%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU504^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.VLnXGIrDWc true
% Computer : n006.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 04:54:49 PM UTC 2025
% Result : Theorem 2.55s 3.09s
% Output : Refutation 2.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/1.02 % Problem : SEU504^1 : TPTP v9.2.0. Released v3.7.0.
% 0.12/1.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.VLnXGIrDWc true
% 0.16/1.51 % Computer : n006.cluster.edu
% 0.16/1.51 % Model : x86_64 x86_64
% 0.16/1.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/1.51 % Memory : 8042.1875MB
% 0.16/1.51 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/1.51 % CPULimit : 300
% 0.16/1.51 % WCLimit : 300
% 0.16/1.51 % DateTime : Wed Oct 1 16:05:09 EDT 2025
% 0.19/1.53 % CPUTime :
% 0.19/1.53 % Running portfolio for 300 s
% 0.19/1.53 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/1.54 % Number of cores: 8
% 0.19/1.56 % Python version: Python 3.6.8
% 0.19/1.57 % Running in HO mode
% 0.63/2.27 % Total configuration time : 828
% 0.63/2.27 % Estimated wc time : 1656
% 0.63/2.27 % Estimated cpu time (8 cpus) : 207.0
% 1.45/2.58 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.53/2.63 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.53/2.66 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.54/2.69 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.54/2.69 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.54/2.73 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.57/2.74 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.57/2.76 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 2.55/3.09 % Solved by lams/40_noforms.sh.
% 2.55/3.09 % done 6 iterations in 0.233s
% 2.55/3.09 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 2.55/3.09 % SZS output start Refutation
% 2.55/3.09 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 2.55/3.09 thf(setunionAx_type, type, setunionAx: $o).
% 2.55/3.09 thf(omegaSAx_type, type, omegaSAx: $o).
% 2.55/3.09 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 2.55/3.09 thf(emptysetE_type, type, emptysetE: $o).
% 2.55/3.09 thf(in_type, type, in: $i > $i > $o).
% 2.55/3.09 thf(sk__77_type, type, sk__77: $i).
% 2.55/3.09 thf(sk__76_type, type, sk__76: $i > $o).
% 2.55/3.09 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 2.55/3.09 thf(zip_tseitin_2_type, type, zip_tseitin_2: $i > $i > $i > $o).
% 2.55/3.09 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $i > $o).
% 2.55/3.09 thf(powersetAx_type, type, powersetAx: $o).
% 2.55/3.09 thf(notinemptyset_type, type, notinemptyset: $o).
% 2.55/3.09 thf(emptyset_type, type, emptyset: $i).
% 2.55/3.09 thf(zip_tseitin_3_type, type, zip_tseitin_3: $i > $i > $i > ($i > $i > $o) > $o).
% 2.55/3.09 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 2.55/3.09 thf(descr_type, type, descr: ($i > $o) > $i).
% 2.55/3.09 thf(exuE1_type, type, exuE1: $o).
% 2.55/3.09 thf(prop2set_type, type, prop2set: $o > $i).
% 2.55/3.09 thf(omega0Ax_type, type, omega0Ax: $o).
% 2.55/3.09 thf(prop2setE_type, type, prop2setE: $o).
% 2.55/3.09 thf(setextAx_type, type, setextAx: $o).
% 2.55/3.09 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 2.55/3.09 thf(setunion_type, type, setunion: $i > $i).
% 2.55/3.09 thf(descrp_type, type, descrp: $o).
% 2.55/3.09 thf(foundationAx_type, type, foundationAx: $o).
% 2.55/3.09 thf(emptysetAx_type, type, emptysetAx: $o).
% 2.55/3.09 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 2.55/3.09 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 2.55/3.09 thf(exu_type, type, exu: ($i > $o) > $o).
% 2.55/3.09 thf(omega_type, type, omega: $i).
% 2.55/3.09 thf(powerset_type, type, powerset: $i > $i).
% 2.55/3.09 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 2.55/3.09 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 2.55/3.09 thf(replAx_type, type, replAx: $o).
% 2.55/3.09 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 2.55/3.09 thf(notinemptyset, axiom, notinemptyset =
% 2.55/3.09 (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 2.55/3.09 thf('0', plain,
% 2.55/3.09 (( notinemptyset ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(emptysetimpfalse, axiom, emptysetimpfalse =
% 2.55/3.09 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( $false ) ))).
% 2.55/3.09 thf('1', plain,
% 2.55/3.09 (( emptysetimpfalse ) =
% 2.55/3.09 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( $false ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(emptysetE, axiom, emptysetE =
% 2.55/3.09 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( ![Xphi:$o]: ( Xphi ) ) ))).
% 2.55/3.09 thf('2', plain,
% 2.55/3.09 (( emptysetE ) =
% 2.55/3.09 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( ![X6:$o]: ( X6 ) ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(prop2setE, axiom, prop2setE =
% 2.55/3.09 (![Xphi:$o,Xx:$i]: ( ( in @ Xx @ ( prop2set @ Xphi ) ) => ( Xphi ) ))).
% 2.55/3.09 thf('3', plain,
% 2.55/3.09 (( prop2setE ) =
% 2.55/3.09 ( ![X4:$o,X6:$i]: ( ( in @ X6 @ ( prop2set @ X4 ) ) => ( X4 ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(exuE1, axiom, exuE1 =
% 2.55/3.09 (![Xphi:( $i > $o )]:
% 2.55/3.09 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 2.55/3.09 ( ?[Xx:$i]:
% 2.55/3.09 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 2.55/3.09 ( Xphi @ Xx ) ) ) ))).
% 2.55/3.09 thf('4', plain,
% 2.55/3.09 (( exuE1 ) =
% 2.55/3.09 ( ![X4:( $i > $o )]:
% 2.55/3.09 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 2.55/3.09 ( ?[X6:$i]:
% 2.55/3.09 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) &
% 2.55/3.09 ( X4 @ X6 ) ) ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(dsetconstrER, axiom, dsetconstrER =
% 2.55/3.09 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 2.55/3.09 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 2.55/3.09 ( Xphi @ Xx ) ))).
% 2.55/3.09 thf('5', plain,
% 2.55/3.09 (( dsetconstrER ) =
% 2.55/3.09 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 2.55/3.09 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 2.55/3.09 ( X6 @ X8 ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(dsetconstrEL, axiom, dsetconstrEL =
% 2.55/3.09 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 2.55/3.09 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 2.55/3.09 ( in @ Xx @ A ) ))).
% 2.55/3.09 thf('6', plain,
% 2.55/3.09 (( dsetconstrEL ) =
% 2.55/3.09 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 2.55/3.09 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 2.55/3.09 ( in @ X8 @ X4 ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(dsetconstrI, axiom, dsetconstrI =
% 2.55/3.09 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 2.55/3.09 ( ( in @ Xx @ A ) =>
% 2.55/3.09 ( ( Xphi @ Xx ) =>
% 2.55/3.09 ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 2.55/3.09 thf('7', plain,
% 2.55/3.09 (( dsetconstrI ) =
% 2.55/3.09 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 2.55/3.09 ( ( in @ X8 @ X4 ) =>
% 2.55/3.09 ( ( X6 @ X8 ) =>
% 2.55/3.09 ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(descrp, axiom, descrp =
% 2.55/3.09 (![Xphi:( $i > $o )]:
% 2.55/3.09 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 2.55/3.09 ( Xphi @ ( descr @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 2.55/3.09 thf('8', plain,
% 2.55/3.09 (( descrp ) =
% 2.55/3.09 ( ![X4:( $i > $o )]:
% 2.55/3.09 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 2.55/3.09 ( X4 @ ( descr @ ( ^[V_2:$i]: ( X4 @ V_2 ) ) ) ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(wellorderingAx, axiom, wellorderingAx =
% 2.55/3.09 (![A:$i]:
% 2.55/3.09 ( ?[B:$i]:
% 2.55/3.09 ( ( ![C:$i]:
% 2.55/3.09 ( ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) &
% 2.55/3.09 ( ?[Xx:$i]: ( in @ Xx @ C ) ) ) =>
% 2.55/3.09 ( ?[D:$i,Xx:$i]:
% 2.55/3.09 ( ( ![E:$i]:
% 2.55/3.09 ( ( in @ E @ B ) =>
% 2.55/3.09 ( ( ![Xy:$i]: ( ( in @ Xy @ E ) => ( in @ Xy @ D ) ) ) |
% 2.55/3.09 ( in @ Xx @ E ) ) ) ) &
% 2.55/3.09 ( ~( ?[Xy:$i]: ( ( in @ Xy @ C ) & ( in @ Xy @ D ) ) ) ) &
% 2.55/3.09 ( in @ Xx @ C ) & ( in @ D @ B ) ) ) ) ) &
% 2.55/3.09 ( ![C:$i,D:$i]:
% 2.55/3.09 ( ( ( in @ C @ B ) & ( in @ D @ B ) ) =>
% 2.55/3.09 ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ D ) ) ) |
% 2.55/3.09 ( ![Xx:$i]: ( ( in @ Xx @ D ) => ( in @ Xx @ C ) ) ) ) ) ) &
% 2.55/3.09 ( ![Xx:$i,Xy:$i]:
% 2.55/3.09 ( ( ( in @ Xx @ A ) & ( in @ Xy @ A ) ) =>
% 2.55/3.09 ( ( ![C:$i]:
% 2.55/3.09 ( ( in @ C @ B ) => ( ( in @ Xx @ C ) <=> ( in @ Xy @ C ) ) ) ) =>
% 2.55/3.09 ( ( Xx ) = ( Xy ) ) ) ) ) &
% 2.55/3.09 ( ![C:$i]:
% 2.55/3.09 ( ( in @ C @ B ) =>
% 2.55/3.09 ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) ) ) ) ))).
% 2.55/3.09 thf('9', plain,
% 2.55/3.09 (( wellorderingAx ) =
% 2.55/3.09 ( ![X4:$i]:
% 2.55/3.09 ( ?[X6:$i]:
% 2.55/3.09 ( ( ![X8:$i]:
% 2.55/3.09 ( ( ( ![X10:$i]: ( ( in @ X10 @ X8 ) => ( in @ X10 @ X4 ) ) ) &
% 2.55/3.09 ( ?[X12:$i]: ( in @ X12 @ X8 ) ) ) =>
% 2.55/3.09 ( ?[X14:$i,X16:$i]:
% 2.55/3.09 ( ( ![X18:$i]:
% 2.55/3.09 ( ( in @ X18 @ X6 ) =>
% 2.55/3.09 ( ( ![X20:$i]:
% 2.55/3.09 ( ( in @ X20 @ X18 ) => ( in @ X20 @ X14 ) ) ) |
% 2.55/3.09 ( in @ X16 @ X18 ) ) ) ) &
% 2.55/3.09 ( ~( ?[X22:$i]: ( ( in @ X22 @ X8 ) & ( in @ X22 @ X14 ) ) ) ) &
% 2.55/3.09 ( in @ X16 @ X8 ) & ( in @ X14 @ X6 ) ) ) ) ) &
% 2.55/3.09 ( ![X24:$i,X26:$i]:
% 2.55/3.09 ( ( ( in @ X24 @ X6 ) & ( in @ X26 @ X6 ) ) =>
% 2.55/3.09 ( ( ![X28:$i]: ( ( in @ X28 @ X24 ) => ( in @ X28 @ X26 ) ) ) |
% 2.55/3.09 ( ![X30:$i]: ( ( in @ X30 @ X26 ) => ( in @ X30 @ X24 ) ) ) ) ) ) &
% 2.55/3.09 ( ![X32:$i,X34:$i]:
% 2.55/3.09 ( ( ( in @ X32 @ X4 ) & ( in @ X34 @ X4 ) ) =>
% 2.55/3.09 ( ( ![X36:$i]:
% 2.55/3.09 ( ( in @ X36 @ X6 ) =>
% 2.55/3.09 ( ( in @ X32 @ X36 ) <=> ( in @ X34 @ X36 ) ) ) ) =>
% 2.55/3.09 ( ( X32 ) = ( X34 ) ) ) ) ) &
% 2.55/3.09 ( ![X38:$i]:
% 2.55/3.09 ( ( in @ X38 @ X6 ) =>
% 2.55/3.09 ( ![X40:$i]: ( ( in @ X40 @ X38 ) => ( in @ X40 @ X4 ) ) ) ) ) ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(foundationAx, axiom, foundationAx =
% 2.55/3.09 (![A:$i]:
% 2.55/3.09 ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) =>
% 2.55/3.09 ( ?[B:$i]:
% 2.55/3.09 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ A ) & ( in @ Xx @ B ) ) ) ) &
% 2.55/3.09 ( in @ B @ A ) ) ) ))).
% 2.55/3.09 thf('10', plain,
% 2.55/3.09 (( foundationAx ) =
% 2.55/3.09 ( ![X4:$i]:
% 2.55/3.09 ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) =>
% 2.55/3.09 ( ?[X8:$i]:
% 2.55/3.09 ( ( ~( ?[X10:$i]: ( ( in @ X10 @ X4 ) & ( in @ X10 @ X8 ) ) ) ) &
% 2.55/3.09 ( in @ X8 @ X4 ) ) ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(replAx, axiom, replAx =
% 2.55/3.09 (![Xphi:( $i > $i > $o ),A:$i]:
% 2.55/3.09 ( ( ![Xx:$i]:
% 2.55/3.09 ( ( in @ Xx @ A ) => ( exu @ ( ^[Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) ) ) =>
% 2.55/3.09 ( ?[B:$i]:
% 2.55/3.09 ( ![Xx:$i]:
% 2.55/3.09 ( ( in @ Xx @ B ) <=>
% 2.55/3.09 ( ?[Xy:$i]: ( ( Xphi @ Xy @ Xx ) & ( in @ Xy @ A ) ) ) ) ) ) ))).
% 2.55/3.09 thf('11', plain,
% 2.55/3.09 (( replAx ) =
% 2.55/3.09 ( ![X4:( $i > $i > $o ),X6:$i]:
% 2.55/3.09 ( ( ![X8:$i]:
% 2.55/3.09 ( ( in @ X8 @ X6 ) => ( exu @ ( ^[V_1:$i]: ( X4 @ X8 @ V_1 ) ) ) ) ) =>
% 2.55/3.09 ( ?[X10:$i]:
% 2.55/3.09 ( ![X12:$i]:
% 2.55/3.09 ( ( in @ X12 @ X10 ) <=>
% 2.55/3.09 ( ?[X14:$i]: ( ( X4 @ X14 @ X12 ) & ( in @ X14 @ X6 ) ) ) ) ) ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(omegaIndAx, axiom, omegaIndAx =
% 2.55/3.09 (![A:$i]:
% 2.55/3.09 ( ( ( in @ emptyset @ A ) &
% 2.55/3.09 ( ![Xx:$i]:
% 2.55/3.09 ( ( ( in @ Xx @ omega ) & ( in @ Xx @ A ) ) =>
% 2.55/3.09 ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) ) =>
% 2.55/3.09 ( ![Xx:$i]: ( ( in @ Xx @ omega ) => ( in @ Xx @ A ) ) ) ))).
% 2.55/3.09 thf('12', plain,
% 2.55/3.09 (( omegaIndAx ) =
% 2.55/3.09 ( ![X4:$i]:
% 2.55/3.09 ( ( ( in @ emptyset @ X4 ) &
% 2.55/3.09 ( ![X6:$i]:
% 2.55/3.09 ( ( ( in @ X6 @ omega ) & ( in @ X6 @ X4 ) ) =>
% 2.55/3.09 ( in @ ( setadjoin @ X6 @ X6 ) @ X4 ) ) ) ) =>
% 2.55/3.09 ( ![X8:$i]: ( ( in @ X8 @ omega ) => ( in @ X8 @ X4 ) ) ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(omegaSAx, axiom, omegaSAx =
% 2.55/3.09 (![Xx:$i]:
% 2.55/3.09 ( ( in @ Xx @ omega ) => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ))).
% 2.55/3.09 thf('13', plain,
% 2.55/3.09 (( omegaSAx ) =
% 2.55/3.09 ( ![X4:$i]:
% 2.55/3.09 ( ( in @ X4 @ omega ) => ( in @ ( setadjoin @ X4 @ X4 ) @ omega ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(omega0Ax, axiom,(( omega0Ax ) = (in @ emptyset @ omega))).
% 2.55/3.09 thf('14', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 2.55/3.09 inference('simplify_rw_rule', [status(thm)], [omega0Ax])).
% 2.55/3.09 thf('15', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(setunionAx, axiom, setunionAx =
% 2.55/3.09 (![A:$i,Xx:$i]:
% 2.55/3.09 ( ( in @ Xx @ ( setunion @ A ) ) <=>
% 2.55/3.09 ( ?[B:$i]: ( ( in @ B @ A ) & ( in @ Xx @ B ) ) ) ))).
% 2.55/3.09 thf('16', plain,
% 2.55/3.09 (( setunionAx ) =
% 2.55/3.09 ( ![X4:$i,X6:$i]:
% 2.55/3.09 ( ( in @ X6 @ ( setunion @ X4 ) ) <=>
% 2.55/3.09 ( ?[X8:$i]: ( ( in @ X8 @ X4 ) & ( in @ X6 @ X8 ) ) ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(powersetAx, axiom, powersetAx =
% 2.55/3.09 (![A:$i,B:$i]:
% 2.55/3.09 ( ( in @ B @ ( powerset @ A ) ) <=>
% 2.55/3.09 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 2.55/3.09 thf('17', plain,
% 2.55/3.09 (( powersetAx ) =
% 2.55/3.09 ( ![X4:$i,X6:$i]:
% 2.55/3.09 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 2.55/3.09 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(setadjoinAx, axiom, setadjoinAx =
% 2.55/3.09 (![Xx:$i,A:$i,Xy:$i]:
% 2.55/3.09 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 2.55/3.09 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 2.55/3.09 thf('18', plain,
% 2.55/3.09 (( setadjoinAx ) =
% 2.55/3.09 ( ![X4:$i,X6:$i,X8:$i]:
% 2.55/3.09 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 2.55/3.09 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(emptysetAx, axiom, emptysetAx = (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 2.55/3.09 thf('19', plain,
% 2.55/3.09 (( emptysetAx ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(setextAx, axiom, setextAx =
% 2.55/3.09 (![A:$i,B:$i]:
% 2.55/3.09 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) <=> ( in @ Xx @ B ) ) ) =>
% 2.55/3.09 ( ( A ) = ( B ) ) ))).
% 2.55/3.09 thf('20', plain,
% 2.55/3.09 (( setextAx ) =
% 2.55/3.09 ( ![X4:$i,X6:$i]:
% 2.55/3.09 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 2.55/3.09 ( ( X4 ) = ( X6 ) ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(exu, axiom,(( exu ) =
% 2.55/3.09 (^[Xphi:( $i > $o )]:
% 2.55/3.09 ( ?[Xx:$i]:
% 2.55/3.09 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) & ( Xphi @ Xx ) ) )))).
% 2.55/3.09 thf('21', plain,
% 2.55/3.09 (( exu ) =
% 2.55/3.09 ( ^[Xphi:( $i > $o )]:
% 2.55/3.09 ( ?[Xx:$i]:
% 2.55/3.09 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 2.55/3.09 ( Xphi @ Xx ) ) ) )),
% 2.55/3.09 inference('simplify_rw_rule', [status(thm)], [exu])).
% 2.55/3.09 thf('22', plain,
% 2.55/3.09 (( exu ) =
% 2.55/3.09 ( ^[V_1:( $i > $o )]:
% 2.55/3.09 ( ?[X4:$i]:
% 2.55/3.09 ( ( ![X6:$i]: ( ( V_1 @ X6 ) => ( ( X4 ) = ( X6 ) ) ) ) &
% 2.55/3.09 ( V_1 @ X4 ) ) ) )),
% 2.55/3.09 define([status(thm)])).
% 2.55/3.09 thf(exuE3e, conjecture,
% 2.55/3.09 (( setextAx ) =>
% 2.55/3.09 ( ( emptysetAx ) =>
% 2.55/3.09 ( ( setadjoinAx ) =>
% 2.55/3.09 ( ( powersetAx ) =>
% 2.55/3.09 ( ( setunionAx ) =>
% 2.55/3.09 ( ( omega0Ax ) =>
% 2.55/3.09 ( ( omegaSAx ) =>
% 2.55/3.09 ( ( omegaIndAx ) =>
% 2.55/3.09 ( ( replAx ) =>
% 2.55/3.09 ( ( foundationAx ) =>
% 2.55/3.09 ( ( wellorderingAx ) =>
% 2.55/3.09 ( ( descrp ) =>
% 2.55/3.09 ( ( dsetconstrI ) =>
% 2.55/3.09 ( ( dsetconstrEL ) =>
% 2.55/3.09 ( ( dsetconstrER ) =>
% 2.55/3.09 ( ( exuE1 ) =>
% 2.55/3.09 ( ( prop2setE ) =>
% 2.55/3.09 ( ( emptysetE ) =>
% 2.55/3.09 ( ( emptysetimpfalse ) =>
% 2.55/3.09 ( ( notinemptyset ) =>
% 2.55/3.09 ( ![Xphi:( $i > $o )]:
% 2.55/3.09 ( ( exu @
% 2.55/3.09 ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 2.55/3.09 ( ?[Xx:$i]: ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 2.55/3.09 thf(zf_stmt_0, conjecture,
% 2.55/3.09 (( ![X4:$i,X6:$i]:
% 2.55/3.09 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 2.55/3.09 ( ( X4 ) = ( X6 ) ) ) ) =>
% 2.55/3.09 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 2.55/3.09 ( ( ![X12:$i,X14:$i,X16:$i]:
% 2.55/3.09 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 2.55/3.09 ( ( in @ X16 @ X14 ) | ( ( X16 ) = ( X12 ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X18:$i,X20:$i]:
% 2.55/3.09 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 2.55/3.09 ( ![X22:$i]: ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X24:$i,X26:$i]:
% 2.55/3.09 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 2.55/3.09 ( ?[X28:$i]: ( ( in @ X26 @ X28 ) & ( in @ X28 @ X24 ) ) ) ) ) =>
% 2.55/3.09 ( ( in @ emptyset @ omega ) =>
% 2.55/3.09 ( ( ![X30:$i]:
% 2.55/3.09 ( ( in @ X30 @ omega ) =>
% 2.55/3.09 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 2.55/3.09 ( ( ![X32:$i]:
% 2.55/3.09 ( ( ( ![X34:$i]:
% 2.55/3.09 ( ( ( in @ X34 @ X32 ) & ( in @ X34 @ omega ) ) =>
% 2.55/3.09 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) &
% 2.55/3.09 ( in @ emptyset @ X32 ) ) =>
% 2.55/3.09 ( ![X36:$i]:
% 2.55/3.09 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 2.55/3.09 ( ( ![X42:$i]:
% 2.55/3.09 ( ( in @ X42 @ X40 ) =>
% 2.55/3.09 ( ?[X44:$i]:
% 2.55/3.09 ( ( X38 @ X42 @ X44 ) &
% 2.55/3.09 ( ![X46:$i]:
% 2.55/3.09 ( ( X38 @ X42 @ X46 ) =>
% 2.55/3.09 ( ( X44 ) = ( X46 ) ) ) ) ) ) ) ) =>
% 2.55/3.09 ( ?[X48:$i]:
% 2.55/3.09 ( ![X50:$i]:
% 2.55/3.09 ( ( in @ X50 @ X48 ) <=>
% 2.55/3.09 ( ?[X52:$i]:
% 2.55/3.09 ( ( in @ X52 @ X40 ) & ( X38 @ X52 @ X50 ) ) ) ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X54:$i]:
% 2.55/3.09 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 2.55/3.09 ( ?[X58:$i]:
% 2.55/3.09 ( ( in @ X58 @ X54 ) &
% 2.55/3.09 ( ~( ?[X60:$i]:
% 2.55/3.09 ( ( in @ X60 @ X58 ) & ( in @ X60 @ X54 ) ) ) ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X62:$i]:
% 2.55/3.09 ( ?[X64:$i]:
% 2.55/3.09 ( ( ![X96:$i]:
% 2.55/3.09 ( ( in @ X96 @ X64 ) =>
% 2.55/3.09 ( ![X98:$i]:
% 2.55/3.09 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) &
% 2.55/3.09 ( ![X90:$i,X92:$i]:
% 2.55/3.09 ( ( ( in @ X92 @ X62 ) & ( in @ X90 @ X62 ) ) =>
% 2.55/3.09 ( ( ![X94:$i]:
% 2.55/3.09 ( ( in @ X94 @ X64 ) =>
% 2.55/3.09 ( ( in @ X90 @ X94 ) <=>
% 2.55/3.09 ( in @ X92 @ X94 ) ) ) ) =>
% 2.55/3.09 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 2.55/3.09 ( ![X82:$i,X84:$i]:
% 2.55/3.09 ( ( ( in @ X84 @ X64 ) & ( in @ X82 @ X64 ) ) =>
% 2.55/3.09 ( ( ![X88:$i]:
% 2.55/3.09 ( ( in @ X88 @ X84 ) =>
% 2.55/3.09 ( in @ X88 @ X82 ) ) ) |
% 2.55/3.09 ( ![X86:$i]:
% 2.55/3.09 ( ( in @ X86 @ X82 ) =>
% 2.55/3.09 ( in @ X86 @ X84 ) ) ) ) ) ) &
% 2.55/3.09 ( ![X66:$i]:
% 2.55/3.09 ( ( ( ?[X70:$i]: ( in @ X70 @ X66 ) ) &
% 2.55/3.09 ( ![X68:$i]:
% 2.55/3.09 ( ( in @ X68 @ X66 ) =>
% 2.55/3.09 ( in @ X68 @ X62 ) ) ) ) =>
% 2.55/3.09 ( ?[X72:$i,X74:$i]:
% 2.55/3.09 ( ( in @ X72 @ X64 ) &
% 2.55/3.09 ( in @ X74 @ X66 ) &
% 2.55/3.09 ( ~( ?[X80:$i]:
% 2.55/3.09 ( ( in @ X80 @ X72 ) &
% 2.55/3.09 ( in @ X80 @ X66 ) ) ) ) &
% 2.55/3.09 ( ![X76:$i]:
% 2.55/3.09 ( ( in @ X76 @ X64 ) =>
% 2.55/3.09 ( ( in @ X74 @ X76 ) |
% 2.55/3.09 ( ![X78:$i]:
% 2.55/3.09 ( ( in @ X78 @ X76 ) =>
% 2.55/3.09 ( in @ X78 @ X72 ) ) ) ) ) ) ) ) ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X100:( $i > $o )]:
% 2.55/3.09 ( ( ?[X102:$i]:
% 2.55/3.09 ( ( X100 @ X102 ) &
% 2.55/3.09 ( ![X104:$i]:
% 2.55/3.09 ( ( X100 @ X104 ) =>
% 2.55/3.09 ( ( X102 ) = ( X104 ) ) ) ) ) ) =>
% 2.55/3.09 ( X100 @
% 2.55/3.09 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 2.55/3.09 ( ( in @ X110 @ X106 ) =>
% 2.55/3.09 ( ( X108 @ X110 ) =>
% 2.55/3.09 ( in @
% 2.55/3.09 X110 @
% 2.55/3.09 ( dsetconstr @
% 2.55/3.09 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 2.55/3.09 ( ( in @
% 2.55/3.09 X116 @
% 2.55/3.09 ( dsetconstr @
% 2.55/3.09 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 2.55/3.09 ( in @ X116 @ X112 ) ) ) =>
% 2.55/3.09 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 2.55/3.09 ( ( in @
% 2.55/3.09 X122 @
% 2.55/3.09 ( dsetconstr @
% 2.55/3.09 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 2.55/3.09 ( X120 @ X122 ) ) ) =>
% 2.55/3.09 ( ( ![X124:( $i > $o )]:
% 2.55/3.09 ( ( ?[X126:$i]:
% 2.55/3.09 ( ( X124 @ X126 ) &
% 2.55/3.09 ( ![X128:$i]:
% 2.55/3.09 ( ( X124 @ X128 ) =>
% 2.55/3.09 ( ( X126 ) = ( X128 ) ) ) ) ) ) =>
% 2.55/3.09 ( ?[X130:$i]:
% 2.55/3.09 ( ( X124 @ X130 ) &
% 2.55/3.09 ( ![X132:$i]:
% 2.55/3.09 ( ( X124 @ X132 ) =>
% 2.55/3.09 ( ( X130 ) = ( X132 ) ) ) ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X134:$o,X136:$i]:
% 2.55/3.09 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 2.55/3.09 ( X134 ) ) ) =>
% 2.55/3.09 ( ( ![X138:$i]:
% 2.55/3.09 ( ( in @ X138 @ emptyset ) =>
% 2.55/3.09 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 2.55/3.09 ( ( ![X142:$i]:
% 2.55/3.09 ( ( in @ X142 @ emptyset ) =>
% 2.55/3.09 ( $false ) ) ) =>
% 2.55/3.09 ( ( ![X144:$i]:
% 2.55/3.09 ( ~( in @ X144 @ emptyset ) ) ) =>
% 2.55/3.09 ( ![X146:( $i > $o )]:
% 2.55/3.09 ( ( ?[X148:$i]:
% 2.55/3.09 ( ( X146 @ X148 ) &
% 2.55/3.09 ( ![X150:$i]:
% 2.55/3.09 ( ( X146 @ X150 ) =>
% 2.55/3.09 ( ( X148 ) = ( X150 ) ) ) ) ) ) =>
% 2.55/3.09 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 2.55/3.09 thf(zf_stmt_1, type, zip_tseitin_3 : $i > $i > $i > ( $i > $i > $o ) > $o).
% 2.55/3.09 thf(zf_stmt_2, axiom,
% 2.55/3.09 (![X52:$i,X50:$i,X40:$i,X38:( $i > $i > $o )]:
% 2.55/3.09 ( ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) <=>
% 2.55/3.09 ( ( X38 @ X52 @ X50 ) & ( in @ X52 @ X40 ) ) ))).
% 2.55/3.09 thf(zf_stmt_3, type, zip_tseitin_2 : $i > $i > $i > $o).
% 2.55/3.09 thf(zf_stmt_4, axiom,
% 2.55/3.09 (![X28:$i,X26:$i,X24:$i]:
% 2.55/3.09 ( ( zip_tseitin_2 @ X28 @ X26 @ X24 ) <=>
% 2.55/3.09 ( ( in @ X28 @ X24 ) & ( in @ X26 @ X28 ) ) ))).
% 2.55/3.09 thf(zf_stmt_5, type, zip_tseitin_1 : $i > $i > $i > $o).
% 2.55/3.09 thf(zf_stmt_6, axiom,
% 2.55/3.09 (![X22:$i,X20:$i,X18:$i]:
% 2.55/3.09 ( ( zip_tseitin_1 @ X22 @ X20 @ X18 ) <=>
% 2.55/3.09 ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ))).
% 2.55/3.09 thf(zf_stmt_7, type, zip_tseitin_0 : $i > $i > $i > $o).
% 2.55/3.09 thf(zf_stmt_8, axiom,
% 2.55/3.09 (![X16:$i,X14:$i,X12:$i]:
% 2.55/3.09 ( ( zip_tseitin_0 @ X16 @ X14 @ X12 ) <=>
% 2.55/3.09 ( ( ( X16 ) = ( X12 ) ) | ( in @ X16 @ X14 ) ) ))).
% 2.55/3.09 thf(zf_stmt_9, conjecture,
% 2.55/3.09 (( ![X4:$i,X6:$i]:
% 2.55/3.09 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 2.55/3.09 ( ( X4 ) = ( X6 ) ) ) ) =>
% 2.55/3.09 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 2.55/3.09 ( ( ![X12:$i,X14:$i,X16:$i]:
% 2.55/3.09 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 2.55/3.09 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 2.55/3.09 ( ( ![X18:$i,X20:$i]:
% 2.55/3.09 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 2.55/3.09 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 2.55/3.09 ( ( ![X24:$i,X26:$i]:
% 2.55/3.09 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 2.55/3.09 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 2.55/3.09 ( ( in @ emptyset @ omega ) =>
% 2.55/3.09 ( ( ![X30:$i]:
% 2.55/3.09 ( ( in @ X30 @ omega ) =>
% 2.55/3.09 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 2.55/3.09 ( ( ![X32:$i]:
% 2.55/3.09 ( ( ( in @ emptyset @ X32 ) &
% 2.55/3.09 ( ![X34:$i]:
% 2.55/3.09 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 2.55/3.09 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 2.55/3.09 ( ![X36:$i]:
% 2.55/3.09 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 2.55/3.09 ( ( ![X42:$i]:
% 2.55/3.09 ( ( in @ X42 @ X40 ) =>
% 2.55/3.09 ( ?[X44:$i]:
% 2.55/3.09 ( ( ![X46:$i]:
% 2.55/3.09 ( ( X38 @ X42 @ X46 ) =>
% 2.55/3.09 ( ( X44 ) = ( X46 ) ) ) ) &
% 2.55/3.09 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 2.55/3.09 ( ?[X48:$i]:
% 2.55/3.09 ( ![X50:$i]:
% 2.55/3.09 ( ( in @ X50 @ X48 ) <=>
% 2.55/3.09 ( ?[X52:$i]:
% 2.55/3.09 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X54:$i]:
% 2.55/3.09 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 2.55/3.09 ( ?[X58:$i]:
% 2.55/3.09 ( ( ~( ?[X60:$i]:
% 2.55/3.09 ( ( in @ X60 @ X54 ) & ( in @ X60 @ X58 ) ) ) ) &
% 2.55/3.09 ( in @ X58 @ X54 ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X62:$i]:
% 2.55/3.09 ( ?[X64:$i]:
% 2.55/3.09 ( ( ![X66:$i]:
% 2.55/3.09 ( ( ( ![X68:$i]:
% 2.55/3.09 ( ( in @ X68 @ X66 ) =>
% 2.55/3.09 ( in @ X68 @ X62 ) ) ) &
% 2.55/3.09 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 2.55/3.09 ( ?[X72:$i,X74:$i]:
% 2.55/3.09 ( ( ![X76:$i]:
% 2.55/3.09 ( ( in @ X76 @ X64 ) =>
% 2.55/3.09 ( ( ![X78:$i]:
% 2.55/3.09 ( ( in @ X78 @ X76 ) =>
% 2.55/3.09 ( in @ X78 @ X72 ) ) ) |
% 2.55/3.09 ( in @ X74 @ X76 ) ) ) ) &
% 2.55/3.09 ( ~( ?[X80:$i]:
% 2.55/3.09 ( ( in @ X80 @ X66 ) &
% 2.55/3.09 ( in @ X80 @ X72 ) ) ) ) &
% 2.55/3.09 ( in @ X74 @ X66 ) & ( in @ X72 @ X64 ) ) ) ) ) &
% 2.55/3.09 ( ![X82:$i,X84:$i]:
% 2.55/3.09 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 2.55/3.09 ( ( ![X86:$i]:
% 2.55/3.09 ( ( in @ X86 @ X82 ) =>
% 2.55/3.09 ( in @ X86 @ X84 ) ) ) |
% 2.55/3.09 ( ![X88:$i]:
% 2.55/3.09 ( ( in @ X88 @ X84 ) =>
% 2.55/3.09 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 2.55/3.09 ( ![X90:$i,X92:$i]:
% 2.55/3.09 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 2.55/3.09 ( ( ![X94:$i]:
% 2.55/3.09 ( ( in @ X94 @ X64 ) =>
% 2.55/3.09 ( ( in @ X90 @ X94 ) <=>
% 2.55/3.09 ( in @ X92 @ X94 ) ) ) ) =>
% 2.55/3.09 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 2.55/3.09 ( ![X96:$i]:
% 2.55/3.09 ( ( in @ X96 @ X64 ) =>
% 2.55/3.09 ( ![X98:$i]:
% 2.55/3.09 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X100:( $i > $o )]:
% 2.55/3.09 ( ( ?[X102:$i]:
% 2.55/3.09 ( ( ![X104:$i]:
% 2.55/3.09 ( ( X100 @ X104 ) =>
% 2.55/3.09 ( ( X102 ) = ( X104 ) ) ) ) &
% 2.55/3.09 ( X100 @ X102 ) ) ) =>
% 2.55/3.09 ( X100 @
% 2.55/3.09 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 2.55/3.09 ( ( in @ X110 @ X106 ) =>
% 2.55/3.09 ( ( X108 @ X110 ) =>
% 2.55/3.09 ( in @
% 2.55/3.09 X110 @
% 2.55/3.09 ( dsetconstr @
% 2.55/3.09 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 2.55/3.09 ( ( in @
% 2.55/3.09 X116 @
% 2.55/3.09 ( dsetconstr @
% 2.55/3.09 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 2.55/3.09 ( in @ X116 @ X112 ) ) ) =>
% 2.55/3.09 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 2.55/3.09 ( ( in @
% 2.55/3.09 X122 @
% 2.55/3.09 ( dsetconstr @
% 2.55/3.09 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 2.55/3.09 ( X120 @ X122 ) ) ) =>
% 2.55/3.09 ( ( ![X124:( $i > $o )]:
% 2.55/3.09 ( ( ?[X126:$i]:
% 2.55/3.09 ( ( ![X128:$i]:
% 2.55/3.09 ( ( X124 @ X128 ) =>
% 2.55/3.09 ( ( X126 ) = ( X128 ) ) ) ) &
% 2.55/3.09 ( X124 @ X126 ) ) ) =>
% 2.55/3.09 ( ?[X130:$i]:
% 2.55/3.09 ( ( ![X132:$i]:
% 2.55/3.09 ( ( X124 @ X132 ) =>
% 2.55/3.09 ( ( X130 ) = ( X132 ) ) ) ) &
% 2.55/3.09 ( X124 @ X130 ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X134:$o,X136:$i]:
% 2.55/3.09 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 2.55/3.09 ( X134 ) ) ) =>
% 2.55/3.09 ( ( ![X138:$i]:
% 2.55/3.09 ( ( in @ X138 @ emptyset ) =>
% 2.55/3.09 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 2.55/3.09 ( ( ![X142:$i]:
% 2.55/3.09 ( ~( in @ X142 @ emptyset ) ) ) =>
% 2.55/3.09 ( ( ![X144:$i]:
% 2.55/3.09 ( ~( in @ X144 @ emptyset ) ) ) =>
% 2.55/3.09 ( ![X146:( $i > $o )]:
% 2.55/3.09 ( ( ?[X148:$i]:
% 2.55/3.09 ( ( ![X150:$i]:
% 2.55/3.09 ( ( X146 @ X150 ) =>
% 2.55/3.09 ( ( X148 ) = ( X150 ) ) ) ) &
% 2.55/3.09 ( X146 @ X148 ) ) ) =>
% 2.55/3.09 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 2.55/3.09 thf(zf_stmt_10, negated_conjecture,
% 2.55/3.09 (~( ( ![X4:$i,X6:$i]:
% 2.55/3.09 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 2.55/3.09 ( ( X4 ) = ( X6 ) ) ) ) =>
% 2.55/3.09 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 2.55/3.09 ( ( ![X12:$i,X14:$i,X16:$i]:
% 2.55/3.09 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 2.55/3.09 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 2.55/3.09 ( ( ![X18:$i,X20:$i]:
% 2.55/3.09 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 2.55/3.09 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 2.55/3.09 ( ( ![X24:$i,X26:$i]:
% 2.55/3.09 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 2.55/3.09 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 2.55/3.09 ( ( in @ emptyset @ omega ) =>
% 2.55/3.09 ( ( ![X30:$i]:
% 2.55/3.09 ( ( in @ X30 @ omega ) =>
% 2.55/3.09 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 2.55/3.09 ( ( ![X32:$i]:
% 2.55/3.09 ( ( ( in @ emptyset @ X32 ) &
% 2.55/3.09 ( ![X34:$i]:
% 2.55/3.09 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 2.55/3.09 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 2.55/3.09 ( ![X36:$i]:
% 2.55/3.09 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 2.55/3.09 ( ( ![X42:$i]:
% 2.55/3.09 ( ( in @ X42 @ X40 ) =>
% 2.55/3.09 ( ?[X44:$i]:
% 2.55/3.09 ( ( ![X46:$i]:
% 2.55/3.09 ( ( X38 @ X42 @ X46 ) =>
% 2.55/3.09 ( ( X44 ) = ( X46 ) ) ) ) &
% 2.55/3.09 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 2.55/3.09 ( ?[X48:$i]:
% 2.55/3.09 ( ![X50:$i]:
% 2.55/3.09 ( ( in @ X50 @ X48 ) <=>
% 2.55/3.09 ( ?[X52:$i]:
% 2.55/3.09 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X54:$i]:
% 2.55/3.09 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 2.55/3.09 ( ?[X58:$i]:
% 2.55/3.09 ( ( ~( ?[X60:$i]:
% 2.55/3.09 ( ( in @ X60 @ X54 ) &
% 2.55/3.09 ( in @ X60 @ X58 ) ) ) ) &
% 2.55/3.09 ( in @ X58 @ X54 ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X62:$i]:
% 2.55/3.09 ( ?[X64:$i]:
% 2.55/3.09 ( ( ![X66:$i]:
% 2.55/3.09 ( ( ( ![X68:$i]:
% 2.55/3.09 ( ( in @ X68 @ X66 ) =>
% 2.55/3.09 ( in @ X68 @ X62 ) ) ) &
% 2.55/3.09 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 2.55/3.09 ( ?[X72:$i,X74:$i]:
% 2.55/3.09 ( ( ![X76:$i]:
% 2.55/3.09 ( ( in @ X76 @ X64 ) =>
% 2.55/3.09 ( ( ![X78:$i]:
% 2.55/3.09 ( ( in @ X78 @ X76 ) =>
% 2.55/3.09 ( in @ X78 @ X72 ) ) ) |
% 2.55/3.09 ( in @ X74 @ X76 ) ) ) ) &
% 2.55/3.09 ( ~( ?[X80:$i]:
% 2.55/3.09 ( ( in @ X80 @ X66 ) &
% 2.55/3.09 ( in @ X80 @ X72 ) ) ) ) &
% 2.55/3.09 ( in @ X74 @ X66 ) &
% 2.55/3.09 ( in @ X72 @ X64 ) ) ) ) ) &
% 2.55/3.09 ( ![X82:$i,X84:$i]:
% 2.55/3.09 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 2.55/3.09 ( ( ![X86:$i]:
% 2.55/3.09 ( ( in @ X86 @ X82 ) =>
% 2.55/3.09 ( in @ X86 @ X84 ) ) ) |
% 2.55/3.09 ( ![X88:$i]:
% 2.55/3.09 ( ( in @ X88 @ X84 ) =>
% 2.55/3.09 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 2.55/3.09 ( ![X90:$i,X92:$i]:
% 2.55/3.09 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 2.55/3.09 ( ( ![X94:$i]:
% 2.55/3.09 ( ( in @ X94 @ X64 ) =>
% 2.55/3.09 ( ( in @ X90 @ X94 ) <=>
% 2.55/3.09 ( in @ X92 @ X94 ) ) ) ) =>
% 2.55/3.09 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 2.55/3.09 ( ![X96:$i]:
% 2.55/3.09 ( ( in @ X96 @ X64 ) =>
% 2.55/3.09 ( ![X98:$i]:
% 2.55/3.09 ( ( in @ X98 @ X96 ) =>
% 2.55/3.09 ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X100:( $i > $o )]:
% 2.55/3.09 ( ( ?[X102:$i]:
% 2.55/3.09 ( ( ![X104:$i]:
% 2.55/3.09 ( ( X100 @ X104 ) =>
% 2.55/3.09 ( ( X102 ) = ( X104 ) ) ) ) &
% 2.55/3.09 ( X100 @ X102 ) ) ) =>
% 2.55/3.09 ( X100 @
% 2.55/3.09 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 2.55/3.09 ( ( in @ X110 @ X106 ) =>
% 2.55/3.09 ( ( X108 @ X110 ) =>
% 2.55/3.09 ( in @
% 2.55/3.09 X110 @
% 2.55/3.09 ( dsetconstr @
% 2.55/3.09 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 2.55/3.09 ( ( in @
% 2.55/3.09 X116 @
% 2.55/3.09 ( dsetconstr @
% 2.55/3.09 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 2.55/3.09 ( in @ X116 @ X112 ) ) ) =>
% 2.55/3.09 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 2.55/3.09 ( ( in @
% 2.55/3.09 X122 @
% 2.55/3.09 ( dsetconstr @
% 2.55/3.09 X118 @
% 2.55/3.09 ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 2.55/3.09 ( X120 @ X122 ) ) ) =>
% 2.55/3.09 ( ( ![X124:( $i > $o )]:
% 2.55/3.09 ( ( ?[X126:$i]:
% 2.55/3.09 ( ( ![X128:$i]:
% 2.55/3.09 ( ( X124 @ X128 ) =>
% 2.55/3.09 ( ( X126 ) = ( X128 ) ) ) ) &
% 2.55/3.09 ( X124 @ X126 ) ) ) =>
% 2.55/3.09 ( ?[X130:$i]:
% 2.55/3.09 ( ( ![X132:$i]:
% 2.55/3.09 ( ( X124 @ X132 ) =>
% 2.55/3.09 ( ( X130 ) = ( X132 ) ) ) ) &
% 2.55/3.09 ( X124 @ X130 ) ) ) ) ) =>
% 2.55/3.09 ( ( ![X134:$o,X136:$i]:
% 2.55/3.09 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 2.55/3.09 ( X134 ) ) ) =>
% 2.55/3.09 ( ( ![X138:$i]:
% 2.55/3.09 ( ( in @ X138 @ emptyset ) =>
% 2.55/3.09 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 2.55/3.09 ( ( ![X142:$i]:
% 2.55/3.09 ( ~( in @ X142 @ emptyset ) ) ) =>
% 2.55/3.09 ( ( ![X144:$i]:
% 2.55/3.09 ( ~( in @ X144 @ emptyset ) ) ) =>
% 2.55/3.09 ( ![X146:( $i > $o )]:
% 2.55/3.09 ( ( ?[X148:$i]:
% 2.55/3.09 ( ( ![X150:$i]:
% 2.55/3.09 ( ( X146 @ X150 ) =>
% 2.55/3.09 ( ( X148 ) = ( X150 ) ) ) ) &
% 2.55/3.09 ( X146 @ X148 ) ) ) =>
% 2.55/3.09 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 2.55/3.09 inference('cnf.neg', [status(esa)], [zf_stmt_9])).
% 2.55/3.09 thf(zip_derived_cl44, plain, ( (sk__76 @ sk__77)),
% 2.55/3.09 inference('cnf', [status(esa)], [zf_stmt_10])).
% 2.55/3.09 thf(zip_derived_cl43, plain, (![X40 : $i]: ~ (sk__76 @ X40)),
% 2.55/3.09 inference('cnf', [status(esa)], [zf_stmt_10])).
% 2.55/3.09 thf(zip_derived_cl65, plain, ($false),
% 2.55/3.09 inference('sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl43])).
% 2.55/3.09
% 2.55/3.09 % SZS output end Refutation
% 2.55/3.09
% 2.55/3.09
% 2.55/3.09 % Terminating...
% 2.85/3.24 % Runner terminated.
% 2.86/3.28 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------