%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU500^1 : 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.OLfk55IDw4 true
% Computer : n016.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 04:54:48 PM UTC 2025
% Result : Theorem 1.71s 1.43s
% Output : Refutation 1.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SEU500^1 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.OLfk55IDw4 true
% 0.12/0.38 % Computer : n016.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8042.1875MB
% 0.12/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Oct 1 16:13:08 EDT 2025
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Running portfolio for 300 s
% 0.12/0.38 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39 % Number of cores: 8
% 0.12/0.39 % Python version: Python 3.6.8
% 0.12/0.39 % Running in HO mode
% 0.55/0.78 % Total configuration time : 828
% 0.55/0.78 % Estimated wc time : 1656
% 0.55/0.78 % Estimated cpu time (8 cpus) : 207.0
% 0.56/1.10 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/1.12 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.56/1.12 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.54/1.16 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.56/1.19 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.56/1.20 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.56/1.22 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.56/1.22 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.71/1.43 % Solved by lams/40_c_ic.sh.
% 1.71/1.43 % done 26 iterations in 0.218s
% 1.71/1.43 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.71/1.43 % SZS output start Refutation
% 1.71/1.43 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 1.71/1.43 thf(setunionAx_type, type, setunionAx: $o).
% 1.71/1.43 thf(omegaSAx_type, type, omegaSAx: $o).
% 1.71/1.43 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 1.71/1.43 thf(in_type, type, in: $i > $i > $o).
% 1.71/1.43 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 1.71/1.43 thf(powersetAx_type, type, powersetAx: $o).
% 1.71/1.43 thf(sk__71_type, type, sk__71: $i).
% 1.71/1.43 thf(emptyset_type, type, emptyset: $i).
% 1.71/1.43 thf(zip_tseitin_3_type, type, zip_tseitin_3: $i > $i > $i > ($i > $i > $o) > $o).
% 1.71/1.43 thf(descr_type, type, descr: ($i > $o) > $i).
% 1.71/1.43 thf(exuE1_type, type, exuE1: $o).
% 1.71/1.43 thf(prop2set_type, type, prop2set: $o > $i).
% 1.71/1.43 thf(zip_tseitin_2_type, type, zip_tseitin_2: $i > $i > $i > $o).
% 1.71/1.43 thf(omega0Ax_type, type, omega0Ax: $o).
% 1.71/1.43 thf(setextAx_type, type, setextAx: $o).
% 1.71/1.43 thf(setunion_type, type, setunion: $i > $i).
% 1.71/1.43 thf(descrp_type, type, descrp: $o).
% 1.71/1.43 thf(foundationAx_type, type, foundationAx: $o).
% 1.71/1.43 thf(emptysetAx_type, type, emptysetAx: $o).
% 1.71/1.43 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 1.71/1.43 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 1.71/1.43 thf(exu_type, type, exu: ($i > $o) > $o).
% 1.71/1.43 thf(sk__70_type, type, sk__70: $o).
% 1.71/1.43 thf(omega_type, type, omega: $i).
% 1.71/1.43 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $i > $o).
% 1.71/1.43 thf(powerset_type, type, powerset: $i > $i).
% 1.71/1.43 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 1.71/1.43 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 1.71/1.43 thf(replAx_type, type, replAx: $o).
% 1.71/1.43 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 1.71/1.43 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 1.71/1.43 thf(prop2set, axiom,(( prop2set ) =
% 1.71/1.43 (^[Xphi:$o]:
% 1.71/1.43 ( dsetconstr @ ( powerset @ emptyset ) @ ( ^[Xx:$i]: ( Xphi ) ) )))).
% 1.71/1.43 thf('0', plain,
% 1.71/1.43 (( prop2set ) =
% 1.71/1.43 ( ^[Xphi:$o]:
% 1.71/1.43 ( dsetconstr @ ( powerset @ emptyset ) @ ( ^[Xx:$i]: ( Xphi ) ) ) )),
% 1.71/1.43 inference('simplify_rw_rule', [status(thm)], [prop2set])).
% 1.71/1.43 thf('1', plain,
% 1.71/1.43 (( prop2set ) =
% 1.71/1.43 ( ^[V_1:$o]:
% 1.71/1.43 ( dsetconstr @ ( powerset @ emptyset ) @ ( ^[V_2:$i]: ( V_1 ) ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(exuE1, axiom, exuE1 =
% 1.71/1.43 (![Xphi:( $i > $o )]:
% 1.71/1.43 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 1.71/1.43 ( ?[Xx:$i]:
% 1.71/1.43 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 1.71/1.43 ( Xphi @ Xx ) ) ) ))).
% 1.71/1.43 thf('2', plain,
% 1.71/1.43 (( exuE1 ) =
% 1.71/1.43 ( ![X4:( $i > $o )]:
% 1.71/1.43 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 1.71/1.43 ( ?[X6:$i]:
% 1.71/1.43 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) &
% 1.71/1.43 ( X4 @ X6 ) ) ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(dsetconstrER, axiom, dsetconstrER =
% 1.71/1.43 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 1.71/1.43 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 1.71/1.43 ( Xphi @ Xx ) ))).
% 1.71/1.43 thf('3', plain,
% 1.71/1.43 (( dsetconstrER ) =
% 1.71/1.43 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 1.71/1.43 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 1.71/1.43 ( X6 @ X8 ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(dsetconstrEL, axiom, dsetconstrEL =
% 1.71/1.43 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 1.71/1.43 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 1.71/1.43 ( in @ Xx @ A ) ))).
% 1.71/1.43 thf('4', plain,
% 1.71/1.43 (( dsetconstrEL ) =
% 1.71/1.43 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 1.71/1.43 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 1.71/1.43 ( in @ X8 @ X4 ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(dsetconstrI, axiom, dsetconstrI =
% 1.71/1.43 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 1.71/1.43 ( ( in @ Xx @ A ) =>
% 1.71/1.43 ( ( Xphi @ Xx ) =>
% 1.71/1.43 ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 1.71/1.43 thf('5', plain,
% 1.71/1.43 (( dsetconstrI ) =
% 1.71/1.43 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 1.71/1.43 ( ( in @ X8 @ X4 ) =>
% 1.71/1.43 ( ( X6 @ X8 ) =>
% 1.71/1.43 ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(descrp, axiom, descrp =
% 1.71/1.43 (![Xphi:( $i > $o )]:
% 1.71/1.43 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 1.71/1.43 ( Xphi @ ( descr @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 1.71/1.43 thf('6', plain,
% 1.71/1.43 (( descrp ) =
% 1.71/1.43 ( ![X4:( $i > $o )]:
% 1.71/1.43 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 1.71/1.43 ( X4 @ ( descr @ ( ^[V_2:$i]: ( X4 @ V_2 ) ) ) ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(wellorderingAx, axiom, wellorderingAx =
% 1.71/1.43 (![A:$i]:
% 1.71/1.43 ( ?[B:$i]:
% 1.71/1.43 ( ( ![C:$i]:
% 1.71/1.43 ( ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) &
% 1.71/1.43 ( ?[Xx:$i]: ( in @ Xx @ C ) ) ) =>
% 1.71/1.43 ( ?[D:$i,Xx:$i]:
% 1.71/1.43 ( ( ![E:$i]:
% 1.71/1.43 ( ( in @ E @ B ) =>
% 1.71/1.43 ( ( ![Xy:$i]: ( ( in @ Xy @ E ) => ( in @ Xy @ D ) ) ) |
% 1.71/1.43 ( in @ Xx @ E ) ) ) ) &
% 1.71/1.43 ( ~( ?[Xy:$i]: ( ( in @ Xy @ C ) & ( in @ Xy @ D ) ) ) ) &
% 1.71/1.43 ( in @ Xx @ C ) & ( in @ D @ B ) ) ) ) ) &
% 1.71/1.43 ( ![C:$i,D:$i]:
% 1.71/1.43 ( ( ( in @ C @ B ) & ( in @ D @ B ) ) =>
% 1.71/1.43 ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ D ) ) ) |
% 1.71/1.43 ( ![Xx:$i]: ( ( in @ Xx @ D ) => ( in @ Xx @ C ) ) ) ) ) ) &
% 1.71/1.43 ( ![Xx:$i,Xy:$i]:
% 1.71/1.43 ( ( ( in @ Xx @ A ) & ( in @ Xy @ A ) ) =>
% 1.71/1.43 ( ( ![C:$i]:
% 1.71/1.43 ( ( in @ C @ B ) => ( ( in @ Xx @ C ) <=> ( in @ Xy @ C ) ) ) ) =>
% 1.71/1.43 ( ( Xx ) = ( Xy ) ) ) ) ) &
% 1.71/1.43 ( ![C:$i]:
% 1.71/1.43 ( ( in @ C @ B ) =>
% 1.71/1.43 ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) ) ) ) ))).
% 1.71/1.43 thf('7', plain,
% 1.71/1.43 (( wellorderingAx ) =
% 1.71/1.43 ( ![X4:$i]:
% 1.71/1.43 ( ?[X6:$i]:
% 1.71/1.43 ( ( ![X8:$i]:
% 1.71/1.43 ( ( ( ![X10:$i]: ( ( in @ X10 @ X8 ) => ( in @ X10 @ X4 ) ) ) &
% 1.71/1.43 ( ?[X12:$i]: ( in @ X12 @ X8 ) ) ) =>
% 1.71/1.43 ( ?[X14:$i,X16:$i]:
% 1.71/1.43 ( ( ![X18:$i]:
% 1.71/1.43 ( ( in @ X18 @ X6 ) =>
% 1.71/1.43 ( ( ![X20:$i]:
% 1.71/1.43 ( ( in @ X20 @ X18 ) => ( in @ X20 @ X14 ) ) ) |
% 1.71/1.43 ( in @ X16 @ X18 ) ) ) ) &
% 1.71/1.43 ( ~( ?[X22:$i]: ( ( in @ X22 @ X8 ) & ( in @ X22 @ X14 ) ) ) ) &
% 1.71/1.43 ( in @ X16 @ X8 ) & ( in @ X14 @ X6 ) ) ) ) ) &
% 1.71/1.43 ( ![X24:$i,X26:$i]:
% 1.71/1.43 ( ( ( in @ X24 @ X6 ) & ( in @ X26 @ X6 ) ) =>
% 1.71/1.43 ( ( ![X28:$i]: ( ( in @ X28 @ X24 ) => ( in @ X28 @ X26 ) ) ) |
% 1.71/1.43 ( ![X30:$i]: ( ( in @ X30 @ X26 ) => ( in @ X30 @ X24 ) ) ) ) ) ) &
% 1.71/1.43 ( ![X32:$i,X34:$i]:
% 1.71/1.43 ( ( ( in @ X32 @ X4 ) & ( in @ X34 @ X4 ) ) =>
% 1.71/1.43 ( ( ![X36:$i]:
% 1.71/1.43 ( ( in @ X36 @ X6 ) =>
% 1.71/1.43 ( ( in @ X32 @ X36 ) <=> ( in @ X34 @ X36 ) ) ) ) =>
% 1.71/1.43 ( ( X32 ) = ( X34 ) ) ) ) ) &
% 1.71/1.43 ( ![X38:$i]:
% 1.71/1.43 ( ( in @ X38 @ X6 ) =>
% 1.71/1.43 ( ![X40:$i]: ( ( in @ X40 @ X38 ) => ( in @ X40 @ X4 ) ) ) ) ) ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(foundationAx, axiom, foundationAx =
% 1.71/1.43 (![A:$i]:
% 1.71/1.43 ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) =>
% 1.71/1.43 ( ?[B:$i]:
% 1.71/1.43 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ A ) & ( in @ Xx @ B ) ) ) ) &
% 1.71/1.43 ( in @ B @ A ) ) ) ))).
% 1.71/1.43 thf('8', plain,
% 1.71/1.43 (( foundationAx ) =
% 1.71/1.43 ( ![X4:$i]:
% 1.71/1.43 ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) =>
% 1.71/1.43 ( ?[X8:$i]:
% 1.71/1.43 ( ( ~( ?[X10:$i]: ( ( in @ X10 @ X4 ) & ( in @ X10 @ X8 ) ) ) ) &
% 1.71/1.43 ( in @ X8 @ X4 ) ) ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(replAx, axiom, replAx =
% 1.71/1.43 (![Xphi:( $i > $i > $o ),A:$i]:
% 1.71/1.43 ( ( ![Xx:$i]:
% 1.71/1.43 ( ( in @ Xx @ A ) => ( exu @ ( ^[Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) ) ) =>
% 1.71/1.43 ( ?[B:$i]:
% 1.71/1.43 ( ![Xx:$i]:
% 1.71/1.43 ( ( in @ Xx @ B ) <=>
% 1.71/1.43 ( ?[Xy:$i]: ( ( Xphi @ Xy @ Xx ) & ( in @ Xy @ A ) ) ) ) ) ) ))).
% 1.71/1.43 thf('9', plain,
% 1.71/1.43 (( replAx ) =
% 1.71/1.43 ( ![X4:( $i > $i > $o ),X6:$i]:
% 1.71/1.43 ( ( ![X8:$i]:
% 1.71/1.43 ( ( in @ X8 @ X6 ) => ( exu @ ( ^[V_1:$i]: ( X4 @ X8 @ V_1 ) ) ) ) ) =>
% 1.71/1.43 ( ?[X10:$i]:
% 1.71/1.43 ( ![X12:$i]:
% 1.71/1.43 ( ( in @ X12 @ X10 ) <=>
% 1.71/1.43 ( ?[X14:$i]: ( ( X4 @ X14 @ X12 ) & ( in @ X14 @ X6 ) ) ) ) ) ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(omegaIndAx, axiom, omegaIndAx =
% 1.71/1.43 (![A:$i]:
% 1.71/1.43 ( ( ( in @ emptyset @ A ) &
% 1.71/1.43 ( ![Xx:$i]:
% 1.71/1.43 ( ( ( in @ Xx @ omega ) & ( in @ Xx @ A ) ) =>
% 1.71/1.43 ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) ) =>
% 1.71/1.43 ( ![Xx:$i]: ( ( in @ Xx @ omega ) => ( in @ Xx @ A ) ) ) ))).
% 1.71/1.43 thf('10', plain,
% 1.71/1.43 (( omegaIndAx ) =
% 1.71/1.43 ( ![X4:$i]:
% 1.71/1.43 ( ( ( in @ emptyset @ X4 ) &
% 1.71/1.43 ( ![X6:$i]:
% 1.71/1.43 ( ( ( in @ X6 @ omega ) & ( in @ X6 @ X4 ) ) =>
% 1.71/1.43 ( in @ ( setadjoin @ X6 @ X6 ) @ X4 ) ) ) ) =>
% 1.71/1.43 ( ![X8:$i]: ( ( in @ X8 @ omega ) => ( in @ X8 @ X4 ) ) ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(omegaSAx, axiom, omegaSAx =
% 1.71/1.43 (![Xx:$i]:
% 1.71/1.43 ( ( in @ Xx @ omega ) => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ))).
% 1.71/1.43 thf('11', plain,
% 1.71/1.43 (( omegaSAx ) =
% 1.71/1.43 ( ![X4:$i]:
% 1.71/1.43 ( ( in @ X4 @ omega ) => ( in @ ( setadjoin @ X4 @ X4 ) @ omega ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(omega0Ax, axiom,(( omega0Ax ) = (in @ emptyset @ omega))).
% 1.71/1.43 thf('12', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 1.71/1.43 inference('simplify_rw_rule', [status(thm)], [omega0Ax])).
% 1.71/1.43 thf('13', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(setunionAx, axiom, setunionAx =
% 1.71/1.43 (![A:$i,Xx:$i]:
% 1.71/1.43 ( ( in @ Xx @ ( setunion @ A ) ) <=>
% 1.71/1.43 ( ?[B:$i]: ( ( in @ B @ A ) & ( in @ Xx @ B ) ) ) ))).
% 1.71/1.43 thf('14', plain,
% 1.71/1.43 (( setunionAx ) =
% 1.71/1.43 ( ![X4:$i,X6:$i]:
% 1.71/1.43 ( ( in @ X6 @ ( setunion @ X4 ) ) <=>
% 1.71/1.43 ( ?[X8:$i]: ( ( in @ X8 @ X4 ) & ( in @ X6 @ X8 ) ) ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(powersetAx, axiom, powersetAx =
% 1.71/1.43 (![A:$i,B:$i]:
% 1.71/1.43 ( ( in @ B @ ( powerset @ A ) ) <=>
% 1.71/1.43 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 1.71/1.43 thf('15', plain,
% 1.71/1.43 (( powersetAx ) =
% 1.71/1.43 ( ![X4:$i,X6:$i]:
% 1.71/1.43 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 1.71/1.43 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(setadjoinAx, axiom, setadjoinAx =
% 1.71/1.43 (![Xx:$i,A:$i,Xy:$i]:
% 1.71/1.43 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 1.71/1.43 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 1.71/1.43 thf('16', plain,
% 1.71/1.43 (( setadjoinAx ) =
% 1.71/1.43 ( ![X4:$i,X6:$i,X8:$i]:
% 1.71/1.43 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 1.71/1.43 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(emptysetAx, axiom, emptysetAx = (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 1.71/1.43 thf('17', plain,
% 1.71/1.43 (( emptysetAx ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(setextAx, axiom, setextAx =
% 1.71/1.43 (![A:$i,B:$i]:
% 1.71/1.43 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) <=> ( in @ Xx @ B ) ) ) =>
% 1.71/1.43 ( ( A ) = ( B ) ) ))).
% 1.71/1.43 thf('18', plain,
% 1.71/1.43 (( setextAx ) =
% 1.71/1.43 ( ![X4:$i,X6:$i]:
% 1.71/1.43 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 1.71/1.43 ( ( X4 ) = ( X6 ) ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(exu, axiom,(( exu ) =
% 1.71/1.43 (^[Xphi:( $i > $o )]:
% 1.71/1.43 ( ?[Xx:$i]:
% 1.71/1.43 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) & ( Xphi @ Xx ) ) )))).
% 1.71/1.43 thf('19', plain,
% 1.71/1.43 (( exu ) =
% 1.71/1.43 ( ^[Xphi:( $i > $o )]:
% 1.71/1.43 ( ?[Xx:$i]:
% 1.71/1.43 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 1.71/1.43 ( Xphi @ Xx ) ) ) )),
% 1.71/1.43 inference('simplify_rw_rule', [status(thm)], [exu])).
% 1.71/1.43 thf('20', plain,
% 1.71/1.43 (( exu ) =
% 1.71/1.43 ( ^[V_1:( $i > $o )]:
% 1.71/1.43 ( ?[X4:$i]:
% 1.71/1.43 ( ( ![X6:$i]: ( ( V_1 @ X6 ) => ( ( X4 ) = ( X6 ) ) ) ) &
% 1.71/1.43 ( V_1 @ X4 ) ) ) )),
% 1.71/1.43 define([status(thm)])).
% 1.71/1.43 thf(prop2setE, conjecture,
% 1.71/1.43 (( setextAx ) =>
% 1.71/1.43 ( ( emptysetAx ) =>
% 1.71/1.43 ( ( setadjoinAx ) =>
% 1.71/1.43 ( ( powersetAx ) =>
% 1.71/1.43 ( ( setunionAx ) =>
% 1.71/1.43 ( ( omega0Ax ) =>
% 1.71/1.43 ( ( omegaSAx ) =>
% 1.71/1.43 ( ( omegaIndAx ) =>
% 1.71/1.43 ( ( replAx ) =>
% 1.71/1.43 ( ( foundationAx ) =>
% 1.71/1.43 ( ( wellorderingAx ) =>
% 1.71/1.43 ( ( descrp ) =>
% 1.71/1.43 ( ( dsetconstrI ) =>
% 1.71/1.43 ( ( dsetconstrEL ) =>
% 1.71/1.43 ( ( dsetconstrER ) =>
% 1.71/1.43 ( ( exuE1 ) =>
% 1.71/1.43 ( ![Xphi:$o,Xx:$i]:
% 1.71/1.43 ( ( in @ Xx @ ( prop2set @ Xphi ) ) =>
% 1.71/1.43 ( Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 1.71/1.43 thf(zf_stmt_0, conjecture,
% 1.71/1.43 (( ![X4:$i,X6:$i]:
% 1.71/1.43 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 1.71/1.43 ( ( X4 ) = ( X6 ) ) ) ) =>
% 1.71/1.43 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 1.71/1.43 ( ( ![X12:$i,X14:$i,X16:$i]:
% 1.71/1.43 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 1.71/1.43 ( ( in @ X16 @ X14 ) | ( ( X16 ) = ( X12 ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X18:$i,X20:$i]:
% 1.71/1.43 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 1.71/1.43 ( ![X22:$i]: ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X24:$i,X26:$i]:
% 1.71/1.43 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 1.71/1.43 ( ?[X28:$i]: ( ( in @ X26 @ X28 ) & ( in @ X28 @ X24 ) ) ) ) ) =>
% 1.71/1.43 ( ( in @ emptyset @ omega ) =>
% 1.71/1.43 ( ( ![X30:$i]:
% 1.71/1.43 ( ( in @ X30 @ omega ) =>
% 1.71/1.43 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 1.71/1.43 ( ( ![X32:$i]:
% 1.71/1.43 ( ( ( ![X34:$i]:
% 1.71/1.43 ( ( ( in @ X34 @ X32 ) & ( in @ X34 @ omega ) ) =>
% 1.71/1.43 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) &
% 1.71/1.43 ( in @ emptyset @ X32 ) ) =>
% 1.71/1.43 ( ![X36:$i]:
% 1.71/1.43 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 1.71/1.43 ( ( ![X42:$i]:
% 1.71/1.43 ( ( in @ X42 @ X40 ) =>
% 1.71/1.43 ( ?[X44:$i]:
% 1.71/1.43 ( ( X38 @ X42 @ X44 ) &
% 1.71/1.43 ( ![X46:$i]:
% 1.71/1.43 ( ( X38 @ X42 @ X46 ) =>
% 1.71/1.43 ( ( X44 ) = ( X46 ) ) ) ) ) ) ) ) =>
% 1.71/1.43 ( ?[X48:$i]:
% 1.71/1.43 ( ![X50:$i]:
% 1.71/1.43 ( ( in @ X50 @ X48 ) <=>
% 1.71/1.43 ( ?[X52:$i]:
% 1.71/1.43 ( ( in @ X52 @ X40 ) & ( X38 @ X52 @ X50 ) ) ) ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X54:$i]:
% 1.71/1.43 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 1.71/1.43 ( ?[X58:$i]:
% 1.71/1.43 ( ( in @ X58 @ X54 ) &
% 1.71/1.43 ( ~( ?[X60:$i]:
% 1.71/1.43 ( ( in @ X60 @ X58 ) & ( in @ X60 @ X54 ) ) ) ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X62:$i]:
% 1.71/1.43 ( ?[X64:$i]:
% 1.71/1.43 ( ( ![X96:$i]:
% 1.71/1.43 ( ( in @ X96 @ X64 ) =>
% 1.71/1.43 ( ![X98:$i]:
% 1.71/1.43 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) &
% 1.71/1.43 ( ![X90:$i,X92:$i]:
% 1.71/1.43 ( ( ( in @ X92 @ X62 ) & ( in @ X90 @ X62 ) ) =>
% 1.71/1.43 ( ( ![X94:$i]:
% 1.71/1.43 ( ( in @ X94 @ X64 ) =>
% 1.71/1.43 ( ( in @ X90 @ X94 ) <=>
% 1.71/1.43 ( in @ X92 @ X94 ) ) ) ) =>
% 1.71/1.43 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 1.71/1.43 ( ![X82:$i,X84:$i]:
% 1.71/1.43 ( ( ( in @ X84 @ X64 ) & ( in @ X82 @ X64 ) ) =>
% 1.71/1.43 ( ( ![X88:$i]:
% 1.71/1.43 ( ( in @ X88 @ X84 ) =>
% 1.71/1.43 ( in @ X88 @ X82 ) ) ) |
% 1.71/1.43 ( ![X86:$i]:
% 1.71/1.43 ( ( in @ X86 @ X82 ) =>
% 1.71/1.43 ( in @ X86 @ X84 ) ) ) ) ) ) &
% 1.71/1.43 ( ![X66:$i]:
% 1.71/1.43 ( ( ( ?[X70:$i]: ( in @ X70 @ X66 ) ) &
% 1.71/1.43 ( ![X68:$i]:
% 1.71/1.43 ( ( in @ X68 @ X66 ) =>
% 1.71/1.43 ( in @ X68 @ X62 ) ) ) ) =>
% 1.71/1.43 ( ?[X72:$i,X74:$i]:
% 1.71/1.43 ( ( in @ X72 @ X64 ) &
% 1.71/1.43 ( in @ X74 @ X66 ) &
% 1.71/1.43 ( ~( ?[X80:$i]:
% 1.71/1.43 ( ( in @ X80 @ X72 ) &
% 1.71/1.43 ( in @ X80 @ X66 ) ) ) ) &
% 1.71/1.43 ( ![X76:$i]:
% 1.71/1.43 ( ( in @ X76 @ X64 ) =>
% 1.71/1.43 ( ( in @ X74 @ X76 ) |
% 1.71/1.43 ( ![X78:$i]:
% 1.71/1.43 ( ( in @ X78 @ X76 ) =>
% 1.71/1.43 ( in @ X78 @ X72 ) ) ) ) ) ) ) ) ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X100:( $i > $o )]:
% 1.71/1.43 ( ( ?[X102:$i]:
% 1.71/1.43 ( ( X100 @ X102 ) &
% 1.71/1.43 ( ![X104:$i]:
% 1.71/1.43 ( ( X100 @ X104 ) =>
% 1.71/1.43 ( ( X102 ) = ( X104 ) ) ) ) ) ) =>
% 1.71/1.43 ( X100 @
% 1.71/1.43 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 1.71/1.43 ( ( in @ X110 @ X106 ) =>
% 1.71/1.43 ( ( X108 @ X110 ) =>
% 1.71/1.43 ( in @
% 1.71/1.43 X110 @
% 1.71/1.43 ( dsetconstr @
% 1.71/1.43 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 1.71/1.43 ( ( in @
% 1.71/1.43 X116 @
% 1.71/1.43 ( dsetconstr @
% 1.71/1.43 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 1.71/1.43 ( in @ X116 @ X112 ) ) ) =>
% 1.71/1.43 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 1.71/1.43 ( ( in @
% 1.71/1.43 X122 @
% 1.71/1.43 ( dsetconstr @
% 1.71/1.43 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 1.71/1.43 ( X120 @ X122 ) ) ) =>
% 1.71/1.43 ( ( ![X124:( $i > $o )]:
% 1.71/1.43 ( ( ?[X126:$i]:
% 1.71/1.43 ( ( X124 @ X126 ) &
% 1.71/1.43 ( ![X128:$i]:
% 1.71/1.43 ( ( X124 @ X128 ) =>
% 1.71/1.43 ( ( X126 ) = ( X128 ) ) ) ) ) ) =>
% 1.71/1.43 ( ?[X130:$i]:
% 1.71/1.43 ( ( X124 @ X130 ) &
% 1.71/1.43 ( ![X132:$i]:
% 1.71/1.43 ( ( X124 @ X132 ) =>
% 1.71/1.43 ( ( X130 ) = ( X132 ) ) ) ) ) ) ) ) =>
% 1.71/1.43 ( ![X134:$o,X136:$i]:
% 1.71/1.43 ( ( in @
% 1.71/1.43 X136 @
% 1.71/1.43 ( dsetconstr @
% 1.71/1.43 ( powerset @ emptyset ) @
% 1.71/1.43 ( ^[V_5:$i]: ( X134 ) ) ) ) =>
% 1.71/1.43 ( X134 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 1.71/1.43 thf(zf_stmt_1, type, zip_tseitin_3 : $i > $i > $i > ( $i > $i > $o ) > $o).
% 1.71/1.43 thf(zf_stmt_2, axiom,
% 1.71/1.43 (![X52:$i,X50:$i,X40:$i,X38:( $i > $i > $o )]:
% 1.71/1.43 ( ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) <=>
% 1.71/1.43 ( ( X38 @ X52 @ X50 ) & ( in @ X52 @ X40 ) ) ))).
% 1.71/1.43 thf(zf_stmt_3, type, zip_tseitin_2 : $i > $i > $i > $o).
% 1.71/1.43 thf(zf_stmt_4, axiom,
% 1.71/1.43 (![X28:$i,X26:$i,X24:$i]:
% 1.71/1.43 ( ( zip_tseitin_2 @ X28 @ X26 @ X24 ) <=>
% 1.71/1.43 ( ( in @ X28 @ X24 ) & ( in @ X26 @ X28 ) ) ))).
% 1.71/1.43 thf(zf_stmt_5, type, zip_tseitin_1 : $i > $i > $i > $o).
% 1.71/1.43 thf(zf_stmt_6, axiom,
% 1.71/1.43 (![X22:$i,X20:$i,X18:$i]:
% 1.71/1.43 ( ( zip_tseitin_1 @ X22 @ X20 @ X18 ) <=>
% 1.71/1.43 ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ))).
% 1.71/1.43 thf(zf_stmt_7, type, zip_tseitin_0 : $i > $i > $i > $o).
% 1.71/1.43 thf(zf_stmt_8, axiom,
% 1.71/1.43 (![X16:$i,X14:$i,X12:$i]:
% 1.71/1.43 ( ( zip_tseitin_0 @ X16 @ X14 @ X12 ) <=>
% 1.71/1.43 ( ( ( X16 ) = ( X12 ) ) | ( in @ X16 @ X14 ) ) ))).
% 1.71/1.43 thf(zf_stmt_9, conjecture,
% 1.71/1.43 (( ![X4:$i,X6:$i]:
% 1.71/1.43 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 1.71/1.43 ( ( X4 ) = ( X6 ) ) ) ) =>
% 1.71/1.43 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 1.71/1.43 ( ( ![X12:$i,X14:$i,X16:$i]:
% 1.71/1.43 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 1.71/1.43 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 1.71/1.43 ( ( ![X18:$i,X20:$i]:
% 1.71/1.43 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 1.71/1.43 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 1.71/1.43 ( ( ![X24:$i,X26:$i]:
% 1.71/1.43 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 1.71/1.43 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 1.71/1.43 ( ( in @ emptyset @ omega ) =>
% 1.71/1.43 ( ( ![X30:$i]:
% 1.71/1.43 ( ( in @ X30 @ omega ) =>
% 1.71/1.43 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 1.71/1.43 ( ( ![X32:$i]:
% 1.71/1.43 ( ( ( in @ emptyset @ X32 ) &
% 1.71/1.43 ( ![X34:$i]:
% 1.71/1.43 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 1.71/1.43 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 1.71/1.43 ( ![X36:$i]:
% 1.71/1.43 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 1.71/1.43 ( ( ![X42:$i]:
% 1.71/1.43 ( ( in @ X42 @ X40 ) =>
% 1.71/1.43 ( ?[X44:$i]:
% 1.71/1.43 ( ( ![X46:$i]:
% 1.71/1.43 ( ( X38 @ X42 @ X46 ) =>
% 1.71/1.43 ( ( X44 ) = ( X46 ) ) ) ) &
% 1.71/1.43 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 1.71/1.43 ( ?[X48:$i]:
% 1.71/1.43 ( ![X50:$i]:
% 1.71/1.43 ( ( in @ X50 @ X48 ) <=>
% 1.71/1.43 ( ?[X52:$i]:
% 1.71/1.43 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X54:$i]:
% 1.71/1.43 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 1.71/1.43 ( ?[X58:$i]:
% 1.71/1.43 ( ( ~( ?[X60:$i]:
% 1.71/1.43 ( ( in @ X60 @ X54 ) & ( in @ X60 @ X58 ) ) ) ) &
% 1.71/1.43 ( in @ X58 @ X54 ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X62:$i]:
% 1.71/1.43 ( ?[X64:$i]:
% 1.71/1.43 ( ( ![X66:$i]:
% 1.71/1.43 ( ( ( ![X68:$i]:
% 1.71/1.43 ( ( in @ X68 @ X66 ) =>
% 1.71/1.43 ( in @ X68 @ X62 ) ) ) &
% 1.71/1.43 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 1.71/1.43 ( ?[X72:$i,X74:$i]:
% 1.71/1.43 ( ( ![X76:$i]:
% 1.71/1.43 ( ( in @ X76 @ X64 ) =>
% 1.71/1.43 ( ( ![X78:$i]:
% 1.71/1.43 ( ( in @ X78 @ X76 ) =>
% 1.71/1.43 ( in @ X78 @ X72 ) ) ) |
% 1.71/1.43 ( in @ X74 @ X76 ) ) ) ) &
% 1.71/1.43 ( ~( ?[X80:$i]:
% 1.71/1.43 ( ( in @ X80 @ X66 ) &
% 1.71/1.43 ( in @ X80 @ X72 ) ) ) ) &
% 1.71/1.43 ( in @ X74 @ X66 ) & ( in @ X72 @ X64 ) ) ) ) ) &
% 1.71/1.43 ( ![X82:$i,X84:$i]:
% 1.71/1.43 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 1.71/1.43 ( ( ![X86:$i]:
% 1.71/1.43 ( ( in @ X86 @ X82 ) =>
% 1.71/1.43 ( in @ X86 @ X84 ) ) ) |
% 1.71/1.43 ( ![X88:$i]:
% 1.71/1.43 ( ( in @ X88 @ X84 ) =>
% 1.71/1.43 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 1.71/1.43 ( ![X90:$i,X92:$i]:
% 1.71/1.43 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 1.71/1.43 ( ( ![X94:$i]:
% 1.71/1.43 ( ( in @ X94 @ X64 ) =>
% 1.71/1.43 ( ( in @ X90 @ X94 ) <=>
% 1.71/1.43 ( in @ X92 @ X94 ) ) ) ) =>
% 1.71/1.43 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 1.71/1.43 ( ![X96:$i]:
% 1.71/1.43 ( ( in @ X96 @ X64 ) =>
% 1.71/1.43 ( ![X98:$i]:
% 1.71/1.43 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X100:( $i > $o )]:
% 1.71/1.43 ( ( ?[X102:$i]:
% 1.71/1.43 ( ( ![X104:$i]:
% 1.71/1.43 ( ( X100 @ X104 ) =>
% 1.71/1.43 ( ( X102 ) = ( X104 ) ) ) ) &
% 1.71/1.43 ( X100 @ X102 ) ) ) =>
% 1.71/1.43 ( X100 @
% 1.71/1.43 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 1.71/1.43 ( ( in @ X110 @ X106 ) =>
% 1.71/1.43 ( ( X108 @ X110 ) =>
% 1.71/1.43 ( in @
% 1.71/1.43 X110 @
% 1.71/1.43 ( dsetconstr @
% 1.71/1.43 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 1.71/1.43 ( ( in @
% 1.71/1.43 X116 @
% 1.71/1.43 ( dsetconstr @
% 1.71/1.43 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 1.71/1.43 ( in @ X116 @ X112 ) ) ) =>
% 1.71/1.43 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 1.71/1.43 ( ( in @
% 1.71/1.43 X122 @
% 1.71/1.43 ( dsetconstr @
% 1.71/1.43 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 1.71/1.43 ( X120 @ X122 ) ) ) =>
% 1.71/1.43 ( ( ![X124:( $i > $o )]:
% 1.71/1.43 ( ( ?[X126:$i]:
% 1.71/1.43 ( ( ![X128:$i]:
% 1.71/1.43 ( ( X124 @ X128 ) =>
% 1.71/1.43 ( ( X126 ) = ( X128 ) ) ) ) &
% 1.71/1.43 ( X124 @ X126 ) ) ) =>
% 1.71/1.43 ( ?[X130:$i]:
% 1.71/1.43 ( ( ![X132:$i]:
% 1.71/1.43 ( ( X124 @ X132 ) =>
% 1.71/1.43 ( ( X130 ) = ( X132 ) ) ) ) &
% 1.71/1.43 ( X124 @ X130 ) ) ) ) ) =>
% 1.71/1.43 ( ![X134:$o,X136:$i]:
% 1.71/1.43 ( ( in @
% 1.71/1.43 X136 @
% 1.71/1.43 ( dsetconstr @
% 1.71/1.43 ( powerset @ emptyset ) @
% 1.71/1.43 ( ^[V_5:$i]: ( X134 ) ) ) ) =>
% 1.71/1.43 ( X134 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 1.71/1.43 thf(zf_stmt_10, negated_conjecture,
% 1.71/1.43 (~( ( ![X4:$i,X6:$i]:
% 1.71/1.43 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 1.71/1.43 ( ( X4 ) = ( X6 ) ) ) ) =>
% 1.71/1.43 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 1.71/1.43 ( ( ![X12:$i,X14:$i,X16:$i]:
% 1.71/1.43 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 1.71/1.43 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 1.71/1.43 ( ( ![X18:$i,X20:$i]:
% 1.71/1.43 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 1.71/1.43 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 1.71/1.43 ( ( ![X24:$i,X26:$i]:
% 1.71/1.43 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 1.71/1.43 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 1.71/1.43 ( ( in @ emptyset @ omega ) =>
% 1.71/1.43 ( ( ![X30:$i]:
% 1.71/1.43 ( ( in @ X30 @ omega ) =>
% 1.71/1.43 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 1.71/1.43 ( ( ![X32:$i]:
% 1.71/1.43 ( ( ( in @ emptyset @ X32 ) &
% 1.71/1.43 ( ![X34:$i]:
% 1.71/1.43 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 1.71/1.43 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 1.71/1.43 ( ![X36:$i]:
% 1.71/1.43 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 1.71/1.43 ( ( ![X42:$i]:
% 1.71/1.43 ( ( in @ X42 @ X40 ) =>
% 1.71/1.43 ( ?[X44:$i]:
% 1.71/1.43 ( ( ![X46:$i]:
% 1.71/1.43 ( ( X38 @ X42 @ X46 ) =>
% 1.71/1.43 ( ( X44 ) = ( X46 ) ) ) ) &
% 1.71/1.43 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 1.71/1.43 ( ?[X48:$i]:
% 1.71/1.43 ( ![X50:$i]:
% 1.71/1.43 ( ( in @ X50 @ X48 ) <=>
% 1.71/1.43 ( ?[X52:$i]:
% 1.71/1.43 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X54:$i]:
% 1.71/1.43 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 1.71/1.43 ( ?[X58:$i]:
% 1.71/1.43 ( ( ~( ?[X60:$i]:
% 1.71/1.43 ( ( in @ X60 @ X54 ) &
% 1.71/1.43 ( in @ X60 @ X58 ) ) ) ) &
% 1.71/1.43 ( in @ X58 @ X54 ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X62:$i]:
% 1.71/1.43 ( ?[X64:$i]:
% 1.71/1.43 ( ( ![X66:$i]:
% 1.71/1.43 ( ( ( ![X68:$i]:
% 1.71/1.43 ( ( in @ X68 @ X66 ) =>
% 1.71/1.43 ( in @ X68 @ X62 ) ) ) &
% 1.71/1.43 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 1.71/1.43 ( ?[X72:$i,X74:$i]:
% 1.71/1.43 ( ( ![X76:$i]:
% 1.71/1.43 ( ( in @ X76 @ X64 ) =>
% 1.71/1.43 ( ( ![X78:$i]:
% 1.71/1.43 ( ( in @ X78 @ X76 ) =>
% 1.71/1.43 ( in @ X78 @ X72 ) ) ) |
% 1.71/1.43 ( in @ X74 @ X76 ) ) ) ) &
% 1.71/1.43 ( ~( ?[X80:$i]:
% 1.71/1.43 ( ( in @ X80 @ X66 ) &
% 1.71/1.43 ( in @ X80 @ X72 ) ) ) ) &
% 1.71/1.43 ( in @ X74 @ X66 ) &
% 1.71/1.43 ( in @ X72 @ X64 ) ) ) ) ) &
% 1.71/1.43 ( ![X82:$i,X84:$i]:
% 1.71/1.43 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 1.71/1.43 ( ( ![X86:$i]:
% 1.71/1.43 ( ( in @ X86 @ X82 ) =>
% 1.71/1.43 ( in @ X86 @ X84 ) ) ) |
% 1.71/1.43 ( ![X88:$i]:
% 1.71/1.43 ( ( in @ X88 @ X84 ) =>
% 1.71/1.43 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 1.71/1.43 ( ![X90:$i,X92:$i]:
% 1.71/1.43 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 1.71/1.43 ( ( ![X94:$i]:
% 1.71/1.43 ( ( in @ X94 @ X64 ) =>
% 1.71/1.43 ( ( in @ X90 @ X94 ) <=>
% 1.71/1.43 ( in @ X92 @ X94 ) ) ) ) =>
% 1.71/1.43 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 1.71/1.43 ( ![X96:$i]:
% 1.71/1.43 ( ( in @ X96 @ X64 ) =>
% 1.71/1.43 ( ![X98:$i]:
% 1.71/1.43 ( ( in @ X98 @ X96 ) =>
% 1.71/1.43 ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X100:( $i > $o )]:
% 1.71/1.43 ( ( ?[X102:$i]:
% 1.71/1.43 ( ( ![X104:$i]:
% 1.71/1.43 ( ( X100 @ X104 ) =>
% 1.71/1.43 ( ( X102 ) = ( X104 ) ) ) ) &
% 1.71/1.43 ( X100 @ X102 ) ) ) =>
% 1.71/1.43 ( X100 @
% 1.71/1.43 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 1.71/1.43 ( ( in @ X110 @ X106 ) =>
% 1.71/1.43 ( ( X108 @ X110 ) =>
% 1.71/1.43 ( in @
% 1.71/1.43 X110 @
% 1.71/1.43 ( dsetconstr @
% 1.71/1.43 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 1.71/1.43 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 1.71/1.43 ( ( in @
% 1.71/1.43 X116 @
% 1.71/1.43 ( dsetconstr @
% 1.71/1.43 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 1.71/1.43 ( in @ X116 @ X112 ) ) ) =>
% 1.71/1.43 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 1.71/1.43 ( ( in @
% 1.71/1.43 X122 @
% 1.71/1.43 ( dsetconstr @
% 1.71/1.43 X118 @
% 1.71/1.43 ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 1.71/1.43 ( X120 @ X122 ) ) ) =>
% 1.71/1.43 ( ( ![X124:( $i > $o )]:
% 1.71/1.43 ( ( ?[X126:$i]:
% 1.71/1.43 ( ( ![X128:$i]:
% 1.71/1.43 ( ( X124 @ X128 ) =>
% 1.71/1.43 ( ( X126 ) = ( X128 ) ) ) ) &
% 1.71/1.43 ( X124 @ X126 ) ) ) =>
% 1.71/1.43 ( ?[X130:$i]:
% 1.71/1.43 ( ( ![X132:$i]:
% 1.71/1.43 ( ( X124 @ X132 ) =>
% 1.71/1.43 ( ( X130 ) = ( X132 ) ) ) ) &
% 1.71/1.43 ( X124 @ X130 ) ) ) ) ) =>
% 1.71/1.43 ( ![X134:$o,X136:$i]:
% 1.71/1.43 ( ( in @
% 1.71/1.43 X136 @
% 1.71/1.43 ( dsetconstr @
% 1.71/1.43 ( powerset @ emptyset ) @
% 1.71/1.43 ( ^[V_5:$i]: ( X134 ) ) ) ) =>
% 1.71/1.43 ( X134 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 1.71/1.43 inference('cnf.neg', [status(esa)], [zf_stmt_9])).
% 1.71/1.43 thf(zip_derived_cl41, plain,
% 1.71/1.43 ( (in @ sk__71 @
% 1.71/1.43 (dsetconstr @ (powerset @ emptyset) @ (^[Y0 : $i]: (sk__70))))),
% 1.71/1.43 inference('cnf', [status(esa)], [zf_stmt_10])).
% 1.71/1.43 thf(zip_derived_cl40, plain, (~ (sk__70)),
% 1.71/1.43 inference('cnf', [status(esa)], [zf_stmt_10])).
% 1.71/1.43 thf(zip_derived_cl58, plain,
% 1.71/1.43 ( (in @ sk__71 @
% 1.71/1.43 (dsetconstr @ (powerset @ emptyset) @ (^[Y0 : $i]: ($false))))),
% 1.71/1.43 inference('demod', [status(thm)], [zip_derived_cl41, zip_derived_cl40])).
% 1.71/1.43 thf(zip_derived_cl39, plain,
% 1.71/1.43 (![X34 : $i > $o, X35 : $i, X36 : $i]:
% 1.71/1.43 ( (X34 @ X35)
% 1.71/1.43 | ~ (in @ X35 @ (dsetconstr @ X36 @ (^[Y0 : $i]: (X34 @ Y0)))))),
% 1.71/1.43 inference('cnf', [status(esa)], [zf_stmt_10])).
% 1.71/1.43 thf(zip_derived_cl79, plain,
% 1.71/1.43 (![X34 : $i > $o, X35 : $i, X36 : $i]:
% 1.71/1.43 ( (X34 @ X35) | ~ (in @ X35 @ (dsetconstr @ X36 @ X34)))),
% 1.71/1.43 inference('ho_norm', [status(thm)], [zip_derived_cl39])).
% 1.71/1.43 thf(zip_derived_cl92, plain, ( ((^[Y0 : $i]: ($false)) @ sk__71)),
% 1.71/1.43 inference('sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl79])).
% 1.71/1.43 thf(zip_derived_cl101, plain, ($false),
% 1.71/1.43 inference('ho_norm', [status(thm)], [zip_derived_cl92])).
% 1.71/1.43
% 1.71/1.43 % SZS output end Refutation
% 1.71/1.43
% 1.71/1.43
% 1.71/1.43 % Terminating...
% 1.86/1.60 % Runner terminated.
% 1.86/1.62 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------