%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM672^4 : TPTP v9.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.mrCSjjxqGp true
% Computer : n017.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 04:47:56 PM UTC 2025
% Result : Theorem 44.33s 8.68s
% Output : Refutation 44.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM672^4 : TPTP v9.2.0. Released v7.1.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.mrCSjjxqGp true
% 0.07/0.33 % Computer : n017.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8042.1875MB
% 0.07/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Wed Oct 1 16:49:08 EDT 2025
% 0.07/0.33 % CPUTime :
% 0.07/0.33 % Running portfolio for 300 s
% 0.07/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.33 % Number of cores: 8
% 0.07/0.33 % Python version: Python 3.6.8
% 0.07/0.33 % Running in HO mode
% 0.12/0.51 % Total configuration time : 828
% 0.12/0.51 % Estimated wc time : 1656
% 0.12/0.51 % Estimated cpu time (8 cpus) : 207.0
% 0.92/0.67 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.92/0.67 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.92/0.68 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.92/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.92/0.68 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.92/0.69 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.92/0.69 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.92/0.69 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 44.33/8.68 % Solved by lams/40_b.comb.sh.
% 44.33/8.68 % done 400 iterations in 7.874s
% 44.33/8.68 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 44.33/8.68 % SZS output start Refutation
% 44.33/8.68 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
% 44.33/8.68 thf(nat_type, type, nat: $i).
% 44.33/8.68 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 44.33/8.68 thf(in_type, type, in: $i > $i > $o).
% 44.33/8.68 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 44.33/8.68 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 44.33/8.68 thf('#sk4_type', type, '#sk4': $i).
% 44.33/8.68 thf(ap_type, type, ap: $i > $i > $i).
% 44.33/8.68 thf(emptyset_type, type, emptyset: $i).
% 44.33/8.68 thf('#sk2_type', type, '#sk2': $i).
% 44.33/8.68 thf('#sk3_type', type, '#sk3': $i).
% 44.33/8.68 thf(omega_type, type, omega: $i).
% 44.33/8.68 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 44.33/8.68 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 44.33/8.68 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 44.33/8.68 thf(plus_type, type, plus: $i > $i).
% 44.33/8.68 thf(iii_type, type, iii: $i > $i > $o).
% 44.33/8.68 thf(n_pl_type, type, n_pl: $i > $i > $i).
% 44.33/8.68 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 44.33/8.68 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 44.33/8.68 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 44.33/8.68 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 44.33/8.68 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 44.33/8.68 thf(satz19c, conjecture,
% 44.33/8.68 (all_of @
% 44.33/8.68 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 44.33/8.68 ( ^[X0:$i]:
% 44.33/8.68 ( all_of @
% 44.33/8.68 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 44.33/8.68 ( ^[X1:$i]:
% 44.33/8.68 ( all_of @
% 44.33/8.68 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 44.33/8.68 ( ^[X2:$i]:
% 44.33/8.68 ( ( iii @ X0 @ X1 ) =>
% 44.33/8.68 ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) ) ) ) ) ) ))).
% 44.33/8.68 thf(zf_stmt_0, negated_conjecture,
% 44.33/8.68 (~( all_of @
% 44.33/8.68 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 44.33/8.68 ( ^[X0:$i]:
% 44.33/8.68 ( all_of @
% 44.33/8.68 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 44.33/8.68 ( ^[X1:$i]:
% 44.33/8.68 ( all_of @
% 44.33/8.68 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 44.33/8.68 ( ^[X2:$i]:
% 44.33/8.68 ( ( iii @ X0 @ X1 ) =>
% 44.33/8.68 ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) ) ) ) ) ) ) )),
% 44.33/8.68 inference('cnf.neg', [status(esa)], [satz19c])).
% 44.33/8.68 thf(zip_derived_cl159, plain,
% 44.33/8.68 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 44.33/8.68 (^[Y0 : $i]:
% 44.33/8.68 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 44.33/8.68 (^[Y1 : $i]:
% 44.33/8.68 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @
% 44.33/8.68 (^[Y2 : $i]:
% 44.33/8.68 (((iii @ Y0 @ Y1) => (iii @ (n_pl @ Y0 @ Y2) @
% 44.33/8.68 (n_pl @ Y1 @ Y2))))))))))),
% 44.33/8.68 inference('cnf', [status(esa)], [zf_stmt_0])).
% 44.33/8.68 thf(zip_derived_cl160, plain,
% 44.33/8.68 (~ (all_of @ ((('#C') @ in @ nat)) @
% 44.33/8.68 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 44.33/8.68 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#S') @
% 44.33/8.68 ((('#B') @ ((('#B') @ ('#B'))) @
% 44.33/8.68 ((('#B') @ ((('#B') @ (=>))) @ iii)))))) @
% 44.33/8.68 ((('#C') @ ((('#B') @ ('#B') @
% 44.33/8.68 ((('#B') @ ('#S') @
% 44.33/8.68 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))) @
% 44.33/8.68 n_pl)))))))))),
% 44.33/8.68 inference('lams2combs', [status(thm)], [zip_derived_cl159])).
% 44.33/8.68 thf(def_nat, axiom,(( nat ) =
% 44.33/8.68 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))).
% 44.33/8.68 thf('0', plain,
% 44.33/8.68 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )),
% 44.33/8.68 define([status(thm)])).
% 44.33/8.68 thf(zip_derived_cl493, plain,
% 44.33/8.68 (~ (all_of @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 44.33/8.68 ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 44.33/8.68 ((('#B') @ ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset)))))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#S') @
% 44.33/8.68 ((('#B') @ ((('#B') @ ('#B'))) @
% 44.33/8.68 ((('#B') @ ((('#B') @ (=>))) @ iii)))))) @
% 44.33/8.68 ((('#C') @ ((('#B') @ ('#B') @
% 44.33/8.68 ((('#B') @ ('#S') @
% 44.33/8.68 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))) @
% 44.33/8.68 n_pl)))))))))),
% 44.33/8.68 inference('rw', [status(thm)], [zip_derived_cl160, '0'])).
% 44.33/8.68 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 44.33/8.68 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 44.33/8.68 thf('1', plain,
% 44.33/8.68 (![X0:( $i > $o ),X1:( $i > $o )]:
% 44.33/8.68 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 44.33/8.68 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 44.33/8.68 inference('rw.lit', [status(esa)], [def_all_of])).
% 44.33/8.68 thf(zip_derived_cl494, plain,
% 44.33/8.68 (~ (((!!) @ (^[Y0 : $i]:
% 44.33/8.68 (((is_of @ Y0 @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 44.33/8.68 ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset)))))) @
% 44.33/8.68 ((('#B') @ ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset)))))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#S') @
% 44.33/8.68 ((('#B') @ ((('#B') @ ('#B'))) @
% 44.33/8.68 ((('#B') @ ((('#B') @ (=>))) @ iii)))))) @
% 44.33/8.68 ((('#C') @ ((('#B') @ ('#B') @
% 44.33/8.68 ((('#B') @ ('#S') @
% 44.33/8.68 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))) @
% 44.33/8.68 n_pl)))))) @
% 44.33/8.68 Y0)))))))),
% 44.33/8.68 inference('rw_clause', [status(thm)], [zip_derived_cl493, '1'])).
% 44.33/8.68 thf(zip_derived_cl495, plain,
% 44.33/8.68 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 44.33/8.68 ((('#C') @ is_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset))))))))) @
% 44.33/8.68 ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 44.33/8.68 ((('#B') @ ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset)))))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#S') @
% 44.33/8.68 ((('#B') @ ((('#B') @ ('#B'))) @
% 44.33/8.68 ((('#B') @ ((('#B') @ (=>))) @ iii)))))) @
% 44.33/8.68 ((('#C') @ ((('#B') @ ('#B') @
% 44.33/8.68 ((('#B') @ ('#S') @
% 44.33/8.68 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))) @
% 44.33/8.68 n_pl))))))))))))),
% 44.33/8.68 inference('comb-normalize', [status(thm)], [zip_derived_cl494])).
% 44.33/8.68 thf(zip_derived_cl496, plain,
% 44.33/8.68 (~ (((is_of @ '#sk2' @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 44.33/8.68 (all_of @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 44.33/8.68 ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (iii @ '#sk2'))))) @
% 44.33/8.68 ((('#B') @ ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))))) @
% 44.33/8.68 n_pl)))))))))),
% 44.33/8.68 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl495])).
% 44.33/8.68 thf(def_is_of, axiom,(( is_of @ (X1)@ (X0)) = ((X0 @ X1)))).
% 44.33/8.68 thf('2', plain,
% 44.33/8.68 (![X0:( $i > $o ),X1:$i]: ( ( is_of @ X1 @ X0 ) = ( X0 @ X1 ) )),
% 44.33/8.68 define([status(thm)])).
% 44.33/8.68 thf(zip_derived_cl497, plain,
% 44.33/8.68 (~ (((in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 44.33/8.68 (all_of @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 44.33/8.68 ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (iii @ '#sk2'))))) @
% 44.33/8.68 ((('#B') @ ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))))) @
% 44.33/8.68 n_pl)))))))))),
% 44.33/8.68 inference('rw', [status(thm)], [zip_derived_cl496, '2'])).
% 44.33/8.68 thf(zip_derived_cl499, plain,
% 44.33/8.68 (~ (all_of @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 44.33/8.68 ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (iii @ '#sk2'))))) @
% 44.33/8.68 ((('#B') @ ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))))) @ n_pl)))))))),
% 44.33/8.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl497])).
% 44.33/8.68 thf(zip_derived_cl500, plain,
% 44.33/8.68 (~ (((!!) @ (^[Y0 : $i]:
% 44.33/8.68 (((is_of @ Y0 @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 44.33/8.68 ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset)))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#B') @
% 44.33/8.68 ((('#B') @ (=>) @ (iii @ '#sk2'))))) @
% 44.33/8.68 ((('#B') @ ((('#S') @ ((('#B') @ iii @
% 44.33/8.68 (n_pl @ '#sk2'))))) @
% 44.33/8.68 n_pl)))) @
% 44.33/8.68 Y0)))))))),
% 44.33/8.68 inference('rw_clause', [status(thm)], [zip_derived_cl499, '1'])).
% 44.33/8.68 thf(zip_derived_cl501, plain,
% 44.33/8.68 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 44.33/8.68 ((('#C') @ is_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset))))))))) @
% 44.33/8.68 ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#B') @
% 44.33/8.68 ((('#B') @ (=>) @ (iii @ '#sk2'))))) @
% 44.33/8.68 ((('#B') @ ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))))) @
% 44.33/8.68 n_pl))))))))))),
% 44.33/8.68 inference('comb-normalize', [status(thm)], [zip_derived_cl500])).
% 44.33/8.68 thf(zip_derived_cl502, plain,
% 44.33/8.68 (~ (((is_of @ '#sk3' @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 44.33/8.68 (all_of @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 44.33/8.68 ((('#B') @ (((=>) @ (iii @ '#sk2' @ '#sk3'))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @ (n_pl @ '#sk3'))))))))),
% 44.33/8.68 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl501])).
% 44.33/8.68 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 44.33/8.68 thf('3', plain,
% 44.33/8.68 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 44.33/8.68 define([status(thm)])).
% 44.33/8.68 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))).
% 44.33/8.68 thf('4', plain,
% 44.33/8.68 (![X1:$i,X0:$i]:
% 44.33/8.68 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 44.33/8.68 define([status(thm)])).
% 44.33/8.68 thf(zip_derived_cl503, plain,
% 44.33/8.68 (~ (((in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 44.33/8.68 (all_of @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 44.33/8.68 ((('#B') @ (((=>) @ (l_some @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ '#sk3' @ '#sk2')))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @ (n_pl @ '#sk3'))))))))),
% 44.33/8.68 inference('rw', [status(thm)], [zip_derived_cl502, '2', '0', '3', '4'])).
% 44.33/8.68 thf(zip_derived_cl505, plain,
% 44.33/8.68 (~ (all_of @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 44.33/8.68 ((('#B') @ (((=>) @ (l_some @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ '#sk3' @ '#sk2')))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @ (n_pl @ '#sk3'))))))),
% 44.33/8.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl503])).
% 44.33/8.68 thf(zip_derived_cl506, plain,
% 44.33/8.68 (~ (((!!) @ (^[Y0 : $i]:
% 44.33/8.68 (((is_of @ Y0 @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 44.33/8.68 ((('#B') @ (((=>) @ (l_some @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ '#sk3' @ '#sk2')))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @
% 44.33/8.68 (n_pl @ '#sk3'))) @
% 44.33/8.68 Y0)))))))),
% 44.33/8.68 inference('rw_clause', [status(thm)], [zip_derived_cl505, '1'])).
% 44.33/8.68 thf(zip_derived_cl507, plain,
% 44.33/8.68 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 44.33/8.68 ((('#C') @ is_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset))))))))) @
% 44.33/8.68 ((('#B') @ (((=>) @ (l_some @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ '#sk3' @ '#sk2')))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @
% 44.33/8.68 (n_pl @ '#sk3')))))))))),
% 44.33/8.68 inference('comb-normalize', [status(thm)], [zip_derived_cl506])).
% 44.33/8.68 thf(zip_derived_cl508, plain,
% 44.33/8.68 (~ (((is_of @ '#sk4' @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 44.33/8.68 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ '#sk3' @ '#sk2')) => (iii @
% 44.33/8.68 (n_pl @ '#sk2' @ '#sk4') @ (n_pl @ '#sk3' @ '#sk4'))))))),
% 44.33/8.68 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl507])).
% 44.33/8.68 thf(def_n_pl, axiom,(( n_pl @ (X0)@ (X1)) = ((ap @ (plus @ X0) @ X1)))).
% 44.33/8.68 thf('5', plain,
% 44.33/8.68 (![X1:$i,X0:$i]: ( ( n_pl @ X0 @ X1 ) = ( ap @ ( plus @ X0 ) @ X1 ) )),
% 44.33/8.68 define([status(thm)])).
% 44.33/8.68 thf(zip_derived_cl509, plain,
% 44.33/8.68 (~ (((in @ '#sk4' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 44.33/8.68 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ '#sk3' @ '#sk2')) => (l_some @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk4') @
% 44.33/8.68 (ap @ (plus @ '#sk2') @ '#sk4')))))))),
% 44.33/8.68 inference('rw', [status(thm)],
% 44.33/8.68 [zip_derived_cl508, '2', '0', '3', '5', '5', '4'])).
% 44.33/8.68 thf(zip_derived_cl511, plain,
% 44.33/8.68 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ '#sk3' @ '#sk2')) => (l_some @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk4') @
% 44.33/8.68 (ap @ (plus @ '#sk2') @ '#sk4')))))),
% 44.33/8.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl509])).
% 44.33/8.68 thf(zip_derived_cl513, plain,
% 44.33/8.68 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk4') @
% 44.33/8.68 (ap @ (plus @ '#sk2') @ '#sk4')))),
% 44.33/8.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl511])).
% 44.33/8.68 thf(satz19a, axiom,
% 44.33/8.68 (all_of @
% 44.33/8.68 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 44.33/8.68 ( ^[X0:$i]:
% 44.33/8.68 ( all_of @
% 44.33/8.68 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 44.33/8.68 ( ^[X1:$i]:
% 44.33/8.68 ( all_of @
% 44.33/8.68 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 44.33/8.68 ( ^[X2:$i]:
% 44.33/8.68 ( ( d_29_ii @ X0 @ X1 ) =>
% 44.33/8.68 ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) ) ) ) ) ) ))).
% 44.33/8.68 thf(zip_derived_cl155, plain,
% 44.33/8.68 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 44.33/8.68 (^[Y0 : $i]:
% 44.33/8.68 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 44.33/8.68 (^[Y1 : $i]:
% 44.33/8.68 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @
% 44.33/8.68 (^[Y2 : $i]:
% 44.33/8.68 (((d_29_ii @ Y0 @ Y1) => (d_29_ii @ (n_pl @ Y0 @ Y2) @
% 44.33/8.68 (n_pl @ Y1 @ Y2))))))))))),
% 44.33/8.68 inference('cnf', [status(esa)], [satz19a])).
% 44.33/8.68 thf(zip_derived_cl156, plain,
% 44.33/8.68 ( (all_of @ ((('#C') @ in @ nat)) @
% 44.33/8.68 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 44.33/8.68 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#S') @
% 44.33/8.68 ((('#B') @ ((('#B') @ ('#B'))) @
% 44.33/8.68 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))) @
% 44.33/8.68 ((('#C') @ ((('#B') @ ('#B') @
% 44.33/8.68 ((('#B') @ ('#S') @
% 44.33/8.68 ((('#B') @ ((('#B') @ d_29_ii)) @ n_pl)))))) @
% 44.33/8.68 n_pl)))))))))),
% 44.33/8.68 inference('lams2combs', [status(thm)], [zip_derived_cl155])).
% 44.33/8.68 thf(zip_derived_cl1037, plain,
% 44.33/8.68 ( (all_of @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 44.33/8.68 ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 44.33/8.68 ((('#B') @ ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset)))))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#S') @
% 44.33/8.68 ((('#B') @ ((('#B') @ ('#B'))) @
% 44.33/8.68 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))) @
% 44.33/8.68 ((('#C') @ ((('#B') @ ('#B') @
% 44.33/8.68 ((('#B') @ ('#S') @
% 44.33/8.68 ((('#B') @ ((('#B') @ d_29_ii)) @ n_pl)))))) @
% 44.33/8.68 n_pl)))))))))),
% 44.33/8.68 inference('rw', [status(thm)], [zip_derived_cl156, '0'])).
% 44.33/8.68 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 44.33/8.68 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 44.33/8.68 thf('6', plain,
% 44.33/8.68 (![X0:( $i > $o ),X1:( $i > $o )]:
% 44.33/8.68 ( ( all_of @ X0 @ X1 ) <=>
% 44.33/8.68 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 44.33/8.68 inference('rw.lit', [status(esa)], [def_all_of])).
% 44.33/8.68 thf(zip_derived_cl1038, plain,
% 44.33/8.68 ( (((!!) @ (^[Y0 : $i]:
% 44.33/8.68 (((is_of @ Y0 @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 44.33/8.68 ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset)))))) @
% 44.33/8.68 ((('#B') @ ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset)))))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#S') @
% 44.33/8.68 ((('#B') @ ((('#B') @ ('#B'))) @
% 44.33/8.68 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))) @
% 44.33/8.68 ((('#C') @ ((('#B') @ ('#B') @
% 44.33/8.68 ((('#B') @ ('#S') @
% 44.33/8.68 ((('#B') @ ((('#B') @ d_29_ii)) @
% 44.33/8.68 n_pl)))))) @
% 44.33/8.68 n_pl)))))) @
% 44.33/8.68 Y0)))))))),
% 44.33/8.68 inference('rw_clause', [status(thm)], [zip_derived_cl1037, '6'])).
% 44.33/8.68 thf(zip_derived_cl1039, plain,
% 44.33/8.68 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 44.33/8.68 ((('#C') @ is_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 44.33/8.68 ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 44.33/8.68 ((('#B') @ ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset)))))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#S') @
% 44.33/8.68 ((('#B') @ ((('#B') @ ('#B'))) @
% 44.33/8.68 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))) @
% 44.33/8.68 ((('#C') @ ((('#B') @ ('#B') @
% 44.33/8.68 ((('#B') @ ('#S') @
% 44.33/8.68 ((('#B') @ ((('#B') @ d_29_ii)) @ n_pl)))))) @
% 44.33/8.68 n_pl))))))))))))),
% 44.33/8.68 inference('comb-normalize', [status(thm)], [zip_derived_cl1038])).
% 44.33/8.68 thf(zip_derived_cl1040, plain,
% 44.33/8.68 (![X2 : $i]:
% 44.33/8.68 (((is_of @ X2 @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 44.33/8.68 (all_of @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 44.33/8.68 ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (d_29_ii @ X2))))) @
% 44.33/8.68 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X2))))) @
% 44.33/8.68 n_pl)))))))))),
% 44.33/8.68 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1039])).
% 44.33/8.68 thf(zip_derived_cl1041, plain,
% 44.33/8.68 (![X2 : $i]:
% 44.33/8.68 (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 44.33/8.68 (all_of @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 44.33/8.68 ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (d_29_ii @ X2))))) @
% 44.33/8.68 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X2))))) @
% 44.33/8.68 n_pl)))))))))),
% 44.33/8.68 inference('rw', [status(thm)], [zip_derived_cl1040, '2'])).
% 44.33/8.68 thf(zip_derived_cl1042, plain,
% 44.33/8.68 (![X2 : $i]:
% 44.33/8.68 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 44.33/8.68 | (all_of @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 44.33/8.68 ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#B') @
% 44.33/8.68 ((('#B') @ (=>) @ (d_29_ii @ X2))))) @
% 44.33/8.68 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X2))))) @
% 44.33/8.68 n_pl))))))))),
% 44.33/8.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1041])).
% 44.33/8.68 thf(zip_derived_cl1043, plain,
% 44.33/8.68 (![X0 : $i]:
% 44.33/8.68 ( (((!!) @ (^[Y0 : $i]:
% 44.33/8.68 (((is_of @ Y0 @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 44.33/8.68 ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset)))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#B') @
% 44.33/8.68 ((('#B') @ (=>) @ (d_29_ii @ X0))))) @
% 44.33/8.68 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @
% 44.33/8.68 (n_pl @ X0))))) @
% 44.33/8.68 n_pl)))) @
% 44.33/8.68 Y0)))))))
% 44.33/8.68 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 44.33/8.68 inference('rw_clause', [status(thm)], [zip_derived_cl1042, '6'])).
% 44.33/8.68 thf(zip_derived_cl1044, plain,
% 44.33/8.68 (![X0 : $i]:
% 44.33/8.68 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 44.33/8.68 ((('#C') @ is_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset))))))))) @
% 44.33/8.68 ((('#B') @ (all_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset)))))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ ('#B') @
% 44.33/8.68 ((('#B') @ (=>) @ (d_29_ii @ X0))))) @
% 44.33/8.68 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @
% 44.33/8.68 (n_pl @ X0))))) @
% 44.33/8.68 n_pl))))))))))
% 44.33/8.68 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 44.33/8.68 inference('comb-normalize', [status(thm)], [zip_derived_cl1043])).
% 44.33/8.68 thf(zip_derived_cl1045, plain,
% 44.33/8.68 (![X0 : $i, X2 : $i]:
% 44.33/8.68 ( (((is_of @ X2 @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 44.33/8.68 (all_of @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 44.33/8.68 ((('#B') @ (((=>) @ (d_29_ii @ X0 @ X2))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @ (n_pl @ X2))))))))
% 44.33/8.68 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 44.33/8.68 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1044])).
% 44.33/8.68 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) =
% 44.33/8.68 ((n_some @ (diffprop @ X0 @ X1))))).
% 44.33/8.68 thf('7', plain,
% 44.33/8.68 (![X1:$i,X0:$i]:
% 44.33/8.68 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 44.33/8.68 define([status(thm)])).
% 44.33/8.68 thf(zip_derived_cl1046, plain,
% 44.33/8.68 (![X0 : $i, X2 : $i]:
% 44.33/8.68 ( (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 44.33/8.68 (all_of @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 44.33/8.68 ((('#B') @ (((=>) @ (l_some @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ X0 @ X2)))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @ (n_pl @ X2))))))))
% 44.33/8.68 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 44.33/8.68 inference('rw', [status(thm)], [zip_derived_cl1045, '2', '0', '3', '7'])).
% 44.33/8.68 thf(zip_derived_cl1047, plain,
% 44.33/8.68 (![X0 : $i, X2 : $i]:
% 44.33/8.68 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 44.33/8.68 | (all_of @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 44.33/8.68 ((('#B') @ (((=>) @ (l_some @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ X0 @ X2)))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @ (n_pl @ X2))))))
% 44.33/8.68 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 44.33/8.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1046])).
% 44.33/8.68 thf(zip_derived_cl1048, plain,
% 44.33/8.68 (![X0 : $i, X1 : $i]:
% 44.33/8.68 ( (((!!) @ (^[Y0 : $i]:
% 44.33/8.68 (((is_of @ Y0 @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 44.33/8.68 ((('#B') @ (((=>) @ (l_some @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ X0 @ X1)))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @
% 44.33/8.68 (n_pl @ X1))) @
% 44.33/8.68 Y0)))))))
% 44.33/8.68 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 44.33/8.68 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 44.33/8.68 inference('rw_clause', [status(thm)], [zip_derived_cl1047, '6'])).
% 44.33/8.68 thf(zip_derived_cl1049, plain,
% 44.33/8.68 (![X0 : $i, X1 : $i]:
% 44.33/8.68 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 44.33/8.68 ((('#C') @ is_of @
% 44.33/8.68 ((('#C') @ in @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset))))))))) @
% 44.33/8.68 ((('#B') @ (((=>) @ (l_some @
% 44.33/8.68 (d_Sep @ omega @
% 44.33/8.68 ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ X0 @ X1)))) @
% 44.33/8.68 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @
% 44.33/8.68 (n_pl @ X1)))))))))
% 44.33/8.68 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 44.33/8.68 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 44.33/8.68 inference('comb-normalize', [status(thm)], [zip_derived_cl1048])).
% 44.33/8.68 thf(zip_derived_cl1050, plain,
% 44.33/8.68 (![X0 : $i, X1 : $i, X3 : $i]:
% 44.33/8.68 ( (((is_of @ X3 @
% 44.33/8.68 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 44.33/8.68 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ X0 @ X1)) => (d_29_ii @ (n_pl @ X0 @ X3) @
% 44.33/8.68 (n_pl @ X1 @ X3))))))
% 44.33/8.68 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 44.33/8.68 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 44.33/8.68 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1049])).
% 44.33/8.68 thf(zip_derived_cl1051, plain,
% 44.33/8.68 (![X0 : $i, X1 : $i, X3 : $i]:
% 44.33/8.68 ( (((in @ X3 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 44.33/8.68 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ X0 @ X1)) => (l_some @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ (ap @ (plus @ X0) @ X3) @ (ap @ (plus @ X1) @ X3)))))))
% 44.33/8.68 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 44.33/8.68 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 44.33/8.68 inference('rw', [status(thm)],
% 44.33/8.68 [zip_derived_cl1050, '2', '0', '3', '5', '5', '7'])).
% 44.33/8.68 thf(zip_derived_cl1052, plain,
% 44.33/8.68 (![X0 : $i, X1 : $i, X3 : $i]:
% 44.33/8.68 (~ (in @ X3 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 44.33/8.68 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ X0 @ X1)) => (l_some @
% 44.33/8.68 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ (ap @ (plus @ X0) @ X3) @ (ap @ (plus @ X1) @ X3)))))
% 44.33/8.68 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 44.33/8.68 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 44.33/8.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1051])).
% 44.33/8.68 thf(zip_derived_cl1053, plain,
% 44.33/8.68 (![X0 : $i, X1 : $i, X3 : $i]:
% 44.33/8.68 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ X0 @ X1))
% 44.33/8.68 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ (ap @ (plus @ X0) @ X3) @ (ap @ (plus @ X1) @ X3)))
% 44.33/8.68 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 44.33/8.68 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 44.33/8.68 | ~ (in @ X3 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 44.33/8.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1052])).
% 44.33/8.68 thf(zip_derived_cl5077, plain,
% 44.33/8.68 ((~ (in @ '#sk4' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 44.33/8.68 | ~ (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 44.33/8.68 | ~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 44.33/8.68 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ '#sk3' @ '#sk2')))),
% 44.33/8.68 inference('sup+', [status(thm)], [zip_derived_cl513, zip_derived_cl1053])).
% 44.33/8.68 thf(zip_derived_cl510, plain,
% 44.33/8.68 ( (in @ '#sk4' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 44.33/8.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl509])).
% 44.33/8.68 thf(zip_derived_cl504, plain,
% 44.33/8.68 ( (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 44.33/8.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl503])).
% 44.33/8.68 thf(zip_derived_cl498, plain,
% 44.33/8.68 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 44.33/8.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl497])).
% 44.33/8.68 thf(zip_derived_cl512, plain,
% 44.33/8.68 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 44.33/8.68 (diffprop @ '#sk3' @ '#sk2'))),
% 44.33/8.68 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl511])).
% 44.33/8.68 thf(zip_derived_cl5119, plain, ($false),
% 44.33/8.68 inference('demod', [status(thm)],
% 44.33/8.68 [zip_derived_cl5077, zip_derived_cl510, zip_derived_cl504,
% 44.33/8.68 zip_derived_cl498, zip_derived_cl512])).
% 44.33/8.68
% 44.33/8.68 % SZS output end Refutation
% 44.33/8.68
% 44.33/8.68
% 44.33/8.68 % Terminating...
% 44.84/8.83 % Runner terminated.
% 44.84/8.84 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------