%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM699^4 : TPTP v9.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.RcYDreyUIn true
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:48:03 PM UTC 2025
% Result : Theorem 89.43s 11.90s
% Output : Refutation 89.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM699^4 : TPTP v9.2.0. Released v7.1.0.
% 0.03/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.RcYDreyUIn true
% 0.14/0.35 % Computer : n020.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 16:17:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.36 % 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
% 0.59/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.59/0.76 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.59/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.59/0.78 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.59/0.78 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.59/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.59/0.78 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.79 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 89.43/11.90 % Solved by lams/40_b.comb.sh.
% 89.43/11.90 % done 275 iterations in 11.074s
% 89.43/11.90 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 89.43/11.90 % SZS output start Refutation
% 89.43/11.90 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
% 89.43/11.90 thf(nat_type, type, nat: $i).
% 89.43/11.90 thf(moreis_type, type, moreis: $i > $i > $o).
% 89.43/11.90 thf(lessis_type, type, lessis: $i > $i > $o).
% 89.43/11.90 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 89.43/11.90 thf(in_type, type, in: $i > $i > $o).
% 89.43/11.90 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 89.43/11.90 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 89.43/11.90 thf(emptyset_type, type, emptyset: $i).
% 89.43/11.90 thf(d_Sing_type, type, d_Sing: $i > $i).
% 89.43/11.90 thf(n_is_type, type, n_is: $i > $i > $o).
% 89.43/11.90 thf(imp_type, type, imp: $o > $o > $o).
% 89.43/11.90 thf('#sk2_type', type, '#sk2': $i).
% 89.43/11.90 thf(omega_type, type, omega: $i).
% 89.43/11.90 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 89.43/11.90 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 89.43/11.90 thf(binunion_type, type, binunion: $i > $i > $i).
% 89.43/11.90 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 89.43/11.90 thf(l_or_type, type, l_or: $o > $o > $o).
% 89.43/11.90 thf(ordsucc_type, type, ordsucc: $i > $i).
% 89.43/11.90 thf(d_not_type, type, d_not: $o > $o).
% 89.43/11.90 thf('#sk3_type', type, '#sk3': $i).
% 89.43/11.90 thf(iii_type, type, iii: $i > $i > $o).
% 89.43/11.90 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 89.43/11.90 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 89.43/11.90 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 89.43/11.90 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 89.43/11.90 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 89.43/11.90 thf(satz25c, conjecture,
% 89.43/11.90 (all_of @
% 89.43/11.90 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 89.43/11.90 ( ^[X0:$i]:
% 89.43/11.90 ( all_of @
% 89.43/11.90 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 89.43/11.90 ( ^[X1:$i]:
% 89.43/11.90 ( ( iii @ X1 @ X0 ) => ( lessis @ ( ordsucc @ X1 ) @ X0 ) ) ) ) ))).
% 89.43/11.90 thf(zf_stmt_0, negated_conjecture,
% 89.43/11.90 (~( all_of @
% 89.43/11.90 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 89.43/11.90 ( ^[X0:$i]:
% 89.43/11.90 ( all_of @
% 89.43/11.90 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 89.43/11.90 ( ^[X1:$i]:
% 89.43/11.90 ( ( iii @ X1 @ X0 ) => ( lessis @ ( ordsucc @ X1 ) @ X0 ) ) ) ) ) )),
% 89.43/11.90 inference('cnf.neg', [status(esa)], [satz25c])).
% 89.43/11.90 thf(zip_derived_cl217, plain,
% 89.43/11.90 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 89.43/11.90 (^[Y0 : $i]:
% 89.43/11.90 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 89.43/11.90 (^[Y1 : $i]:
% 89.43/11.90 (((iii @ Y1 @ Y0) => (lessis @ (ordsucc @ Y1) @ Y0)))))))),
% 89.43/11.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 89.43/11.90 thf(zip_derived_cl218, plain,
% 89.43/11.90 (~ (all_of @ ((('#C') @ in @ nat)) @
% 89.43/11.90 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ ('#S') @
% 89.43/11.90 ((('#B') @ ((('#B') @ (=>))) @ ((('#C') @ iii)))))) @
% 89.43/11.90 ((('#C') @ ((('#B') @ lessis @ ordsucc)))))))))),
% 89.43/11.90 inference('lams2combs', [status(thm)], [zip_derived_cl217])).
% 89.43/11.90 thf(def_nat, axiom,(( nat ) =
% 89.43/11.90 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))).
% 89.43/11.90 thf('0', plain,
% 89.43/11.90 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )),
% 89.43/11.90 define([status(thm)])).
% 89.43/11.90 thf(zip_derived_cl378, plain,
% 89.43/11.90 (~ (all_of @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 89.43/11.90 ((('#B') @ (all_of @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ ('#S') @
% 89.43/11.90 ((('#B') @ ((('#B') @ (=>))) @ ((('#C') @ iii)))))) @
% 89.43/11.90 ((('#C') @ ((('#B') @ lessis @ ordsucc)))))))))),
% 89.43/11.90 inference('rw', [status(thm)], [zip_derived_cl218, '0'])).
% 89.43/11.90 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 89.43/11.90 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 89.43/11.90 thf('1', plain,
% 89.43/11.90 (![X0:( $i > $o ),X1:( $i > $o )]:
% 89.43/11.90 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 89.43/11.90 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 89.43/11.90 inference('rw.lit', [status(esa)], [def_all_of])).
% 89.43/11.90 thf(zip_derived_cl379, plain,
% 89.43/11.90 (~ (((!!) @ (^[Y0 : $i]:
% 89.43/11.90 (((is_of @ Y0 @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 89.43/11.90 ((('#B') @ (all_of @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @
% 89.43/11.90 ((('#C') @ (!=) @ emptyset)))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ ('#S') @
% 89.43/11.90 ((('#B') @ ((('#B') @ (=>))) @
% 89.43/11.90 ((('#C') @ iii)))))) @
% 89.43/11.90 ((('#C') @ ((('#B') @ lessis @ ordsucc)))))) @
% 89.43/11.90 Y0)))))))),
% 89.43/11.90 inference('rw_clause', [status(thm)], [zip_derived_cl378, '1'])).
% 89.43/11.90 thf(zip_derived_cl380, plain,
% 89.43/11.90 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 89.43/11.90 ((('#C') @ is_of @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @
% 89.43/11.90 ((('#C') @ (!=) @ emptyset))))))))) @
% 89.43/11.90 ((('#B') @ (all_of @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ ('#S') @
% 89.43/11.90 ((('#B') @ ((('#B') @ (=>))) @
% 89.43/11.90 ((('#C') @ iii)))))) @
% 89.43/11.90 ((('#C') @ ((('#B') @ lessis @ ordsucc))))))))))))),
% 89.43/11.90 inference('comb-normalize', [status(thm)], [zip_derived_cl379])).
% 89.43/11.90 thf(zip_derived_cl381, plain,
% 89.43/11.90 (~ (((is_of @ '#sk2' @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 89.43/11.90 (all_of @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ iii @ '#sk2')))) @
% 89.43/11.90 ((('#C') @ ((('#B') @ lessis @ ordsucc)) @ '#sk2')))))))),
% 89.43/11.90 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl380])).
% 89.43/11.90 thf(def_is_of, axiom,(( is_of @ (X1)@ (X0)) = ((X0 @ X1)))).
% 89.43/11.90 thf('2', plain,
% 89.43/11.90 (![X0:( $i > $o ),X1:$i]: ( ( is_of @ X1 @ X0 ) = ( X0 @ X1 ) )),
% 89.43/11.90 define([status(thm)])).
% 89.43/11.90 thf(zip_derived_cl382, plain,
% 89.43/11.90 (~ (((in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 89.43/11.90 (all_of @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ iii @ '#sk2')))) @
% 89.43/11.90 ((('#C') @ ((('#B') @ lessis @ ordsucc)) @ '#sk2')))))))),
% 89.43/11.90 inference('rw', [status(thm)], [zip_derived_cl381, '2'])).
% 89.43/11.90 thf(zip_derived_cl384, plain,
% 89.43/11.90 (~ (all_of @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ iii @ '#sk2')))) @
% 89.43/11.90 ((('#C') @ ((('#B') @ lessis @ ordsucc)) @ '#sk2')))))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl382])).
% 89.43/11.90 thf(zip_derived_cl385, plain,
% 89.43/11.90 (~ (((!!) @ (^[Y0 : $i]:
% 89.43/11.90 (((is_of @ Y0 @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 89.43/11.90 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ iii @ '#sk2')))) @
% 89.43/11.90 ((('#C') @ ((('#B') @ lessis @ ordsucc)) @ '#sk2')) @
% 89.43/11.90 Y0)))))))),
% 89.43/11.90 inference('rw_clause', [status(thm)], [zip_derived_cl384, '1'])).
% 89.43/11.90 thf(zip_derived_cl386, plain,
% 89.43/11.90 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 89.43/11.90 ((('#C') @ is_of @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @
% 89.43/11.90 ((('#C') @ (!=) @ emptyset))))))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ iii @ '#sk2')))) @
% 89.43/11.90 ((('#C') @ ((('#B') @ lessis @ ordsucc)) @ '#sk2'))))))))),
% 89.43/11.90 inference('comb-normalize', [status(thm)], [zip_derived_cl385])).
% 89.43/11.90 thf(zip_derived_cl387, plain,
% 89.43/11.90 (~ (((is_of @ '#sk3' @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 89.43/11.90 (((iii @ '#sk3' @ '#sk2') => (lessis @ (ordsucc @ '#sk3') @ '#sk2')))))),
% 89.43/11.90 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl386])).
% 89.43/11.90 thf(def_ordsucc, axiom,(( ordsucc @ (X0)) =
% 89.43/11.90 ((binunion @ X0 @ (d_Sing @ X0))))).
% 89.43/11.90 thf('3', plain,
% 89.43/11.90 (![X0:$i]: ( ( ordsucc @ X0 ) = ( binunion @ X0 @ ( d_Sing @ X0 ) ) )),
% 89.43/11.90 define([status(thm)])).
% 89.43/11.90 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 89.43/11.90 thf('4', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 89.43/11.90 define([status(thm)])).
% 89.43/11.90 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 89.43/11.90 thf('5', plain,
% 89.43/11.90 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 89.43/11.90 define([status(thm)])).
% 89.43/11.90 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 89.43/11.90 thf('6', plain,
% 89.43/11.90 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 89.43/11.90 define([status(thm)])).
% 89.43/11.90 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))).
% 89.43/11.90 thf('7', plain,
% 89.43/11.90 (![X1:$i,X0:$i]:
% 89.43/11.90 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 89.43/11.90 define([status(thm)])).
% 89.43/11.90 thf(def_lessis, axiom,(( lessis @ (X0)@ (X1)) =
% 89.43/11.90 ((l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1))))).
% 89.43/11.90 thf('8', plain,
% 89.43/11.90 (![X1:$i,X0:$i]:
% 89.43/11.90 ( ( lessis @ X0 @ X1 ) =
% 89.43/11.90 ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
% 89.43/11.90 define([status(thm)])).
% 89.43/11.90 thf(zip_derived_cl388, plain,
% 89.43/11.90 (~ (((in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 89.43/11.90 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ '#sk2' @ '#sk3')) => (imp @
% 89.43/11.90 (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ '#sk2' @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')))) @
% 89.43/11.90 ($false)) @
% 89.43/11.90 (n_is @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')) @ '#sk2'))))))),
% 89.43/11.90 inference('rw', [status(thm)],
% 89.43/11.90 [zip_derived_cl387, '2', '3', '4', '5', '0', '6', '6', '7',
% 89.43/11.90 '7', '8'])).
% 89.43/11.90 thf(zip_derived_cl390, plain,
% 89.43/11.90 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ '#sk2' @ '#sk3')) => (imp @
% 89.43/11.90 (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ '#sk2' @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')))) @
% 89.43/11.90 ($false)) @
% 89.43/11.90 (n_is @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')) @ '#sk2'))))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl388])).
% 89.43/11.90 thf(zip_derived_cl392, plain,
% 89.43/11.90 (~ (imp @
% 89.43/11.90 (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ '#sk2' @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')))) @
% 89.43/11.90 ($false)) @
% 89.43/11.90 (n_is @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')) @ '#sk2'))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl390])).
% 89.43/11.90 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 89.43/11.90 thf('9', plain,
% 89.43/11.90 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 89.43/11.90 inference('rw.lit', [status(esa)], [def_imp])).
% 89.43/11.90 thf(zip_derived_cl393, plain,
% 89.43/11.90 (~ (((imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ '#sk2' @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')))) @
% 89.43/11.90 ($false)) => (n_is @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')) @
% 89.43/11.90 '#sk2')))),
% 89.43/11.90 inference('rw_clause', [status(thm)], [zip_derived_cl392, '9'])).
% 89.43/11.90 thf(zip_derived_cl394, plain,
% 89.43/11.90 ( (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ '#sk2' @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')))) @
% 89.43/11.90 ($false))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl393])).
% 89.43/11.90 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 89.43/11.90 thf('10', plain,
% 89.43/11.90 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 89.43/11.90 inference('rw.lit', [status(esa)], [def_imp])).
% 89.43/11.90 thf(zip_derived_cl396, plain,
% 89.43/11.90 ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ '#sk2' @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')))) =>
% 89.43/11.90 ($false)))),
% 89.43/11.90 inference('rw_clause', [status(thm)], [zip_derived_cl394, '10'])).
% 89.43/11.90 thf(zip_derived_cl397, plain,
% 89.43/11.90 ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ '#sk2' @ (binunion @ '#sk3' @ (d_Sing @ '#sk3'))))))),
% 89.43/11.90 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl396])).
% 89.43/11.90 thf(zip_derived_cl398, plain,
% 89.43/11.90 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ '#sk2' @ (binunion @ '#sk3' @ (d_Sing @ '#sk3'))))),
% 89.43/11.90 inference('simplify nested equalities', [status(thm)],
% 89.43/11.90 [zip_derived_cl397])).
% 89.43/11.90 thf(satz25a, axiom,
% 89.43/11.90 (all_of @
% 89.43/11.90 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 89.43/11.90 ( ^[X0:$i]:
% 89.43/11.90 ( all_of @
% 89.43/11.90 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 89.43/11.90 ( ^[X1:$i]:
% 89.43/11.90 ( ( d_29_ii @ X1 @ X0 ) => ( moreis @ X1 @ ( ordsucc @ X0 ) ) ) ) ) ))).
% 89.43/11.90 thf(zip_derived_cl213, plain,
% 89.43/11.90 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 89.43/11.90 (^[Y0 : $i]:
% 89.43/11.90 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 89.43/11.90 (^[Y1 : $i]:
% 89.43/11.90 (((d_29_ii @ Y1 @ Y0) => (moreis @ Y1 @ (ordsucc @ Y0))))))))),
% 89.43/11.90 inference('cnf', [status(esa)], [satz25a])).
% 89.43/11.90 thf(zip_derived_cl214, plain,
% 89.43/11.90 ( (all_of @ ((('#C') @ in @ nat)) @
% 89.43/11.90 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ ('#S') @
% 89.43/11.90 ((('#B') @ ((('#B') @ (=>))) @ ((('#C') @ d_29_ii)))))) @
% 89.43/11.90 ((('#B') @ ((('#C') @ moreis)) @ ordsucc)))))))),
% 89.43/11.90 inference('lams2combs', [status(thm)], [zip_derived_cl213])).
% 89.43/11.90 thf(zip_derived_cl697, plain,
% 89.43/11.90 ( (all_of @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 89.43/11.90 ((('#B') @ (all_of @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ ('#S') @
% 89.43/11.90 ((('#B') @ ((('#B') @ (=>))) @ ((('#C') @ d_29_ii)))))) @
% 89.43/11.90 ((('#B') @ ((('#C') @ moreis)) @ ordsucc)))))))),
% 89.43/11.90 inference('rw', [status(thm)], [zip_derived_cl214, '0'])).
% 89.43/11.90 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 89.43/11.90 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 89.43/11.90 thf('11', plain,
% 89.43/11.90 (![X0:( $i > $o ),X1:( $i > $o )]:
% 89.43/11.90 ( ( all_of @ X0 @ X1 ) <=>
% 89.43/11.90 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 89.43/11.90 inference('rw.lit', [status(esa)], [def_all_of])).
% 89.43/11.90 thf(zip_derived_cl698, plain,
% 89.43/11.90 ( (((!!) @ (^[Y0 : $i]:
% 89.43/11.90 (((is_of @ Y0 @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 89.43/11.90 ((('#B') @ (all_of @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @
% 89.43/11.90 ((('#C') @ (!=) @ emptyset)))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ ('#S') @
% 89.43/11.90 ((('#B') @ ((('#B') @ (=>))) @
% 89.43/11.90 ((('#C') @ d_29_ii)))))) @
% 89.43/11.90 ((('#B') @ ((('#C') @ moreis)) @ ordsucc)))) @
% 89.43/11.90 Y0)))))))),
% 89.43/11.90 inference('rw_clause', [status(thm)], [zip_derived_cl697, '11'])).
% 89.43/11.90 thf(zip_derived_cl699, plain,
% 89.43/11.90 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 89.43/11.90 ((('#C') @ is_of @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 89.43/11.90 ((('#B') @ (all_of @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ ('#S') @
% 89.43/11.90 ((('#B') @ ((('#B') @ (=>))) @
% 89.43/11.90 ((('#C') @ d_29_ii)))))) @
% 89.43/11.90 ((('#B') @ ((('#C') @ moreis)) @ ordsucc))))))))))),
% 89.43/11.90 inference('comb-normalize', [status(thm)], [zip_derived_cl698])).
% 89.43/11.90 thf(zip_derived_cl700, plain,
% 89.43/11.90 (![X2 : $i]:
% 89.43/11.90 (((is_of @ X2 @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 89.43/11.90 (all_of @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ d_29_ii @ X2)))) @
% 89.43/11.90 ((('#C') @ moreis @ (ordsucc @ X2))))))))),
% 89.43/11.90 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl699])).
% 89.43/11.90 thf(zip_derived_cl701, plain,
% 89.43/11.90 (![X2 : $i]:
% 89.43/11.90 (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 89.43/11.90 (all_of @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ d_29_ii @ X2)))) @
% 89.43/11.90 ((('#C') @ moreis @ (binunion @ X2 @ (d_Sing @ X2)))))))))),
% 89.43/11.90 inference('rw', [status(thm)], [zip_derived_cl700, '2', '3'])).
% 89.43/11.90 thf(zip_derived_cl702, plain,
% 89.43/11.90 (![X2 : $i]:
% 89.43/11.90 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | (all_of @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ d_29_ii @ X2)))) @
% 89.43/11.90 ((('#C') @ moreis @ (binunion @ X2 @ (d_Sing @ X2))))))))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl701])).
% 89.43/11.90 thf(zip_derived_cl703, plain,
% 89.43/11.90 (![X0 : $i]:
% 89.43/11.90 ( (((!!) @ (^[Y0 : $i]:
% 89.43/11.90 (((is_of @ Y0 @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 89.43/11.90 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ d_29_ii @ X0)))) @
% 89.43/11.90 ((('#C') @ moreis @ (binunion @ X0 @ (d_Sing @ X0)))) @
% 89.43/11.90 Y0)))))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('rw_clause', [status(thm)], [zip_derived_cl702, '11'])).
% 89.43/11.90 thf(zip_derived_cl704, plain,
% 89.43/11.90 (![X0 : $i]:
% 89.43/11.90 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 89.43/11.90 ((('#C') @ is_of @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @
% 89.43/11.90 ((('#C') @ (!=) @ emptyset))))))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ d_29_ii @ X0)))) @
% 89.43/11.90 ((('#C') @ moreis @ (binunion @ X0 @ (d_Sing @ X0))))))))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('comb-normalize', [status(thm)], [zip_derived_cl703])).
% 89.43/11.90 thf(zip_derived_cl705, plain,
% 89.43/11.90 (![X0 : $i, X2 : $i]:
% 89.43/11.90 ( (((is_of @ X2 @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 89.43/11.90 (((d_29_ii @ X2 @ X0) => (moreis @ X2 @
% 89.43/11.90 (binunion @ X0 @ (d_Sing @ X0)))))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl704])).
% 89.43/11.90 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) =
% 89.43/11.90 ((n_some @ (diffprop @ X0 @ X1))))).
% 89.43/11.90 thf('12', plain,
% 89.43/11.90 (![X1:$i,X0:$i]:
% 89.43/11.90 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 89.43/11.90 define([status(thm)])).
% 89.43/11.90 thf(def_moreis, axiom,(( moreis @ (X0)@ (X1)) =
% 89.43/11.90 ((l_or @ (d_29_ii @ X0 @ X1) @ (n_is @ X0 @ X1))))).
% 89.43/11.90 thf('13', plain,
% 89.43/11.90 (![X1:$i,X0:$i]:
% 89.43/11.90 ( ( moreis @ X0 @ X1 ) =
% 89.43/11.90 ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
% 89.43/11.90 define([status(thm)])).
% 89.43/11.90 thf(zip_derived_cl706, plain,
% 89.43/11.90 (![X0 : $i, X2 : $i]:
% 89.43/11.90 ( (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 89.43/11.90 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X2 @ X0)) => (imp @
% 89.43/11.90 (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X2 @ (binunion @ X0 @ (d_Sing @ X0)))) @
% 89.43/11.90 ($false)) @
% 89.43/11.90 (n_is @ X2 @ (binunion @ X0 @ (d_Sing @ X0))))))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('rw', [status(thm)],
% 89.43/11.90 [zip_derived_cl705, '2', '4', '5', '0', '6', '6', '12', '12',
% 89.43/11.90 '13'])).
% 89.43/11.90 thf(zip_derived_cl707, plain,
% 89.43/11.90 (![X0 : $i, X2 : $i]:
% 89.43/11.90 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X2 @ X0)) => (imp @
% 89.43/11.90 (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X2 @ (binunion @ X0 @ (d_Sing @ X0)))) @
% 89.43/11.90 ($false)) @
% 89.43/11.90 (n_is @ X2 @ (binunion @ X0 @ (d_Sing @ X0))))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl706])).
% 89.43/11.90 thf(zip_derived_cl708, plain,
% 89.43/11.90 (![X0 : $i, X2 : $i]:
% 89.43/11.90 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X2 @ X0))
% 89.43/11.90 | (imp @
% 89.43/11.90 (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X2 @ (binunion @ X0 @ (d_Sing @ X0)))) @
% 89.43/11.90 ($false)) @
% 89.43/11.90 (n_is @ X2 @ (binunion @ X0 @ (d_Sing @ X0))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl707])).
% 89.43/11.90 thf(zip_derived_cl709, plain,
% 89.43/11.90 (![X0 : $i, X1 : $i]:
% 89.43/11.90 ( (((imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ (binunion @ X1 @ (d_Sing @ X1)))) @
% 89.43/11.90 ($false)) => (n_is @ X0 @ (binunion @ X1 @ (d_Sing @ X1)))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X1)))),
% 89.43/11.90 inference('rw_clause', [status(thm)], [zip_derived_cl708, '10'])).
% 89.43/11.90 thf(zip_derived_cl710, plain,
% 89.43/11.90 (![X0 : $i, X1 : $i]:
% 89.43/11.90 (~ (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ (binunion @ X1 @ (d_Sing @ X1)))) @
% 89.43/11.90 ($false))
% 89.43/11.90 | (n_is @ X0 @ (binunion @ X1 @ (d_Sing @ X1)))
% 89.43/11.90 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X1))
% 89.43/11.90 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl709])).
% 89.43/11.90 thf(zip_derived_cl711, plain,
% 89.43/11.90 (![X0 : $i, X1 : $i]:
% 89.43/11.90 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ (binunion @ X1 @ (d_Sing @ X1)))) => ($false)))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X1))
% 89.43/11.90 | (n_is @ X0 @ (binunion @ X1 @ (d_Sing @ X1))))),
% 89.43/11.90 inference('rw_clause', [status(thm)], [zip_derived_cl710, '9'])).
% 89.43/11.90 thf(zip_derived_cl712, plain,
% 89.43/11.90 (![X0 : $i, X1 : $i]:
% 89.43/11.90 (~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ (binunion @ X1 @ (d_Sing @ X1))))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X1))
% 89.43/11.90 | (n_is @ X0 @ (binunion @ X1 @ (d_Sing @ X1))))),
% 89.43/11.90 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl711])).
% 89.43/11.90 thf(zip_derived_cl713, plain,
% 89.43/11.90 (![X0 : $i, X1 : $i]:
% 89.43/11.90 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ (binunion @ X1 @ (d_Sing @ X1))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X1))
% 89.43/11.90 | (n_is @ X0 @ (binunion @ X1 @ (d_Sing @ X1))))),
% 89.43/11.90 inference('simplify nested equalities', [status(thm)],
% 89.43/11.90 [zip_derived_cl712])).
% 89.43/11.90 thf(zip_derived_cl4072, plain,
% 89.43/11.90 (( (n_is @ '#sk2' @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')))
% 89.43/11.90 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ '#sk2' @ '#sk3'))
% 89.43/11.90 | ~ (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('sup+', [status(thm)], [zip_derived_cl398, zip_derived_cl713])).
% 89.43/11.90 thf(suc_p, axiom,
% 89.43/11.90 (all_of @
% 89.43/11.90 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 89.43/11.90 ( ^[X0:$i]: ( is_of @ ( ordsucc @ X0 ) @ ( ^[X1:$i]: ( in @ X1 @ nat ) ) ) ))).
% 89.43/11.90 thf(zip_derived_cl59, plain,
% 89.43/11.90 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 89.43/11.90 (^[Y0 : $i]: (is_of @ (ordsucc @ Y0) @ (^[Y1 : $i]: (in @ Y1 @ nat)))))),
% 89.43/11.90 inference('cnf', [status(esa)], [suc_p])).
% 89.43/11.90 thf(zip_derived_cl60, plain,
% 89.43/11.90 ( (all_of @ ((('#C') @ in @ nat)) @
% 89.43/11.90 ((('#C') @ ((('#B') @ is_of @ ordsucc)) @ ((('#C') @ in @ nat)))))),
% 89.43/11.90 inference('lams2combs', [status(thm)], [zip_derived_cl59])).
% 89.43/11.90 thf(zip_derived_cl324, plain,
% 89.43/11.90 ( (all_of @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 89.43/11.90 ((('#C') @ ((('#B') @ is_of @ ordsucc)) @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))),
% 89.43/11.90 inference('rw', [status(thm)], [zip_derived_cl60, '0'])).
% 89.43/11.90 thf(zip_derived_cl325, plain,
% 89.43/11.90 ( (((!!) @ (^[Y0 : $i]:
% 89.43/11.90 (((is_of @ Y0 @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 89.43/11.90 ((('#C') @ ((('#B') @ is_of @ ordsucc)) @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 89.43/11.90 Y0)))))))),
% 89.43/11.90 inference('rw_clause', [status(thm)], [zip_derived_cl324, '11'])).
% 89.43/11.90 thf(zip_derived_cl326, plain,
% 89.43/11.90 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 89.43/11.90 ((('#C') @ is_of @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 89.43/11.90 ((('#C') @ ((('#B') @ is_of @ ordsucc)) @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))))))),
% 89.43/11.90 inference('comb-normalize', [status(thm)], [zip_derived_cl325])).
% 89.43/11.90 thf(zip_derived_cl327, plain,
% 89.43/11.90 (![X2 : $i]:
% 89.43/11.90 (((is_of @ X2 @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 89.43/11.90 (is_of @ (ordsucc @ X2) @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))),
% 89.43/11.90 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl326])).
% 89.43/11.90 thf(zip_derived_cl328, plain,
% 89.43/11.90 (![X2 : $i]:
% 89.43/11.90 (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 89.43/11.90 (in @ (binunion @ X2 @ (d_Sing @ X2)) @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 89.43/11.90 inference('rw', [status(thm)], [zip_derived_cl327, '2', '2', '3'])).
% 89.43/11.90 thf(zip_derived_cl329, plain,
% 89.43/11.90 (![X2 : $i]:
% 89.43/11.90 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | (in @ (binunion @ X2 @ (d_Sing @ X2)) @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl328])).
% 89.43/11.90 thf(zip_derived_cl398, plain,
% 89.43/11.90 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ '#sk2' @ (binunion @ '#sk3' @ (d_Sing @ '#sk3'))))),
% 89.43/11.90 inference('simplify nested equalities', [status(thm)],
% 89.43/11.90 [zip_derived_cl397])).
% 89.43/11.90 thf(satz13, axiom,
% 89.43/11.90 (all_of @
% 89.43/11.90 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 89.43/11.90 ( ^[X0:$i]:
% 89.43/11.90 ( all_of @
% 89.43/11.90 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 89.43/11.90 ( ^[X1:$i]: ( ( moreis @ X0 @ X1 ) => ( lessis @ X1 @ X0 ) ) ) ) ))).
% 89.43/11.90 thf(zip_derived_cl107, plain,
% 89.43/11.90 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 89.43/11.90 (^[Y0 : $i]:
% 89.43/11.90 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 89.43/11.90 (^[Y1 : $i]: (((moreis @ Y0 @ Y1) => (lessis @ Y1 @ Y0)))))))),
% 89.43/11.90 inference('cnf', [status(esa)], [satz13])).
% 89.43/11.90 thf(zip_derived_cl108, plain,
% 89.43/11.90 ( (all_of @ ((('#C') @ in @ nat)) @
% 89.43/11.90 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ ('#S') @
% 89.43/11.90 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @
% 89.43/11.90 ((('#C') @ lessis)))))))),
% 89.43/11.90 inference('lams2combs', [status(thm)], [zip_derived_cl107])).
% 89.43/11.90 thf(zip_derived_cl476, plain,
% 89.43/11.90 ( (all_of @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 89.43/11.90 ((('#B') @ (all_of @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ ('#S') @
% 89.43/11.90 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @
% 89.43/11.90 ((('#C') @ lessis)))))))),
% 89.43/11.90 inference('rw', [status(thm)], [zip_derived_cl108, '0'])).
% 89.43/11.90 thf(zip_derived_cl477, plain,
% 89.43/11.90 ( (((!!) @ (^[Y0 : $i]:
% 89.43/11.90 (((is_of @ Y0 @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 89.43/11.90 ((('#B') @ (all_of @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @
% 89.43/11.90 ((('#C') @ (!=) @ emptyset)))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ ('#S') @
% 89.43/11.90 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @
% 89.43/11.90 ((('#C') @ lessis)))) @
% 89.43/11.90 Y0)))))))),
% 89.43/11.90 inference('rw_clause', [status(thm)], [zip_derived_cl476, '11'])).
% 89.43/11.90 thf(zip_derived_cl478, plain,
% 89.43/11.90 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 89.43/11.90 ((('#C') @ is_of @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 89.43/11.90 ((('#B') @ (all_of @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ ('#S') @
% 89.43/11.90 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @
% 89.43/11.90 ((('#C') @ lessis))))))))))),
% 89.43/11.90 inference('comb-normalize', [status(thm)], [zip_derived_cl477])).
% 89.43/11.90 thf(zip_derived_cl479, plain,
% 89.43/11.90 (![X2 : $i]:
% 89.43/11.90 (((is_of @ X2 @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 89.43/11.90 (all_of @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X2))) @
% 89.43/11.90 ((('#C') @ lessis @ X2)))))))),
% 89.43/11.90 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl478])).
% 89.43/11.90 thf(zip_derived_cl480, plain,
% 89.43/11.90 (![X2 : $i]:
% 89.43/11.90 (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 89.43/11.90 (all_of @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X2))) @
% 89.43/11.90 ((('#C') @ lessis @ X2)))))))),
% 89.43/11.90 inference('rw', [status(thm)], [zip_derived_cl479, '2'])).
% 89.43/11.90 thf(zip_derived_cl481, plain,
% 89.43/11.90 (![X2 : $i]:
% 89.43/11.90 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | (all_of @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X2))) @
% 89.43/11.90 ((('#C') @ lessis @ X2))))))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl480])).
% 89.43/11.90 thf(zip_derived_cl482, plain,
% 89.43/11.90 (![X0 : $i]:
% 89.43/11.90 ( (((!!) @ (^[Y0 : $i]:
% 89.43/11.90 (((is_of @ Y0 @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 89.43/11.90 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X0))) @
% 89.43/11.90 ((('#C') @ lessis @ X0)) @ Y0)))))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('rw_clause', [status(thm)], [zip_derived_cl481, '11'])).
% 89.43/11.90 thf(zip_derived_cl483, plain,
% 89.43/11.90 (![X0 : $i]:
% 89.43/11.90 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 89.43/11.90 ((('#C') @ is_of @
% 89.43/11.90 ((('#C') @ in @
% 89.43/11.90 (d_Sep @ omega @
% 89.43/11.90 ((('#C') @ (!=) @ emptyset))))))))) @
% 89.43/11.90 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X0))) @
% 89.43/11.90 ((('#C') @ lessis @ X0))))))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('comb-normalize', [status(thm)], [zip_derived_cl482])).
% 89.43/11.90 thf(zip_derived_cl484, plain,
% 89.43/11.90 (![X0 : $i, X2 : $i]:
% 89.43/11.90 ( (((is_of @ X2 @
% 89.43/11.90 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 89.43/11.90 (((moreis @ X0 @ X2) => (lessis @ X2 @ X0)))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl483])).
% 89.43/11.90 thf(zip_derived_cl485, plain,
% 89.43/11.90 (![X0 : $i, X2 : $i]:
% 89.43/11.90 ( (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 89.43/11.90 (((imp @
% 89.43/11.90 (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X2)) @
% 89.43/11.90 ($false)) @
% 89.43/11.90 (n_is @ X0 @ X2)) => (imp @
% 89.43/11.90 (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X2)) @
% 89.43/11.90 ($false)) @
% 89.43/11.90 (n_is @ X2 @ X0))))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('rw', [status(thm)],
% 89.43/11.90 [zip_derived_cl484, '2', '4', '5', '5', '0', '6', '12', '7',
% 89.43/11.90 '13', '8'])).
% 89.43/11.90 thf(zip_derived_cl486, plain,
% 89.43/11.90 (![X0 : $i, X2 : $i]:
% 89.43/11.90 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | (((imp @
% 89.43/11.90 (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X2)) @
% 89.43/11.90 ($false)) @
% 89.43/11.90 (n_is @ X0 @ X2)) => (imp @
% 89.43/11.90 (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X2)) @
% 89.43/11.90 ($false)) @
% 89.43/11.90 (n_is @ X2 @ X0))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])).
% 89.43/11.90 thf(zip_derived_cl487, plain,
% 89.43/11.90 (![X0 : $i, X2 : $i]:
% 89.43/11.90 (~ (imp @
% 89.43/11.90 (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X2)) @
% 89.43/11.90 ($false)) @
% 89.43/11.90 (n_is @ X0 @ X2))
% 89.43/11.90 | (imp @
% 89.43/11.90 (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X2)) @
% 89.43/11.90 ($false)) @
% 89.43/11.90 (n_is @ X2 @ X0))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl486])).
% 89.43/11.90 thf(zip_derived_cl488, plain,
% 89.43/11.90 (![X0 : $i, X1 : $i]:
% 89.43/11.90 (~ (((imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X1 @ X0)) @
% 89.43/11.90 ($false)) => (n_is @ X1 @ X0)))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | (imp @
% 89.43/11.90 (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X1 @ X0)) @
% 89.43/11.90 ($false)) @
% 89.43/11.90 (n_is @ X0 @ X1)))),
% 89.43/11.90 inference('rw_clause', [status(thm)], [zip_derived_cl487, '9'])).
% 89.43/11.90 thf(zip_derived_cl489, plain,
% 89.43/11.90 (![X0 : $i, X1 : $i]:
% 89.43/11.90 ( (((imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X1)) @
% 89.43/11.90 ($false)) => (n_is @ X1 @ X0)))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (((imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X1)) @
% 89.43/11.90 ($false)) => (n_is @ X0 @ X1))))),
% 89.43/11.90 inference('rw_clause', [status(thm)], [zip_derived_cl488, '10'])).
% 89.43/11.90 thf(zip_derived_cl490, plain,
% 89.43/11.90 (![X0 : $i, X1 : $i]:
% 89.43/11.90 (~ (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X1)) @
% 89.43/11.90 ($false))
% 89.43/11.90 | (n_is @ X1 @ X0)
% 89.43/11.90 | ~ (((imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X1)) @
% 89.43/11.90 ($false)) => (n_is @ X0 @ X1)))
% 89.43/11.90 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl489])).
% 89.43/11.90 thf(zip_derived_cl491, plain,
% 89.43/11.90 (![X0 : $i, X1 : $i]:
% 89.43/11.90 (~ (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X1)) @
% 89.43/11.90 ($false))
% 89.43/11.90 | (n_is @ X1 @ X0)
% 89.43/11.90 | ~ ((($true) => (n_is @ X0 @ X1)))
% 89.43/11.90 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('local_rewriting', [status(thm)], [zip_derived_cl490])).
% 89.43/11.90 thf(zip_derived_cl492, plain,
% 89.43/11.90 (![X0 : $i, X1 : $i]:
% 89.43/11.90 (~ (imp @
% 89.43/11.90 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X1)) @
% 89.43/11.90 ($false))
% 89.43/11.90 | (n_is @ X1 @ X0)
% 89.43/11.90 | ~ (n_is @ X0 @ X1)
% 89.43/11.90 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl491])).
% 89.43/11.90 thf(zip_derived_cl493, plain,
% 89.43/11.90 (![X0 : $i, X1 : $i]:
% 89.43/11.90 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X1)) => ($false)))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (n_is @ X0 @ X1)
% 89.43/11.90 | (n_is @ X1 @ X0))),
% 89.43/11.90 inference('rw_clause', [status(thm)], [zip_derived_cl492, '9'])).
% 89.43/11.90 thf(zip_derived_cl494, plain,
% 89.43/11.90 (![X0 : $i, X1 : $i]:
% 89.43/11.90 (~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X1))))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (n_is @ X0 @ X1)
% 89.43/11.90 | (n_is @ X1 @ X0))),
% 89.43/11.90 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl493])).
% 89.43/11.90 thf(zip_derived_cl495, plain,
% 89.43/11.90 (![X0 : $i, X1 : $i]:
% 89.43/11.90 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ X0 @ X1))
% 89.43/11.90 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (n_is @ X0 @ X1)
% 89.43/11.90 | (n_is @ X1 @ X0))),
% 89.43/11.90 inference('simplify nested equalities', [status(thm)],
% 89.43/11.90 [zip_derived_cl494])).
% 89.43/11.90 thf(zip_derived_cl2676, plain,
% 89.43/11.90 (( (n_is @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')) @ '#sk2')
% 89.43/11.90 | ~ (n_is @ '#sk2' @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')))
% 89.43/11.90 | ~ (in @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')) @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('sup+', [status(thm)], [zip_derived_cl398, zip_derived_cl495])).
% 89.43/11.90 thf(zip_derived_cl395, plain,
% 89.43/11.90 (~ (n_is @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')) @ '#sk2')),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl393])).
% 89.43/11.90 thf(zip_derived_cl383, plain,
% 89.43/11.90 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl382])).
% 89.43/11.90 thf(zip_derived_cl2679, plain,
% 89.43/11.90 ((~ (n_is @ '#sk2' @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')))
% 89.43/11.90 | ~ (in @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')) @
% 89.43/11.90 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 89.43/11.90 inference('demod', [status(thm)],
% 89.43/11.90 [zip_derived_cl2676, zip_derived_cl395, zip_derived_cl383])).
% 89.43/11.90 thf(zip_derived_cl2682, plain,
% 89.43/11.90 ((~ (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 89.43/11.90 | ~ (n_is @ '#sk2' @ (binunion @ '#sk3' @ (d_Sing @ '#sk3'))))),
% 89.43/11.90 inference('sup-', [status(thm)], [zip_derived_cl329, zip_derived_cl2679])).
% 89.43/11.90 thf(zip_derived_cl389, plain,
% 89.43/11.90 ( (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl388])).
% 89.43/11.90 thf(zip_derived_cl2687, plain,
% 89.43/11.90 (~ (n_is @ '#sk2' @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')))),
% 89.43/11.90 inference('demod', [status(thm)], [zip_derived_cl2682, zip_derived_cl389])).
% 89.43/11.90 thf(zip_derived_cl391, plain,
% 89.43/11.90 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 89.43/11.90 (diffprop @ '#sk2' @ '#sk3'))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl390])).
% 89.43/11.90 thf(zip_derived_cl389, plain,
% 89.43/11.90 ( (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl388])).
% 89.43/11.90 thf(zip_derived_cl383, plain,
% 89.43/11.90 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 89.43/11.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl382])).
% 89.43/11.90 thf(zip_derived_cl4083, plain, ($false),
% 89.43/11.90 inference('demod', [status(thm)],
% 89.43/11.90 [zip_derived_cl4072, zip_derived_cl2687, zip_derived_cl391,
% 89.43/11.90 zip_derived_cl389, zip_derived_cl383])).
% 89.43/11.90
% 89.43/11.90 % SZS output end Refutation
% 89.43/11.90
% 89.43/11.90
% 89.43/11.90 % Terminating...
% 90.19/12.01 % Runner terminated.
% 90.19/12.03 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------