%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM785^4 : TPTP v9.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.GQ6BdogSJH true
% Computer : n005.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 04:48:20 PM UTC 2025
% Result : Theorem 96.37s 12.76s
% Output : Refutation 96.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM785^4 : TPTP v9.2.0. Released v7.1.0.
% 0.03/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.GQ6BdogSJH true
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 1 16:31:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.58/0.66 % Total configuration time : 828
% 0.58/0.66 % Estimated wc time : 1656
% 0.58/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.59/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.59/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.59/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.59/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.59/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.59/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.59/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 10.97/1.98 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 96.37/12.76 % Solved by lams/40_b.comb.sh.
% 96.37/12.76 % done 342 iterations in 11.942s
% 96.37/12.76 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 96.37/12.76 % SZS output start Refutation
% 96.37/12.76 thf(rt_is_type, type, rt_is: $i > $i > $o).
% 96.37/12.76 thf('#ty_enc13_type', type, '#ty_enc13': (($o > $o > $o) > ($i > $o) > $i >
% 96.37/12.76 $o > $o) >
% 96.37/12.76 ($i > $o > $o > $o) > $i >
% 96.37/12.76 ($i > $o) > $i > $o > $o).
% 96.37/12.76 thf(lessf_type, type, lessf: $i > $i > $o).
% 96.37/12.76 thf(inf_type, type, inf: $i > $i > $o).
% 96.37/12.76 thf(orec3_type, type, orec3: $o > $o > $o > $o).
% 96.37/12.76 thf(rt_less_type, type, rt_less: $i > $i > $o).
% 96.37/12.76 thf(and3_type, type, and3: $o > $o > $o > $o).
% 96.37/12.76 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 96.37/12.76 thf(in_type, type, in: $i > $i > $o).
% 96.37/12.76 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 96.37/12.76 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 96.37/12.76 thf('#sk2_type', type, '#sk2': $i).
% 96.37/12.76 thf('#ty_enc8_type', type, '#ty_enc8': ($i > $i > $o) > $i > $i > $o).
% 96.37/12.76 thf('#ty_enc14_type', type, '#ty_enc14': ($o > $o > $o > $o) > ($i > $o) >
% 96.37/12.76 $i > $o > $o > $o).
% 96.37/12.76 thf(l_ec_type, type, l_ec: $o > $o > $o).
% 96.37/12.76 thf(ect_type, type, ect: $i > ($i > $i > $o) > $i).
% 96.37/12.76 thf('#ty_enc15_type', type, '#ty_enc15': ($o > $o > $o) > ($i > $o) > $i > $o > $o).
% 96.37/12.76 thf(imp_type, type, imp: $o > $o > $o).
% 96.37/12.76 thf(rat_type, type, rat: $i).
% 96.37/12.76 thf(rt_lessis_type, type, rt_lessis: $i > $i > $o).
% 96.37/12.76 thf(ec3_type, type, ec3: $o > $o > $o > $o).
% 96.37/12.76 thf(frac_type, type, frac: $i).
% 96.37/12.76 thf(e_in_type, type, e_in: $i > ($i > $o) > $i > $i).
% 96.37/12.76 thf(n_eq_type, type, n_eq: $i > $i > $o).
% 96.37/12.76 thf(d_and_type, type, d_and: $o > $o > $o).
% 96.37/12.76 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 96.37/12.76 thf(ecect_type, type, ecect: $i > ($i > $i > $o) > $i > $i).
% 96.37/12.76 thf(anec_type, type, anec: $i > ($i > $i > $o) > $i > $o).
% 96.37/12.76 thf('#ty_enc9_type', type, '#ty_enc9': (($i > $o) > $o) > ($i > $i > $o) > $i > $o).
% 96.37/12.76 thf(l_or_type, type, l_or: $o > $o > $o).
% 96.37/12.76 thf(class_type, type, class: $i > $i).
% 96.37/12.76 thf('#ty_enc10_type', type, '#ty_enc10': ($i > ($i > $o) > $i > $o) >
% 96.37/12.76 ($i > $i > $o) > $i > $i > $o).
% 96.37/12.76 thf(moref_type, type, moref: $i > $i > $o).
% 96.37/12.76 thf('#ty_enc12_type', type, '#ty_enc12': ($i > ($i > $o) > $i > $o > $o) >
% 96.37/12.76 ($i > $o) > $i > $i > $o > $o).
% 96.37/12.76 thf(d_not_type, type, d_not: $o > $o).
% 96.37/12.76 thf('#ty_enc16_type', type, '#ty_enc16': ($i > $o > $o) > ($i > $o) > $i > $o).
% 96.37/12.76 thf(power_type, type, power: $i > $i).
% 96.37/12.76 thf(or3_type, type, or3: $o > $o > $o > $o).
% 96.37/12.76 thf('#ty_enc11_type', type, '#ty_enc11': (($i > $o > $o) > ($i > $o) > $i > $o) >
% 96.37/12.76 ($i > $i > $o > $o) > $i >
% 96.37/12.76 ($i > $o) > $i > $o).
% 96.37/12.76 thf(rt_more_type, type, rt_more: $i > $i > $o).
% 96.37/12.76 thf(e_is_type, type, e_is: $i > $i > $i > $o).
% 96.37/12.76 thf('#sk3_type', type, '#sk3': $i).
% 96.37/12.76 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 96.37/12.76 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 96.37/12.76 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 96.37/12.76 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 96.37/12.76 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 96.37/12.76 thf(satz81d, conjecture,
% 96.37/12.76 (all_of @
% 96.37/12.76 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @
% 96.37/12.76 ( ^[X0:$i]:
% 96.37/12.76 ( all_of @
% 96.37/12.76 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @
% 96.37/12.76 ( ^[X1:$i]:
% 96.37/12.76 ( ( rt_lessis @ X0 @ X1 ) => ( d_not @ ( rt_more @ X0 @ X1 ) ) ) ) ) ))).
% 96.37/12.76 thf(zf_stmt_0, negated_conjecture,
% 96.37/12.76 (~( all_of @
% 96.37/12.76 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @
% 96.37/12.76 ( ^[X0:$i]:
% 96.37/12.76 ( all_of @
% 96.37/12.76 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @
% 96.37/12.76 ( ^[X1:$i]:
% 96.37/12.76 ( ( rt_lessis @ X0 @ X1 ) => ( d_not @ ( rt_more @ X0 @ X1 ) ) ) ) ) ) )),
% 96.37/12.76 inference('cnf.neg', [status(esa)], [satz81d])).
% 96.37/12.76 thf(zip_derived_cl499, plain,
% 96.37/12.76 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @
% 96.37/12.76 (^[Y0 : $i]:
% 96.37/12.76 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @
% 96.37/12.76 (^[Y1 : $i]:
% 96.37/12.76 (((rt_lessis @ Y0 @ Y1) => (d_not @ (rt_more @ Y0 @ Y1))))))))),
% 96.37/12.76 inference('cnf', [status(esa)], [zf_stmt_0])).
% 96.37/12.76 thf(zip_derived_cl500, plain,
% 96.37/12.76 (~ (all_of @ ((('#C') @ in @ rat)) @
% 96.37/12.76 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))) @
% 96.37/12.76 ((('#B') @ ((('#B') @ d_not)) @ rt_more)))))))),
% 96.37/12.76 inference('lams2combs', [status(thm)], [zip_derived_cl499])).
% 96.37/12.76 thf(def_ect, axiom,(( ect @ (X0)@ (X1)) =
% 96.37/12.76 ((d_Sep @ (power @ X0) @ (anec @ X0 @ X1))))).
% 96.37/12.76 thf('0', plain,
% 96.37/12.76 (![X1:( $i > $i > $o ),X0:$i]:
% 96.37/12.76 ( ( ect @ X0 @ X1 ) = ( d_Sep @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(def_rat, axiom,(( rat ) = ((ect @ frac @ n_eq)))).
% 96.37/12.76 thf('1', plain, (( rat ) = ( ect @ frac @ n_eq )), define([status(thm)])).
% 96.37/12.76 thf(zip_derived_cl636, plain,
% 96.37/12.76 (~ (all_of @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 96.37/12.76 ((('#B') @ (all_of @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))) @
% 96.37/12.76 ((('#B') @ ((('#B') @ d_not)) @ rt_more)))))))),
% 96.37/12.76 inference('rw', [status(thm)], [zip_derived_cl500, '0', '1'])).
% 96.37/12.76 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 96.37/12.76 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 96.37/12.76 thf('2', plain,
% 96.37/12.76 (![X0:( $i > $o ),X1:( $i > $o )]:
% 96.37/12.76 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 96.37/12.76 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 96.37/12.76 inference('rw.lit', [status(esa)], [def_all_of])).
% 96.37/12.76 thf(zip_derived_cl637, plain,
% 96.37/12.76 (~ (((!!) @ (^[Y0 : $i]:
% 96.37/12.76 (((is_of @ Y0 @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.37/12.76 ((('#B') @ (all_of @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @
% 96.37/12.76 (anec @ frac @ n_eq))))) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))) @
% 96.37/12.76 ((('#B') @ ((('#B') @ d_not)) @ rt_more)))) @
% 96.37/12.76 Y0)))))))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl636, '2'])).
% 96.37/12.76 thf(zip_derived_cl638, plain,
% 96.37/12.76 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 96.37/12.76 ((('#C') @ is_of @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @
% 96.37/12.76 (anec @ frac @ n_eq)))))))) @
% 96.37/12.76 ((('#B') @ (all_of @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @
% 96.37/12.76 (anec @ frac @ n_eq))))) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))) @
% 96.37/12.76 ((('#B') @ ((('#B') @ d_not)) @ rt_more))))))))))),
% 96.37/12.76 inference('comb-normalize', [status(thm)], [zip_derived_cl637])).
% 96.37/12.76 thf(zip_derived_cl639, plain,
% 96.37/12.76 (~ (((is_of @ '#sk2' @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.37/12.76 (all_of @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 96.37/12.76 ((('#S') @ ((('#B') @ (=>) @ (rt_lessis @ '#sk2'))) @
% 96.37/12.76 ((('#B') @ d_not @ (rt_more @ '#sk2'))))))))),
% 96.37/12.76 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl638])).
% 96.37/12.76 thf(zip_derived_cl640, plain,
% 96.37/12.76 ( (is_of @ '#sk2' @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl639])).
% 96.37/12.76 thf(zip_derived_cl8883, plain,
% 96.37/12.76 ( (is_of @ '#sk2' @
% 96.37/12.76 ('#ty_enc8' @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))),
% 96.37/12.76 inference('remove_ty_args', [status(thm)], [zip_derived_cl640])).
% 96.37/12.76 thf(zip_derived_cl641, plain,
% 96.37/12.76 (~ (all_of @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 96.37/12.76 ((('#S') @ ((('#B') @ (=>) @ (rt_lessis @ '#sk2'))) @
% 96.37/12.76 ((('#B') @ d_not @ (rt_more @ '#sk2'))))))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl639])).
% 96.37/12.76 thf(zip_derived_cl642, plain,
% 96.37/12.76 (~ (((!!) @ (^[Y0 : $i]:
% 96.37/12.76 (((is_of @ Y0 @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.37/12.76 ((('#S') @ ((('#B') @ (=>) @ (rt_lessis @ '#sk2'))) @
% 96.37/12.76 ((('#B') @ d_not @ (rt_more @ '#sk2'))) @ Y0)))))))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl641, '2'])).
% 96.37/12.76 thf(zip_derived_cl643, plain,
% 96.37/12.76 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 96.37/12.76 ((('#C') @ is_of @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @
% 96.37/12.76 (anec @ frac @ n_eq)))))))) @
% 96.37/12.76 ((('#S') @ ((('#B') @ (=>) @ (rt_lessis @ '#sk2'))) @
% 96.37/12.76 ((('#B') @ d_not @ (rt_more @ '#sk2')))))))))),
% 96.37/12.76 inference('comb-normalize', [status(thm)], [zip_derived_cl642])).
% 96.37/12.76 thf(zip_derived_cl644, plain,
% 96.37/12.76 (~ (((is_of @ '#sk3' @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.37/12.76 (((rt_lessis @ '#sk2' @ '#sk3') => (d_not @
% 96.37/12.76 (rt_more @ '#sk2' @ '#sk3'))))))),
% 96.37/12.76 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl643])).
% 96.37/12.76 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 96.37/12.76 thf('3', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 96.37/12.76 thf('4', plain,
% 96.37/12.76 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))).
% 96.37/12.76 thf('5', plain,
% 96.37/12.76 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(def_e_in, axiom,(( e_in @ (X1)@ (X2)@ (X0)) = ((X0)))).
% 96.37/12.76 thf('6', plain,
% 96.37/12.76 (![X2:( $i > $o ),X1:$i,X0:$i]: ( ( e_in @ X1 @ X2 @ X0 ) = ( X0 ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(def_ecect, axiom,(( ecect @ (X0)@ (X1)@ (X2)) =
% 96.37/12.76 ((e_in @ (power @ X0) @ (anec @ X0 @ X1) @ X2)))).
% 96.37/12.76 thf('7', plain,
% 96.37/12.76 (![X2:$i,X1:( $i > $i > $o ),X0:$i]:
% 96.37/12.76 ( ( ecect @ X0 @ X1 @ X2 ) =
% 96.37/12.76 ( e_in @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) @ X2 ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(def_rt_is, axiom,(( rt_is @ (X0)@ (X1)) = ((e_is @ rat @ X0 @ X1)))).
% 96.37/12.76 thf('8', plain,
% 96.37/12.76 (![X1:$i,X0:$i]: ( ( rt_is @ X0 @ X1 ) = ( e_is @ rat @ X0 @ X1 ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(def_class, axiom,(( class @ (X0)) = ((ecect @ frac @ n_eq @ X0)))).
% 96.37/12.76 thf('9', plain,
% 96.37/12.76 (![X0:$i]: ( ( class @ X0 ) = ( ecect @ frac @ n_eq @ X0 ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(def_rt_more, axiom,(( rt_more @ (X0)@ (X1)) =
% 96.37/12.76 ((l_some @ frac @
% 96.37/12.76 (^[Y0 : $i]:
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 (^[Y1 : $i]:
% 96.37/12.76 (and3 @ (inf @ Y0 @ (class @ X0)) @ (inf @ Y1 @ (class @ X1)) @
% 96.37/12.76 (moref @ Y0 @ Y1))))))))).
% 96.37/12.76 thf('10', plain,
% 96.37/12.76 (![X1:$i,X0:$i]:
% 96.37/12.76 ( ( rt_more @ X0 @ X1 ) =
% 96.37/12.76 ( l_some @
% 96.37/12.76 frac @
% 96.37/12.76 ( ^[V_1:$i]:
% 96.37/12.76 ( l_some @
% 96.37/12.76 frac @
% 96.37/12.76 ( ^[V_2:$i]:
% 96.37/12.76 ( and3 @
% 96.37/12.76 ( inf @ V_1 @ ( class @ X0 ) ) @
% 96.37/12.76 ( inf @ V_2 @ ( class @ X1 ) ) @ ( moref @ V_1 @ V_2 ) ) ) ) ) ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(def_rt_less, axiom,(( rt_less @ (X0)@ (X1)) =
% 96.37/12.76 ((l_some @ frac @
% 96.37/12.76 (^[Y0 : $i]:
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 (^[Y1 : $i]:
% 96.37/12.76 (and3 @ (inf @ Y0 @ (class @ X0)) @ (inf @ Y1 @ (class @ X1)) @
% 96.37/12.76 (lessf @ Y0 @ Y1))))))))).
% 96.37/12.76 thf('11', plain,
% 96.37/12.76 (![X1:$i,X0:$i]:
% 96.37/12.76 ( ( rt_less @ X0 @ X1 ) =
% 96.37/12.76 ( l_some @
% 96.37/12.76 frac @
% 96.37/12.76 ( ^[V_1:$i]:
% 96.37/12.76 ( l_some @
% 96.37/12.76 frac @
% 96.37/12.76 ( ^[V_2:$i]:
% 96.37/12.76 ( and3 @
% 96.37/12.76 ( inf @ V_1 @ ( class @ X0 ) ) @
% 96.37/12.76 ( inf @ V_2 @ ( class @ X1 ) ) @ ( lessf @ V_1 @ V_2 ) ) ) ) ) ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(def_rt_lessis, axiom,(( rt_lessis @ (X0)@ (X1)) =
% 96.37/12.76 ((l_or @ (rt_less @ X0 @ X1) @ (rt_is @ X0 @ X1))))).
% 96.37/12.76 thf('12', plain,
% 96.37/12.76 (![X1:$i,X0:$i]:
% 96.37/12.76 ( ( rt_lessis @ X0 @ X1 ) =
% 96.37/12.76 ( l_or @ ( rt_less @ X0 @ X1 ) @ ( rt_is @ X0 @ X1 ) ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(zip_derived_cl645, plain,
% 96.37/12.76 (~ (((is_of @ '#sk3' @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.37/12.76 (((imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ '#sk2')))))) @
% 96.37/12.76 ((('#C') @ inf @ '#sk3')))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false)) @
% 96.37/12.76 ((('#sk2') = ('#sk3')))) => (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ '#sk2')))))) @
% 96.37/12.76 ((('#C') @ inf @ '#sk3')))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false))))))),
% 96.37/12.76 inference('rw', [status(thm)],
% 96.37/12.76 [zip_derived_cl644, '3', '3', '4', '5', '6', '6', '0', '7',
% 96.37/12.76 '7', '1', '8', '9', '9', '10', '11', '12'])).
% 96.37/12.76 thf(zip_derived_cl646, plain,
% 96.37/12.76 ( (is_of @ '#sk3' @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl645])).
% 96.37/12.76 thf(zip_derived_cl8884, plain,
% 96.37/12.76 ( (is_of @ '#sk3' @
% 96.37/12.76 ('#ty_enc8' @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))),
% 96.37/12.76 inference('remove_ty_args', [status(thm)], [zip_derived_cl646])).
% 96.37/12.76 thf(zip_derived_cl647, plain,
% 96.37/12.76 (~ (((imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ '#sk2')))))) @
% 96.37/12.76 ((('#C') @ inf @ '#sk3')))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false)) @
% 96.37/12.76 ((('#sk2') = ('#sk3')))) => (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ '#sk2')))))) @
% 96.37/12.76 ((('#C') @ inf @ '#sk3')))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false))))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl645])).
% 96.37/12.76 thf(zip_derived_cl649, plain,
% 96.37/12.76 (~ (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ '#sk2')))))) @
% 96.37/12.76 ((('#C') @ inf @ '#sk3')))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl647])).
% 96.37/12.76 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 96.37/12.76 thf('13', plain,
% 96.37/12.76 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 96.37/12.76 inference('rw.lit', [status(esa)], [def_imp])).
% 96.37/12.76 thf(zip_derived_cl651, plain,
% 96.37/12.76 (~ (((l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ '#sk2')))))) @
% 96.37/12.76 ((('#C') @ inf @ '#sk3')))))) @
% 96.37/12.76 moref))))) =>
% 96.37/12.76 ($false)))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl649, '13'])).
% 96.37/12.76 thf(zip_derived_cl653, plain,
% 96.37/12.76 (~ (((~) @ (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ '#sk2')))))) @
% 96.37/12.76 ((('#C') @ inf @ '#sk3')))))) @
% 96.37/12.76 moref)))))))),
% 96.37/12.76 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl651])).
% 96.37/12.76 thf(zip_derived_cl654, plain,
% 96.37/12.76 ( (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ '#sk2')))))) @
% 96.37/12.76 ((('#C') @ inf @ '#sk3')))))) @
% 96.37/12.76 moref)))))),
% 96.37/12.76 inference('simplify nested equalities', [status(thm)],
% 96.37/12.76 [zip_derived_cl653])).
% 96.37/12.76 thf(zip_derived_cl8885, plain,
% 96.37/12.76 ( (l_some @ frac @
% 96.37/12.76 ('#ty_enc9' @ (l_some @ frac) @
% 96.37/12.76 ('#ty_enc10' @
% 96.37/12.76 ('#ty_enc11' @ '#ty_enc16' @
% 96.37/12.76 ('#ty_enc12' @
% 96.37/12.76 ('#ty_enc13' @ '#ty_enc15' @
% 96.37/12.76 ('#ty_enc14' @ and3 @ ('#ty_enc8' @ inf @ '#sk2'))) @
% 96.37/12.76 ('#ty_enc8' @ inf @ '#sk3'))) @
% 96.37/12.76 moref)))),
% 96.37/12.76 inference('remove_ty_args', [status(thm)], [zip_derived_cl654])).
% 96.37/12.76 thf(zip_derived_cl654, plain,
% 96.37/12.76 ( (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ '#sk2')))))) @
% 96.37/12.76 ((('#C') @ inf @ '#sk3')))))) @
% 96.37/12.76 moref)))))),
% 96.37/12.76 inference('simplify nested equalities', [status(thm)],
% 96.37/12.76 [zip_derived_cl653])).
% 96.37/12.76 thf(satz81, axiom,
% 96.37/12.76 (all_of @
% 96.37/12.76 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @
% 96.37/12.76 ( ^[X0:$i]:
% 96.37/12.76 ( all_of @
% 96.37/12.76 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @
% 96.37/12.76 ( ^[X1:$i]:
% 96.37/12.76 ( orec3 @
% 96.37/12.76 ( rt_is @ X0 @ X1 ) @ ( rt_more @ X0 @ X1 ) @
% 96.37/12.76 ( rt_less @ X0 @ X1 ) ) ) ) ))).
% 96.37/12.76 thf(zip_derived_cl489, plain,
% 96.37/12.76 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @
% 96.37/12.76 (^[Y0 : $i]:
% 96.37/12.76 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @
% 96.37/12.76 (^[Y1 : $i]:
% 96.37/12.76 (orec3 @ (rt_is @ Y0 @ Y1) @ (rt_more @ Y0 @ Y1) @
% 96.37/12.76 (rt_less @ Y0 @ Y1))))))),
% 96.37/12.76 inference('cnf', [status(esa)], [satz81])).
% 96.37/12.76 thf(zip_derived_cl490, plain,
% 96.37/12.76 ( (all_of @ ((('#C') @ in @ rat)) @
% 96.37/12.76 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#B') @ ((('#B') @ orec3)) @ rt_is)))) @
% 96.37/12.76 rt_more)))) @
% 96.37/12.76 rt_less)))))),
% 96.37/12.76 inference('lams2combs', [status(thm)], [zip_derived_cl489])).
% 96.37/12.76 thf(zip_derived_cl1710, plain,
% 96.37/12.76 ( (all_of @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 96.37/12.76 ((('#B') @ (all_of @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#B') @ ((('#B') @ orec3)) @ rt_is)))) @
% 96.37/12.76 rt_more)))) @
% 96.37/12.76 rt_less)))))),
% 96.37/12.76 inference('rw', [status(thm)], [zip_derived_cl490, '0', '1'])).
% 96.37/12.76 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 96.37/12.76 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 96.37/12.76 thf('14', plain,
% 96.37/12.76 (![X0:( $i > $o ),X1:( $i > $o )]:
% 96.37/12.76 ( ( all_of @ X0 @ X1 ) <=>
% 96.37/12.76 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 96.37/12.76 inference('rw.lit', [status(esa)], [def_all_of])).
% 96.37/12.76 thf(zip_derived_cl1711, plain,
% 96.37/12.76 ( (((!!) @ (^[Y0 : $i]:
% 96.37/12.76 (((is_of @ Y0 @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.37/12.76 ((('#B') @ (all_of @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @
% 96.37/12.76 (anec @ frac @ n_eq))))) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#B') @ ((('#B') @ orec3)) @
% 96.37/12.76 rt_is)))) @
% 96.37/12.76 rt_more)))) @
% 96.37/12.76 rt_less)) @
% 96.37/12.76 Y0)))))))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl1710, '14'])).
% 96.37/12.76 thf(zip_derived_cl1712, plain,
% 96.37/12.76 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 96.37/12.76 ((('#C') @ is_of @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @
% 96.37/12.76 (anec @ frac @ n_eq)))))))) @
% 96.37/12.76 ((('#B') @ (all_of @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#B') @ ((('#B') @ orec3)) @
% 96.37/12.76 rt_is)))) @
% 96.37/12.76 rt_more)))) @
% 96.37/12.76 rt_less))))))))),
% 96.37/12.76 inference('comb-normalize', [status(thm)], [zip_derived_cl1711])).
% 96.37/12.76 thf(zip_derived_cl1713, plain,
% 96.37/12.76 (![X2 : $i]:
% 96.37/12.76 (((is_of @ X2 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.37/12.76 (all_of @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 96.37/12.76 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X2))) @
% 96.37/12.76 (rt_more @ X2))) @
% 96.37/12.76 (rt_less @ X2))))))),
% 96.37/12.76 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1712])).
% 96.37/12.76 thf(zip_derived_cl1714, plain,
% 96.37/12.76 (![X2 : $i]:
% 96.37/12.76 (~ (is_of @ X2 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | (all_of @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 96.37/12.76 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X2))) @
% 96.37/12.76 (rt_more @ X2))) @
% 96.37/12.76 (rt_less @ X2)))))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1713])).
% 96.37/12.76 thf(zip_derived_cl1715, plain,
% 96.37/12.76 (![X0 : $i]:
% 96.37/12.76 ( (((!!) @ (^[Y0 : $i]:
% 96.37/12.76 (((is_of @ Y0 @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.37/12.76 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X0))) @
% 96.37/12.76 (rt_more @ X0))) @
% 96.37/12.76 (rt_less @ X0) @ Y0)))))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl1714, '14'])).
% 96.37/12.76 thf(zip_derived_cl1716, plain,
% 96.37/12.76 (![X0 : $i]:
% 96.37/12.76 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 96.37/12.76 ((('#C') @ is_of @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @
% 96.37/12.76 (anec @ frac @ n_eq)))))))) @
% 96.37/12.76 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X0))) @
% 96.37/12.76 (rt_more @ X0))) @
% 96.37/12.76 (rt_less @ X0)))))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('comb-normalize', [status(thm)], [zip_derived_cl1715])).
% 96.37/12.76 thf(zip_derived_cl1717, plain,
% 96.37/12.76 (![X0 : $i, X2 : $i]:
% 96.37/12.76 ( (((is_of @ X2 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.37/12.76 (orec3 @ (rt_is @ X0 @ X2) @ (rt_more @ X0 @ X2) @
% 96.37/12.76 (rt_less @ X0 @ X2))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1716])).
% 96.37/12.76 thf(def_l_ec, axiom,(( l_ec @ (X0)@ (X1)) = ((imp @ X0 @ (d_not @ X1))))).
% 96.37/12.76 thf('15', plain,
% 96.37/12.76 (![X1:$o,X0:$o]: ( ( l_ec @ X0 @ X1 ) = ( imp @ X0 @ ( d_not @ X1 ) ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(def_d_and, axiom,(( d_and @ (X0)@ (X1)) = ((d_not @ (l_ec @ X0 @ X1))))).
% 96.37/12.76 thf('16', plain,
% 96.37/12.76 (![X1:$o,X0:$o]: ( ( d_and @ X0 @ X1 ) = ( d_not @ ( l_ec @ X0 @ X1 ) ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(def_or3, axiom,(( or3 @ (X0)@ (X1)@ (X2)) =
% 96.37/12.76 ((l_or @ X0 @ (l_or @ X1 @ X2))))).
% 96.37/12.76 thf('17', plain,
% 96.37/12.76 (![X2:$o,X1:$o,X0:$o]:
% 96.37/12.76 ( ( or3 @ X0 @ X1 @ X2 ) = ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(def_and3, axiom,(( and3 @ (X0)@ (X1)@ (X2)) =
% 96.37/12.76 ((d_and @ X0 @ (d_and @ X1 @ X2))))).
% 96.37/12.76 thf('18', plain,
% 96.37/12.76 (![X2:$o,X1:$o,X0:$o]:
% 96.37/12.76 ( ( and3 @ X0 @ X1 @ X2 ) = ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(def_ec3, axiom,(( ec3 @ (X0)@ (X1)@ (X2)) =
% 96.37/12.76 ((and3 @ (l_ec @ X0 @ X1) @ (l_ec @ X1 @ X2) @ (l_ec @ X2 @ X0))))).
% 96.37/12.76 thf('19', plain,
% 96.37/12.76 (![X2:$o,X1:$o,X0:$o]:
% 96.37/12.76 ( ( ec3 @ X0 @ X1 @ X2 ) =
% 96.37/12.76 ( and3 @ ( l_ec @ X0 @ X1 ) @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X0 ) ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(def_orec3, axiom,(( orec3 @ (X0)@ (X1)@ (X2)) =
% 96.37/12.76 ((d_and @ (or3 @ X0 @ X1 @ X2) @ (ec3 @ X0 @ X1 @ X2))))).
% 96.37/12.76 thf('20', plain,
% 96.37/12.76 (![X2:$o,X1:$o,X0:$o]:
% 96.37/12.76 ( ( orec3 @ X0 @ X1 @ X2 ) =
% 96.37/12.76 ( d_and @ ( or3 @ X0 @ X1 @ X2 ) @ ( ec3 @ X0 @ X1 @ X2 ) ) )),
% 96.37/12.76 define([status(thm)])).
% 96.37/12.76 thf(zip_derived_cl1718, plain,
% 96.37/12.76 (![X0 : $i, X2 : $i]:
% 96.37/12.76 ( (((is_of @ X2 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
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% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('rw', [status(thm)],
% 96.37/12.76 [zip_derived_cl1717, '3', '3', '3', '3', '3', '3', '3', '3',
% 96.37/12.76 '3', '15', '15', '15', '15', '15', '15', '16', '16', '16',
% 96.37/12.76 '4', '4', '17', '18', '19', '20', '5', '6', '6', '0', '7',
% 96.37/12.76 '7', '1', '8', '9', '9', '10', '11'])).
% 96.37/12.76 thf(zip_derived_cl1719, plain,
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% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X2)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false)) @
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% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
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% 96.37/12.76 ($false))) @
% 96.37/12.76 ($false))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1718])).
% 96.37/12.76 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 96.37/12.76 thf('21', plain,
% 96.37/12.76 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 96.37/12.76 inference('rw.lit', [status(esa)], [def_imp])).
% 96.37/12.76 thf(zip_derived_cl1720, plain,
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% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false)) @
% 96.37/12.76 (l_some @ frac @
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% 96.37/12.76 ($false)) @
% 96.37/12.76 ($false))) =>
% 96.37/12.76 ($false)))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl1719, '21'])).
% 96.37/12.76 thf(zip_derived_cl1721, plain,
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% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false)) @
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% 96.37/12.76 ($false))) @
% 96.37/12.76 ($false)) @
% 96.37/12.76 ($false)))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('simplify boolean subterms', [status(thm)],
% 96.37/12.76 [zip_derived_cl1720])).
% 96.37/12.76 thf(zip_derived_cl1722, plain,
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% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false)) @
% 96.37/12.76 (l_some @ frac @
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% 96.37/12.76 (imp @
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% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
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% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
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% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 (imp @ (((X0) = (X1))) @ ($false))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 ($false)) @
% 96.37/12.76 ($false)))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('simplify boolean subterms', [status(thm)],
% 96.37/12.76 [zip_derived_cl1731])).
% 96.37/12.76 thf(zip_derived_cl1734, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 (~ (imp @
% 96.37/12.76 (imp @ (((X0) = (X1))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 (imp @ (((X0) = (X1))) @ ($false))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 ($false)) @
% 96.37/12.76 ($false)))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('simplify nested equalities', [status(thm)],
% 96.37/12.76 [zip_derived_cl1733])).
% 96.37/12.76 thf(zip_derived_cl1735, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 (~ (((imp @ (((X1) = (X0))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false))) =>
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 (imp @ (((X1) = (X0))) @ ($false))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 ($false)) @
% 96.37/12.76 ($false))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl1734, '13'])).
% 96.37/12.76 thf(zip_derived_cl1739, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 ( (imp @ (((X1) = (X0))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false)))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1735])).
% 96.37/12.76 thf(zip_derived_cl1742, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 ( (((((X1) = (X0))) => (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl1739, '21'])).
% 96.37/12.76 thf(zip_derived_cl1745, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 (~ (((X1) = (X0)))
% 96.37/12.76 | (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1742])).
% 96.37/12.76 thf(zip_derived_cl1751, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 (((X1) != (X0))
% 96.37/12.76 | (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('simplify nested equalities', [status(thm)],
% 96.37/12.76 [zip_derived_cl1745])).
% 96.37/12.76 thf(zip_derived_cl1752, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 ( (((l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 moref))))) =>
% 96.37/12.76 ($false)))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ((X1) != (X0)))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl1751, '21'])).
% 96.37/12.76 thf(zip_derived_cl1756, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 ( (((~) @ (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 moref)))))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ((X1) != (X0)))),
% 96.37/12.76 inference('simplify boolean subterms', [status(thm)],
% 96.37/12.76 [zip_derived_cl1752])).
% 96.37/12.76 thf(zip_derived_cl1757, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 (~ (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 moref)))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ((X1) != (X0)))),
% 96.37/12.76 inference('simplify nested equalities', [status(thm)],
% 96.37/12.76 [zip_derived_cl1756])).
% 96.37/12.76 thf(zip_derived_cl8740, plain,
% 96.37/12.76 (((('#sk2') != ('#sk3'))
% 96.37/12.76 | ~ (is_of @ '#sk2' @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ '#sk3' @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('sup-', [status(thm)], [zip_derived_cl654, zip_derived_cl1757])).
% 96.37/12.76 thf(zip_derived_cl640, plain,
% 96.37/12.76 ( (is_of @ '#sk2' @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl639])).
% 96.37/12.76 thf(zip_derived_cl646, plain,
% 96.37/12.76 ( (is_of @ '#sk3' @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl645])).
% 96.37/12.76 thf(zip_derived_cl8767, plain, ((('#sk2') != ('#sk3'))),
% 96.37/12.76 inference('demod', [status(thm)],
% 96.37/12.76 [zip_derived_cl8740, zip_derived_cl640, zip_derived_cl646])).
% 96.37/12.76 thf(zip_derived_cl648, plain,
% 96.37/12.76 ( (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ '#sk2')))))) @
% 96.37/12.76 ((('#C') @ inf @ '#sk3')))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false)) @
% 96.37/12.76 ((('#sk2') = ('#sk3'))))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl647])).
% 96.37/12.76 thf(zip_derived_cl650, plain,
% 96.37/12.76 ( (((imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ '#sk2')))))) @
% 96.37/12.76 ((('#C') @ inf @ '#sk3')))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false)) => ((('#sk2') = ('#sk3')))))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl648, '21'])).
% 96.37/12.76 thf(zip_derived_cl652, plain,
% 96.37/12.76 ((~ (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ '#sk2')))))) @
% 96.37/12.76 ((('#C') @ inf @ '#sk3')))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false))
% 96.37/12.76 | ((('#sk2') = ('#sk3'))))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl650])).
% 96.37/12.76 thf(zip_derived_cl655, plain,
% 96.37/12.76 ((~ (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ '#sk2')))))) @
% 96.37/12.76 ((('#C') @ inf @ '#sk3')))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false))
% 96.37/12.76 | (('#sk2') = ('#sk3')))),
% 96.37/12.76 inference('simplify nested equalities', [status(thm)],
% 96.37/12.76 [zip_derived_cl652])).
% 96.37/12.76 thf(zip_derived_cl656, plain,
% 96.37/12.76 ((~ (((l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ '#sk2')))))) @
% 96.37/12.76 ((('#C') @ inf @ '#sk3')))))) @
% 96.37/12.76 lessf))))) =>
% 96.37/12.76 ($false)))
% 96.37/12.76 | (('#sk2') = ('#sk3')))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl655, '13'])).
% 96.37/12.76 thf(zip_derived_cl657, plain,
% 96.37/12.76 ((~ (((~) @ (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ '#sk2')))))) @
% 96.37/12.76 ((('#C') @ inf @ '#sk3')))))) @
% 96.37/12.76 lessf)))))))
% 96.37/12.76 | (('#sk2') = ('#sk3')))),
% 96.37/12.76 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl656])).
% 96.37/12.76 thf(zip_derived_cl658, plain,
% 96.37/12.76 (( (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ '#sk2')))))) @
% 96.37/12.76 ((('#C') @ inf @ '#sk3')))))) @
% 96.37/12.76 lessf)))))
% 96.37/12.76 | (('#sk2') = ('#sk3')))),
% 96.37/12.76 inference('simplify nested equalities', [status(thm)],
% 96.37/12.76 [zip_derived_cl657])).
% 96.37/12.76 thf(zip_derived_cl8886, plain,
% 96.37/12.76 (( (l_some @ frac @
% 96.37/12.76 ('#ty_enc9' @ (l_some @ frac) @
% 96.37/12.76 ('#ty_enc10' @
% 96.37/12.76 ('#ty_enc11' @ '#ty_enc16' @
% 96.37/12.76 ('#ty_enc12' @
% 96.37/12.76 ('#ty_enc13' @ '#ty_enc15' @
% 96.37/12.76 ('#ty_enc14' @ and3 @ ('#ty_enc8' @ inf @ '#sk2'))) @
% 96.37/12.76 ('#ty_enc8' @ inf @ '#sk3'))) @
% 96.37/12.76 lessf)))
% 96.37/12.76 | (('#sk2') = ('#sk3')))),
% 96.37/12.76 inference('remove_ty_args', [status(thm)], [zip_derived_cl658])).
% 96.37/12.76 thf(satz81b, axiom,
% 96.37/12.76 (all_of @
% 96.37/12.76 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @
% 96.37/12.76 ( ^[X0:$i]:
% 96.37/12.76 ( all_of @
% 96.37/12.76 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @
% 96.37/12.76 ( ^[X1:$i]:
% 96.37/12.76 ( ec3 @
% 96.37/12.76 ( rt_is @ X0 @ X1 ) @ ( rt_more @ X0 @ X1 ) @
% 96.37/12.76 ( rt_less @ X0 @ X1 ) ) ) ) ))).
% 96.37/12.76 thf(zip_derived_cl493, plain,
% 96.37/12.76 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @
% 96.37/12.76 (^[Y0 : $i]:
% 96.37/12.76 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @
% 96.37/12.76 (^[Y1 : $i]:
% 96.37/12.76 (ec3 @ (rt_is @ Y0 @ Y1) @ (rt_more @ Y0 @ Y1) @
% 96.37/12.76 (rt_less @ Y0 @ Y1))))))),
% 96.37/12.76 inference('cnf', [status(esa)], [satz81b])).
% 96.37/12.76 thf(zip_derived_cl494, plain,
% 96.37/12.76 ( (all_of @ ((('#C') @ in @ rat)) @
% 96.37/12.76 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#B') @ ((('#B') @ ec3)) @ rt_is)))) @
% 96.37/12.76 rt_more)))) @
% 96.37/12.76 rt_less)))))),
% 96.37/12.76 inference('lams2combs', [status(thm)], [zip_derived_cl493])).
% 96.37/12.76 thf(zip_derived_cl1833, plain,
% 96.37/12.76 ( (all_of @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 96.37/12.76 ((('#B') @ (all_of @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#B') @ ((('#B') @ ec3)) @ rt_is)))) @
% 96.37/12.76 rt_more)))) @
% 96.37/12.76 rt_less)))))),
% 96.37/12.76 inference('rw', [status(thm)], [zip_derived_cl494, '0', '1'])).
% 96.37/12.76 thf(zip_derived_cl1834, plain,
% 96.37/12.76 ( (((!!) @ (^[Y0 : $i]:
% 96.37/12.76 (((is_of @ Y0 @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.37/12.76 ((('#B') @ (all_of @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @
% 96.37/12.76 (anec @ frac @ n_eq))))) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#B') @ ((('#B') @ ec3)) @
% 96.37/12.76 rt_is)))) @
% 96.37/12.76 rt_more)))) @
% 96.37/12.76 rt_less)) @
% 96.37/12.76 Y0)))))))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl1833, '14'])).
% 96.37/12.76 thf(zip_derived_cl1835, plain,
% 96.37/12.76 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 96.37/12.76 ((('#C') @ is_of @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @
% 96.37/12.76 (anec @ frac @ n_eq)))))))) @
% 96.37/12.76 ((('#B') @ (all_of @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#B') @ ((('#B') @ ec3)) @
% 96.37/12.76 rt_is)))) @
% 96.37/12.76 rt_more)))) @
% 96.37/12.76 rt_less))))))))),
% 96.37/12.76 inference('comb-normalize', [status(thm)], [zip_derived_cl1834])).
% 96.37/12.76 thf(zip_derived_cl1836, plain,
% 96.37/12.76 (![X2 : $i]:
% 96.37/12.76 (((is_of @ X2 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.37/12.76 (all_of @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 96.37/12.76 ((('#S') @ ((('#S') @ ((('#B') @ ec3 @ (rt_is @ X2))) @
% 96.37/12.76 (rt_more @ X2))) @
% 96.37/12.76 (rt_less @ X2))))))),
% 96.37/12.76 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1835])).
% 96.37/12.76 thf(zip_derived_cl1837, plain,
% 96.37/12.76 (![X2 : $i]:
% 96.37/12.76 (~ (is_of @ X2 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | (all_of @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 96.37/12.76 ((('#S') @ ((('#S') @ ((('#B') @ ec3 @ (rt_is @ X2))) @
% 96.37/12.76 (rt_more @ X2))) @
% 96.37/12.76 (rt_less @ X2)))))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1836])).
% 96.37/12.76 thf(zip_derived_cl1838, plain,
% 96.37/12.76 (![X0 : $i]:
% 96.37/12.76 ( (((!!) @ (^[Y0 : $i]:
% 96.37/12.76 (((is_of @ Y0 @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.37/12.76 ((('#S') @ ((('#S') @ ((('#B') @ ec3 @ (rt_is @ X0))) @
% 96.37/12.76 (rt_more @ X0))) @
% 96.37/12.76 (rt_less @ X0) @ Y0)))))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl1837, '14'])).
% 96.37/12.76 thf(zip_derived_cl1839, plain,
% 96.37/12.76 (![X0 : $i]:
% 96.37/12.76 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 96.37/12.76 ((('#C') @ is_of @
% 96.37/12.76 ((('#C') @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @
% 96.37/12.76 (anec @ frac @ n_eq)))))))) @
% 96.37/12.76 ((('#S') @ ((('#S') @ ((('#B') @ ec3 @ (rt_is @ X0))) @
% 96.37/12.76 (rt_more @ X0))) @
% 96.37/12.76 (rt_less @ X0)))))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('comb-normalize', [status(thm)], [zip_derived_cl1838])).
% 96.37/12.76 thf(zip_derived_cl1840, plain,
% 96.37/12.76 (![X0 : $i, X2 : $i]:
% 96.37/12.76 ( (((is_of @ X2 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.37/12.76 (ec3 @ (rt_is @ X0 @ X2) @ (rt_more @ X0 @ X2) @
% 96.37/12.76 (rt_less @ X0 @ X2))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1839])).
% 96.37/12.76 thf(zip_derived_cl1841, plain,
% 96.37/12.76 (![X0 : $i, X2 : $i]:
% 96.37/12.76 ( (((is_of @ X2 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @ (((X0) = (X2))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X2)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X2)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X2)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X2)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 (imp @ (((X0) = (X2))) @ ($false))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 ($false)) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 ($false))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('rw', [status(thm)],
% 96.37/12.76 [zip_derived_cl1840, '3', '3', '3', '3', '3', '3', '3', '15',
% 96.37/12.76 '15', '15', '15', '15', '16', '16', '18', '19', '5', '6',
% 96.37/12.76 '6', '0', '7', '7', '1', '8', '9', '9', '10', '11'])).
% 96.37/12.76 thf(zip_derived_cl1842, plain,
% 96.37/12.76 (![X0 : $i, X2 : $i]:
% 96.37/12.76 (~ (is_of @ X2 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @ (((X0) = (X2))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X2)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X2)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X2)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X2)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 (imp @ (((X0) = (X2))) @ ($false))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 ($false)) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 ($false))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1841])).
% 96.37/12.76 thf(zip_derived_cl1843, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 ( (((imp @
% 96.37/12.76 (imp @ (((X0) = (X1))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 (imp @ (((X0) = (X1))) @ ($false))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 ($false)) @
% 96.37/12.76 ($false))) =>
% 96.37/12.76 ($false)))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl1842, '21'])).
% 96.37/12.76 thf(zip_derived_cl1844, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 ( (((~) @ (imp @
% 96.37/12.76 (imp @ (((X0) = (X1))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 (imp @ (((X0) = (X1))) @ ($false))) @
% 96.37/12.76 ($false))) @
% 96.37/12.76 ($false)) @
% 96.37/12.76 ($false)))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('simplify boolean subterms', [status(thm)],
% 96.37/12.76 [zip_derived_cl1843])).
% 96.37/12.76 thf(zip_derived_cl1845, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 (~ (imp @
% 96.37/12.76 (imp @ (((X0) = (X1))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
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% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
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% 96.37/12.76 thf(zip_derived_cl1850, plain,
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% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
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% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('simplify boolean subterms', [status(thm)],
% 96.37/12.76 [zip_derived_cl1850])).
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% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('simplify nested equalities', [status(thm)],
% 96.37/12.76 [zip_derived_cl1852])).
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% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl1853, '21'])).
% 96.37/12.76 thf(zip_derived_cl1857, plain,
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% 96.37/12.76 ($false)))))
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% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('simplify boolean subterms', [status(thm)],
% 96.37/12.76 [zip_derived_cl1854])).
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% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('simplify nested equalities', [status(thm)],
% 96.37/12.76 [zip_derived_cl1857])).
% 96.37/12.76 thf(zip_derived_cl1859, plain,
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% 96.37/12.76 (~ (((imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false))) =>
% 96.37/12.76 (imp @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 (imp @ (((X1) = (X0))) @ ($false))) @
% 96.37/12.76 ($false))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl1858, '13'])).
% 96.37/12.76 thf(zip_derived_cl1862, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 ( (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 moref))))) @
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false)))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1859])).
% 96.37/12.76 thf(zip_derived_cl1864, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 ( (((l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 moref))))) =>
% 96.37/12.76 (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl1862, '21'])).
% 96.37/12.76 thf(zip_derived_cl1866, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 (~ (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 moref)))))
% 96.37/12.76 | (imp @
% 96.37/12.76 (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 lessf))))) @
% 96.37/12.76 ($false))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.37/12.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1864])).
% 96.37/12.76 thf(zip_derived_cl1870, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 ( (((l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 lessf))))) =>
% 96.37/12.76 ($false)))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 moref))))))),
% 96.37/12.76 inference('rw_clause', [status(thm)], [zip_derived_cl1866, '21'])).
% 96.37/12.76 thf(zip_derived_cl1872, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 ( (((~) @ (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 lessf)))))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 moref))))))),
% 96.37/12.76 inference('simplify boolean subterms', [status(thm)],
% 96.37/12.76 [zip_derived_cl1870])).
% 96.37/12.76 thf(zip_derived_cl1873, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 (~ (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 lessf)))))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.37/12.76 | ~ (l_some @ frac @
% 96.37/12.76 ((('#B') @ (l_some @ frac) @
% 96.37/12.76 ((('#S') @ ((('#B') @ ('#S') @
% 96.37/12.76 ((('#C') @ ((('#B') @ ('#B') @
% 96.37/12.76 ((('#B') @ and3 @
% 96.37/12.76 ((('#C') @ inf @ X1)))))) @
% 96.37/12.76 ((('#C') @ inf @ X0)))))) @
% 96.37/12.76 moref))))))),
% 96.37/12.76 inference('simplify nested equalities', [status(thm)],
% 96.37/12.76 [zip_derived_cl1872])).
% 96.37/12.76 thf(zip_derived_cl8921, plain,
% 96.37/12.76 (![X0 : $i, X1 : $i]:
% 96.37/12.76 (~ (l_some @ frac @
% 96.37/12.76 ('#ty_enc9' @ (l_some @ frac) @
% 96.37/12.76 ('#ty_enc10' @
% 96.37/12.76 ('#ty_enc11' @ '#ty_enc16' @
% 96.37/12.76 ('#ty_enc12' @
% 96.37/12.76 ('#ty_enc13' @ '#ty_enc15' @
% 96.37/12.76 ('#ty_enc14' @ and3 @ ('#ty_enc8' @ inf @ X1))) @
% 96.37/12.76 ('#ty_enc8' @ inf @ X0))) @
% 96.37/12.76 lessf)))
% 96.37/12.76 | ~ (is_of @ X0 @
% 96.37/12.76 ('#ty_enc8' @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))
% 96.37/12.76 | ~ (is_of @ X1 @
% 96.37/12.76 ('#ty_enc8' @ in @
% 96.37/12.76 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))
% 96.37/12.76 | ~ (l_some @ frac @
% 96.37/12.76 ('#ty_enc9' @ (l_some @ frac) @
% 96.37/12.76 ('#ty_enc10' @
% 96.37/12.76 ('#ty_enc11' @ '#ty_enc16' @
% 96.37/12.76 ('#ty_enc12' @
% 96.37/12.76 ('#ty_enc13' @ '#ty_enc15' @
% 96.37/12.76 ('#ty_enc14' @ and3 @ ('#ty_enc8' @ inf @ X1))) @
% 96.37/12.76 ('#ty_enc8' @ inf @ X0))) @
% 96.37/12.76 moref))))),
% 96.37/12.76 inference('remove_ty_args', [status(thm)], [zip_derived_cl1873])).
% 96.37/12.76 thf(zip_derived_cl9016, plain, ($false),
% 96.37/12.76 inference('eprover', [status(thm)],
% 96.37/12.76 [zip_derived_cl8883, zip_derived_cl8884, zip_derived_cl8885,
% 96.37/12.76 zip_derived_cl8767, zip_derived_cl8886, zip_derived_cl8921])).
% 96.37/12.76
% 96.37/12.76 % SZS output end Refutation
% 96.37/12.76
% 96.37/12.76
% 96.37/12.77 % Terminating...
% 96.40/12.84 % Runner terminated.
% 96.40/12.84 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------