%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM656^4 : 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.MoZIIPok4G 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 04:47:50 PM UTC 2025
% Result : Theorem 18.51s 3.02s
% Output : Refutation 18.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.19 % Problem : NUM656^4 : TPTP v9.2.0. Released v7.1.0.
% 0.11/0.20 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.MoZIIPok4G true
% 0.13/0.44 % Computer : n005.cluster.edu
% 0.13/0.44 % Model : x86_64 x86_64
% 0.13/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.44 % Memory : 8042.1875MB
% 0.13/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.44 % CPULimit : 300
% 0.13/0.44 % WCLimit : 300
% 0.13/0.44 % DateTime : Wed Oct 1 16:42:38 EDT 2025
% 0.13/0.44 % CPUTime :
% 0.13/0.44 % Running portfolio for 300 s
% 0.13/0.44 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.44 % Number of cores: 8
% 0.13/0.45 % Python version: Python 3.6.8
% 0.13/0.45 % Running in HO mode
% 0.50/0.73 % Total configuration time : 828
% 0.50/0.73 % Estimated wc time : 1656
% 0.50/0.73 % Estimated cpu time (8 cpus) : 207.0
% 0.50/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.50/0.82 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.50/0.83 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.50/0.83 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.50/0.83 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.50/0.83 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.50/0.83 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.50/0.83 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 9.22/1.89 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 18.51/3.02 % Solved by lams/40_b.comb.sh.
% 18.51/3.02 % done 140 iterations in 2.139s
% 18.51/3.02 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 18.51/3.02 % SZS output start Refutation
% 18.51/3.02 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
% 18.51/3.02 thf('#sk2_type', type, '#sk2': $i).
% 18.51/3.02 thf(nat_type, type, nat: $i).
% 18.51/3.02 thf(lessis_type, type, lessis: $i > $i > $o).
% 18.51/3.02 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 18.51/3.02 thf(in_type, type, in: $i > $i > $o).
% 18.51/3.02 thf('#sk3_type', type, '#sk3': $i).
% 18.51/3.02 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 18.51/3.02 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 18.51/3.02 thf(emptyset_type, type, emptyset: $i).
% 18.51/3.02 thf(n_is_type, type, n_is: $i > $i > $o).
% 18.51/3.02 thf(imp_type, type, imp: $o > $o > $o).
% 18.51/3.02 thf(omega_type, type, omega: $i).
% 18.51/3.02 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 18.51/3.02 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 18.51/3.02 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 18.51/3.02 thf(l_or_type, type, l_or: $o > $o > $o).
% 18.51/3.02 thf(d_not_type, type, d_not: $o > $o).
% 18.51/3.02 thf(iii_type, type, iii: $i > $i > $o).
% 18.51/3.02 thf(e_is_type, type, e_is: $i > $i > $i > $o).
% 18.51/3.02 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 18.51/3.02 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 18.51/3.02 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 18.51/3.02 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 18.51/3.02 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 18.51/3.02 thf(satz10g, conjecture,
% 18.51/3.02 (all_of @
% 18.51/3.02 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 18.51/3.02 ( ^[X0:$i]:
% 18.51/3.02 ( all_of @
% 18.51/3.02 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 18.51/3.02 ( ^[X1:$i]:
% 18.51/3.02 ( ( d_29_ii @ X0 @ X1 ) => ( d_not @ ( lessis @ X0 @ X1 ) ) ) ) ) ))).
% 18.51/3.02 thf(zf_stmt_0, negated_conjecture,
% 18.51/3.02 (~( all_of @
% 18.51/3.02 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 18.51/3.02 ( ^[X0:$i]:
% 18.51/3.02 ( all_of @
% 18.51/3.02 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 18.51/3.02 ( ^[X1:$i]:
% 18.51/3.02 ( ( d_29_ii @ X0 @ X1 ) => ( d_not @ ( lessis @ X0 @ X1 ) ) ) ) ) ) )),
% 18.51/3.02 inference('cnf.neg', [status(esa)], [satz10g])).
% 18.51/3.02 thf(zip_derived_cl101, plain,
% 18.51/3.02 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 18.51/3.02 (^[Y0 : $i]:
% 18.51/3.02 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 18.51/3.02 (^[Y1 : $i]:
% 18.51/3.02 (((d_29_ii @ Y0 @ Y1) => (d_not @ (lessis @ Y0 @ Y1))))))))),
% 18.51/3.02 inference('cnf', [status(esa)], [zf_stmt_0])).
% 18.51/3.02 thf(zip_derived_cl102, plain,
% 18.51/3.02 (~ (all_of @ ((('#C') @ in @ nat)) @
% 18.51/3.02 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 18.51/3.02 ((('#S') @ ((('#B') @ ('#S') @
% 18.51/3.02 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 18.51/3.02 ((('#B') @ ((('#B') @ d_not)) @ lessis)))))))),
% 18.51/3.02 inference('lams2combs', [status(thm)], [zip_derived_cl101])).
% 18.51/3.02 thf(def_nat, axiom,(( nat ) =
% 18.51/3.02 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))).
% 18.51/3.02 thf('0', plain,
% 18.51/3.02 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )),
% 18.51/3.02 define([status(thm)])).
% 18.51/3.02 thf(zip_derived_cl169, plain,
% 18.51/3.02 (~ (all_of @
% 18.51/3.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 18.51/3.02 ((('#B') @ (all_of @
% 18.51/3.02 ((('#C') @ in @
% 18.51/3.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 18.51/3.02 ((('#S') @ ((('#B') @ ('#S') @
% 18.51/3.02 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 18.51/3.02 ((('#B') @ ((('#B') @ d_not)) @ lessis)))))))),
% 18.51/3.02 inference('rw', [status(thm)], [zip_derived_cl102, '0'])).
% 18.51/3.02 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 18.51/3.02 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 18.51/3.02 thf('1', plain,
% 18.51/3.02 (![X0:( $i > $o ),X1:( $i > $o )]:
% 18.51/3.02 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 18.51/3.02 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 18.51/3.02 inference('rw.lit', [status(esa)], [def_all_of])).
% 18.51/3.02 thf(zip_derived_cl170, plain,
% 18.51/3.02 (~ (((!!) @ (^[Y0 : $i]:
% 18.51/3.02 (((is_of @ Y0 @
% 18.51/3.02 ((('#C') @ in @
% 18.51/3.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 18.51/3.02 ((('#B') @ (all_of @
% 18.51/3.02 ((('#C') @ in @
% 18.51/3.02 (d_Sep @ omega @
% 18.51/3.02 ((('#C') @ (!=) @ emptyset)))))) @
% 18.51/3.02 ((('#S') @ ((('#B') @ ('#S') @
% 18.51/3.02 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 18.51/3.02 ((('#B') @ ((('#B') @ d_not)) @ lessis)))) @
% 18.51/3.02 Y0)))))))),
% 18.51/3.02 inference('rw_clause', [status(thm)], [zip_derived_cl169, '1'])).
% 18.51/3.02 thf(zip_derived_cl171, plain,
% 18.51/3.02 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 18.51/3.02 ((('#C') @ is_of @
% 18.51/3.02 ((('#C') @ in @
% 18.51/3.02 (d_Sep @ omega @
% 18.51/3.02 ((('#C') @ (!=) @ emptyset))))))))) @
% 18.51/3.02 ((('#B') @ (all_of @
% 18.51/3.02 ((('#C') @ in @
% 18.51/3.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 18.51/3.02 ((('#S') @ ((('#B') @ ('#S') @
% 18.51/3.02 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 18.51/3.02 ((('#B') @ ((('#B') @ d_not)) @ lessis))))))))))),
% 18.51/3.02 inference('comb-normalize', [status(thm)], [zip_derived_cl170])).
% 18.51/3.02 thf(zip_derived_cl172, plain,
% 18.51/3.02 (~ (((is_of @ '#sk2' @
% 18.51/3.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 18.51/3.02 (all_of @
% 18.51/3.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 18.51/3.02 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk2'))) @
% 18.51/3.02 ((('#B') @ d_not @ (lessis @ '#sk2'))))))))),
% 18.51/3.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl171])).
% 18.51/3.02 thf(def_is_of, axiom,(( is_of @ (X1)@ (X0)) = ((X0 @ X1)))).
% 18.51/3.02 thf('2', plain,
% 18.51/3.02 (![X0:( $i > $o ),X1:$i]: ( ( is_of @ X1 @ X0 ) = ( X0 @ X1 ) )),
% 18.51/3.02 define([status(thm)])).
% 18.51/3.02 thf(zip_derived_cl173, plain,
% 18.51/3.02 (~ (((in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 18.51/3.02 (all_of @
% 18.51/3.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 18.51/3.02 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk2'))) @
% 18.51/3.02 ((('#B') @ d_not @ (lessis @ '#sk2'))))))))),
% 18.51/3.02 inference('rw', [status(thm)], [zip_derived_cl172, '2'])).
% 18.51/3.02 thf(zip_derived_cl175, plain,
% 18.51/3.02 (~ (all_of @
% 18.51/3.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 18.51/3.02 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk2'))) @
% 18.51/3.02 ((('#B') @ d_not @ (lessis @ '#sk2'))))))),
% 18.51/3.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])).
% 18.51/3.02 thf(zip_derived_cl176, plain,
% 18.51/3.02 (~ (((!!) @ (^[Y0 : $i]:
% 18.51/3.02 (((is_of @ Y0 @
% 18.51/3.02 ((('#C') @ in @
% 18.51/3.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 18.51/3.02 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk2'))) @
% 18.51/3.02 ((('#B') @ d_not @ (lessis @ '#sk2'))) @ Y0)))))))),
% 18.51/3.02 inference('rw_clause', [status(thm)], [zip_derived_cl175, '1'])).
% 18.51/3.02 thf(zip_derived_cl177, plain,
% 18.51/3.02 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 18.51/3.02 ((('#C') @ is_of @
% 18.51/3.02 ((('#C') @ in @
% 18.51/3.02 (d_Sep @ omega @
% 18.51/3.02 ((('#C') @ (!=) @ emptyset))))))))) @
% 18.51/3.02 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk2'))) @
% 18.51/3.02 ((('#B') @ d_not @ (lessis @ '#sk2')))))))))),
% 18.51/3.02 inference('comb-normalize', [status(thm)], [zip_derived_cl176])).
% 18.51/3.02 thf(zip_derived_cl178, plain,
% 18.51/3.02 (~ (((is_of @ '#sk3' @
% 18.51/3.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 18.51/3.02 (((d_29_ii @ '#sk2' @ '#sk3') => (d_not @
% 18.51/3.02 (lessis @ '#sk2' @ '#sk3'))))))),
% 18.51/3.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl177])).
% 18.51/3.02 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 18.51/3.02 thf('3', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 18.51/3.02 define([status(thm)])).
% 18.51/3.02 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 18.51/3.02 thf('4', plain,
% 18.51/3.02 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 18.51/3.02 define([status(thm)])).
% 18.51/3.02 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))).
% 18.51/3.02 thf('5', plain,
% 18.51/3.02 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )),
% 18.51/3.02 define([status(thm)])).
% 18.51/3.02 thf(def_n_is, axiom,(( n_is @ (X0)@ (X1)) = ((e_is @ nat @ X0 @ X1)))).
% 18.51/3.02 thf('6', plain,
% 18.51/3.02 (![X1:$i,X0:$i]: ( ( n_is @ X0 @ X1 ) = ( e_is @ nat @ X0 @ X1 ) )),
% 18.51/3.02 define([status(thm)])).
% 18.51/3.02 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 18.51/3.02 thf('7', plain,
% 18.51/3.02 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 18.51/3.02 define([status(thm)])).
% 18.51/3.02 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) =
% 18.51/3.02 ((n_some @ (diffprop @ X0 @ X1))))).
% 18.51/3.02 thf('8', plain,
% 18.51/3.02 (![X1:$i,X0:$i]:
% 18.51/3.02 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 18.51/3.02 define([status(thm)])).
% 18.51/3.02 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))).
% 18.51/3.02 thf('9', plain,
% 18.51/3.02 (![X1:$i,X0:$i]:
% 18.51/3.02 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 18.51/3.02 define([status(thm)])).
% 18.51/3.02 thf(def_lessis, axiom,(( lessis @ (X0)@ (X1)) =
% 18.51/3.02 ((l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1))))).
% 18.51/3.02 thf('10', plain,
% 18.51/3.02 (![X1:$i,X0:$i]:
% 18.51/3.02 ( ( lessis @ X0 @ X1 ) =
% 18.51/3.02 ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
% 18.51/3.02 define([status(thm)])).
% 18.51/3.02 thf(zip_derived_cl179, plain,
% 18.51/3.02 (~ (((in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 18.51/3.02 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk2' @ '#sk3')) => (imp @
% 18.51/3.02 (imp @
% 18.51/3.02 (imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk3' @ '#sk2')) @
% 18.51/3.02 ($false)) @
% 18.51/3.02 ((('#sk2') = ('#sk3')))) @
% 18.51/3.02 ($false))))))),
% 18.51/3.02 inference('rw', [status(thm)],
% 18.51/3.02 [zip_derived_cl178, '2', '3', '3', '4', '5', '0', '6', '7',
% 18.51/3.02 '7', '8', '9', '10'])).
% 18.51/3.02 thf(zip_derived_cl181, plain,
% 18.51/3.02 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk2' @ '#sk3')) => (imp @
% 18.51/3.02 (imp @
% 18.51/3.02 (imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk3' @ '#sk2')) @
% 18.51/3.02 ($false)) @
% 18.51/3.02 ((('#sk2') = ('#sk3')))) @
% 18.51/3.02 ($false))))),
% 18.51/3.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])).
% 18.51/3.02 thf(zip_derived_cl183, plain,
% 18.51/3.02 (~ (imp @
% 18.51/3.02 (imp @
% 18.51/3.02 (imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk3' @ '#sk2')) @
% 18.51/3.02 ($false)) @
% 18.51/3.02 ((('#sk2') = ('#sk3')))) @
% 18.51/3.02 ($false))),
% 18.51/3.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl181])).
% 18.51/3.02 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 18.51/3.02 thf('11', plain,
% 18.51/3.02 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 18.51/3.02 inference('rw.lit', [status(esa)], [def_imp])).
% 18.51/3.02 thf(zip_derived_cl184, plain,
% 18.51/3.02 (~ (((imp @
% 18.51/3.02 (imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk3' @ '#sk2')) @
% 18.51/3.02 ($false)) @
% 18.51/3.02 ((('#sk2') = ('#sk3')))) => ($false)))),
% 18.51/3.02 inference('rw_clause', [status(thm)], [zip_derived_cl183, '11'])).
% 18.51/3.02 thf(zip_derived_cl185, plain,
% 18.51/3.02 (~ (((~) @ (imp @
% 18.51/3.02 (imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk3' @ '#sk2')) @
% 18.51/3.02 ($false)) @
% 18.51/3.02 ((('#sk2') = ('#sk3'))))))),
% 18.51/3.02 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl184])).
% 18.51/3.02 thf(zip_derived_cl186, plain,
% 18.51/3.02 ( (imp @
% 18.51/3.02 (imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk3' @ '#sk2')) @
% 18.51/3.02 ($false)) @
% 18.51/3.02 ((('#sk2') = ('#sk3'))))),
% 18.51/3.02 inference('simplify nested equalities', [status(thm)],
% 18.51/3.02 [zip_derived_cl185])).
% 18.51/3.02 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 18.51/3.02 thf('12', plain,
% 18.51/3.02 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 18.51/3.02 inference('rw.lit', [status(esa)], [def_imp])).
% 18.51/3.02 thf(zip_derived_cl187, plain,
% 18.51/3.02 ( (((imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk3' @ '#sk2')) @
% 18.51/3.02 ($false)) => ((('#sk2') = ('#sk3')))))),
% 18.51/3.02 inference('rw_clause', [status(thm)], [zip_derived_cl186, '12'])).
% 18.51/3.02 thf(zip_derived_cl188, plain,
% 18.51/3.02 ((~ (imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk3' @ '#sk2')) @
% 18.51/3.02 ($false))
% 18.51/3.02 | ((('#sk2') = ('#sk3'))))),
% 18.51/3.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl187])).
% 18.51/3.02 thf(zip_derived_cl189, plain,
% 18.51/3.02 ((~ (imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk3' @ '#sk2')) @
% 18.51/3.02 ($false))
% 18.51/3.02 | (('#sk2') = ('#sk3')))),
% 18.51/3.02 inference('simplify nested equalities', [status(thm)],
% 18.51/3.02 [zip_derived_cl188])).
% 18.51/3.02 thf(zip_derived_cl190, plain,
% 18.51/3.02 ((~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk3' @ '#sk2')) => ($false)))
% 18.51/3.02 | (('#sk2') = ('#sk3')))),
% 18.51/3.02 inference('rw_clause', [status(thm)], [zip_derived_cl189, '11'])).
% 18.51/3.02 thf(zip_derived_cl191, plain,
% 18.51/3.02 ((~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk3' @ '#sk2'))))
% 18.51/3.02 | (('#sk2') = ('#sk3')))),
% 18.51/3.02 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl190])).
% 18.51/3.02 thf(zip_derived_cl192, plain,
% 18.51/3.02 (( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk3' @ '#sk2'))
% 18.51/3.02 | (('#sk2') = ('#sk3')))),
% 18.51/3.02 inference('simplify nested equalities', [status(thm)],
% 18.51/3.02 [zip_derived_cl191])).
% 18.51/3.02 thf(satz10d, axiom,
% 18.51/3.02 (all_of @
% 18.51/3.02 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 18.51/3.02 ( ^[X0:$i]:
% 18.51/3.02 ( all_of @
% 18.51/3.02 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 18.51/3.02 ( ^[X1:$i]:
% 18.51/3.02 ( ( lessis @ X0 @ X1 ) => ( d_not @ ( d_29_ii @ X0 @ X1 ) ) ) ) ) ))).
% 18.51/3.02 thf(zip_derived_cl95, plain,
% 18.51/3.02 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 18.51/3.02 (^[Y0 : $i]:
% 18.51/3.02 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 18.51/3.02 (^[Y1 : $i]:
% 18.51/3.02 (((lessis @ Y0 @ Y1) => (d_not @ (d_29_ii @ Y0 @ Y1))))))))),
% 18.51/3.02 inference('cnf', [status(esa)], [satz10d])).
% 18.51/3.02 thf(zip_derived_cl96, plain,
% 18.51/3.02 ( (all_of @ ((('#C') @ in @ nat)) @
% 18.51/3.02 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 18.51/3.02 ((('#S') @ ((('#B') @ ('#S') @
% 18.51/3.02 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @
% 18.51/3.02 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))))),
% 18.51/3.02 inference('lams2combs', [status(thm)], [zip_derived_cl95])).
% 18.51/3.02 thf(zip_derived_cl321, plain,
% 18.51/3.02 ( (all_of @
% 18.51/3.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 18.51/3.02 ((('#B') @ (all_of @
% 18.51/3.02 ((('#C') @ in @
% 18.51/3.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 18.51/3.02 ((('#S') @ ((('#B') @ ('#S') @
% 18.51/3.02 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @
% 18.51/3.02 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))))),
% 18.51/3.02 inference('rw', [status(thm)], [zip_derived_cl96, '0'])).
% 18.51/3.02 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 18.51/3.02 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 18.51/3.02 thf('13', plain,
% 18.51/3.02 (![X0:( $i > $o ),X1:( $i > $o )]:
% 18.51/3.02 ( ( all_of @ X0 @ X1 ) <=>
% 18.51/3.02 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 18.51/3.02 inference('rw.lit', [status(esa)], [def_all_of])).
% 18.51/3.02 thf(zip_derived_cl322, plain,
% 18.51/3.02 ( (((!!) @ (^[Y0 : $i]:
% 18.51/3.02 (((is_of @ Y0 @
% 18.51/3.02 ((('#C') @ in @
% 18.51/3.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 18.51/3.02 ((('#B') @ (all_of @
% 18.51/3.02 ((('#C') @ in @
% 18.51/3.02 (d_Sep @ omega @
% 18.51/3.02 ((('#C') @ (!=) @ emptyset)))))) @
% 18.51/3.02 ((('#S') @ ((('#B') @ ('#S') @
% 18.51/3.02 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @
% 18.51/3.02 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))) @
% 18.51/3.02 Y0)))))))),
% 18.51/3.02 inference('rw_clause', [status(thm)], [zip_derived_cl321, '13'])).
% 18.51/3.02 thf(zip_derived_cl323, plain,
% 18.51/3.02 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 18.51/3.02 ((('#C') @ is_of @
% 18.51/3.02 ((('#C') @ in @
% 18.51/3.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 18.51/3.02 ((('#B') @ (all_of @
% 18.51/3.02 ((('#C') @ in @
% 18.51/3.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 18.51/3.02 ((('#S') @ ((('#B') @ ('#S') @
% 18.51/3.02 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @
% 18.51/3.02 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii))))))))))),
% 18.51/3.02 inference('comb-normalize', [status(thm)], [zip_derived_cl322])).
% 18.51/3.02 thf(zip_derived_cl324, plain,
% 18.51/3.02 (![X2 : $i]:
% 18.51/3.02 (((is_of @ X2 @
% 18.51/3.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 18.51/3.02 (all_of @
% 18.51/3.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 18.51/3.02 ((('#S') @ ((('#B') @ (=>) @ (lessis @ X2))) @
% 18.51/3.02 ((('#B') @ d_not @ (d_29_ii @ X2))))))))),
% 18.51/3.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl323])).
% 18.51/3.02 thf(zip_derived_cl325, plain,
% 18.51/3.02 (![X2 : $i]:
% 18.51/3.02 (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 18.51/3.02 (all_of @
% 18.51/3.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 18.51/3.02 ((('#S') @ ((('#B') @ (=>) @ (lessis @ X2))) @
% 18.51/3.02 ((('#B') @ d_not @ (d_29_ii @ X2))))))))),
% 18.51/3.02 inference('rw', [status(thm)], [zip_derived_cl324, '2'])).
% 18.51/3.02 thf(zip_derived_cl326, plain,
% 18.51/3.02 (![X2 : $i]:
% 18.51/3.02 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | (all_of @
% 18.51/3.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 18.51/3.02 ((('#S') @ ((('#B') @ (=>) @ (lessis @ X2))) @
% 18.51/3.02 ((('#B') @ d_not @ (d_29_ii @ X2)))))))),
% 18.51/3.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl325])).
% 18.51/3.02 thf(zip_derived_cl327, plain,
% 18.51/3.02 (![X0 : $i]:
% 18.51/3.02 ( (((!!) @ (^[Y0 : $i]:
% 18.51/3.02 (((is_of @ Y0 @
% 18.51/3.02 ((('#C') @ in @
% 18.51/3.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 18.51/3.02 ((('#S') @ ((('#B') @ (=>) @ (lessis @ X0))) @
% 18.51/3.02 ((('#B') @ d_not @ (d_29_ii @ X0))) @ Y0)))))))
% 18.51/3.02 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 18.51/3.02 inference('rw_clause', [status(thm)], [zip_derived_cl326, '13'])).
% 18.51/3.02 thf(zip_derived_cl328, plain,
% 18.51/3.02 (![X0 : $i]:
% 18.51/3.02 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 18.51/3.02 ((('#C') @ is_of @
% 18.51/3.02 ((('#C') @ in @
% 18.51/3.02 (d_Sep @ omega @
% 18.51/3.02 ((('#C') @ (!=) @ emptyset))))))))) @
% 18.51/3.02 ((('#S') @ ((('#B') @ (=>) @ (lessis @ X0))) @
% 18.51/3.02 ((('#B') @ d_not @ (d_29_ii @ X0)))))))))
% 18.51/3.02 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 18.51/3.02 inference('comb-normalize', [status(thm)], [zip_derived_cl327])).
% 18.51/3.02 thf(zip_derived_cl329, plain,
% 18.51/3.02 (![X0 : $i, X2 : $i]:
% 18.51/3.02 ( (((is_of @ X2 @
% 18.51/3.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 18.51/3.02 (((lessis @ X0 @ X2) => (d_not @ (d_29_ii @ X0 @ X2))))))
% 18.51/3.02 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 18.51/3.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl328])).
% 18.51/3.02 thf(zip_derived_cl330, plain,
% 18.51/3.02 (![X0 : $i, X2 : $i]:
% 18.51/3.02 ( (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 18.51/3.02 (((imp @
% 18.51/3.02 (imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X2 @ X0)) @
% 18.51/3.02 ($false)) @
% 18.51/3.02 (((X0) = (X2)))) => (imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X0 @ X2)) @
% 18.51/3.02 ($false))))))
% 18.51/3.02 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 18.51/3.02 inference('rw', [status(thm)],
% 18.51/3.02 [zip_derived_cl329, '2', '3', '3', '4', '5', '0', '6', '7',
% 18.51/3.02 '7', '8', '9', '10'])).
% 18.51/3.02 thf(zip_derived_cl331, plain,
% 18.51/3.02 (![X0 : $i, X2 : $i]:
% 18.51/3.02 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | (((imp @
% 18.51/3.02 (imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X2 @ X0)) @
% 18.51/3.02 ($false)) @
% 18.51/3.02 (((X0) = (X2)))) => (imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X0 @ X2)) @
% 18.51/3.02 ($false))))
% 18.51/3.02 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 18.51/3.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl330])).
% 18.51/3.02 thf(zip_derived_cl332, plain,
% 18.51/3.02 (![X0 : $i, X2 : $i]:
% 18.51/3.02 (~ (imp @
% 18.51/3.02 (imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X2 @ X0)) @
% 18.51/3.02 ($false)) @
% 18.51/3.02 (((X0) = (X2))))
% 18.51/3.02 | (imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X0 @ X2)) @
% 18.51/3.02 ($false))
% 18.51/3.02 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 18.51/3.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl331])).
% 18.51/3.02 thf(zip_derived_cl333, plain,
% 18.51/3.02 (![X0 : $i, X1 : $i]:
% 18.51/3.02 (~ (((imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X0 @ X1)) @
% 18.51/3.02 ($false)) => (((X1) = (X0)))))
% 18.51/3.02 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | (imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X1 @ X0)) @
% 18.51/3.02 ($false)))),
% 18.51/3.02 inference('rw_clause', [status(thm)], [zip_derived_cl332, '11'])).
% 18.51/3.02 thf(zip_derived_cl334, plain,
% 18.51/3.02 (![X0 : $i, X1 : $i]:
% 18.51/3.02 ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X0 @ X1)) => ($false)))
% 18.51/3.02 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (((imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X1 @ X0)) @
% 18.51/3.02 ($false)) => (((X0) = (X1))))))),
% 18.51/3.02 inference('rw_clause', [status(thm)], [zip_derived_cl333, '12'])).
% 18.51/3.02 thf(zip_derived_cl335, plain,
% 18.51/3.02 (![X0 : $i, X1 : $i]:
% 18.51/3.02 ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X0 @ X1))))
% 18.51/3.02 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (((imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X1 @ X0)) @
% 18.51/3.02 ($false)) => (((X0) = (X1))))))),
% 18.51/3.02 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl334])).
% 18.51/3.02 thf(zip_derived_cl336, plain,
% 18.51/3.02 (![X0 : $i, X1 : $i]:
% 18.51/3.02 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X0 @ X1))
% 18.51/3.02 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (((imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X1 @ X0)) @
% 18.51/3.02 ($false)) => (((X0) = (X1))))))),
% 18.51/3.02 inference('simplify nested equalities', [status(thm)],
% 18.51/3.02 [zip_derived_cl335])).
% 18.51/3.02 thf(zip_derived_cl337, plain,
% 18.51/3.02 (![X0 : $i, X1 : $i]:
% 18.51/3.02 ( (imp @
% 18.51/3.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X1 @ X0)) @
% 18.51/3.02 ($false))
% 18.51/3.02 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X0 @ X1)))),
% 18.51/3.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl336])).
% 18.51/3.02 thf(zip_derived_cl339, plain,
% 18.51/3.02 (![X0 : $i, X1 : $i]:
% 18.51/3.02 ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X0 @ X1)) => ($false)))
% 18.51/3.02 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X1 @ X0))
% 18.51/3.02 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 18.51/3.02 inference('rw_clause', [status(thm)], [zip_derived_cl337, '12'])).
% 18.51/3.02 thf(zip_derived_cl341, plain,
% 18.51/3.02 (![X0 : $i, X1 : $i]:
% 18.51/3.02 ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X0 @ X1))))
% 18.51/3.02 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X1 @ X0))
% 18.51/3.02 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 18.51/3.02 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl339])).
% 18.51/3.02 thf(zip_derived_cl342, plain,
% 18.51/3.02 (![X0 : $i, X1 : $i]:
% 18.51/3.02 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X0 @ X1))
% 18.51/3.02 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X1 @ X0))
% 18.51/3.02 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 18.51/3.02 inference('simplify nested equalities', [status(thm)],
% 18.51/3.02 [zip_derived_cl341])).
% 18.51/3.02 thf(zip_derived_cl1824, plain,
% 18.51/3.02 (((('#sk2') = ('#sk3'))
% 18.51/3.02 | ~ (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk2' @ '#sk3')))),
% 18.51/3.02 inference('sup-', [status(thm)], [zip_derived_cl192, zip_derived_cl342])).
% 18.51/3.02 thf(zip_derived_cl180, plain,
% 18.51/3.02 ( (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 18.51/3.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])).
% 18.51/3.02 thf(zip_derived_cl174, plain,
% 18.51/3.02 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 18.51/3.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])).
% 18.51/3.02 thf(zip_derived_cl182, plain,
% 18.51/3.02 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk2' @ '#sk3'))),
% 18.51/3.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl181])).
% 18.51/3.02 thf(zip_derived_cl1838, plain, ((('#sk2') = ('#sk3'))),
% 18.51/3.02 inference('demod', [status(thm)],
% 18.51/3.02 [zip_derived_cl1824, zip_derived_cl180, zip_derived_cl174,
% 18.51/3.02 zip_derived_cl182])).
% 18.51/3.02 thf(zip_derived_cl182, plain,
% 18.51/3.02 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ '#sk2' @ '#sk3'))),
% 18.51/3.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl181])).
% 18.51/3.02 thf(zip_derived_cl338, plain,
% 18.51/3.02 (![X0 : $i, X1 : $i]:
% 18.51/3.02 (~ (((X0) = (X1)))
% 18.51/3.02 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X0 @ X1)))),
% 18.51/3.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl336])).
% 18.51/3.02 thf(zip_derived_cl340, plain,
% 18.51/3.02 (![X0 : $i, X1 : $i]:
% 18.51/3.02 (((X0) != (X1))
% 18.51/3.02 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 18.51/3.02 (diffprop @ X0 @ X1)))),
% 18.51/3.02 inference('simplify nested equalities', [status(thm)],
% 18.51/3.02 [zip_derived_cl338])).
% 18.51/3.02 thf(zip_derived_cl1416, plain,
% 18.51/3.02 ((~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | ~ (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 18.51/3.02 | (('#sk2') != ('#sk3')))),
% 18.51/3.02 inference('sup-', [status(thm)], [zip_derived_cl182, zip_derived_cl340])).
% 18.51/3.02 thf(zip_derived_cl174, plain,
% 18.51/3.02 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 18.51/3.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])).
% 18.51/3.02 thf(zip_derived_cl180, plain,
% 18.51/3.02 ( (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 18.51/3.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])).
% 18.51/3.02 thf(zip_derived_cl1420, plain, ((('#sk2') != ('#sk3'))),
% 18.51/3.02 inference('demod', [status(thm)],
% 18.51/3.02 [zip_derived_cl1416, zip_derived_cl174, zip_derived_cl180])).
% 18.51/3.02 thf(zip_derived_cl1839, plain, ($false),
% 18.51/3.02 inference('simplify_reflect-', [status(thm)],
% 18.51/3.02 [zip_derived_cl1838, zip_derived_cl1420])).
% 18.51/3.02
% 18.51/3.02 % SZS output end Refutation
% 18.51/3.02
% 18.51/3.02
% 18.51/3.02 % Terminating...
% 19.11/3.22 % Runner terminated.
% 19.11/3.24 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------