.57/0.81 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 0.57/0.81 thf(emptysetE_type, type, emptysetE: $o).
% 0.57/0.81 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 0.57/0.81 thf(in_type, type, in: $i > $i > $o).
% 0.57/0.81 thf(emptyI_type, type, emptyI: $o).
% 0.57/0.81 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 0.57/0.81 thf(sk__98_type, type, sk__98: $i).
% 0.57/0.81 thf(powersetAx_type, type, powersetAx: $o).
% 0.57/0.81 thf(notinemptyset_type, type, notinemptyset: $o).
% 0.57/0.81 thf(emptyset_type, type, emptyset: $i).
% 0.57/0.81 thf(setext_type, type, setext: $o).
% 0.57/0.81 thf(setbeta_type, type, setbeta: $o).
% 0.57/0.81 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 0.57/0.81 thf(descr_type, type, descr: ($i > $o) > $i).
% 0.57/0.81 thf(exuE1_type, type, exuE1: $o).
% 0.57/0.81 thf(prop2set_type, type, prop2set: $o > $i).
% 0.57/0.81 thf(nonemptyI_type, type, nonemptyI: $o).
% 0.57/0.81 thf(omega0Ax_type, type, omega0Ax: $o).
% 0.57/0.81 thf(prop2setE_type, type, prop2setE: $o).
% 0.57/0.81 thf(setextAx_type, type, setextAx: $o).
% 0.57/0.81 thf(zip_tseitin_2_type, type, zip_tseitin_2: $i > $i > $i > $o).
% 0.57/0.81 thf(setunion_type, type, setunion: $i > $i).
% 0.57/0.81 thf(descrp_type, type, descrp: $o).
% 0.57/0.81 thf(foundationAx_type, type, foundationAx: $o).
% 0.57/0.81 thf(emptysetAx_type, type, emptysetAx: $o).
% 0.57/0.81 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 0.57/0.81 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 0.57/0.81 thf(exu_type, type, exu: ($i > $o) > $o).
% 0.57/0.81 thf(sk__99_type, type, sk__99: $i).
% 0.57/0.81 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 0.57/0.81 thf(omega_type, type, omega: $i).
% 0.57/0.81 thf(exuE3e_type, type, exuE3e: $o).
% 0.57/0.81 thf(powerset_type, type, powerset: $i > $i).
% 0.57/0.81 thf(zip_tseitin_3_type, type, zip_tseitin_3: $i > $i > $i > ($i > $i > $o) > $o).
% 0.57/0.81 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 0.57/0.81 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 0.57/0.81 thf(replAx_type, type, replAx: $o).
% 0.57/0.81 thf(nonempty_type, type, nonempty: $i > $o).
% 0.57/0.81 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 0.57/0.81 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $i > $o).
% 0.57/0.81 thf(nonemptyI, axiom, nonemptyI =
% 0.57/0.81 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 0.57/0.81 ( ( in @ Xx @ A ) =>
% 0.57/0.81 ( ( Xphi @ Xx ) =>
% 0.57/0.81 ( nonempty @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 0.57/0.81 thf('0', plain,
% 0.57/0.81 (( nonemptyI ) =
% 0.57/0.81 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 0.57/0.81 ( ( in @ X8 @ X4 ) =>
% 0.57/0.81 ( ( X6 @ X8 ) =>
% 0.57/0.81 ( nonempty @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(nonemptyE1, axiom, nonemptyE1 =
% 0.57/0.81 (![A:$i]: ( ( nonempty @ A ) => ( ?[Xx:$i]: ( in @ Xx @ A ) ) ))).
% 0.57/0.81 thf('1', plain,
% 0.57/0.81 (( nonemptyE1 ) =
% 0.57/0.81 ( ![X4:$i]: ( ( nonempty @ X4 ) => ( ?[X6:$i]: ( in @ X6 @ X4 ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(nonempty, axiom,(( nonempty ) = (^[Xx:$i]: ( ( Xx ) != ( emptyset ) )))).
% 0.57/0.81 thf('2', plain, (( nonempty ) = ( ^[Xx:$i]: ( ( Xx ) != ( emptyset ) ) )),
% 0.57/0.81 inference('simplify_rw_rule', [status(thm)], [nonempty])).
% 0.57/0.81 thf('3', plain, (( nonempty ) = ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(setbeta, axiom, setbeta =
% 0.57/0.81 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 0.57/0.81 ( ( in @ Xx @ A ) =>
% 0.57/0.81 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) <=>
% 0.57/0.81 ( Xphi @ Xx ) ) ))).
% 0.57/0.81 thf('4', plain,
% 0.57/0.81 (( setbeta ) =
% 0.57/0.81 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 0.57/0.81 ( ( in @ X8 @ X4 ) =>
% 0.57/0.81 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) <=>
% 0.57/0.81 ( X6 @ X8 ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(noeltsimpempty, axiom, noeltsimpempty =
% 0.57/0.81 (![A:$i]:
% 0.57/0.81 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 0.57/0.81 thf('5', plain,
% 0.57/0.81 (( noeltsimpempty ) =
% 0.57/0.81 ( ![X4:$i]:
% 0.57/0.81 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(emptyI, axiom, emptyI =
% 0.57/0.81 (![A:$i]:
% 0.57/0.81 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 0.57/0.81 thf('6', plain,
% 0.57/0.81 (( emptyI ) =
% 0.57/0.81 ( ![X4:$i]:
% 0.57/0.81 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(setext, axiom, setext =
% 0.57/0.81 (![A:$i,B:$i]:
% 0.57/0.81 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 0.57/0.81 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 0.57/0.81 ( ( A ) = ( B ) ) ) ))).
% 0.57/0.81 thf('7', plain,
% 0.57/0.81 (( setext ) =
% 0.57/0.81 ( ![X4:$i,X6:$i]:
% 0.57/0.81 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 0.57/0.81 ( ( ![X10:$i]: ( ( in @ X10 @ X6 ) => ( in @ X10 @ X4 ) ) ) =>
% 0.57/0.81 ( ( X4 ) = ( X6 ) ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(exuE3e, axiom, exuE3e =
% 0.57/0.81 (![Xphi:( $i > $o )]:
% 0.57/0.81 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) => ( ?[Xx:$i]: ( Xphi @ Xx ) ) ))).
% 0.57/0.81 thf('8', plain,
% 0.57/0.81 (( exuE3e ) =
% 0.57/0.81 ( ![X4:( $i > $o )]:
% 0.57/0.81 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) => ( ?[X6:$i]: ( X4 @ X6 ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(notinemptyset, axiom, notinemptyset =
% 0.57/0.81 (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 0.57/0.81 thf('9', plain,
% 0.57/0.81 (( notinemptyset ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(emptysetimpfalse, axiom, emptysetimpfalse =
% 0.57/0.81 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( $false ) ))).
% 0.57/0.81 thf('10', plain,
% 0.57/0.81 (( emptysetimpfalse ) =
% 0.57/0.81 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( $false ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(emptysetE, axiom, emptysetE =
% 0.57/0.81 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( ![Xphi:$o]: ( Xphi ) ) ))).
% 0.57/0.81 thf('11', plain,
% 0.57/0.81 (( emptysetE ) =
% 0.57/0.81 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( ![X6:$o]: ( X6 ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(prop2setE, axiom, prop2setE =
% 0.57/0.81 (![Xphi:$o,Xx:$i]: ( ( in @ Xx @ ( prop2set @ Xphi ) ) => ( Xphi ) ))).
% 0.57/0.81 thf('12', plain,
% 0.57/0.81 (( prop2setE ) =
% 0.57/0.81 ( ![X4:$o,X6:$i]: ( ( in @ X6 @ ( prop2set @ X4 ) ) => ( X4 ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(prop2set, axiom,(( prop2set ) =
% 0.57/0.81 (^[Xphi:$o]:
% 0.57/0.81 ( dsetconstr @ ( powerset @ emptyset ) @ ( ^[Xx:$i]: ( Xphi ) ) )))).
% 0.57/0.81 thf('13', plain,
% 0.57/0.81 (( prop2set ) =
% 0.57/0.81 ( ^[Xphi:$o]:
% 0.57/0.81 ( dsetconstr @ ( powerset @ emptyset ) @ ( ^[Xx:$i]: ( Xphi ) ) ) )),
% 0.57/0.81 inference('simplify_rw_rule', [status(thm)], [prop2set])).
% 0.57/0.81 thf('14', plain,
% 0.57/0.81 (( prop2set ) =
% 0.57/0.81 ( ^[V_1:$o]:
% 0.57/0.81 ( dsetconstr @ ( powerset @ emptyset ) @ ( ^[V_2:$i]: ( V_1 ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(exuE1, axiom, exuE1 =
% 0.57/0.81 (![Xphi:( $i > $o )]:
% 0.57/0.81 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 0.57/0.81 ( ?[Xx:$i]:
% 0.57/0.81 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 0.57/0.81 ( Xphi @ Xx ) ) ) ))).
% 0.57/0.81 thf('15', plain,
% 0.57/0.81 (( exuE1 ) =
% 0.57/0.81 ( ![X4:( $i > $o )]:
% 0.57/0.81 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 0.57/0.81 ( ?[X6:$i]:
% 0.57/0.81 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) &
% 0.57/0.81 ( X4 @ X6 ) ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(dsetconstrER, axiom, dsetconstrER =
% 0.57/0.81 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 0.57/0.81 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 0.57/0.81 ( Xphi @ Xx ) ))).
% 0.57/0.81 thf('16', plain,
% 0.57/0.81 (( dsetconstrER ) =
% 0.57/0.81 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 0.57/0.81 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 0.57/0.81 ( X6 @ X8 ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(dsetconstrEL, axiom, dsetconstrEL =
% 0.57/0.81 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 0.57/0.81 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 0.57/0.81 ( in @ Xx @ A ) ))).
% 0.57/0.81 thf('17', plain,
% 0.57/0.81 (( dsetconstrEL ) =
% 0.57/0.81 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 0.57/0.81 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 0.57/0.81 ( in @ X8 @ X4 ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(dsetconstrI, axiom, dsetconstrI =
% 0.57/0.81 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 0.57/0.81 ( ( in @ Xx @ A ) =>
% 0.57/0.81 ( ( Xphi @ Xx ) =>
% 0.57/0.81 ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 0.57/0.81 thf('18', plain,
% 0.57/0.81 (( dsetconstrI ) =
% 0.57/0.81 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 0.57/0.81 ( ( in @ X8 @ X4 ) =>
% 0.57/0.81 ( ( X6 @ X8 ) =>
% 0.57/0.81 ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(descrp, axiom, descrp =
% 0.57/0.81 (![Xphi:( $i > $o )]:
% 0.57/0.81 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 0.57/0.81 ( Xphi @ ( descr @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 0.57/0.81 thf('19', plain,
% 0.57/0.81 (( descrp ) =
% 0.57/0.81 ( ![X4:( $i > $o )]:
% 0.57/0.81 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 0.57/0.81 ( X4 @ ( descr @ ( ^[V_2:$i]: ( X4 @ V_2 ) ) ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(wellorderingAx, axiom, wellorderingAx =
% 0.57/0.81 (![A:$i]:
% 0.57/0.81 ( ?[B:$i]:
% 0.57/0.81 ( ( ![C:$i]:
% 0.57/0.81 ( ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) &
% 0.57/0.81 ( ?[Xx:$i]: ( in @ Xx @ C ) ) ) =>
% 0.57/0.81 ( ?[D:$i,Xx:$i]:
% 0.57/0.81 ( ( ![E:$i]:
% 0.57/0.81 ( ( in @ E @ B ) =>
% 0.57/0.81 ( ( ![Xy:$i]: ( ( in @ Xy @ E ) => ( in @ Xy @ D ) ) ) |
% 0.57/0.81 ( in @ Xx @ E ) ) ) ) &
% 0.57/0.81 ( ~( ?[Xy:$i]: ( ( in @ Xy @ C ) & ( in @ Xy @ D ) ) ) ) &
% 0.57/0.81 ( in @ Xx @ C ) & ( in @ D @ B ) ) ) ) ) &
% 0.57/0.81 ( ![C:$i,D:$i]:
% 0.57/0.81 ( ( ( in @ C @ B ) & ( in @ D @ B ) ) =>
% 0.57/0.81 ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ D ) ) ) |
% 0.57/0.81 ( ![Xx:$i]: ( ( in @ Xx @ D ) => ( in @ Xx @ C ) ) ) ) ) ) &
% 0.57/0.81 ( ![Xx:$i,Xy:$i]:
% 0.57/0.81 ( ( ( in @ Xx @ A ) & ( in @ Xy @ A ) ) =>
% 0.57/0.81 ( ( ![C:$i]:
% 0.57/0.81 ( ( in @ C @ B ) => ( ( in @ Xx @ C ) <=> ( in @ Xy @ C ) ) ) ) =>
% 0.57/0.81 ( ( Xx ) = ( Xy ) ) ) ) ) &
% 0.57/0.81 ( ![C:$i]:
% 0.57/0.81 ( ( in @ C @ B ) =>
% 0.57/0.81 ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) ) ) ) ))).
% 0.57/0.81 thf('20', plain,
% 0.57/0.81 (( wellorderingAx ) =
% 0.57/0.81 ( ![X4:$i]:
% 0.57/0.81 ( ?[X6:$i]:
% 0.57/0.81 ( ( ![X8:$i]:
% 0.57/0.81 ( ( ( ![X10:$i]: ( ( in @ X10 @ X8 ) => ( in @ X10 @ X4 ) ) ) &
% 0.57/0.81 ( ?[X12:$i]: ( in @ X12 @ X8 ) ) ) =>
% 0.57/0.81 ( ?[X14:$i,X16:$i]:
% 0.57/0.81 ( ( ![X18:$i]:
% 0.57/0.81 ( ( in @ X18 @ X6 ) =>
% 0.57/0.81 ( ( ![X20:$i]:
% 0.57/0.81 ( ( in @ X20 @ X18 ) => ( in @ X20 @ X14 ) ) ) |
% 0.57/0.81 ( in @ X16 @ X18 ) ) ) ) &
% 0.57/0.81 ( ~( ?[X22:$i]: ( ( in @ X22 @ X8 ) & ( in @ X22 @ X14 ) ) ) ) &
% 0.57/0.81 ( in @ X16 @ X8 ) & ( in @ X14 @ X6 ) ) ) ) ) &
% 0.57/0.81 ( ![X24:$i,X26:$i]:
% 0.57/0.81 ( ( ( in @ X24 @ X6 ) & ( in @ X26 @ X6 ) ) =>
% 0.57/0.81 ( ( ![X28:$i]: ( ( in @ X28 @ X24 ) => ( in @ X28 @ X26 ) ) ) |
% 0.57/0.81 ( ![X30:$i]: ( ( in @ X30 @ X26 ) => ( in @ X30 @ X24 ) ) ) ) ) ) &
% 0.57/0.81 ( ![X32:$i,X34:$i]:
% 0.57/0.81 ( ( ( in @ X32 @ X4 ) & ( in @ X34 @ X4 ) ) =>
% 0.57/0.81 ( ( ![X36:$i]:
% 0.57/0.81 ( ( in @ X36 @ X6 ) =>
% 0.57/0.81 ( ( in @ X32 @ X36 ) <=> ( in @ X34 @ X36 ) ) ) ) =>
% 0.57/0.81 ( ( X32 ) = ( X34 ) ) ) ) ) &
% 0.57/0.81 ( ![X38:$i]:
% 0.57/0.81 ( ( in @ X38 @ X6 ) =>
% 0.57/0.81 ( ![X40:$i]: ( ( in @ X40 @ X38 ) => ( in @ X40 @ X4 ) ) ) ) ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(foundationAx, axiom, foundationAx =
% 0.57/0.81 (![A:$i]:
% 0.57/0.81 ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) =>
% 0.57/0.81 ( ?[B:$i]:
% 0.57/0.81 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ A ) & ( in @ Xx @ B ) ) ) ) &
% 0.57/0.81 ( in @ B @ A ) ) ) ))).
% 0.57/0.81 thf('21', plain,
% 0.57/0.81 (( foundationAx ) =
% 0.57/0.81 ( ![X4:$i]:
% 0.57/0.81 ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) =>
% 0.57/0.81 ( ?[X8:$i]:
% 0.57/0.81 ( ( ~( ?[X10:$i]: ( ( in @ X10 @ X4 ) & ( in @ X10 @ X8 ) ) ) ) &
% 0.57/0.81 ( in @ X8 @ X4 ) ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(replAx, axiom, replAx =
% 0.57/0.81 (![Xphi:( $i > $i > $o ),A:$i]:
% 0.57/0.81 ( ( ![Xx:$i]:
% 0.57/0.81 ( ( in @ Xx @ A ) => ( exu @ ( ^[Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) ) ) =>
% 0.57/0.81 ( ?[B:$i]:
% 0.57/0.81 ( ![Xx:$i]:
% 0.57/0.81 ( ( in @ Xx @ B ) <=>
% 0.57/0.81 ( ?[Xy:$i]: ( ( Xphi @ Xy @ Xx ) & ( in @ Xy @ A ) ) ) ) ) ) ))).
% 0.57/0.81 thf('22', plain,
% 0.57/0.81 (( replAx ) =
% 0.57/0.81 ( ![X4:( $i > $i > $o ),X6:$i]:
% 0.57/0.81 ( ( ![X8:$i]:
% 0.57/0.81 ( ( in @ X8 @ X6 ) => ( exu @ ( ^[V_1:$i]: ( X4 @ X8 @ V_1 ) ) ) ) ) =>
% 0.57/0.81 ( ?[X10:$i]:
% 0.57/0.81 ( ![X12:$i]:
% 0.57/0.81 ( ( in @ X12 @ X10 ) <=>
% 0.57/0.81 ( ?[X14:$i]: ( ( X4 @ X14 @ X12 ) & ( in @ X14 @ X6 ) ) ) ) ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(omegaIndAx, axiom, omegaIndAx =
% 0.57/0.81 (![A:$i]:
% 0.57/0.81 ( ( ( in @ emptyset @ A ) &
% 0.57/0.81 ( ![Xx:$i]:
% 0.57/0.81 ( ( ( in @ Xx @ omega ) & ( in @ Xx @ A ) ) =>
% 0.57/0.81 ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) ) =>
% 0.57/0.81 ( ![Xx:$i]: ( ( in @ Xx @ omega ) => ( in @ Xx @ A ) ) ) ))).
% 0.57/0.81 thf('23', plain,
% 0.57/0.81 (( omegaIndAx ) =
% 0.57/0.81 ( ![X4:$i]:
% 0.57/0.81 ( ( ( in @ emptyset @ X4 ) &
% 0.57/0.81 ( ![X6:$i]:
% 0.57/0.81 ( ( ( in @ X6 @ omega ) & ( in @ X6 @ X4 ) ) =>
% 0.57/0.81 ( in @ ( setadjoin @ X6 @ X6 ) @ X4 ) ) ) ) =>
% 0.57/0.81 ( ![X8:$i]: ( ( in @ X8 @ omega ) => ( in @ X8 @ X4 ) ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(omegaSAx, axiom, omegaSAx =
% 0.57/0.81 (![Xx:$i]:
% 0.57/0.81 ( ( in @ Xx @ omega ) => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ))).
% 0.57/0.81 thf('24', plain,
% 0.57/0.81 (( omegaSAx ) =
% 0.57/0.81 ( ![X4:$i]:
% 0.57/0.81 ( ( in @ X4 @ omega ) => ( in @ ( setadjoin @ X4 @ X4 ) @ omega ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(omega0Ax, axiom,(( omega0Ax ) = (in @ emptyset @ omega))).
% 0.57/0.81 thf('25', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 0.57/0.81 inference('simplify_rw_rule', [status(thm)], [omega0Ax])).
% 0.57/0.81 thf('26', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(setunionAx, axiom, setunionAx =
% 0.57/0.81 (![A:$i,Xx:$i]:
% 0.57/0.81 ( ( in @ Xx @ ( setunion @ A ) ) <=>
% 0.57/0.81 ( ?[B:$i]: ( ( in @ B @ A ) & ( in @ Xx @ B ) ) ) ))).
% 0.57/0.81 thf('27', plain,
% 0.57/0.81 (( setunionAx ) =
% 0.57/0.81 ( ![X4:$i,X6:$i]:
% 0.57/0.81 ( ( in @ X6 @ ( setunion @ X4 ) ) <=>
% 0.57/0.81 ( ?[X8:$i]: ( ( in @ X8 @ X4 ) & ( in @ X6 @ X8 ) ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(powersetAx, axiom, powersetAx =
% 0.57/0.81 (![A:$i,B:$i]:
% 0.57/0.81 ( ( in @ B @ ( powerset @ A ) ) <=>
% 0.57/0.81 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 0.57/0.81 thf('28', plain,
% 0.57/0.81 (( powersetAx ) =
% 0.57/0.81 ( ![X4:$i,X6:$i]:
% 0.57/0.81 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 0.57/0.81 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(setadjoinAx, axiom, setadjoinAx =
% 0.57/0.81 (![Xx:$i,A:$i,Xy:$i]:
% 0.57/0.81 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 0.57/0.81 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 0.57/0.81 thf('29', plain,
% 0.57/0.81 (( setadjoinAx ) =
% 0.57/0.81 ( ![X4:$i,X6:$i,X8:$i]:
% 0.57/0.81 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.57/0.81 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(emptysetAx, axiom, emptysetAx = (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 0.57/0.81 thf('30', plain,
% 0.57/0.81 (( emptysetAx ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(setextAx, axiom, setextAx =
% 0.57/0.81 (![A:$i,B:$i]:
% 0.57/0.81 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) <=> ( in @ Xx @ B ) ) ) =>
% 0.57/0.81 ( ( A ) = ( B ) ) ))).
% 0.57/0.81 thf('31', plain,
% 0.57/0.81 (( setextAx ) =
% 0.57/0.81 ( ![X4:$i,X6:$i]:
% 0.57/0.81 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 0.57/0.81 ( ( X4 ) = ( X6 ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(exu, axiom,(( exu ) =
% 0.57/0.81 (^[Xphi:( $i > $o )]:
% 0.57/0.81 ( ?[Xx:$i]:
% 0.57/0.81 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) & ( Xphi @ Xx ) ) )))).
% 0.57/0.81 thf('32', plain,
% 0.57/0.81 (( exu ) =
% 0.57/0.81 ( ^[Xphi:( $i > $o )]:
% 0.57/0.81 ( ?[Xx:$i]:
% 0.57/0.81 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 0.57/0.81 ( Xphi @ Xx ) ) ) )),
% 0.57/0.81 inference('simplify_rw_rule', [status(thm)], [exu])).
% 0.57/0.81 thf('33', plain,
% 0.57/0.81 (( exu ) =
% 0.57/0.81 ( ^[V_1:( $i > $o )]:
% 0.57/0.81 ( ?[X4:$i]:
% 0.57/0.81 ( ( ![X6:$i]: ( ( V_1 @ X6 ) => ( ( X4 ) = ( X6 ) ) ) ) &
% 0.57/0.81 ( V_1 @ X4 ) ) ) )),
% 0.57/0.81 define([status(thm)])).
% 0.57/0.81 thf(nonemptyI1, conjecture,
% 0.57/0.81 (( setextAx ) =>
% 0.57/0.81 ( ( emptysetAx ) =>
% 0.57/0.81 ( ( setadjoinAx ) =>
% 0.57/0.81 ( ( powersetAx ) =>
% 0.57/0.81 ( ( setunionAx ) =>
% 0.57/0.81 ( ( omega0Ax ) =>
% 0.57/0.81 ( ( omegaSAx ) =>
% 0.57/0.81 ( ( omegaIndAx ) =>
% 0.57/0.81 ( ( replAx ) =>
% 0.57/0.81 ( ( foundationAx ) =>
% 0.57/0.81 ( ( wellorderingAx ) =>
% 0.57/0.81 ( ( descrp ) =>
% 0.57/0.81 ( ( dsetconstrI ) =>
% 0.57/0.81 ( ( dsetconstrEL ) =>
% 0.57/0.81 ( ( dsetconstrER ) =>
% 0.57/0.81 ( ( exuE1 ) =>
% 0.57/0.81 ( ( prop2setE ) =>
% 0.57/0.81 ( ( emptysetE ) =>
% 0.57/0.81 ( ( emptysetimpfalse ) =>
% 0.57/0.81 ( ( notinemptyset ) =>
% 0.57/0.81 ( ( exuE3e ) =>
% 0.57/0.81 ( ( setext ) =>
% 0.57/0.81 ( ( emptyI ) =>
% 0.57/0.81 ( ( noeltsimpempty ) =>
% 0.57/0.81 ( ( setbeta ) =>
% 0.57/0.81 ( ( nonemptyE1 ) =>
% 0.57/0.81 ( ( nonemptyI ) =>
% 0.57/0.81 ( ![A:$i]:
% 0.57/0.81 ( ( ?[Xx:$i]:
% 0.57/0.81 ( in @ Xx @ A ) ) =>
% 0.57/0.81 ( nonempty @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.57/0.81 thf(zf_stmt_0, conjecture,
% 0.57/0.81 (( ![X4:$i,X6:$i]:
% 0.57/0.81 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 0.57/0.81 ( ( X4 ) = ( X6 ) ) ) ) =>
% 0.57/0.81 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 0.57/0.81 ( ( ![X12:$i,X14:$i,X16:$i]:
% 0.57/0.81 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 0.57/0.81 ( ( in @ X16 @ X14 ) | ( ( X16 ) = ( X12 ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X18:$i,X20:$i]:
% 0.57/0.81 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 0.57/0.81 ( ![X22:$i]: ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X24:$i,X26:$i]:
% 0.57/0.81 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 0.57/0.81 ( ?[X28:$i]: ( ( in @ X26 @ X28 ) & ( in @ X28 @ X24 ) ) ) ) ) =>
% 0.57/0.81 ( ( in @ emptyset @ omega ) =>
% 0.57/0.81 ( ( ![X30:$i]:
% 0.57/0.81 ( ( in @ X30 @ omega ) =>
% 0.57/0.81 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 0.57/0.81 ( ( ![X32:$i]:
% 0.57/0.81 ( ( ( ![X34:$i]:
% 0.57/0.81 ( ( ( in @ X34 @ X32 ) & ( in @ X34 @ omega ) ) =>
% 0.57/0.81 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) &
% 0.57/0.81 ( in @ emptyset @ X32 ) ) =>
% 0.57/0.81 ( ![X36:$i]:
% 0.57/0.81 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 0.57/0.81 ( ( ![X42:$i]:
% 0.57/0.81 ( ( in @ X42 @ X40 ) =>
% 0.57/0.81 ( ?[X44:$i]:
% 0.57/0.81 ( ( X38 @ X42 @ X44 ) &
% 0.57/0.81 ( ![X46:$i]:
% 0.57/0.81 ( ( X38 @ X42 @ X46 ) =>
% 0.57/0.81 ( ( X44 ) = ( X46 ) ) ) ) ) ) ) ) =>
% 0.57/0.81 ( ?[X48:$i]:
% 0.57/0.81 ( ![X50:$i]:
% 0.57/0.81 ( ( in @ X50 @ X48 ) <=>
% 0.57/0.81 ( ?[X52:$i]:
% 0.57/0.81 ( ( in @ X52 @ X40 ) & ( X38 @ X52 @ X50 ) ) ) ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X54:$i]:
% 0.57/0.81 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 0.57/0.81 ( ?[X58:$i]:
% 0.57/0.81 ( ( in @ X58 @ X54 ) &
% 0.57/0.81 ( ~( ?[X60:$i]:
% 0.57/0.81 ( ( in @ X60 @ X58 ) & ( in @ X60 @ X54 ) ) ) ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X62:$i]:
% 0.57/0.81 ( ?[X64:$i]:
% 0.57/0.81 ( ( ![X96:$i]:
% 0.57/0.81 ( ( in @ X96 @ X64 ) =>
% 0.57/0.81 ( ![X98:$i]:
% 0.57/0.81 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) &
% 0.57/0.81 ( ![X90:$i,X92:$i]:
% 0.57/0.81 ( ( ( in @ X92 @ X62 ) & ( in @ X90 @ X62 ) ) =>
% 0.57/0.81 ( ( ![X94:$i]:
% 0.57/0.81 ( ( in @ X94 @ X64 ) =>
% 0.57/0.81 ( ( in @ X90 @ X94 ) <=>
% 0.57/0.81 ( in @ X92 @ X94 ) ) ) ) =>
% 0.57/0.81 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 0.57/0.81 ( ![X82:$i,X84:$i]:
% 0.57/0.81 ( ( ( in @ X84 @ X64 ) & ( in @ X82 @ X64 ) ) =>
% 0.57/0.81 ( ( ![X88:$i]:
% 0.57/0.81 ( ( in @ X88 @ X84 ) =>
% 0.57/0.81 ( in @ X88 @ X82 ) ) ) |
% 0.57/0.81 ( ![X86:$i]:
% 0.57/0.81 ( ( in @ X86 @ X82 ) =>
% 0.57/0.81 ( in @ X86 @ X84 ) ) ) ) ) ) &
% 0.57/0.81 ( ![X66:$i]:
% 0.57/0.81 ( ( ( ?[X70:$i]: ( in @ X70 @ X66 ) ) &
% 0.57/0.81 ( ![X68:$i]:
% 0.57/0.81 ( ( in @ X68 @ X66 ) =>
% 0.57/0.81 ( in @ X68 @ X62 ) ) ) ) =>
% 0.57/0.81 ( ?[X72:$i,X74:$i]:
% 0.57/0.81 ( ( in @ X72 @ X64 ) &
% 0.57/0.81 ( in @ X74 @ X66 ) &
% 0.57/0.81 ( ~( ?[X80:$i]:
% 0.57/0.81 ( ( in @ X80 @ X72 ) &
% 0.57/0.81 ( in @ X80 @ X66 ) ) ) ) &
% 0.57/0.81 ( ![X76:$i]:
% 0.57/0.81 ( ( in @ X76 @ X64 ) =>
% 0.57/0.81 ( ( in @ X74 @ X76 ) |
% 0.57/0.81 ( ![X78:$i]:
% 0.57/0.81 ( ( in @ X78 @ X76 ) =>
% 0.57/0.81 ( in @ X78 @ X72 ) ) ) ) ) ) ) ) ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X100:( $i > $o )]:
% 0.57/0.81 ( ( ?[X102:$i]:
% 0.57/0.81 ( ( X100 @ X102 ) &
% 0.57/0.81 ( ![X104:$i]:
% 0.57/0.81 ( ( X100 @ X104 ) =>
% 0.57/0.81 ( ( X102 ) = ( X104 ) ) ) ) ) ) =>
% 0.57/0.81 ( X100 @
% 0.57/0.81 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 0.57/0.81 ( ( in @ X110 @ X106 ) =>
% 0.57/0.81 ( ( X108 @ X110 ) =>
% 0.57/0.81 ( in @
% 0.57/0.81 X110 @
% 0.57/0.81 ( dsetconstr @
% 0.57/0.81 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 0.57/0.81 ( ( in @
% 0.57/0.81 X116 @
% 0.57/0.81 ( dsetconstr @
% 0.57/0.81 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 0.57/0.81 ( in @ X116 @ X112 ) ) ) =>
% 0.57/0.81 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 0.57/0.81 ( ( in @
% 0.57/0.81 X122 @
% 0.57/0.81 ( dsetconstr @
% 0.57/0.81 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 0.57/0.81 ( X120 @ X122 ) ) ) =>
% 0.57/0.81 ( ( ![X124:( $i > $o )]:
% 0.57/0.81 ( ( ?[X126:$i]:
% 0.57/0.81 ( ( X124 @ X126 ) &
% 0.57/0.81 ( ![X128:$i]:
% 0.57/0.81 ( ( X124 @ X128 ) =>
% 0.57/0.81 ( ( X126 ) = ( X128 ) ) ) ) ) ) =>
% 0.57/0.81 ( ?[X130:$i]:
% 0.57/0.81 ( ( X124 @ X130 ) &
% 0.57/0.81 ( ![X132:$i]:
% 0.57/0.81 ( ( X124 @ X132 ) =>
% 0.57/0.81 ( ( X130 ) = ( X132 ) ) ) ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X134:$o,X136:$i]:
% 0.57/0.81 ( ( in @
% 0.57/0.81 X136 @
% 0.57/0.81 ( dsetconstr @
% 0.57/0.81 ( powerset @ emptyset ) @
% 0.57/0.81 ( ^[V_5:$i]: ( X134 ) ) ) ) =>
% 0.57/0.81 ( X134 ) ) ) =>
% 0.57/0.81 ( ( ![X138:$i]:
% 0.57/0.81 ( ( in @ X138 @ emptyset ) =>
% 0.57/0.81 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 0.57/0.81 ( ( ![X142:$i]:
% 0.57/0.81 ( ( in @ X142 @ emptyset ) =>
% 0.57/0.81 ( $false ) ) ) =>
% 0.57/0.81 ( ( ![X144:$i]:
% 0.57/0.81 ( ~( in @ X144 @ emptyset ) ) ) =>
% 0.57/0.81 ( ( ![X146:( $i > $o )]:
% 0.57/0.81 ( ( ?[X148:$i]:
% 0.57/0.81 ( ( X146 @ X148 ) &
% 0.57/0.81 ( ![X150:$i]:
% 0.57/0.81 ( ( X146 @ X150 ) =>
% 0.57/0.81 ( ( X148 ) = ( X150 ) ) ) ) ) ) =>
% 0.57/0.81 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) =>
% 0.57/0.81 ( ( ![X154:$i,X156:$i]:
% 0.57/0.81 ( ( ![X158:$i]:
% 0.57/0.81 ( ( in @ X158 @ X154 ) =>
% 0.57/0.81 ( in @ X158 @ X156 ) ) ) =>
% 0.57/0.81 ( ( ![X160:$i]:
% 0.57/0.81 ( ( in @ X160 @ X156 ) =>
% 0.57/0.81 ( in @ X160 @ X154 ) ) ) =>
% 0.57/0.81 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X162:$i]:
% 0.57/0.81 ( ( ![X164:$i]:
% 0.57/0.81 ( ~( in @ X164 @ X162 ) ) ) =>
% 0.57/0.81 ( ( X162 ) = ( emptyset ) ) ) ) =>
% 0.57/0.81 ( ( ![X166:$i]:
% 0.57/0.81 ( ( ![X168:$i]:
% 0.57/0.81 ( ~( in @ X168 @ X166 ) ) ) =>
% 0.57/0.81 ( ( X166 ) =
% 0.57/0.81 ( emptyset ) ) ) ) =>
% 0.57/0.81 ( ( ![X170:$i,
% 0.57/0.81 X172:( $i > $o ),
% 0.57/0.81 X174:$i]:
% 0.57/0.81 ( ( in @ X174 @ X170 ) =>
% 0.57/0.81 ( ( in @
% 0.57/0.81 X174 @
% 0.57/0.81 ( dsetconstr @
% 0.57/0.81 X170 @
% 0.57/0.81 ( ^[V_6:$i]:
% 0.57/0.81 ( X172 @ V_6 ) ) ) ) <=>
% 0.57/0.81 ( X172 @ X174 ) ) ) ) =>
% 0.57/0.81 ( ( ![X176:$i]:
% 0.57/0.81 ( ( ( X176 ) !=
% 0.57/0.81 ( emptyset ) ) =>
% 0.57/0.81 ( ?[X178:$i]:
% 0.57/0.81 ( in @ X178 @ X176 ) ) ) ) =>
% 0.57/0.81 ( ( ![X180:$i,
% 0.57/0.81 X182:( $i > $o ),
% 0.57/0.81 X184:$i]:
% 0.57/0.81 ( ( in @ X184 @ X180 ) =>
% 0.57/0.81 ( ( X182 @ X184 ) =>
% 0.57/0.81 ( ( dsetconstr @
% 0.57/0.81 X180 @
% 0.57/0.81 ( ^[
% 0.57/0.81 V_7:$i]:
% 0.57/0.81 (
% 0.57/0.81 X182 @ V_7 ) ) ) !=
% 0.57/0.81 ( emptyset ) ) ) ) ) =>
% 0.57/0.81 ( ![X186:$i]:
% 0.57/0.81 ( ( ?[X188:$i]:
% 0.57/0.81 ( in @
% 0.57/0.81 X188 @ X186 ) ) =>
% 0.57/0.81 ( ( X186 ) !=
% 0.57/0.81 ( emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.57/0.81 thf(zf_stmt_1, type, zip_tseitin_3 : $i > $i > $i > ( $i > $i > $o ) > $o).
% 0.57/0.81 thf(zf_stmt_2, axiom,
% 0.57/0.81 (![X52:$i,X50:$i,X40:$i,X38:( $i > $i > $o )]:
% 0.57/0.81 ( ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) <=>
% 0.57/0.81 ( ( X38 @ X52 @ X50 ) & ( in @ X52 @ X40 ) ) ))).
% 0.57/0.81 thf(zf_stmt_3, type, zip_tseitin_2 : $i > $i > $i > $o).
% 0.57/0.81 thf(zf_stmt_4, axiom,
% 0.57/0.81 (![X28:$i,X26:$i,X24:$i]:
% 0.57/0.81 ( ( zip_tseitin_2 @ X28 @ X26 @ X24 ) <=>
% 0.57/0.81 ( ( in @ X28 @ X24 ) & ( in @ X26 @ X28 ) ) ))).
% 0.57/0.81 thf(zf_stmt_5, type, zip_tseitin_1 : $i > $i > $i > $o).
% 0.57/0.81 thf(zf_stmt_6, axiom,
% 0.57/0.81 (![X22:$i,X20:$i,X18:$i]:
% 0.57/0.81 ( ( zip_tseitin_1 @ X22 @ X20 @ X18 ) <=>
% 0.57/0.81 ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ))).
% 0.57/0.81 thf(zf_stmt_7, type, zip_tseitin_0 : $i > $i > $i > $o).
% 0.57/0.81 thf(zf_stmt_8, axiom,
% 0.57/0.81 (![X16:$i,X14:$i,X12:$i]:
% 0.57/0.81 ( ( zip_tseitin_0 @ X16 @ X14 @ X12 ) <=>
% 0.57/0.81 ( ( ( X16 ) = ( X12 ) ) | ( in @ X16 @ X14 ) ) ))).
% 0.57/0.81 thf(zf_stmt_9, conjecture,
% 0.57/0.81 (( ![X4:$i,X6:$i]:
% 0.57/0.81 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 0.57/0.81 ( ( X4 ) = ( X6 ) ) ) ) =>
% 0.57/0.81 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 0.57/0.81 ( ( ![X12:$i,X14:$i,X16:$i]:
% 0.57/0.81 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 0.57/0.81 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 0.57/0.81 ( ( ![X18:$i,X20:$i]:
% 0.57/0.81 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 0.57/0.81 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 0.57/0.81 ( ( ![X24:$i,X26:$i]:
% 0.57/0.81 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 0.57/0.81 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 0.57/0.81 ( ( in @ emptyset @ omega ) =>
% 0.57/0.81 ( ( ![X30:$i]:
% 0.57/0.81 ( ( in @ X30 @ omega ) =>
% 0.57/0.81 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 0.57/0.81 ( ( ![X32:$i]:
% 0.57/0.81 ( ( ( in @ emptyset @ X32 ) &
% 0.57/0.81 ( ![X34:$i]:
% 0.57/0.81 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 0.57/0.81 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 0.57/0.81 ( ![X36:$i]:
% 0.57/0.81 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 0.57/0.81 ( ( ![X42:$i]:
% 0.57/0.81 ( ( in @ X42 @ X40 ) =>
% 0.57/0.81 ( ?[X44:$i]:
% 0.57/0.81 ( ( ![X46:$i]:
% 0.57/0.81 ( ( X38 @ X42 @ X46 ) =>
% 0.57/0.81 ( ( X44 ) = ( X46 ) ) ) ) &
% 0.57/0.81 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 0.57/0.81 ( ?[X48:$i]:
% 0.57/0.81 ( ![X50:$i]:
% 0.57/0.81 ( ( in @ X50 @ X48 ) <=>
% 0.57/0.81 ( ?[X52:$i]:
% 0.57/0.81 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X54:$i]:
% 0.57/0.81 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 0.57/0.81 ( ?[X58:$i]:
% 0.57/0.81 ( ( ~( ?[X60:$i]:
% 0.57/0.81 ( ( in @ X60 @ X54 ) & ( in @ X60 @ X58 ) ) ) ) &
% 0.57/0.81 ( in @ X58 @ X54 ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X62:$i]:
% 0.57/0.81 ( ?[X64:$i]:
% 0.57/0.81 ( ( ![X66:$i]:
% 0.57/0.81 ( ( ( ![X68:$i]:
% 0.57/0.81 ( ( in @ X68 @ X66 ) =>
% 0.57/0.81 ( in @ X68 @ X62 ) ) ) &
% 0.57/0.81 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 0.57/0.81 ( ?[X72:$i,X74:$i]:
% 0.57/0.81 ( ( ![X76:$i]:
% 0.57/0.81 ( ( in @ X76 @ X64 ) =>
% 0.57/0.81 ( ( ![X78:$i]:
% 0.57/0.81 ( ( in @ X78 @ X76 ) =>
% 0.57/0.81 ( in @ X78 @ X72 ) ) ) |
% 0.57/0.81 ( in @ X74 @ X76 ) ) ) ) &
% 0.57/0.81 ( ~( ?[X80:$i]:
% 0.57/0.81 ( ( in @ X80 @ X66 ) &
% 0.57/0.81 ( in @ X80 @ X72 ) ) ) ) &
% 0.57/0.81 ( in @ X74 @ X66 ) & ( in @ X72 @ X64 ) ) ) ) ) &
% 0.57/0.81 ( ![X82:$i,X84:$i]:
% 0.57/0.81 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 0.57/0.81 ( ( ![X86:$i]:
% 0.57/0.81 ( ( in @ X86 @ X82 ) =>
% 0.57/0.81 ( in @ X86 @ X84 ) ) ) |
% 0.57/0.81 ( ![X88:$i]:
% 0.57/0.81 ( ( in @ X88 @ X84 ) =>
% 0.57/0.81 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 0.57/0.81 ( ![X90:$i,X92:$i]:
% 0.57/0.81 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 0.57/0.81 ( ( ![X94:$i]:
% 0.57/0.81 ( ( in @ X94 @ X64 ) =>
% 0.57/0.81 ( ( in @ X90 @ X94 ) <=>
% 0.57/0.81 ( in @ X92 @ X94 ) ) ) ) =>
% 0.57/0.81 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 0.57/0.81 ( ![X96:$i]:
% 0.57/0.81 ( ( in @ X96 @ X64 ) =>
% 0.57/0.81 ( ![X98:$i]:
% 0.57/0.81 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X100:( $i > $o )]:
% 0.57/0.81 ( ( ?[X102:$i]:
% 0.57/0.81 ( ( ![X104:$i]:
% 0.57/0.81 ( ( X100 @ X104 ) =>
% 0.57/0.81 ( ( X102 ) = ( X104 ) ) ) ) &
% 0.57/0.81 ( X100 @ X102 ) ) ) =>
% 0.57/0.81 ( X100 @
% 0.57/0.81 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 0.57/0.81 ( ( in @ X110 @ X106 ) =>
% 0.57/0.81 ( ( X108 @ X110 ) =>
% 0.57/0.81 ( in @
% 0.57/0.81 X110 @
% 0.57/0.81 ( dsetconstr @
% 0.57/0.81 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 0.57/0.81 ( ( in @
% 0.57/0.81 X116 @
% 0.57/0.81 ( dsetconstr @
% 0.57/0.81 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 0.57/0.81 ( in @ X116 @ X112 ) ) ) =>
% 0.57/0.81 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 0.57/0.81 ( ( in @
% 0.57/0.81 X122 @
% 0.57/0.81 ( dsetconstr @
% 0.57/0.81 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 0.57/0.81 ( X120 @ X122 ) ) ) =>
% 0.57/0.81 ( ( ![X124:( $i > $o )]:
% 0.57/0.81 ( ( ?[X126:$i]:
% 0.57/0.81 ( ( ![X128:$i]:
% 0.57/0.81 ( ( X124 @ X128 ) =>
% 0.57/0.81 ( ( X126 ) = ( X128 ) ) ) ) &
% 0.57/0.81 ( X124 @ X126 ) ) ) =>
% 0.57/0.81 ( ?[X130:$i]:
% 0.57/0.81 ( ( ![X132:$i]:
% 0.57/0.81 ( ( X124 @ X132 ) =>
% 0.57/0.81 ( ( X130 ) = ( X132 ) ) ) ) &
% 0.57/0.81 ( X124 @ X130 ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X134:$o,X136:$i]:
% 0.57/0.81 ( ( in @
% 0.57/0.81 X136 @
% 0.57/0.81 ( dsetconstr @
% 0.57/0.81 ( powerset @ emptyset ) @
% 0.57/0.81 ( ^[V_5:$i]: ( X134 ) ) ) ) =>
% 0.57/0.81 ( X134 ) ) ) =>
% 0.57/0.81 ( ( ![X138:$i]:
% 0.57/0.81 ( ( in @ X138 @ emptyset ) =>
% 0.57/0.81 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 0.57/0.81 ( ( ![X142:$i]:
% 0.57/0.81 ( ~( in @ X142 @ emptyset ) ) ) =>
% 0.57/0.81 ( ( ![X144:$i]:
% 0.57/0.81 ( ~( in @ X144 @ emptyset ) ) ) =>
% 0.57/0.81 ( ( ![X146:( $i > $o )]:
% 0.57/0.81 ( ( ?[X148:$i]:
% 0.57/0.81 ( ( ![X150:$i]:
% 0.57/0.81 ( ( X146 @ X150 ) =>
% 0.57/0.81 ( ( X148 ) = ( X150 ) ) ) ) &
% 0.57/0.81 ( X146 @ X148 ) ) ) =>
% 0.57/0.81 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) =>
% 0.57/0.81 ( ( ![X154:$i,X156:$i]:
% 0.57/0.81 ( ( ![X158:$i]:
% 0.57/0.81 ( ( in @ X158 @ X154 ) =>
% 0.57/0.81 ( in @ X158 @ X156 ) ) ) =>
% 0.57/0.81 ( ( ![X160:$i]:
% 0.57/0.81 ( ( in @ X160 @ X156 ) =>
% 0.57/0.81 ( in @ X160 @ X154 ) ) ) =>
% 0.57/0.81 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X162:$i]:
% 0.57/0.81 ( ( ![X164:$i]:
% 0.57/0.81 ( ~( in @ X164 @ X162 ) ) ) =>
% 0.57/0.81 ( ( X162 ) = ( emptyset ) ) ) ) =>
% 0.57/0.81 ( ( ![X166:$i]:
% 0.57/0.81 ( ( ![X168:$i]:
% 0.57/0.81 ( ~( in @ X168 @ X166 ) ) ) =>
% 0.57/0.81 ( ( X166 ) =
% 0.57/0.81 ( emptyset ) ) ) ) =>
% 0.57/0.81 ( ( ![X170:$i,
% 0.57/0.81 X172:( $i > $o ),
% 0.57/0.81 X174:$i]:
% 0.57/0.81 ( ( in @ X174 @ X170 ) =>
% 0.57/0.81 ( ( in @
% 0.57/0.81 X174 @
% 0.57/0.81 ( dsetconstr @
% 0.57/0.81 X170 @
% 0.57/0.81 ( ^[V_6:$i]:
% 0.57/0.81 ( X172 @ V_6 ) ) ) ) <=>
% 0.57/0.81 ( X172 @ X174 ) ) ) ) =>
% 0.57/0.81 ( ( ![X176:$i]:
% 0.57/0.81 ( ( ( X176 ) !=
% 0.57/0.81 ( emptyset ) ) =>
% 0.57/0.81 ( ?[X178:$i]:
% 0.57/0.81 ( in @ X178 @ X176 ) ) ) ) =>
% 0.57/0.81 ( ( ![X180:$i,
% 0.57/0.81 X182:( $i > $o ),
% 0.57/0.81 X184:$i]:
% 0.57/0.81 ( ( in @ X184 @ X180 ) =>
% 0.57/0.81 ( ( X182 @ X184 ) =>
% 0.57/0.81 ( ( dsetconstr @
% 0.57/0.81 X180 @
% 0.57/0.81 ( ^[
% 0.57/0.81 V_7:$i]:
% 0.57/0.81 (
% 0.57/0.81 X182 @ V_7 ) ) ) !=
% 0.57/0.81 ( emptyset ) ) ) ) ) =>
% 0.57/0.81 ( ![X186:$i]:
% 0.57/0.81 ( ( ?[X188:$i]:
% 0.57/0.81 ( in @
% 0.57/0.81 X188 @ X186 ) ) =>
% 0.57/0.81 ( ( X186 ) !=
% 0.57/0.81 ( emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.57/0.81 thf(zf_stmt_10, negated_conjecture,
% 0.57/0.81 (~( ( ![X4:$i,X6:$i]:
% 0.57/0.81 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 0.57/0.81 ( ( X4 ) = ( X6 ) ) ) ) =>
% 0.57/0.81 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 0.57/0.81 ( ( ![X12:$i,X14:$i,X16:$i]:
% 0.57/0.81 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 0.57/0.81 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 0.57/0.81 ( ( ![X18:$i,X20:$i]:
% 0.57/0.81 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 0.57/0.81 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 0.57/0.81 ( ( ![X24:$i,X26:$i]:
% 0.57/0.81 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 0.57/0.81 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 0.57/0.81 ( ( in @ emptyset @ omega ) =>
% 0.57/0.81 ( ( ![X30:$i]:
% 0.57/0.81 ( ( in @ X30 @ omega ) =>
% 0.57/0.81 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 0.57/0.81 ( ( ![X32:$i]:
% 0.57/0.81 ( ( ( in @ emptyset @ X32 ) &
% 0.57/0.81 ( ![X34:$i]:
% 0.57/0.81 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 0.57/0.81 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 0.57/0.81 ( ![X36:$i]:
% 0.57/0.81 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 0.57/0.81 ( ( ![X42:$i]:
% 0.57/0.81 ( ( in @ X42 @ X40 ) =>
% 0.57/0.81 ( ?[X44:$i]:
% 0.57/0.81 ( ( ![X46:$i]:
% 0.57/0.81 ( ( X38 @ X42 @ X46 ) =>
% 0.57/0.81 ( ( X44 ) = ( X46 ) ) ) ) &
% 0.57/0.81 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 0.57/0.81 ( ?[X48:$i]:
% 0.57/0.81 ( ![X50:$i]:
% 0.57/0.81 ( ( in @ X50 @ X48 ) <=>
% 0.57/0.81 ( ?[X52:$i]:
% 0.57/0.81 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X54:$i]:
% 0.57/0.81 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 0.57/0.81 ( ?[X58:$i]:
% 0.57/0.81 ( ( ~( ?[X60:$i]:
% 0.57/0.81 ( ( in @ X60 @ X54 ) &
% 0.57/0.81 ( in @ X60 @ X58 ) ) ) ) &
% 0.57/0.81 ( in @ X58 @ X54 ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X62:$i]:
% 0.57/0.81 ( ?[X64:$i]:
% 0.57/0.81 ( ( ![X66:$i]:
% 0.57/0.81 ( ( ( ![X68:$i]:
% 0.57/0.81 ( ( in @ X68 @ X66 ) =>
% 0.57/0.81 ( in @ X68 @ X62 ) ) ) &
% 0.57/0.81 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 0.57/0.81 ( ?[X72:$i,X74:$i]:
% 0.57/0.81 ( ( ![X76:$i]:
% 0.57/0.81 ( ( in @ X76 @ X64 ) =>
% 0.57/0.81 ( ( ![X78:$i]:
% 0.57/0.81 ( ( in @ X78 @ X76 ) =>
% 0.57/0.81 ( in @ X78 @ X72 ) ) ) |
% 0.57/0.81 ( in @ X74 @ X76 ) ) ) ) &
% 0.57/0.81 ( ~( ?[X80:$i]:
% 0.57/0.81 ( ( in @ X80 @ X66 ) &
% 0.57/0.81 ( in @ X80 @ X72 ) ) ) ) &
% 0.57/0.81 ( in @ X74 @ X66 ) &
% 0.57/0.81 ( in @ X72 @ X64 ) ) ) ) ) &
% 0.57/0.81 ( ![X82:$i,X84:$i]:
% 0.57/0.81 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 0.57/0.81 ( ( ![X86:$i]:
% 0.57/0.81 ( ( in @ X86 @ X82 ) =>
% 0.57/0.81 ( in @ X86 @ X84 ) ) ) |
% 0.57/0.81 ( ![X88:$i]:
% 0.57/0.81 ( ( in @ X88 @ X84 ) =>
% 0.57/0.81 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 0.57/0.81 ( ![X90:$i,X92:$i]:
% 0.57/0.81 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 0.57/0.81 ( ( ![X94:$i]:
% 0.57/0.81 ( ( in @ X94 @ X64 ) =>
% 0.57/0.81 ( ( in @ X90 @ X94 ) <=>
% 0.57/0.81 ( in @ X92 @ X94 ) ) ) ) =>
% 0.57/0.81 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 0.57/0.81 ( ![X96:$i]:
% 0.57/0.81 ( ( in @ X96 @ X64 ) =>
% 0.57/0.81 ( ![X98:$i]:
% 0.57/0.81 ( ( in @ X98 @ X96 ) =>
% 0.57/0.81 ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X100:( $i > $o )]:
% 0.57/0.81 ( ( ?[X102:$i]:
% 0.57/0.81 ( ( ![X104:$i]:
% 0.57/0.81 ( ( X100 @ X104 ) =>
% 0.57/0.81 ( ( X102 ) = ( X104 ) ) ) ) &
% 0.57/0.81 ( X100 @ X102 ) ) ) =>
% 0.57/0.81 ( X100 @
% 0.57/0.81 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 0.57/0.81 ( ( in @ X110 @ X106 ) =>
% 0.57/0.81 ( ( X108 @ X110 ) =>
% 0.57/0.81 ( in @
% 0.57/0.81 X110 @
% 0.57/0.81 ( dsetconstr @
% 0.57/0.81 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 0.57/0.81 ( ( in @
% 0.57/0.81 X116 @
% 0.57/0.81 ( dsetconstr @
% 0.57/0.81 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 0.57/0.81 ( in @ X116 @ X112 ) ) ) =>
% 0.57/0.81 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 0.57/0.81 ( ( in @
% 0.57/0.81 X122 @
% 0.57/0.81 ( dsetconstr @
% 0.57/0.81 X118 @
% 0.57/0.81 ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 0.57/0.81 ( X120 @ X122 ) ) ) =>
% 0.57/0.81 ( ( ![X124:( $i > $o )]:
% 0.57/0.81 ( ( ?[X126:$i]:
% 0.57/0.81 ( ( ![X128:$i]:
% 0.57/0.81 ( ( X124 @ X128 ) =>
% 0.57/0.81 ( ( X126 ) = ( X128 ) ) ) ) &
% 0.57/0.81 ( X124 @ X126 ) ) ) =>
% 0.57/0.81 ( ?[X130:$i]:
% 0.57/0.81 ( ( ![X132:$i]:
% 0.57/0.81 ( ( X124 @ X132 ) =>
% 0.57/0.81 ( ( X130 ) = ( X132 ) ) ) ) &
% 0.57/0.81 ( X124 @ X130 ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X134:$o,X136:$i]:
% 0.57/0.81 ( ( in @
% 0.57/0.81 X136 @
% 0.57/0.81 ( dsetconstr @
% 0.57/0.81 ( powerset @ emptyset ) @
% 0.57/0.81 ( ^[V_5:$i]: ( X134 ) ) ) ) =>
% 0.57/0.81 ( X134 ) ) ) =>
% 0.57/0.81 ( ( ![X138:$i]:
% 0.57/0.81 ( ( in @ X138 @ emptyset ) =>
% 0.57/0.81 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 0.57/0.81 ( ( ![X142:$i]:
% 0.57/0.81 ( ~( in @ X142 @ emptyset ) ) ) =>
% 0.57/0.81 ( ( ![X144:$i]:
% 0.57/0.81 ( ~( in @ X144 @ emptyset ) ) ) =>
% 0.57/0.81 ( ( ![X146:( $i > $o )]:
% 0.57/0.81 ( ( ?[X148:$i]:
% 0.57/0.81 ( ( ![X150:$i]:
% 0.57/0.81 ( ( X146 @ X150 ) =>
% 0.57/0.81 ( ( X148 ) =
% 0.57/0.81 ( X150 ) ) ) ) &
% 0.57/0.81 ( X146 @ X148 ) ) ) =>
% 0.57/0.81 ( ?[X152:$i]:
% 0.57/0.81 ( X146 @ X152 ) ) ) ) =>
% 0.57/0.81 ( ( ![X154:$i,X156:$i]:
% 0.57/0.81 ( ( ![X158:$i]:
% 0.57/0.81 ( ( in @ X158 @ X154 ) =>
% 0.57/0.81 ( in @ X158 @ X156 ) ) ) =>
% 0.57/0.81 ( ( ![X160:$i]:
% 0.57/0.81 ( ( in @ X160 @ X156 ) =>
% 0.57/0.81 ( in @ X160 @ X154 ) ) ) =>
% 0.57/0.81 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 0.57/0.81 ( ( ![X162:$i]:
% 0.57/0.81 ( ( ![X164:$i]:
% 0.57/0.81 ( ~( in @ X164 @ X162 ) ) ) =>
% 0.57/0.81 ( ( X162 ) =
% 0.57/0.81 ( emptyset ) ) ) ) =>
% 0.57/0.81 ( ( ![X166:$i]:
% 0.57/0.81 ( ( ![X168:$i]:
% 0.57/0.81 ( ~( in @
% 0.57/0.81 X168 @ X166 ) ) ) =>
% 0.57/0.81 ( ( X166 ) =
% 0.57/0.81 ( emptyset ) ) ) ) =>
% 0.57/0.81 ( ( ![X170:$i,
% 0.57/0.81 X172:( $i > $o ),
% 0.57/0.81 X174:$i]:
% 0.57/0.81 ( ( in @ X174 @ X170 ) =>
% 0.57/0.81 ( ( in @
% 0.57/0.81 X174 @
% 0.57/0.81 ( dsetconstr @
% 0.57/0.81 X170 @
% 0.57/0.81 ( ^[V_6:$i]:
% 0.57/0.81 ( X172 @
% 0.57/0.81 V_6 ) ) ) ) <=>
% 0.57/0.81 ( X172 @ X174 ) ) ) ) =>
% 0.57/0.81 ( ( ![X176:$i]:
% 0.57/0.81 ( ( ( X176 ) !=
% 0.57/0.81 ( emptyset ) ) =>
% 0.57/0.81 ( ?[X178:$i]:
% 0.57/0.81 ( in @
% 0.57/0.81 X178 @ X176 ) ) ) ) =>
% 0.57/0.81 ( ( ![X180:$i,
% 0.57/0.81 X182:(
% 0.57/0.81 $i > $o ),
% 0.57/0.81 X184:$i]:
% 0.57/0.81 ( ( in @
% 0.57/0.81 X184 @ X180 ) =>
% 0.57/0.81 ( ( X182 @ X184 ) =>
% 0.57/0.81 ( ( dsetconstr
% 0.57/0.81 @
% 0.57/0.81 X180 @
% 0.57/0.81 (
% 0.57/0.81 ^[
% 0.57/0.81 V_7:$i]:
% 0.57/0.81 (
% 0.57/0.81 X182 @
% 0.57/0.81 V_7 ) ) ) !=
% 0.57/0.81 ( emptyset ) ) ) ) ) =>
% 0.57/0.81 ( ![X186:$i]:
% 0.57/0.81 ( ( ?[X188:$i]:
% 0.57/0.81 ( in @
% 0.57/0.81 X188 @ X186 ) ) =>
% 0.57/0.81 ( ( X186 ) !=
% 0.57/0.81 ( emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 0.57/0.81 inference('cnf.neg', [status(esa)], [zf_stmt_9])).
% 0.57/0.81 thf(zip_derived_cl49, plain, ( (in @ sk__99 @ sk__98)),
% 0.57/0.81 inference('cnf', [status(esa)], [zf_stmt_10])).
% 0.57/0.81 thf(zip_derived_cl48, plain, (((sk__98) = (emptyset))),
% 0.57/0.81 inference('cnf', [status(esa)], [zf_stmt_10])).
% 0.57/0.81 thf(zip_derived_cl74, plain, ( (in @ sk__99 @ emptyset)),
% 0.57/0.81 inference('demod', [status(thm)], [zip_derived_cl49, zip_derived_cl48])).
% 0.57/0.81 thf(zip_derived_cl41, plain, (![X39 : $i]: ~ (in @ X39 @ emptyset)),
% 0.57/0.81 inference('cnf', [status(esa)], [zf_stmt_10])).
% 0.57/0.81 thf(zip_derived_cl76, plain, ($false),
% 0.57/0.81 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl41])).
% 0.57/0.81
% 0.57/0.81 % SZS output end Refutation
% 0.57/0.81
% 0.57/0.81
% 0.57/0.81 % Terminating...
% 1.74/0.88 % Runner terminated.
% 1.74/0.89 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------