%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM655^4 : 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.EiM2bdu9Rd true
% Computer : n002.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 10.29s 1.93s
% Output : Refutation 10.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM655^4 : TPTP v9.2.0. Released v7.1.0.
% 0.03/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.EiM2bdu9Rd true
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 16:38:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.57/0.69 % Total configuration time : 828
% 0.57/0.69 % Estimated wc time : 1656
% 0.57/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.57/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.57/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.58/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.58/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.58/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.58/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 4.52/1.18 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 10.29/1.93 % Solved by lams/40_b.comb.sh.
% 10.29/1.93 % done 173 iterations in 1.135s
% 10.29/1.93 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 10.29/1.93 % SZS output start Refutation
% 10.29/1.93 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
% 10.29/1.93 thf(nat_type, type, nat: $i).
% 10.29/1.93 thf('#sk3_type', type, '#sk3': $i).
% 10.29/1.93 thf('#sk2_type', type, '#sk2': $i).
% 10.29/1.93 thf(moreis_type, type, moreis: $i > $i > $o).
% 10.29/1.93 thf(lessis_type, type, lessis: $i > $i > $o).
% 10.29/1.93 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 10.29/1.93 thf(in_type, type, in: $i > $i > $o).
% 10.29/1.93 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 10.29/1.93 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 10.29/1.93 thf(emptyset_type, type, emptyset: $i).
% 10.29/1.93 thf(n_is_type, type, n_is: $i > $i > $o).
% 10.29/1.93 thf(imp_type, type, imp: $o > $o > $o).
% 10.29/1.93 thf(omega_type, type, omega: $i).
% 10.29/1.93 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 10.29/1.93 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 10.29/1.93 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 10.29/1.93 thf(l_or_type, type, l_or: $o > $o > $o).
% 10.29/1.93 thf(d_not_type, type, d_not: $o > $o).
% 10.29/1.93 thf(iii_type, type, iii: $i > $i > $o).
% 10.29/1.93 thf(e_is_type, type, e_is: $i > $i > $i > $o).
% 10.29/1.93 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 10.29/1.93 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 10.29/1.93 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 10.29/1.93 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 10.29/1.93 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 10.29/1.93 thf(satz10f, conjecture,
% 10.29/1.93 (all_of @
% 10.29/1.93 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 10.29/1.93 ( ^[X0:$i]:
% 10.29/1.93 ( all_of @
% 10.29/1.93 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 10.29/1.93 ( ^[X1:$i]: ( ( d_not @ ( iii @ X0 @ X1 ) ) => ( moreis @ X0 @ X1 ) ) ) ) ))).
% 10.29/1.93 thf(zf_stmt_0, negated_conjecture,
% 10.29/1.93 (~( all_of @
% 10.29/1.93 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 10.29/1.93 ( ^[X0:$i]:
% 10.29/1.93 ( all_of @
% 10.29/1.93 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 10.29/1.93 ( ^[X1:$i]:
% 10.29/1.93 ( ( d_not @ ( iii @ X0 @ X1 ) ) => ( moreis @ X0 @ X1 ) ) ) ) ) )),
% 10.29/1.93 inference('cnf.neg', [status(esa)], [satz10f])).
% 10.29/1.93 thf(zip_derived_cl99, plain,
% 10.29/1.93 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 10.29/1.93 (^[Y0 : $i]:
% 10.29/1.93 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 10.29/1.93 (^[Y1 : $i]: (((d_not @ (iii @ Y0 @ Y1)) => (moreis @ Y0 @ Y1)))))))),
% 10.29/1.93 inference('cnf', [status(esa)], [zf_stmt_0])).
% 10.29/1.93 thf(zip_derived_cl100, plain,
% 10.29/1.93 (~ (all_of @ ((('#C') @ in @ nat)) @
% 10.29/1.93 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 10.29/1.93 ((('#S') @ ((('#B') @ ('#S') @
% 10.29/1.93 ((('#B') @ ((('#B') @ (=>))) @
% 10.29/1.93 ((('#B') @ ((('#B') @ d_not)) @ iii)))))) @
% 10.29/1.93 moreis)))))),
% 10.29/1.93 inference('lams2combs', [status(thm)], [zip_derived_cl99])).
% 10.29/1.93 thf(def_nat, axiom,(( nat ) =
% 10.29/1.93 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))).
% 10.29/1.93 thf('0', plain,
% 10.29/1.93 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )),
% 10.29/1.93 define([status(thm)])).
% 10.29/1.93 thf(zip_derived_cl167, plain,
% 10.29/1.93 (~ (all_of @
% 10.29/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 10.29/1.93 ((('#B') @ (all_of @
% 10.29/1.93 ((('#C') @ in @
% 10.29/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 10.29/1.93 ((('#S') @ ((('#B') @ ('#S') @
% 10.29/1.93 ((('#B') @ ((('#B') @ (=>))) @
% 10.29/1.93 ((('#B') @ ((('#B') @ d_not)) @ iii)))))) @
% 10.29/1.93 moreis)))))),
% 10.29/1.93 inference('rw', [status(thm)], [zip_derived_cl100, '0'])).
% 10.29/1.93 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 10.29/1.93 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 10.29/1.93 thf('1', plain,
% 10.29/1.93 (![X0:( $i > $o ),X1:( $i > $o )]:
% 10.29/1.93 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 10.29/1.93 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 10.29/1.93 inference('rw.lit', [status(esa)], [def_all_of])).
% 10.29/1.93 thf(zip_derived_cl168, plain,
% 10.29/1.93 (~ (((!!) @ (^[Y0 : $i]:
% 10.29/1.93 (((is_of @ Y0 @
% 10.29/1.93 ((('#C') @ in @
% 10.29/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 10.29/1.93 ((('#B') @ (all_of @
% 10.29/1.93 ((('#C') @ in @
% 10.29/1.93 (d_Sep @ omega @
% 10.29/1.93 ((('#C') @ (!=) @ emptyset)))))) @
% 10.29/1.93 ((('#S') @ ((('#B') @ ('#S') @
% 10.29/1.93 ((('#B') @ ((('#B') @ (=>))) @
% 10.29/1.93 ((('#B') @ ((('#B') @ d_not)) @ iii)))))) @
% 10.29/1.93 moreis)) @
% 10.29/1.93 Y0)))))))),
% 10.29/1.93 inference('rw_clause', [status(thm)], [zip_derived_cl167, '1'])).
% 10.29/1.93 thf(zip_derived_cl169, plain,
% 10.29/1.93 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 10.29/1.93 ((('#C') @ is_of @
% 10.29/1.93 ((('#C') @ in @
% 10.29/1.93 (d_Sep @ omega @
% 10.29/1.93 ((('#C') @ (!=) @ emptyset))))))))) @
% 10.29/1.93 ((('#B') @ (all_of @
% 10.29/1.93 ((('#C') @ in @
% 10.29/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 10.29/1.93 ((('#S') @ ((('#B') @ ('#S') @
% 10.29/1.93 ((('#B') @ ((('#B') @ (=>))) @
% 10.29/1.93 ((('#B') @ ((('#B') @ d_not)) @ iii)))))) @
% 10.29/1.93 moreis))))))))),
% 10.29/1.93 inference('comb-normalize', [status(thm)], [zip_derived_cl168])).
% 10.29/1.93 thf(zip_derived_cl170, plain,
% 10.29/1.93 (~ (((is_of @ '#sk2' @
% 10.29/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 10.29/1.93 (all_of @
% 10.29/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 10.29/1.93 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (iii @ '#sk2'))))) @
% 10.29/1.93 (moreis @ '#sk2'))))))),
% 10.29/1.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl169])).
% 10.29/1.93 thf(def_is_of, axiom,(( is_of @ (X1)@ (X0)) = ((X0 @ X1)))).
% 10.29/1.93 thf('2', plain,
% 10.29/1.93 (![X0:( $i > $o ),X1:$i]: ( ( is_of @ X1 @ X0 ) = ( X0 @ X1 ) )),
% 10.29/1.93 define([status(thm)])).
% 10.29/1.93 thf(zip_derived_cl171, plain,
% 10.29/1.93 (~ (((in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 10.29/1.93 (all_of @
% 10.29/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 10.29/1.93 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (iii @ '#sk2'))))) @
% 10.29/1.93 (moreis @ '#sk2'))))))),
% 10.29/1.93 inference('rw', [status(thm)], [zip_derived_cl170, '2'])).
% 10.29/1.93 thf(zip_derived_cl173, plain,
% 10.29/1.93 (~ (all_of @
% 10.29/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 10.29/1.93 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (iii @ '#sk2'))))) @
% 10.29/1.93 (moreis @ '#sk2'))))),
% 10.29/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl171])).
% 10.29/1.93 thf(zip_derived_cl174, plain,
% 10.29/1.93 (~ (((!!) @ (^[Y0 : $i]:
% 10.29/1.93 (((is_of @ Y0 @
% 10.29/1.93 ((('#C') @ in @
% 10.29/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 10.29/1.93 ((('#S') @ ((('#B') @ (=>) @
% 10.29/1.93 ((('#B') @ d_not @ (iii @ '#sk2'))))) @
% 10.29/1.93 (moreis @ '#sk2') @ Y0)))))))),
% 10.29/1.93 inference('rw_clause', [status(thm)], [zip_derived_cl173, '1'])).
% 10.29/1.93 thf(zip_derived_cl175, plain,
% 10.29/1.93 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 10.29/1.93 ((('#C') @ is_of @
% 10.29/1.93 ((('#C') @ in @
% 10.29/1.93 (d_Sep @ omega @
% 10.29/1.93 ((('#C') @ (!=) @ emptyset))))))))) @
% 10.29/1.93 ((('#S') @ ((('#B') @ (=>) @
% 10.29/1.93 ((('#B') @ d_not @ (iii @ '#sk2'))))) @
% 10.29/1.93 (moreis @ '#sk2')))))))),
% 10.29/1.93 inference('comb-normalize', [status(thm)], [zip_derived_cl174])).
% 10.29/1.93 thf(zip_derived_cl176, plain,
% 10.29/1.93 (~ (((is_of @ '#sk3' @
% 10.29/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 10.29/1.93 (((d_not @ (iii @ '#sk2' @ '#sk3')) => (moreis @ '#sk2' @ '#sk3')))))),
% 10.29/1.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl175])).
% 10.29/1.93 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 10.29/1.93 thf('3', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 10.29/1.93 define([status(thm)])).
% 10.29/1.93 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 10.29/1.93 thf('4', plain,
% 10.29/1.93 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 10.29/1.93 define([status(thm)])).
% 10.29/1.93 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))).
% 10.29/1.93 thf('5', plain,
% 10.29/1.93 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )),
% 10.29/1.93 define([status(thm)])).
% 10.29/1.93 thf(def_n_is, axiom,(( n_is @ (X0)@ (X1)) = ((e_is @ nat @ X0 @ X1)))).
% 10.29/1.93 thf('6', plain,
% 10.29/1.93 (![X1:$i,X0:$i]: ( ( n_is @ X0 @ X1 ) = ( e_is @ nat @ X0 @ X1 ) )),
% 10.29/1.93 define([status(thm)])).
% 10.29/1.93 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 10.29/1.93 thf('7', plain,
% 10.29/1.93 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 10.29/1.93 define([status(thm)])).
% 10.29/1.93 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) =
% 10.29/1.93 ((n_some @ (diffprop @ X0 @ X1))))).
% 10.29/1.93 thf('8', plain,
% 10.29/1.93 (![X1:$i,X0:$i]:
% 10.29/1.93 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 10.29/1.93 define([status(thm)])).
% 10.29/1.93 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))).
% 10.29/1.93 thf('9', plain,
% 10.29/1.93 (![X1:$i,X0:$i]:
% 10.29/1.93 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 10.29/1.93 define([status(thm)])).
% 10.29/1.93 thf(def_moreis, axiom,(( moreis @ (X0)@ (X1)) =
% 10.29/1.93 ((l_or @ (d_29_ii @ X0 @ X1) @ (n_is @ X0 @ X1))))).
% 10.29/1.93 thf('10', plain,
% 10.29/1.93 (![X1:$i,X0:$i]:
% 10.29/1.93 ( ( moreis @ X0 @ X1 ) =
% 10.29/1.93 ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
% 10.29/1.93 define([status(thm)])).
% 10.29/1.93 thf(zip_derived_cl177, plain,
% 10.29/1.93 (~ (((in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 10.29/1.93 (((imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk3' @ '#sk2')) @
% 10.29/1.93 ($false)) => (imp @
% 10.29/1.93 (imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk2' @ '#sk3')) @
% 10.29/1.93 ($false)) @
% 10.29/1.93 ((('#sk2') = ('#sk3'))))))))),
% 10.29/1.93 inference('rw', [status(thm)],
% 10.29/1.93 [zip_derived_cl176, '2', '3', '3', '4', '5', '0', '6', '7',
% 10.29/1.93 '7', '8', '9', '10'])).
% 10.29/1.93 thf(zip_derived_cl179, plain,
% 10.29/1.93 (~ (((imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk3' @ '#sk2')) @
% 10.29/1.93 ($false)) => (imp @
% 10.29/1.93 (imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk2' @ '#sk3')) @
% 10.29/1.93 ($false)) @
% 10.29/1.93 ((('#sk2') = ('#sk3'))))))),
% 10.29/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl177])).
% 10.29/1.93 thf(zip_derived_cl181, plain,
% 10.29/1.93 (~ (imp @
% 10.29/1.93 (imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk2' @ '#sk3')) @
% 10.29/1.93 ($false)) @
% 10.29/1.93 ((('#sk2') = ('#sk3'))))),
% 10.29/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])).
% 10.29/1.93 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 10.29/1.93 thf('11', plain,
% 10.29/1.93 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 10.29/1.93 inference('rw.lit', [status(esa)], [def_imp])).
% 10.29/1.93 thf(zip_derived_cl183, plain,
% 10.29/1.93 (~ (((imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk2' @ '#sk3')) @
% 10.29/1.93 ($false)) => ((('#sk2') = ('#sk3')))))),
% 10.29/1.93 inference('rw_clause', [status(thm)], [zip_derived_cl181, '11'])).
% 10.29/1.93 thf(zip_derived_cl186, plain,
% 10.29/1.93 ( (imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk2' @ '#sk3')) @
% 10.29/1.93 ($false))),
% 10.29/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl183])).
% 10.29/1.93 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 10.29/1.93 thf('12', plain,
% 10.29/1.93 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 10.29/1.93 inference('rw.lit', [status(esa)], [def_imp])).
% 10.29/1.93 thf(zip_derived_cl188, plain,
% 10.29/1.93 ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk2' @ '#sk3')) => ($false)))),
% 10.29/1.93 inference('rw_clause', [status(thm)], [zip_derived_cl186, '12'])).
% 10.29/1.93 thf(zip_derived_cl190, plain,
% 10.29/1.93 ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk2' @ '#sk3'))))),
% 10.29/1.93 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl188])).
% 10.29/1.93 thf(zip_derived_cl191, plain,
% 10.29/1.93 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk2' @ '#sk3'))),
% 10.29/1.93 inference('simplify nested equalities', [status(thm)],
% 10.29/1.93 [zip_derived_cl190])).
% 10.29/1.93 thf(zip_derived_cl180, plain,
% 10.29/1.93 ( (imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk3' @ '#sk2')) @
% 10.29/1.93 ($false))),
% 10.29/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])).
% 10.29/1.93 thf(zip_derived_cl182, plain,
% 10.29/1.93 ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk3' @ '#sk2')) => ($false)))),
% 10.29/1.93 inference('rw_clause', [status(thm)], [zip_derived_cl180, '12'])).
% 10.29/1.93 thf(zip_derived_cl184, plain,
% 10.29/1.93 ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk3' @ '#sk2'))))),
% 10.29/1.93 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl182])).
% 10.29/1.93 thf(zip_derived_cl185, plain,
% 10.29/1.93 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk3' @ '#sk2'))),
% 10.29/1.93 inference('simplify nested equalities', [status(thm)],
% 10.29/1.93 [zip_derived_cl184])).
% 10.29/1.93 thf(satz10e, axiom,
% 10.29/1.93 (all_of @
% 10.29/1.93 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 10.29/1.93 ( ^[X0:$i]:
% 10.29/1.93 ( all_of @
% 10.29/1.93 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 10.29/1.93 ( ^[X1:$i]:
% 10.29/1.93 ( ( d_not @ ( d_29_ii @ X0 @ X1 ) ) => ( lessis @ X0 @ X1 ) ) ) ) ))).
% 10.29/1.93 thf(zip_derived_cl97, plain,
% 10.29/1.93 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 10.29/1.93 (^[Y0 : $i]:
% 10.29/1.93 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 10.29/1.93 (^[Y1 : $i]:
% 10.29/1.93 (((d_not @ (d_29_ii @ Y0 @ Y1)) => (lessis @ Y0 @ Y1)))))))),
% 10.29/1.93 inference('cnf', [status(esa)], [satz10e])).
% 10.29/1.93 thf(zip_derived_cl98, plain,
% 10.29/1.93 ( (all_of @ ((('#C') @ in @ nat)) @
% 10.29/1.93 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 10.29/1.93 ((('#S') @ ((('#B') @ ('#S') @
% 10.29/1.93 ((('#B') @ ((('#B') @ (=>))) @
% 10.29/1.93 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))) @
% 10.29/1.93 lessis)))))),
% 10.29/1.93 inference('lams2combs', [status(thm)], [zip_derived_cl97])).
% 10.29/1.93 thf(zip_derived_cl364, plain,
% 10.29/1.93 ( (all_of @
% 10.29/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 10.29/1.93 ((('#B') @ (all_of @
% 10.29/1.93 ((('#C') @ in @
% 10.29/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 10.29/1.93 ((('#S') @ ((('#B') @ ('#S') @
% 10.29/1.93 ((('#B') @ ((('#B') @ (=>))) @
% 10.29/1.93 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))) @
% 10.29/1.93 lessis)))))),
% 10.29/1.93 inference('rw', [status(thm)], [zip_derived_cl98, '0'])).
% 10.29/1.93 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 10.29/1.93 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 10.29/1.93 thf('13', plain,
% 10.29/1.93 (![X0:( $i > $o ),X1:( $i > $o )]:
% 10.29/1.93 ( ( all_of @ X0 @ X1 ) <=>
% 10.29/1.93 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 10.29/1.93 inference('rw.lit', [status(esa)], [def_all_of])).
% 10.29/1.93 thf(zip_derived_cl365, plain,
% 10.29/1.93 ( (((!!) @ (^[Y0 : $i]:
% 10.29/1.93 (((is_of @ Y0 @
% 10.29/1.93 ((('#C') @ in @
% 10.29/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 10.29/1.93 ((('#B') @ (all_of @
% 10.29/1.93 ((('#C') @ in @
% 10.29/1.93 (d_Sep @ omega @
% 10.29/1.93 ((('#C') @ (!=) @ emptyset)))))) @
% 10.29/1.93 ((('#S') @ ((('#B') @ ('#S') @
% 10.29/1.93 ((('#B') @ ((('#B') @ (=>))) @
% 10.29/1.93 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))) @
% 10.29/1.93 lessis)) @
% 10.29/1.93 Y0)))))))),
% 10.29/1.93 inference('rw_clause', [status(thm)], [zip_derived_cl364, '13'])).
% 10.29/1.93 thf(zip_derived_cl366, plain,
% 10.29/1.93 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 10.29/1.93 ((('#C') @ is_of @
% 10.29/1.93 ((('#C') @ in @
% 10.29/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 10.29/1.93 ((('#B') @ (all_of @
% 10.29/1.93 ((('#C') @ in @
% 10.29/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 10.29/1.93 ((('#S') @ ((('#B') @ ('#S') @
% 10.29/1.93 ((('#B') @ ((('#B') @ (=>))) @
% 10.29/1.93 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))) @
% 10.29/1.93 lessis))))))))),
% 10.29/1.93 inference('comb-normalize', [status(thm)], [zip_derived_cl365])).
% 10.29/1.93 thf(zip_derived_cl367, plain,
% 10.29/1.93 (![X2 : $i]:
% 10.29/1.93 (((is_of @ X2 @
% 10.29/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 10.29/1.93 (all_of @
% 10.29/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 10.29/1.93 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (d_29_ii @ X2))))) @
% 10.29/1.93 (lessis @ X2))))))),
% 10.29/1.93 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl366])).
% 10.29/1.93 thf(zip_derived_cl368, plain,
% 10.29/1.93 (![X2 : $i]:
% 10.29/1.93 (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 10.29/1.93 (all_of @
% 10.29/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 10.29/1.93 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (d_29_ii @ X2))))) @
% 10.29/1.93 (lessis @ X2))))))),
% 10.29/1.93 inference('rw', [status(thm)], [zip_derived_cl367, '2'])).
% 10.29/1.93 thf(zip_derived_cl369, plain,
% 10.29/1.93 (![X2 : $i]:
% 10.29/1.93 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | (all_of @
% 10.29/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 10.29/1.93 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (d_29_ii @ X2))))) @
% 10.29/1.93 (lessis @ X2)))))),
% 10.29/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl368])).
% 10.29/1.93 thf(zip_derived_cl370, plain,
% 10.29/1.93 (![X0 : $i]:
% 10.29/1.93 ( (((!!) @ (^[Y0 : $i]:
% 10.29/1.93 (((is_of @ Y0 @
% 10.29/1.93 ((('#C') @ in @
% 10.29/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 10.29/1.93 ((('#S') @ ((('#B') @ (=>) @
% 10.29/1.93 ((('#B') @ d_not @ (d_29_ii @ X0))))) @
% 10.29/1.93 (lessis @ X0) @ Y0)))))))
% 10.29/1.93 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 10.29/1.93 inference('rw_clause', [status(thm)], [zip_derived_cl369, '13'])).
% 10.29/1.93 thf(zip_derived_cl371, plain,
% 10.29/1.93 (![X0 : $i]:
% 10.29/1.93 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 10.29/1.93 ((('#C') @ is_of @
% 10.29/1.93 ((('#C') @ in @
% 10.29/1.93 (d_Sep @ omega @
% 10.29/1.93 ((('#C') @ (!=) @ emptyset))))))))) @
% 10.29/1.93 ((('#S') @ ((('#B') @ (=>) @
% 10.29/1.93 ((('#B') @ d_not @ (d_29_ii @ X0))))) @
% 10.29/1.93 (lessis @ X0)))))))
% 10.29/1.93 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 10.29/1.93 inference('comb-normalize', [status(thm)], [zip_derived_cl370])).
% 10.29/1.93 thf(zip_derived_cl372, plain,
% 10.29/1.93 (![X0 : $i, X2 : $i]:
% 10.29/1.93 ( (((is_of @ X2 @
% 10.29/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 10.29/1.93 (((d_not @ (d_29_ii @ X0 @ X2)) => (lessis @ X0 @ X2)))))
% 10.29/1.93 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 10.29/1.93 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl371])).
% 10.29/1.93 thf(def_lessis, axiom,(( lessis @ (X0)@ (X1)) =
% 10.29/1.93 ((l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1))))).
% 10.29/1.93 thf('14', plain,
% 10.29/1.93 (![X1:$i,X0:$i]:
% 10.29/1.93 ( ( lessis @ X0 @ X1 ) =
% 10.29/1.93 ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
% 10.29/1.93 define([status(thm)])).
% 10.29/1.93 thf(zip_derived_cl373, plain,
% 10.29/1.93 (![X0 : $i, X2 : $i]:
% 10.29/1.93 ( (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 10.29/1.93 (((imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X0 @ X2)) @
% 10.29/1.93 ($false)) => (imp @
% 10.29/1.93 (imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X2 @ X0)) @
% 10.29/1.93 ($false)) @
% 10.29/1.93 (((X0) = (X2))))))))
% 10.29/1.93 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 10.29/1.93 inference('rw', [status(thm)],
% 10.29/1.93 [zip_derived_cl372, '2', '3', '3', '4', '5', '0', '6', '7',
% 10.29/1.93 '7', '8', '9', '14'])).
% 10.29/1.93 thf(zip_derived_cl374, plain,
% 10.29/1.93 (![X0 : $i, X2 : $i]:
% 10.29/1.93 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | (((imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X0 @ X2)) @
% 10.29/1.93 ($false)) => (imp @
% 10.29/1.93 (imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X2 @ X0)) @
% 10.29/1.93 ($false)) @
% 10.29/1.93 (((X0) = (X2))))))
% 10.29/1.93 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 10.29/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl373])).
% 10.29/1.93 thf(zip_derived_cl375, plain,
% 10.29/1.93 (![X0 : $i, X2 : $i]:
% 10.29/1.93 (~ (imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X0 @ X2)) @
% 10.29/1.93 ($false))
% 10.29/1.93 | (imp @
% 10.29/1.93 (imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X2 @ X0)) @
% 10.29/1.93 ($false)) @
% 10.29/1.93 (((X0) = (X2))))
% 10.29/1.93 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | ~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 10.29/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl374])).
% 10.29/1.93 thf(zip_derived_cl376, plain,
% 10.29/1.93 (![X0 : $i, X1 : $i]:
% 10.29/1.93 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X1 @ X0)) => ($false)))
% 10.29/1.93 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | (imp @
% 10.29/1.93 (imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X0 @ X1)) @
% 10.29/1.93 ($false)) @
% 10.29/1.93 (((X1) = (X0)))))),
% 10.29/1.93 inference('rw_clause', [status(thm)], [zip_derived_cl375, '11'])).
% 10.29/1.93 thf(zip_derived_cl377, plain,
% 10.29/1.93 (![X0 : $i, X1 : $i]:
% 10.29/1.93 (~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X1 @ X0))))
% 10.29/1.93 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | (imp @
% 10.29/1.93 (imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X0 @ X1)) @
% 10.29/1.93 ($false)) @
% 10.29/1.93 (((X1) = (X0)))))),
% 10.29/1.93 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl376])).
% 10.29/1.93 thf(zip_derived_cl378, plain,
% 10.29/1.93 (![X0 : $i, X1 : $i]:
% 10.29/1.93 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X1 @ X0))
% 10.29/1.93 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | (imp @
% 10.29/1.93 (imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X0 @ X1)) @
% 10.29/1.93 ($false)) @
% 10.29/1.93 (((X1) = (X0)))))),
% 10.29/1.93 inference('simplify nested equalities', [status(thm)],
% 10.29/1.93 [zip_derived_cl377])).
% 10.29/1.93 thf(zip_derived_cl379, plain,
% 10.29/1.93 (![X0 : $i, X1 : $i]:
% 10.29/1.93 ( (((imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X1 @ X0)) @
% 10.29/1.93 ($false)) => (((X0) = (X1)))))
% 10.29/1.93 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X0 @ X1)))),
% 10.29/1.93 inference('rw_clause', [status(thm)], [zip_derived_cl378, '12'])).
% 10.29/1.93 thf(zip_derived_cl380, plain,
% 10.29/1.93 (![X0 : $i, X1 : $i]:
% 10.29/1.93 (~ (imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X1 @ X0)) @
% 10.29/1.93 ($false))
% 10.29/1.93 | (((X0) = (X1)))
% 10.29/1.93 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X0 @ X1))
% 10.29/1.93 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 10.29/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl379])).
% 10.29/1.93 thf(zip_derived_cl381, plain,
% 10.29/1.93 (![X0 : $i, X1 : $i]:
% 10.29/1.93 (~ (imp @
% 10.29/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X1 @ X0)) @
% 10.29/1.93 ($false))
% 10.29/1.93 | ((X0) = (X1))
% 10.29/1.93 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X0 @ X1))
% 10.29/1.93 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 10.29/1.93 inference('simplify nested equalities', [status(thm)],
% 10.29/1.93 [zip_derived_cl380])).
% 10.29/1.93 thf(zip_derived_cl382, plain,
% 10.29/1.93 (![X0 : $i, X1 : $i]:
% 10.29/1.93 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X1 @ X0)) => ($false)))
% 10.29/1.93 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X0 @ X1))
% 10.29/1.93 | ((X0) = (X1)))),
% 10.29/1.93 inference('rw_clause', [status(thm)], [zip_derived_cl381, '11'])).
% 10.29/1.93 thf(zip_derived_cl383, plain,
% 10.29/1.93 (![X0 : $i, X1 : $i]:
% 10.29/1.93 (~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X1 @ X0))))
% 10.29/1.93 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X0 @ X1))
% 10.29/1.93 | ((X0) = (X1)))),
% 10.29/1.93 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl382])).
% 10.29/1.93 thf(zip_derived_cl384, plain,
% 10.29/1.93 (![X0 : $i, X1 : $i]:
% 10.29/1.93 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X1 @ X0))
% 10.29/1.93 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ X0 @ X1))
% 10.29/1.93 | ((X0) = (X1)))),
% 10.29/1.93 inference('simplify nested equalities', [status(thm)],
% 10.29/1.93 [zip_derived_cl383])).
% 10.29/1.93 thf(zip_derived_cl1989, plain,
% 10.29/1.93 (((('#sk2') = ('#sk3'))
% 10.29/1.93 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk2' @ '#sk3'))
% 10.29/1.93 | ~ (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 10.29/1.93 | ~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 10.29/1.93 inference('sup+', [status(thm)], [zip_derived_cl185, zip_derived_cl384])).
% 10.29/1.93 thf(zip_derived_cl178, plain,
% 10.29/1.93 ( (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 10.29/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl177])).
% 10.29/1.93 thf(zip_derived_cl172, plain,
% 10.29/1.93 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 10.29/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl171])).
% 10.29/1.93 thf(zip_derived_cl2009, plain,
% 10.29/1.93 (((('#sk2') = ('#sk3'))
% 10.29/1.93 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk2' @ '#sk3')))),
% 10.29/1.93 inference('demod', [status(thm)],
% 10.29/1.93 [zip_derived_cl1989, zip_derived_cl178, zip_derived_cl172])).
% 10.29/1.93 thf(zip_derived_cl187, plain, (~ ((('#sk2') = ('#sk3')))),
% 10.29/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl183])).
% 10.29/1.93 thf(zip_derived_cl189, plain, ((('#sk2') != ('#sk3'))),
% 10.29/1.93 inference('simplify nested equalities', [status(thm)],
% 10.29/1.93 [zip_derived_cl187])).
% 10.29/1.93 thf(zip_derived_cl2010, plain,
% 10.29/1.93 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 10.29/1.93 (diffprop @ '#sk2' @ '#sk3'))),
% 10.29/1.93 inference('simplify_reflect-', [status(thm)],
% 10.29/1.93 [zip_derived_cl2009, zip_derived_cl189])).
% 10.29/1.93 thf(zip_derived_cl2041, plain, ($false),
% 10.29/1.93 inference('demod', [status(thm)], [zip_derived_cl191, zip_derived_cl2010])).
% 10.29/1.93
% 10.29/1.93 % SZS output end Refutation
% 10.29/1.93
% 10.29/1.93
% 10.29/1.93 % Terminating...
% 10.29/1.99 % Runner terminated.
% 10.29/1.99 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------