TSTP Solution File: NUM690^4 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM690^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.aA2LAlvtle true
% Computer : n024.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 Aug 31 12:43:29 EDT 2023
% Result : Theorem 54.80s 7.59s
% Output : Refutation 54.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM690^4 : TPTP v8.1.2. Released v7.1.0.
% 0.08/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.aA2LAlvtle true
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 16:23:09 EDT 2023
% 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
% 0.20/0.65 % Total configuration time : 828
% 0.20/0.65 % Estimated wc time : 1656
% 0.20/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.71 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.20/0.77 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.20/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 54.80/7.59 % Solved by lams/40_b.comb.sh.
% 54.80/7.59 % done 519 iterations in 6.763s
% 54.80/7.59 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 54.80/7.59 % SZS output start Refutation
% 54.80/7.59 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
% 54.80/7.59 thf(nat_type, type, nat: $i).
% 54.80/7.59 thf('#sk2_type', type, '#sk2': $i).
% 54.80/7.59 thf(lessis_type, type, lessis: $i > $i > $o).
% 54.80/7.59 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 54.80/7.59 thf(in_type, type, in: $i > $i > $o).
% 54.80/7.59 thf('#sk3_type', type, '#sk3': $i).
% 54.80/7.59 thf('#sk5_type', type, '#sk5': $i).
% 54.80/7.59 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 54.80/7.59 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 54.80/7.59 thf(ap_type, type, ap: $i > $i > $i).
% 54.80/7.59 thf(emptyset_type, type, emptyset: $i).
% 54.80/7.59 thf(n_is_type, type, n_is: $i > $i > $o).
% 54.80/7.59 thf(imp_type, type, imp: $o > $o > $o).
% 54.80/7.59 thf(omega_type, type, omega: $i).
% 54.80/7.59 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 54.80/7.59 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 54.80/7.59 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 54.80/7.59 thf(l_or_type, type, l_or: $o > $o > $o).
% 54.80/7.59 thf(d_not_type, type, d_not: $o > $o).
% 54.80/7.59 thf('#sk4_type', type, '#sk4': $i).
% 54.80/7.59 thf(plus_type, type, plus: $i > $i).
% 54.80/7.59 thf(iii_type, type, iii: $i > $i > $o).
% 54.80/7.59 thf(n_pl_type, type, n_pl: $i > $i > $i).
% 54.80/7.59 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 54.80/7.59 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 54.80/7.59 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 54.80/7.59 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 54.80/7.59 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 54.80/7.59 thf(satz22d, conjecture,
% 54.80/7.59 (all_of @
% 54.80/7.59 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 54.80/7.59 ( ^[X0:$i]:
% 54.80/7.59 ( all_of @
% 54.80/7.59 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 54.80/7.59 ( ^[X1:$i]:
% 54.80/7.59 ( all_of @
% 54.80/7.59 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 54.80/7.59 ( ^[X2:$i]:
% 54.80/7.59 ( all_of @
% 54.80/7.59 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @
% 54.80/7.59 ( ^[X3:$i]:
% 54.80/7.59 ( ( iii @ X0 @ X1 ) =>
% 54.80/7.59 ( ( lessis @ X2 @ X3 ) =>
% 54.80/7.59 ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 54.80/7.59 thf(zf_stmt_0, negated_conjecture,
% 54.80/7.59 (~( all_of @
% 54.80/7.59 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 54.80/7.59 ( ^[X0:$i]:
% 54.80/7.59 ( all_of @
% 54.80/7.59 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 54.80/7.59 ( ^[X1:$i]:
% 54.80/7.59 ( all_of @
% 54.80/7.59 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 54.80/7.59 ( ^[X2:$i]:
% 54.80/7.59 ( all_of @
% 54.80/7.59 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @
% 54.80/7.59 ( ^[X3:$i]:
% 54.80/7.59 ( ( iii @ X0 @ X1 ) =>
% 54.80/7.59 ( ( lessis @ X2 @ X3 ) =>
% 54.80/7.59 ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) )),
% 54.80/7.59 inference('cnf.neg', [status(esa)], [satz22d])).
% 54.80/7.59 thf(zip_derived_cl140, plain,
% 54.80/7.59 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 54.80/7.59 (^[Y0 : $i]:
% 54.80/7.59 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 54.80/7.59 (^[Y1 : $i]:
% 54.80/7.59 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @
% 54.80/7.59 (^[Y2 : $i]:
% 54.80/7.59 (all_of @ (^[Y3 : $i]: (in @ Y3 @ nat)) @
% 54.80/7.59 (^[Y3 : $i]:
% 54.80/7.59 (((iii @ Y0 @ Y1) =>
% 54.80/7.59 (((lessis @ Y2 @ Y3) => (iii @ (n_pl @ Y0 @ Y2) @
% 54.80/7.59 (n_pl @ Y1 @ Y3))))))))))))))),
% 54.80/7.59 inference('cnf', [status(esa)], [zf_stmt_0])).
% 54.80/7.59 thf(zip_derived_cl141, plain,
% 54.80/7.59 (~ (all_of @ ((('#C') @ in @ nat)) @
% 54.80/7.59 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ iii)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 lessis)))))))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#C') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))))) @
% 54.80/7.59 n_pl)))))))))))))),
% 54.80/7.59 inference('lams2combs', [status(thm)], [zip_derived_cl140])).
% 54.80/7.59 thf(def_nat, axiom,(( nat ) =
% 54.80/7.59 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))).
% 54.80/7.59 thf('0', plain,
% 54.80/7.59 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )),
% 54.80/7.59 define([status(thm)])).
% 54.80/7.59 thf(zip_derived_cl575, plain,
% 54.80/7.59 (~ (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ iii)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 lessis)))))))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#C') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))))) @
% 54.80/7.59 n_pl)))))))))))))),
% 54.80/7.59 inference('rw', [status(thm)], [zip_derived_cl141, '0'])).
% 54.80/7.59 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 54.80/7.59 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 54.80/7.59 thf('1', plain,
% 54.80/7.59 (![X0:( $i > $o ),X1:( $i > $o )]:
% 54.80/7.59 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 54.80/7.59 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 54.80/7.59 inference('rw.lit', [status(esa)], [def_all_of])).
% 54.80/7.59 thf(zip_derived_cl576, plain,
% 54.80/7.59 (~ (((!!) @ (^[Y0 : $i]:
% 54.80/7.59 (((is_of @ Y0 @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @
% 54.80/7.59 omega @
% 54.80/7.59 ((('#C') @ (
% 54.80/7.59 !=) @
% 54.80/7.59 emptyset)))))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 iii)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 54.80/7.59 '#S') @
% 54.80/7.59 ((('#B') @ (
% 54.80/7.59 (('#B') @ (
% 54.80/7.59 =>))) @
% 54.80/7.59 lessis)))))))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#C') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ iii)) @
% 54.80/7.59 n_pl)))))))) @
% 54.80/7.59 n_pl)))))))))) @
% 54.80/7.59 Y0)))))))),
% 54.80/7.59 inference('rw_clause', [status(thm)], [zip_derived_cl575, '1'])).
% 54.80/7.59 thf(zip_derived_cl577, plain,
% 54.80/7.59 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 54.80/7.59 ((('#C') @ is_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))))))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (
% 54.80/7.59 !=) @ emptyset)))))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ iii)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 54.80/7.59 '#S') @
% 54.80/7.59 ((('#B') @ (
% 54.80/7.59 (('#B') @ (=>))) @
% 54.80/7.59 lessis)))))))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#C') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ iii)) @
% 54.80/7.59 n_pl)))))))) @
% 54.80/7.59 n_pl))))))))))))))))),
% 54.80/7.59 inference('comb-normalize', [status(thm)], [zip_derived_cl576])).
% 54.80/7.59 thf(zip_derived_cl578, plain,
% 54.80/7.59 (~ (((is_of @ '#sk2' @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ (=>) @ (iii @ '#sk2'))))))) @
% 54.80/7.59 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ lessis)))))) @
% 54.80/7.59 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @ (n_pl @ '#sk2'))))))) @
% 54.80/7.59 n_pl)))))))))))))),
% 54.80/7.59 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl577])).
% 54.80/7.59 thf(zip_derived_cl580, plain,
% 54.80/7.59 (~ (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ (=>) @ (iii @ '#sk2'))))))) @
% 54.80/7.59 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ lessis)))))) @
% 54.80/7.59 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @ (n_pl @ '#sk2'))))))) @
% 54.80/7.59 n_pl)))))))))))),
% 54.80/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
% 54.80/7.59 thf(zip_derived_cl581, plain,
% 54.80/7.59 (~ (((!!) @ (^[Y0 : $i]:
% 54.80/7.59 (((is_of @ Y0 @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ (=>) @ (iii @ '#sk2'))))))) @
% 54.80/7.59 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 lessis)))))) @
% 54.80/7.59 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @
% 54.80/7.59 (n_pl @ '#sk2'))))))) @
% 54.80/7.59 n_pl)))))))) @
% 54.80/7.59 Y0)))))))),
% 54.80/7.59 inference('rw_clause', [status(thm)], [zip_derived_cl580, '1'])).
% 54.80/7.59 thf(zip_derived_cl582, plain,
% 54.80/7.59 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 54.80/7.59 ((('#C') @ is_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))))))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ (=>) @ (iii @ '#sk2'))))))) @
% 54.80/7.59 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 lessis)))))) @
% 54.80/7.59 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @
% 54.80/7.59 (n_pl @ '#sk2'))))))) @
% 54.80/7.59 n_pl))))))))))))))),
% 54.80/7.59 inference('comb-normalize', [status(thm)], [zip_derived_cl581])).
% 54.80/7.59 thf(zip_derived_cl583, plain,
% 54.80/7.59 (~ (((is_of @ '#sk3' @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (((=>) @ (iii @ '#sk2' @ '#sk3'))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @ (n_pl @ '#sk2'))))) @
% 54.80/7.59 (n_pl @ '#sk3'))))))))))))),
% 54.80/7.59 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl582])).
% 54.80/7.59 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 54.80/7.59 thf('2', plain,
% 54.80/7.59 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 54.80/7.59 define([status(thm)])).
% 54.80/7.59 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))).
% 54.80/7.59 thf('3', plain,
% 54.80/7.59 (![X1:$i,X0:$i]:
% 54.80/7.59 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 54.80/7.59 define([status(thm)])).
% 54.80/7.59 thf(zip_derived_cl584, plain,
% 54.80/7.59 (~ (((is_of @ '#sk3' @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ '#sk3' @ '#sk2')))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @ (n_pl @ '#sk2'))))) @
% 54.80/7.59 (n_pl @ '#sk3'))))))))))))),
% 54.80/7.59 inference('rw', [status(thm)], [zip_derived_cl583, '0', '2', '3'])).
% 54.80/7.59 thf(zip_derived_cl586, plain,
% 54.80/7.59 (~ (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ '#sk3' @ '#sk2')))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @ (n_pl @ '#sk2'))))) @
% 54.80/7.59 (n_pl @ '#sk3'))))))))))),
% 54.80/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl584])).
% 54.80/7.59 thf(zip_derived_cl587, plain,
% 54.80/7.59 (~ (((!!) @ (^[Y0 : $i]:
% 54.80/7.59 (((is_of @ Y0 @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @
% 54.80/7.59 emptyset))) @
% 54.80/7.59 (diffprop @ '#sk3' @
% 54.80/7.59 '#sk2')))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @ (n_pl @ '#sk2'))))) @
% 54.80/7.59 (n_pl @ '#sk3'))))))) @
% 54.80/7.59 Y0)))))))),
% 54.80/7.59 inference('rw_clause', [status(thm)], [zip_derived_cl586, '1'])).
% 54.80/7.59 thf(zip_derived_cl588, plain,
% 54.80/7.59 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 54.80/7.59 ((('#C') @ is_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))))))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @
% 54.80/7.59 emptyset))) @
% 54.80/7.59 (diffprop @ '#sk3' @
% 54.80/7.59 '#sk2')))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @ (n_pl @ '#sk2'))))) @
% 54.80/7.59 (n_pl @ '#sk3')))))))))))))),
% 54.80/7.59 inference('comb-normalize', [status(thm)], [zip_derived_cl587])).
% 54.80/7.59 thf(zip_derived_cl589, plain,
% 54.80/7.59 (~ (((is_of @ '#sk4' @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ '#sk3' @ '#sk2')))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ (=>) @ (lessis @ '#sk4'))) @
% 54.80/7.59 ((('#B') @ (iii @ (n_pl @ '#sk2' @ '#sk4')) @ (n_pl @ '#sk3'))))))))))),
% 54.80/7.59 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl588])).
% 54.80/7.59 thf(def_n_pl, axiom,(( n_pl @ (X0)@ (X1)) = ((ap @ (plus @ X0) @ X1)))).
% 54.80/7.59 thf('4', plain,
% 54.80/7.59 (![X1:$i,X0:$i]: ( ( n_pl @ X0 @ X1 ) = ( ap @ ( plus @ X0 ) @ X1 ) )),
% 54.80/7.59 define([status(thm)])).
% 54.80/7.59 thf(zip_derived_cl590, plain,
% 54.80/7.59 (~ (((is_of @ '#sk4' @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ '#sk3' @ '#sk2')))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ (=>) @ (lessis @ '#sk4'))) @
% 54.80/7.59 ((('#B') @ (iii @ (ap @ (plus @ '#sk2') @ '#sk4')) @
% 54.80/7.59 (n_pl @ '#sk3'))))))))))),
% 54.80/7.59 inference('rw', [status(thm)], [zip_derived_cl589, '4'])).
% 54.80/7.59 thf(zip_derived_cl592, plain,
% 54.80/7.59 (~ (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ '#sk3' @ '#sk2')))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ (=>) @ (lessis @ '#sk4'))) @
% 54.80/7.59 ((('#B') @ (iii @ (ap @ (plus @ '#sk2') @ '#sk4')) @
% 54.80/7.59 (n_pl @ '#sk3'))))))))),
% 54.80/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl590])).
% 54.80/7.59 thf(zip_derived_cl593, plain,
% 54.80/7.59 (~ (((!!) @ (^[Y0 : $i]:
% 54.80/7.59 (((is_of @ Y0 @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ '#sk3' @ '#sk2')))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ (=>) @ (lessis @ '#sk4'))) @
% 54.80/7.59 ((('#B') @ (iii @ (ap @ (plus @ '#sk2') @ '#sk4')) @
% 54.80/7.59 (n_pl @ '#sk3'))))) @
% 54.80/7.59 Y0)))))))),
% 54.80/7.59 inference('rw_clause', [status(thm)], [zip_derived_cl592, '1'])).
% 54.80/7.59 thf(zip_derived_cl594, plain,
% 54.80/7.59 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 54.80/7.59 ((('#C') @ is_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))))))))) @
% 54.80/7.59 ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ '#sk3' @ '#sk2')))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ (=>) @ (lessis @ '#sk4'))) @
% 54.80/7.59 ((('#B') @ (iii @ (ap @ (plus @ '#sk2') @ '#sk4')) @
% 54.80/7.59 (n_pl @ '#sk3')))))))))))),
% 54.80/7.59 inference('comb-normalize', [status(thm)], [zip_derived_cl593])).
% 54.80/7.59 thf(zip_derived_cl595, plain,
% 54.80/7.59 (~ (((is_of @ '#sk5' @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ '#sk3' @ '#sk2')) =>
% 54.80/7.59 (((lessis @ '#sk4' @ '#sk5') => (iii @
% 54.80/7.59 (ap @ (plus @ '#sk2') @ '#sk4') @ (n_pl @ '#sk3' @ '#sk5'))))))))),
% 54.80/7.59 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl594])).
% 54.80/7.59 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 54.80/7.59 thf('5', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 54.80/7.59 define([status(thm)])).
% 54.80/7.59 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 54.80/7.59 thf('6', plain,
% 54.80/7.59 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 54.80/7.59 define([status(thm)])).
% 54.80/7.59 thf(def_lessis, axiom,(( lessis @ (X0)@ (X1)) =
% 54.80/7.59 ((l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1))))).
% 54.80/7.59 thf('7', plain,
% 54.80/7.59 (![X1:$i,X0:$i]:
% 54.80/7.59 ( ( lessis @ X0 @ X1 ) =
% 54.80/7.59 ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
% 54.80/7.59 define([status(thm)])).
% 54.80/7.59 thf(zip_derived_cl596, plain,
% 54.80/7.59 (~ (((is_of @ '#sk5' @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ '#sk3' @ '#sk2')) =>
% 54.80/7.59 (((imp @
% 54.80/7.59 (imp @
% 54.80/7.59 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ '#sk5' @ '#sk4')) @
% 54.80/7.59 ($false)) @
% 54.80/7.59 (n_is @ '#sk4' @ '#sk5')) => (l_some @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk5') @
% 54.80/7.59 (ap @ (plus @ '#sk2') @ '#sk4')))))))))),
% 54.80/7.59 inference('rw', [status(thm)],
% 54.80/7.59 [zip_derived_cl595, '5', '6', '0', '2', '2', '4', '3', '3', '7'])).
% 54.80/7.59 thf(zip_derived_cl598, plain,
% 54.80/7.59 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ '#sk3' @ '#sk2')) =>
% 54.80/7.59 (((imp @
% 54.80/7.59 (imp @
% 54.80/7.59 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ '#sk5' @ '#sk4')) @
% 54.80/7.59 ($false)) @
% 54.80/7.59 (n_is @ '#sk4' @ '#sk5')) => (l_some @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk5') @
% 54.80/7.59 (ap @ (plus @ '#sk2') @ '#sk4')))))))),
% 54.80/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl596])).
% 54.80/7.59 thf(zip_derived_cl600, plain,
% 54.80/7.59 (~ (((imp @
% 54.80/7.59 (imp @
% 54.80/7.59 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ '#sk5' @ '#sk4')) @
% 54.80/7.59 ($false)) @
% 54.80/7.59 (n_is @ '#sk4' @ '#sk5')) => (l_some @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk5') @
% 54.80/7.59 (ap @ (plus @ '#sk2') @ '#sk4')))))),
% 54.80/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl598])).
% 54.80/7.59 thf(zip_derived_cl602, plain,
% 54.80/7.59 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk5') @
% 54.80/7.59 (ap @ (plus @ '#sk2') @ '#sk4')))),
% 54.80/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl600])).
% 54.80/7.59 thf(satz19k, axiom,
% 54.80/7.59 (all_of @
% 54.80/7.59 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 54.80/7.59 ( ^[X0:$i]:
% 54.80/7.59 ( all_of @
% 54.80/7.59 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 54.80/7.59 ( ^[X1:$i]:
% 54.80/7.59 ( all_of @
% 54.80/7.59 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 54.80/7.59 ( ^[X2:$i]:
% 54.80/7.59 ( all_of @
% 54.80/7.59 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @
% 54.80/7.59 ( ^[X3:$i]:
% 54.80/7.59 ( ( n_is @ X0 @ X1 ) =>
% 54.80/7.59 ( ( iii @ X2 @ X3 ) =>
% 54.80/7.59 ( iii @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ))).
% 54.80/7.59 thf(zip_derived_cl108, plain,
% 54.80/7.59 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 54.80/7.59 (^[Y0 : $i]:
% 54.80/7.59 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 54.80/7.59 (^[Y1 : $i]:
% 54.80/7.59 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @
% 54.80/7.59 (^[Y2 : $i]:
% 54.80/7.59 (all_of @ (^[Y3 : $i]: (in @ Y3 @ nat)) @
% 54.80/7.59 (^[Y3 : $i]:
% 54.80/7.59 (((n_is @ Y0 @ Y1) =>
% 54.80/7.59 (((iii @ Y2 @ Y3) => (iii @ (n_pl @ Y2 @ Y0) @
% 54.80/7.59 (n_pl @ Y3 @ Y1))))))))))))))),
% 54.80/7.59 inference('cnf', [status(esa)], [satz19k])).
% 54.80/7.59 thf(zip_derived_cl109, plain,
% 54.80/7.59 ( (all_of @ ((('#C') @ in @ nat)) @
% 54.80/7.59 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 iii)))))))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#C') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ iii)) @
% 54.80/7.59 ((('#C') @ n_pl)))))))))) @
% 54.80/7.59 ((('#C') @ n_pl)))))))))))))))),
% 54.80/7.59 inference('lams2combs', [status(thm)], [zip_derived_cl108])).
% 54.80/7.59 thf(zip_derived_cl1295, plain,
% 54.80/7.59 ( (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 iii)))))))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#C') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ iii)) @
% 54.80/7.59 ((('#C') @ n_pl)))))))))) @
% 54.80/7.59 ((('#C') @ n_pl)))))))))))))))),
% 54.80/7.59 inference('rw', [status(thm)], [zip_derived_cl109, '0'])).
% 54.80/7.59 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 54.80/7.59 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 54.80/7.59 thf('8', plain,
% 54.80/7.59 (![X0:( $i > $o ),X1:( $i > $o )]:
% 54.80/7.59 ( ( all_of @ X0 @ X1 ) <=>
% 54.80/7.59 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 54.80/7.59 inference('rw.lit', [status(esa)], [def_all_of])).
% 54.80/7.59 thf(zip_derived_cl1296, plain,
% 54.80/7.59 ( (((!!) @ (^[Y0 : $i]:
% 54.80/7.59 (((is_of @ Y0 @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (
% 54.80/7.59 !=) @ emptyset)))))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 n_is)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 54.80/7.59 '#S') @
% 54.80/7.59 ((('#B') @ (
% 54.80/7.59 (('#B') @ (
% 54.80/7.59 =>))) @
% 54.80/7.59 iii)))))))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#C') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ iii)) @
% 54.80/7.59 ((('#C') @ n_pl)))))))))) @
% 54.80/7.59 ((('#C') @ n_pl)))))))))))) @
% 54.80/7.59 Y0)))))))),
% 54.80/7.59 inference('rw_clause', [status(thm)], [zip_derived_cl1295, '8'])).
% 54.80/7.59 thf(zip_derived_cl1297, plain,
% 54.80/7.59 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 54.80/7.59 ((('#C') @ is_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (
% 54.80/7.59 !=) @ emptyset)))))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 54.80/7.59 '#S') @
% 54.80/7.59 ((('#B') @ (
% 54.80/7.59 (('#B') @ (=>))) @
% 54.80/7.59 iii)))))))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#C') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ iii)) @
% 54.80/7.59 ((('#C') @ n_pl)))))))))) @
% 54.80/7.59 ((('#C') @ n_pl))))))))))))))))))),
% 54.80/7.59 inference('comb-normalize', [status(thm)], [zip_derived_cl1296])).
% 54.80/7.59 thf(zip_derived_cl1298, plain,
% 54.80/7.59 (![X2 : $i]:
% 54.80/7.59 (((is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ (=>) @ (n_is @ X2))))))) @
% 54.80/7.59 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ iii)))))) @
% 54.80/7.59 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @
% 54.80/7.59 ((('#C') @ n_pl @ X2)))))))) @
% 54.80/7.59 ((('#C') @ n_pl)))))))))))))))),
% 54.80/7.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1297])).
% 54.80/7.59 thf(zip_derived_cl1299, plain,
% 54.80/7.59 (![X2 : $i]:
% 54.80/7.59 (~ (is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ (=>) @ (n_is @ X2))))))) @
% 54.80/7.59 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ iii)))))) @
% 54.80/7.59 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @
% 54.80/7.59 ((('#C') @ n_pl @ X2)))))))) @
% 54.80/7.59 ((('#C') @ n_pl))))))))))))))),
% 54.80/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1298])).
% 54.80/7.59 thf(zip_derived_cl1300, plain,
% 54.80/7.59 (![X0 : $i]:
% 54.80/7.59 ( (((!!) @ (^[Y0 : $i]:
% 54.80/7.59 (((is_of @ Y0 @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ (=>) @ (n_is @ X0))))))) @
% 54.80/7.59 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (
% 54.80/7.59 =>))) @
% 54.80/7.59 iii)))))) @
% 54.80/7.59 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @
% 54.80/7.59 ((('#C') @ n_pl @ X0)))))))) @
% 54.80/7.59 ((('#C') @ n_pl)))))))))) @
% 54.80/7.59 Y0)))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('rw_clause', [status(thm)], [zip_derived_cl1299, '8'])).
% 54.80/7.59 thf(zip_derived_cl1301, plain,
% 54.80/7.59 (![X0 : $i]:
% 54.80/7.59 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 54.80/7.59 ((('#C') @ is_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))))))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ (=>) @ (n_is @ X0))))))) @
% 54.80/7.59 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 iii)))))) @
% 54.80/7.59 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @
% 54.80/7.59 ((('#C') @ n_pl @ X0)))))))) @
% 54.80/7.59 ((('#C') @ n_pl))))))))))))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('comb-normalize', [status(thm)], [zip_derived_cl1300])).
% 54.80/7.59 thf(zip_derived_cl1302, plain,
% 54.80/7.59 (![X0 : $i, X2 : $i]:
% 54.80/7.59 ( (((is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ X0 @ X2))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @ ((('#C') @ n_pl @ X0)))))) @
% 54.80/7.59 ((('#C') @ n_pl @ X2)))))))))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1301])).
% 54.80/7.59 thf(zip_derived_cl1303, plain,
% 54.80/7.59 (![X0 : $i, X2 : $i]:
% 54.80/7.59 (~ (is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ X0 @ X2))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @ ((('#C') @ n_pl @ X0)))))) @
% 54.80/7.59 ((('#C') @ n_pl @ X2)))))))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1302])).
% 54.80/7.59 thf(zip_derived_cl1304, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i]:
% 54.80/7.59 ( (((!!) @ (^[Y0 : $i]:
% 54.80/7.59 (((is_of @ Y0 @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ X0 @ X1))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @
% 54.80/7.59 ((('#C') @ n_pl @ X0)))))) @
% 54.80/7.59 ((('#C') @ n_pl @ X1)))))))) @
% 54.80/7.59 Y0)))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('rw_clause', [status(thm)], [zip_derived_cl1303, '8'])).
% 54.80/7.59 thf(zip_derived_cl1305, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i]:
% 54.80/7.59 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 54.80/7.59 ((('#C') @ is_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))))))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ X0 @ X1))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ iii @
% 54.80/7.59 ((('#C') @ n_pl @ X0)))))) @
% 54.80/7.59 ((('#C') @ n_pl @ X1))))))))))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('comb-normalize', [status(thm)], [zip_derived_cl1304])).
% 54.80/7.59 thf(zip_derived_cl1306, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 54.80/7.59 ( (((is_of @ X3 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (((=>) @ (n_is @ X0 @ X1))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ (=>) @ (iii @ X3))) @
% 54.80/7.59 ((('#B') @ (iii @ (n_pl @ X3 @ X0)) @ ((('#C') @ n_pl @ X1)))))))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1305])).
% 54.80/7.59 thf(zip_derived_cl1307, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 54.80/7.59 ( (((is_of @ X3 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (((=>) @ (n_is @ X0 @ X1))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ (=>) @ (iii @ X3))) @
% 54.80/7.59 ((('#B') @ (iii @ (ap @ (plus @ X3) @ X0)) @
% 54.80/7.59 ((('#C') @ n_pl @ X1)))))))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('rw', [status(thm)], [zip_derived_cl1306, '4'])).
% 54.80/7.59 thf(zip_derived_cl1308, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 54.80/7.59 (~ (is_of @ X3 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (((=>) @ (n_is @ X0 @ X1))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ (=>) @ (iii @ X3))) @
% 54.80/7.59 ((('#B') @ (iii @ (ap @ (plus @ X3) @ X0)) @
% 54.80/7.59 ((('#C') @ n_pl @ X1)))))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1307])).
% 54.80/7.59 thf(zip_derived_cl1309, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 54.80/7.59 ( (((!!) @ (^[Y0 : $i]:
% 54.80/7.59 (((is_of @ Y0 @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 ((('#B') @ (((=>) @ (n_is @ X1 @ X0))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ (=>) @ (iii @ X2))) @
% 54.80/7.59 ((('#B') @ (iii @ (ap @ (plus @ X2) @ X1)) @
% 54.80/7.59 ((('#C') @ n_pl @ X0)))))) @
% 54.80/7.59 Y0)))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('rw_clause', [status(thm)], [zip_derived_cl1308, '8'])).
% 54.80/7.59 thf(zip_derived_cl1310, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 54.80/7.59 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 54.80/7.59 ((('#C') @ is_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))))))))) @
% 54.80/7.59 ((('#B') @ (((=>) @ (n_is @ X1 @ X0))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ (=>) @ (iii @ X2))) @
% 54.80/7.59 ((('#B') @ (iii @ (ap @ (plus @ X2) @ X1)) @
% 54.80/7.59 ((('#C') @ n_pl @ X0))))))))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('comb-normalize', [status(thm)], [zip_derived_cl1309])).
% 54.80/7.59 thf(zip_derived_cl1311, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 54.80/7.59 ( (((is_of @ X4 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (((n_is @ X1 @ X0) =>
% 54.80/7.59 (((iii @ X2 @ X4) => (iii @ (ap @ (plus @ X2) @ X1) @
% 54.80/7.59 (n_pl @ X4 @ X0))))))))
% 54.80/7.59 | ~ (is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1310])).
% 54.80/7.59 thf(zip_derived_cl1312, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 54.80/7.59 ( (((is_of @ X4 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (((n_is @ X1 @ X0) =>
% 54.80/7.59 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X4 @ X2)) => (l_some @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ (ap @ (plus @ X4) @ X0) @ (ap @ (plus @ X2) @ X1)))))))))
% 54.80/7.59 | ~ (is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('rw', [status(thm)],
% 54.80/7.59 [zip_derived_cl1311, '0', '2', '2', '4', '3', '3'])).
% 54.80/7.59 thf(zip_derived_cl1313, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 54.80/7.59 (~ (is_of @ X4 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | (((n_is @ X1 @ X0) =>
% 54.80/7.59 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X4 @ X2)) => (l_some @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ (ap @ (plus @ X4) @ X0) @ (ap @ (plus @ X2) @ X1)))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1312])).
% 54.80/7.59 thf(zip_derived_cl1314, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 54.80/7.59 (~ (n_is @ X1 @ X0)
% 54.80/7.59 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X4 @ X2)) => (l_some @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ (ap @ (plus @ X4) @ X0) @ (ap @ (plus @ X2) @ X1)))))
% 54.80/7.59 | ~ (is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X4 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1313])).
% 54.80/7.59 thf(zip_derived_cl1315, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 54.80/7.59 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X4 @ X2))
% 54.80/7.59 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ (ap @ (plus @ X4) @ X0) @ (ap @ (plus @ X2) @ X1)))
% 54.80/7.59 | ~ (is_of @ X4 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (n_is @ X1 @ X0))),
% 54.80/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1314])).
% 54.80/7.59 thf(zip_derived_cl9330, plain,
% 54.80/7.59 ((~ (n_is @ '#sk4' @ '#sk5')
% 54.80/7.59 | ~ (is_of @ '#sk2' @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ '#sk4' @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ '#sk5' @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ '#sk3' @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ '#sk3' @ '#sk2')))),
% 54.80/7.59 inference('sup+', [status(thm)], [zip_derived_cl602, zip_derived_cl1315])).
% 54.80/7.59 thf(zip_derived_cl602, plain,
% 54.80/7.59 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk5') @
% 54.80/7.59 (ap @ (plus @ '#sk2') @ '#sk4')))),
% 54.80/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl600])).
% 54.80/7.59 thf(satz21, axiom,
% 54.80/7.59 (all_of @
% 54.80/7.59 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 54.80/7.59 ( ^[X0:$i]:
% 54.80/7.59 ( all_of @
% 54.80/7.59 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 54.80/7.59 ( ^[X1:$i]:
% 54.80/7.59 ( all_of @
% 54.80/7.59 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 54.80/7.59 ( ^[X2:$i]:
% 54.80/7.59 ( all_of @
% 54.80/7.59 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @
% 54.80/7.59 ( ^[X3:$i]:
% 54.80/7.59 ( ( d_29_ii @ X0 @ X1 ) =>
% 54.80/7.59 ( ( d_29_ii @ X2 @ X3 ) =>
% 54.80/7.59 ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 54.80/7.59 thf(zip_derived_cl130, plain,
% 54.80/7.59 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 54.80/7.59 (^[Y0 : $i]:
% 54.80/7.59 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 54.80/7.59 (^[Y1 : $i]:
% 54.80/7.59 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @
% 54.80/7.59 (^[Y2 : $i]:
% 54.80/7.59 (all_of @ (^[Y3 : $i]: (in @ Y3 @ nat)) @
% 54.80/7.59 (^[Y3 : $i]:
% 54.80/7.59 (((d_29_ii @ Y0 @ Y1) =>
% 54.80/7.59 (((d_29_ii @ Y2 @ Y3) => (d_29_ii @
% 54.80/7.59 (n_pl @ Y0 @ Y2) @ (n_pl @ Y1 @ Y3))))))))))))))),
% 54.80/7.59 inference('cnf', [status(esa)], [satz21])).
% 54.80/7.59 thf(zip_derived_cl131, plain,
% 54.80/7.59 ( (all_of @ ((('#C') @ in @ nat)) @
% 54.80/7.59 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 d_29_ii)))))))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#C') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ d_29_ii)) @ n_pl)))))))) @
% 54.80/7.59 n_pl)))))))))))))),
% 54.80/7.59 inference('lams2combs', [status(thm)], [zip_derived_cl130])).
% 54.80/7.59 thf(zip_derived_cl1165, plain,
% 54.80/7.59 ( (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 d_29_ii)))))))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#C') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ d_29_ii)) @ n_pl)))))))) @
% 54.80/7.59 n_pl)))))))))))))),
% 54.80/7.59 inference('rw', [status(thm)], [zip_derived_cl131, '0'])).
% 54.80/7.59 thf(zip_derived_cl1166, plain,
% 54.80/7.59 ( (((!!) @ (^[Y0 : $i]:
% 54.80/7.59 (((is_of @ Y0 @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (
% 54.80/7.59 !=) @ emptyset)))))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 d_29_ii)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 54.80/7.59 '#S') @
% 54.80/7.59 ((('#B') @ (
% 54.80/7.59 (('#B') @ (
% 54.80/7.59 =>))) @
% 54.80/7.59 d_29_ii)))))))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#C') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ d_29_ii)) @
% 54.80/7.59 n_pl)))))))) @
% 54.80/7.59 n_pl)))))))))) @
% 54.80/7.59 Y0)))))))),
% 54.80/7.59 inference('rw_clause', [status(thm)], [zip_derived_cl1165, '8'])).
% 54.80/7.59 thf(zip_derived_cl1167, plain,
% 54.80/7.59 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 54.80/7.59 ((('#C') @ is_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (
% 54.80/7.59 !=) @ emptyset)))))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 d_29_ii)))))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 54.80/7.59 '#S') @
% 54.80/7.59 ((('#B') @ (
% 54.80/7.59 (('#B') @ (=>))) @
% 54.80/7.59 d_29_ii)))))))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#C') @
% 54.80/7.59 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ d_29_ii)) @
% 54.80/7.59 n_pl)))))))) @
% 54.80/7.59 n_pl))))))))))))))))),
% 54.80/7.59 inference('comb-normalize', [status(thm)], [zip_derived_cl1166])).
% 54.80/7.59 thf(zip_derived_cl1168, plain,
% 54.80/7.59 (![X2 : $i]:
% 54.80/7.59 (((is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ (=>) @ (d_29_ii @ X2))))))) @
% 54.80/7.59 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 d_29_ii)))))) @
% 54.80/7.59 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ d_29_ii @ (n_pl @ X2))))))) @
% 54.80/7.59 n_pl)))))))))))))),
% 54.80/7.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1167])).
% 54.80/7.59 thf(zip_derived_cl1169, plain,
% 54.80/7.59 (![X2 : $i]:
% 54.80/7.59 (~ (is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ (=>) @ (d_29_ii @ X2))))))) @
% 54.80/7.59 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 d_29_ii)))))) @
% 54.80/7.59 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ d_29_ii @ (n_pl @ X2))))))) @
% 54.80/7.59 n_pl))))))))))))),
% 54.80/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1168])).
% 54.80/7.59 thf(zip_derived_cl1170, plain,
% 54.80/7.59 (![X0 : $i]:
% 54.80/7.59 ( (((!!) @ (^[Y0 : $i]:
% 54.80/7.59 (((is_of @ Y0 @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ (=>) @ (d_29_ii @ X0))))))) @
% 54.80/7.59 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (
% 54.80/7.59 =>))) @
% 54.80/7.59 d_29_ii)))))) @
% 54.80/7.59 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ d_29_ii @
% 54.80/7.59 (n_pl @ X0))))))) @
% 54.80/7.59 n_pl)))))))) @
% 54.80/7.59 Y0)))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('rw_clause', [status(thm)], [zip_derived_cl1169, '8'])).
% 54.80/7.59 thf(zip_derived_cl1171, plain,
% 54.80/7.59 (![X0 : $i]:
% 54.80/7.59 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 54.80/7.59 ((('#C') @ is_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))))))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ (=>) @ (d_29_ii @ X0))))))) @
% 54.80/7.59 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 d_29_ii)))))) @
% 54.80/7.59 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ d_29_ii @
% 54.80/7.59 (n_pl @ X0))))))) @
% 54.80/7.59 n_pl))))))))))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('comb-normalize', [status(thm)], [zip_derived_cl1170])).
% 54.80/7.59 thf(zip_derived_cl1172, plain,
% 54.80/7.59 (![X0 : $i, X2 : $i]:
% 54.80/7.59 ( (((is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (((=>) @ (d_29_ii @ X0 @ X2))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ d_29_ii @ (n_pl @ X0))))) @
% 54.80/7.59 (n_pl @ X2))))))))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1171])).
% 54.80/7.59 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) =
% 54.80/7.59 ((n_some @ (diffprop @ X0 @ X1))))).
% 54.80/7.59 thf('9', plain,
% 54.80/7.59 (![X1:$i,X0:$i]:
% 54.80/7.59 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 54.80/7.59 define([status(thm)])).
% 54.80/7.59 thf(zip_derived_cl1173, plain,
% 54.80/7.59 (![X0 : $i, X2 : $i]:
% 54.80/7.59 ( (((is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X0 @ X2)))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ d_29_ii @ (n_pl @ X0))))) @
% 54.80/7.59 (n_pl @ X2))))))))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('rw', [status(thm)], [zip_derived_cl1172, '0', '2', '9'])).
% 54.80/7.59 thf(zip_derived_cl1174, plain,
% 54.80/7.59 (![X0 : $i, X2 : $i]:
% 54.80/7.59 (~ (is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X0 @ X2)))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ d_29_ii @ (n_pl @ X0))))) @
% 54.80/7.59 (n_pl @ X2))))))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1173])).
% 54.80/7.59 thf(zip_derived_cl1175, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i]:
% 54.80/7.59 ( (((!!) @ (^[Y0 : $i]:
% 54.80/7.59 (((is_of @ Y0 @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (
% 54.80/7.59 !=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X0 @ X1)))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @
% 54.80/7.59 d_29_ii)))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ d_29_ii @ (n_pl @ X0))))) @
% 54.80/7.59 (n_pl @ X1))))))) @
% 54.80/7.59 Y0)))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('rw_clause', [status(thm)], [zip_derived_cl1174, '8'])).
% 54.80/7.59 thf(zip_derived_cl1176, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i]:
% 54.80/7.59 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 54.80/7.59 ((('#C') @ is_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))))))))) @
% 54.80/7.59 ((('#B') @ (all_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset)))))) @
% 54.80/7.59 ((('#B') @ ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @
% 54.80/7.59 emptyset))) @
% 54.80/7.59 (diffprop @ X0 @ X1)))))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ ('#S') @
% 54.80/7.59 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 54.80/7.59 ((('#C') @ ((('#B') @ ('#B') @
% 54.80/7.59 ((('#B') @ d_29_ii @ (n_pl @ X0))))) @
% 54.80/7.59 (n_pl @ X1)))))))))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('comb-normalize', [status(thm)], [zip_derived_cl1175])).
% 54.80/7.59 thf(zip_derived_cl1177, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 54.80/7.59 ( (((is_of @ X3 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X0 @ X1)))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X3))) @
% 54.80/7.59 ((('#B') @ (d_29_ii @ (n_pl @ X0 @ X3)) @ (n_pl @ X1))))))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1176])).
% 54.80/7.59 thf(zip_derived_cl1178, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 54.80/7.59 ( (((is_of @ X3 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X0 @ X1)))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X3))) @
% 54.80/7.59 ((('#B') @ (d_29_ii @ (ap @ (plus @ X0) @ X3)) @ (n_pl @ X1))))))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('rw', [status(thm)], [zip_derived_cl1177, '4'])).
% 54.80/7.59 thf(zip_derived_cl1179, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X3 : $i]:
% 54.80/7.59 (~ (is_of @ X3 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | (all_of @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.80/7.59 ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X0 @ X1)))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X3))) @
% 54.80/7.59 ((('#B') @ (d_29_ii @ (ap @ (plus @ X0) @ X3)) @ (n_pl @ X1))))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1178])).
% 54.80/7.59 thf(zip_derived_cl1180, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 54.80/7.59 ( (((!!) @ (^[Y0 : $i]:
% 54.80/7.59 (((is_of @ Y0 @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X1 @ X0)))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X2))) @
% 54.80/7.59 ((('#B') @ (d_29_ii @ (ap @ (plus @ X1) @ X2)) @
% 54.80/7.59 (n_pl @ X0))))) @
% 54.80/7.59 Y0)))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('rw_clause', [status(thm)], [zip_derived_cl1179, '8'])).
% 54.80/7.59 thf(zip_derived_cl1181, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 54.80/7.59 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 54.80/7.59 ((('#C') @ is_of @
% 54.80/7.59 ((('#C') @ in @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))))))))) @
% 54.80/7.59 ((('#B') @ (((=>) @ (l_some @
% 54.80/7.59 (d_Sep @ omega @
% 54.80/7.59 ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X1 @ X0)))) @
% 54.80/7.59 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X2))) @
% 54.80/7.59 ((('#B') @ (d_29_ii @ (ap @ (plus @ X1) @ X2)) @
% 54.80/7.59 (n_pl @ X0)))))))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('comb-normalize', [status(thm)], [zip_derived_cl1180])).
% 54.80/7.59 thf(zip_derived_cl1182, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 54.80/7.59 ( (((is_of @ X4 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X1 @ X0)) =>
% 54.80/7.59 (((d_29_ii @ X2 @ X4) => (d_29_ii @ (ap @ (plus @ X1) @ X2) @
% 54.80/7.59 (n_pl @ X0 @ X4))))))))
% 54.80/7.59 | ~ (is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1181])).
% 54.80/7.59 thf(zip_derived_cl1183, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 54.80/7.59 ( (((is_of @ X4 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.80/7.59 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X1 @ X0)) =>
% 54.80/7.59 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X2 @ X4)) => (l_some @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ (ap @ (plus @ X1) @ X2) @ (ap @ (plus @ X0) @ X4)))))))))
% 54.80/7.59 | ~ (is_of @ X2 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X1 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.80/7.59 inference('rw', [status(thm)],
% 54.80/7.59 [zip_derived_cl1182, '0', '2', '2', '4', '9', '9'])).
% 54.80/7.59 thf(zip_derived_cl1184, plain,
% 54.80/7.59 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 54.80/7.59 (~ (is_of @ X4 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.80/7.59 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X1 @ X0)) =>
% 54.80/7.59 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ X2 @ X4)) => (l_some @
% 54.80/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.80/7.59 (diffprop @ (ap @ (plus @ X1) @ X2) @ (ap @ (plus @ X0) @ X4)))))))
% 54.80/7.59 | ~ (is_of @ X0 @
% 54.80/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.94/7.59 | ~ (is_of @ X1 @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.94/7.59 | ~ (is_of @ X2 @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.94/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1183])).
% 54.94/7.59 thf(zip_derived_cl1185, plain,
% 54.94/7.59 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 54.94/7.59 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ X1 @ X0))
% 54.94/7.59 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ X2 @ X4)) => (l_some @
% 54.94/7.59 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ (ap @ (plus @ X1) @ X2) @ (ap @ (plus @ X0) @ X4)))))
% 54.94/7.59 | ~ (is_of @ X2 @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.94/7.59 | ~ (is_of @ X1 @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.94/7.59 | ~ (is_of @ X0 @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.94/7.59 | ~ (is_of @ X4 @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.94/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1184])).
% 54.94/7.59 thf(zip_derived_cl1186, plain,
% 54.94/7.59 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 54.94/7.59 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ X2 @ X4))
% 54.94/7.59 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ (ap @ (plus @ X1) @ X2) @ (ap @ (plus @ X0) @ X4)))
% 54.94/7.59 | ~ (is_of @ X4 @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.94/7.59 | ~ (is_of @ X0 @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.94/7.59 | ~ (is_of @ X1 @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.94/7.59 | ~ (is_of @ X2 @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.94/7.59 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ X1 @ X0)))),
% 54.94/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1185])).
% 54.94/7.59 thf(zip_derived_cl8876, plain,
% 54.94/7.59 ((~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ '#sk3' @ '#sk2'))
% 54.94/7.59 | ~ (is_of @ '#sk5' @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.94/7.59 | ~ (is_of @ '#sk3' @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.94/7.59 | ~ (is_of @ '#sk2' @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.94/7.59 | ~ (is_of @ '#sk4' @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.94/7.59 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ '#sk5' @ '#sk4')))),
% 54.94/7.59 inference('sup+', [status(thm)], [zip_derived_cl602, zip_derived_cl1186])).
% 54.94/7.59 thf(zip_derived_cl599, plain,
% 54.94/7.59 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ '#sk3' @ '#sk2'))),
% 54.94/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl598])).
% 54.94/7.59 thf(zip_derived_cl597, plain,
% 54.94/7.59 ( (is_of @ '#sk5' @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 54.94/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl596])).
% 54.94/7.59 thf(zip_derived_cl585, plain,
% 54.94/7.59 ( (is_of @ '#sk3' @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 54.94/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl584])).
% 54.94/7.59 thf(zip_derived_cl579, plain,
% 54.94/7.59 ( (is_of @ '#sk2' @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 54.94/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
% 54.94/7.59 thf(zip_derived_cl591, plain,
% 54.94/7.59 ( (is_of @ '#sk4' @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 54.94/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl590])).
% 54.94/7.59 thf(zip_derived_cl8891, plain,
% 54.94/7.59 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ '#sk5' @ '#sk4'))),
% 54.94/7.59 inference('demod', [status(thm)],
% 54.94/7.59 [zip_derived_cl8876, zip_derived_cl599, zip_derived_cl597,
% 54.94/7.59 zip_derived_cl585, zip_derived_cl579, zip_derived_cl591])).
% 54.94/7.59 thf(zip_derived_cl601, plain,
% 54.94/7.59 ( (imp @
% 54.94/7.59 (imp @
% 54.94/7.59 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ '#sk5' @ '#sk4')) @
% 54.94/7.59 ($false)) @
% 54.94/7.59 (n_is @ '#sk4' @ '#sk5'))),
% 54.94/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl600])).
% 54.94/7.59 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 54.94/7.59 thf('10', plain,
% 54.94/7.59 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 54.94/7.59 inference('rw.lit', [status(esa)], [def_imp])).
% 54.94/7.59 thf(zip_derived_cl603, plain,
% 54.94/7.59 ( (((imp @
% 54.94/7.59 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ '#sk5' @ '#sk4')) @
% 54.94/7.59 ($false)) => (n_is @ '#sk4' @ '#sk5')))),
% 54.94/7.59 inference('rw_clause', [status(thm)], [zip_derived_cl601, '10'])).
% 54.94/7.59 thf(zip_derived_cl604, plain,
% 54.94/7.59 ((~ (imp @
% 54.94/7.59 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ '#sk5' @ '#sk4')) @
% 54.94/7.59 ($false))
% 54.94/7.59 | (n_is @ '#sk4' @ '#sk5'))),
% 54.94/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl603])).
% 54.94/7.59 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 54.94/7.59 thf('11', plain,
% 54.94/7.59 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 54.94/7.59 inference('rw.lit', [status(esa)], [def_imp])).
% 54.94/7.59 thf(zip_derived_cl605, plain,
% 54.94/7.59 ((~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ '#sk5' @ '#sk4')) => ($false)))
% 54.94/7.59 | (n_is @ '#sk4' @ '#sk5'))),
% 54.94/7.59 inference('rw_clause', [status(thm)], [zip_derived_cl604, '11'])).
% 54.94/7.59 thf(zip_derived_cl606, plain,
% 54.94/7.59 ((~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ '#sk5' @ '#sk4'))))
% 54.94/7.59 | (n_is @ '#sk4' @ '#sk5'))),
% 54.94/7.59 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl605])).
% 54.94/7.59 thf(zip_derived_cl607, plain,
% 54.94/7.59 (( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ '#sk5' @ '#sk4'))
% 54.94/7.59 | (n_is @ '#sk4' @ '#sk5'))),
% 54.94/7.59 inference('simplify nested equalities', [status(thm)],
% 54.94/7.59 [zip_derived_cl606])).
% 54.94/7.59 thf(zip_derived_cl9011, plain, ( (n_is @ '#sk4' @ '#sk5')),
% 54.94/7.59 inference('sup+', [status(thm)], [zip_derived_cl8891, zip_derived_cl607])).
% 54.94/7.59 thf(zip_derived_cl579, plain,
% 54.94/7.59 ( (is_of @ '#sk2' @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 54.94/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
% 54.94/7.59 thf(zip_derived_cl591, plain,
% 54.94/7.59 ( (is_of @ '#sk4' @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 54.94/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl590])).
% 54.94/7.59 thf(zip_derived_cl597, plain,
% 54.94/7.59 ( (is_of @ '#sk5' @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 54.94/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl596])).
% 54.94/7.59 thf(zip_derived_cl585, plain,
% 54.94/7.59 ( (is_of @ '#sk3' @
% 54.94/7.59 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 54.94/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl584])).
% 54.94/7.59 thf(zip_derived_cl599, plain,
% 54.94/7.59 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.94/7.59 (diffprop @ '#sk3' @ '#sk2'))),
% 54.94/7.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl598])).
% 54.94/7.59 thf(zip_derived_cl9345, plain, ($false),
% 54.94/7.59 inference('demod', [status(thm)],
% 54.94/7.59 [zip_derived_cl9330, zip_derived_cl9011, zip_derived_cl579,
% 54.94/7.59 zip_derived_cl591, zip_derived_cl597, zip_derived_cl585,
% 54.94/7.59 zip_derived_cl599])).
% 54.94/7.59
% 54.94/7.59 % SZS output end Refutation
% 54.94/7.59
% 54.94/7.59
% 54.94/7.59 % Terminating...
% 55.13/7.67 % Runner terminated.
% 55.13/7.68 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------