%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM677^4 : 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.7bB5WWE3uj true
% Computer : n018.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 04:47:57 PM UTC 2025
% Result : Theorem 22.97s 3.54s
% Output : Refutation 22.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM677^4 : TPTP v9.2.0. Released v7.1.0.
% 0.13/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.7bB5WWE3uj true
% 0.13/0.35 % Computer : n018.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 : Wed Oct 1 16:28:38 EDT 2025
% 0.20/0.35 % CPUTime :
% 0.20/0.35 % Running portfolio for 300 s
% 0.20/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.35 % Number of cores: 8
% 0.20/0.35 % Python version: Python 3.6.8
% 0.20/0.35 % Running in HO mode
% 0.55/0.67 % Total configuration time : 828
% 0.55/0.67 % Estimated wc time : 1656
% 0.55/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.55/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.56/0.73 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 22.97/3.54 % Solved by lams/40_b.comb.sh.
% 22.97/3.54 % done 328 iterations in 2.756s
% 22.97/3.54 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 22.97/3.54 % SZS output start Refutation
% 22.97/3.54 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
% 22.97/3.54 thf(nat_type, type, nat: $i).
% 22.97/3.54 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 22.97/3.54 thf(in_type, type, in: $i > $i > $o).
% 22.97/3.54 thf('#sk3_type', type, '#sk3': $i).
% 22.97/3.54 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 22.97/3.54 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 22.97/3.54 thf('#sk2_type', type, '#sk2': $i).
% 22.97/3.54 thf(ap_type, type, ap: $i > $i > $i).
% 22.97/3.54 thf(emptyset_type, type, emptyset: $i).
% 22.97/3.54 thf('#sk4_type', type, '#sk4': $i).
% 22.97/3.54 thf(n_is_type, type, n_is: $i > $i > $o).
% 22.97/3.54 thf(omega_type, type, omega: $i).
% 22.97/3.54 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 22.97/3.54 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 22.97/3.54 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 22.97/3.54 thf(plus_type, type, plus: $i > $i).
% 22.97/3.54 thf('#sk5_type', type, '#sk5': $i).
% 22.97/3.54 thf(e_is_type, type, e_is: $i > $i > $i > $o).
% 22.97/3.54 thf(n_pl_type, type, n_pl: $i > $i > $i).
% 22.97/3.54 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 22.97/3.54 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 22.97/3.54 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 22.97/3.54 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 22.97/3.54 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 22.97/3.54 thf(satz19a, axiom,
% 22.97/3.54 (all_of @
% 22.97/3.54 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 22.97/3.54 ( ^[X0:$i]:
% 22.97/3.54 ( all_of @
% 22.97/3.54 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 22.97/3.54 ( ^[X1:$i]:
% 22.97/3.54 ( all_of @
% 22.97/3.54 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 22.97/3.54 ( ^[X2:$i]:
% 22.97/3.54 ( ( d_29_ii @ X0 @ X1 ) =>
% 22.97/3.54 ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) ) ) ) ) ) ))).
% 22.97/3.54 thf(zip_derived_cl96, plain,
% 22.97/3.54 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 22.97/3.54 (^[Y0 : $i]:
% 22.97/3.54 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 22.97/3.54 (^[Y1 : $i]:
% 22.97/3.54 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @
% 22.97/3.54 (^[Y2 : $i]:
% 22.97/3.54 (((d_29_ii @ Y0 @ Y1) => (d_29_ii @ (n_pl @ Y0 @ Y2) @
% 22.97/3.54 (n_pl @ Y1 @ Y2))))))))))),
% 22.97/3.54 inference('cnf', [status(esa)], [satz19a])).
% 22.97/3.54 thf(zip_derived_cl97, plain,
% 22.97/3.54 ( (all_of @ ((('#C') @ in @ nat)) @
% 22.97/3.54 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 22.97/3.54 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @
% 22.97/3.54 ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.54 ((('#B') @ ((('#B') @ ('#B'))) @
% 22.97/3.54 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))) @
% 22.97/3.54 ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.54 ((('#B') @ ('#S') @
% 22.97/3.54 ((('#B') @ ((('#B') @ d_29_ii)) @ n_pl)))))) @
% 22.97/3.54 n_pl)))))))))),
% 22.97/3.54 inference('lams2combs', [status(thm)], [zip_derived_cl96])).
% 22.97/3.54 thf(def_nat, axiom,(( nat ) =
% 22.97/3.54 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))).
% 22.97/3.54 thf('0', plain,
% 22.97/3.54 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )),
% 22.97/3.54 define([status(thm)])).
% 22.97/3.54 thf(zip_derived_cl846, plain,
% 22.97/3.54 ( (all_of @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 22.97/3.54 ((('#B') @ (all_of @
% 22.97/3.54 ((('#C') @ in @
% 22.97/3.54 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.54 ((('#B') @ ((('#B') @ (all_of @
% 22.97/3.54 ((('#C') @ in @
% 22.97/3.54 (d_Sep @ omega @
% 22.97/3.54 ((('#C') @ (!=) @ emptyset)))))))) @
% 22.97/3.54 ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.54 ((('#B') @ ((('#B') @ ('#B'))) @
% 22.97/3.54 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))) @
% 22.97/3.54 ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.54 ((('#B') @ ('#S') @
% 22.97/3.54 ((('#B') @ ((('#B') @ d_29_ii)) @ n_pl)))))) @
% 22.97/3.54 n_pl)))))))))),
% 22.97/3.54 inference('rw', [status(thm)], [zip_derived_cl97, '0'])).
% 22.97/3.54 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 22.97/3.54 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 22.97/3.54 thf('1', plain,
% 22.97/3.54 (![X0:( $i > $o ),X1:( $i > $o )]:
% 22.97/3.54 ( ( all_of @ X0 @ X1 ) <=>
% 22.97/3.54 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 22.97/3.54 inference('rw.lit', [status(esa)], [def_all_of])).
% 22.97/3.54 thf(zip_derived_cl847, plain,
% 22.97/3.54 ( (((!!) @ (^[Y0 : $i]:
% 22.97/3.54 (((is_of @ Y0 @
% 22.97/3.54 ((('#C') @ in @
% 22.97/3.54 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.54 ((('#B') @ (all_of @
% 22.97/3.54 ((('#C') @ in @
% 22.97/3.54 (d_Sep @ omega @
% 22.97/3.54 ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.54 ((('#B') @ ((('#B') @ (all_of @
% 22.97/3.54 ((('#C') @ in @
% 22.97/3.54 (d_Sep @ omega @
% 22.97/3.54 ((('#C') @ (!=) @ emptyset)))))))) @
% 22.97/3.54 ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.54 ((('#B') @ ((('#B') @ ('#B'))) @
% 22.97/3.54 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))) @
% 22.97/3.54 ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.54 ((('#B') @ ('#S') @
% 22.97/3.54 ((('#B') @ ((('#B') @ d_29_ii)) @
% 22.97/3.54 n_pl)))))) @
% 22.97/3.54 n_pl)))))) @
% 22.97/3.54 Y0)))))))),
% 22.97/3.54 inference('rw_clause', [status(thm)], [zip_derived_cl846, '1'])).
% 22.97/3.54 thf(zip_derived_cl848, plain,
% 22.97/3.54 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 22.97/3.54 ((('#C') @ is_of @
% 22.97/3.54 ((('#C') @ in @
% 22.97/3.54 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 22.97/3.54 ((('#B') @ (all_of @
% 22.97/3.54 ((('#C') @ in @
% 22.97/3.54 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.54 ((('#B') @ ((('#B') @ (all_of @
% 22.97/3.54 ((('#C') @ in @
% 22.97/3.54 (d_Sep @ omega @
% 22.97/3.54 ((('#C') @ (!=) @ emptyset)))))))) @
% 22.97/3.54 ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.54 ((('#B') @ ((('#B') @ ('#B'))) @
% 22.97/3.54 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))) @
% 22.97/3.54 ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.54 ((('#B') @ ('#S') @
% 22.97/3.54 ((('#B') @ ((('#B') @ d_29_ii)) @ n_pl)))))) @
% 22.97/3.54 n_pl))))))))))))),
% 22.97/3.54 inference('comb-normalize', [status(thm)], [zip_derived_cl847])).
% 22.97/3.54 thf(zip_derived_cl849, plain,
% 22.97/3.54 (![X2 : $i]:
% 22.97/3.54 (((is_of @ X2 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.54 (all_of @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 22.97/3.54 ((('#B') @ (all_of @
% 22.97/3.54 ((('#C') @ in @
% 22.97/3.54 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.54 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (d_29_ii @ X2))))) @
% 22.97/3.54 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X2))))) @
% 22.97/3.54 n_pl)))))))))),
% 22.97/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl848])).
% 22.97/3.54 thf(zip_derived_cl850, plain,
% 22.97/3.54 (![X2 : $i]:
% 22.97/3.54 (~ (is_of @ X2 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 22.97/3.54 | (all_of @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 22.97/3.54 ((('#B') @ (all_of @
% 22.97/3.54 ((('#C') @ in @
% 22.97/3.54 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.54 ((('#S') @ ((('#B') @ ('#B') @
% 22.97/3.54 ((('#B') @ (=>) @ (d_29_ii @ X2))))) @
% 22.97/3.54 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X2))))) @
% 22.97/3.54 n_pl))))))))),
% 22.97/3.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl849])).
% 22.97/3.54 thf(zip_derived_cl851, plain,
% 22.97/3.54 (![X0 : $i]:
% 22.97/3.54 ( (((!!) @ (^[Y0 : $i]:
% 22.97/3.54 (((is_of @ Y0 @
% 22.97/3.54 ((('#C') @ in @
% 22.97/3.54 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.54 ((('#B') @ (all_of @
% 22.97/3.54 ((('#C') @ in @
% 22.97/3.54 (d_Sep @ omega @
% 22.97/3.54 ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.54 ((('#S') @ ((('#B') @ ('#B') @
% 22.97/3.54 ((('#B') @ (=>) @ (d_29_ii @ X0))))) @
% 22.97/3.54 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @
% 22.97/3.54 (n_pl @ X0))))) @
% 22.97/3.54 n_pl)))) @
% 22.97/3.54 Y0)))))))
% 22.97/3.54 | ~ (is_of @ X0 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 22.97/3.54 inference('rw_clause', [status(thm)], [zip_derived_cl850, '1'])).
% 22.97/3.54 thf(zip_derived_cl852, plain,
% 22.97/3.54 (![X0 : $i]:
% 22.97/3.54 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 22.97/3.54 ((('#C') @ is_of @
% 22.97/3.54 ((('#C') @ in @
% 22.97/3.54 (d_Sep @ omega @
% 22.97/3.54 ((('#C') @ (!=) @ emptyset))))))))) @
% 22.97/3.54 ((('#B') @ (all_of @
% 22.97/3.54 ((('#C') @ in @
% 22.97/3.54 (d_Sep @ omega @
% 22.97/3.54 ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.54 ((('#S') @ ((('#B') @ ('#B') @
% 22.97/3.54 ((('#B') @ (=>) @ (d_29_ii @ X0))))) @
% 22.97/3.54 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @
% 22.97/3.54 (n_pl @ X0))))) @
% 22.97/3.54 n_pl))))))))))
% 22.97/3.54 | ~ (is_of @ X0 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 22.97/3.54 inference('comb-normalize', [status(thm)], [zip_derived_cl851])).
% 22.97/3.54 thf(zip_derived_cl853, plain,
% 22.97/3.54 (![X0 : $i, X2 : $i]:
% 22.97/3.54 ( (((is_of @ X2 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.54 (all_of @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 22.97/3.54 ((('#B') @ (((=>) @ (d_29_ii @ X0 @ X2))) @
% 22.97/3.54 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @ (n_pl @ X2))))))))
% 22.97/3.54 | ~ (is_of @ X0 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 22.97/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl852])).
% 22.97/3.54 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 22.97/3.54 thf('2', plain,
% 22.97/3.54 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 22.97/3.54 define([status(thm)])).
% 22.97/3.54 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) =
% 22.97/3.54 ((n_some @ (diffprop @ X0 @ X1))))).
% 22.97/3.54 thf('3', plain,
% 22.97/3.54 (![X1:$i,X0:$i]:
% 22.97/3.54 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 22.97/3.54 define([status(thm)])).
% 22.97/3.54 thf(zip_derived_cl854, plain,
% 22.97/3.54 (![X0 : $i, X2 : $i]:
% 22.97/3.54 ( (((is_of @ X2 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.54 (all_of @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 22.97/3.54 ((('#B') @ (((=>) @ (l_some @
% 22.97/3.54 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.54 (diffprop @ X0 @ X2)))) @
% 22.97/3.54 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @ (n_pl @ X2))))))))
% 22.97/3.54 | ~ (is_of @ X0 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 22.97/3.54 inference('rw', [status(thm)], [zip_derived_cl853, '0', '2', '3'])).
% 22.97/3.54 thf(zip_derived_cl855, plain,
% 22.97/3.54 (![X0 : $i, X2 : $i]:
% 22.97/3.54 (~ (is_of @ X2 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 22.97/3.54 | (all_of @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 22.97/3.54 ((('#B') @ (((=>) @ (l_some @
% 22.97/3.54 (d_Sep @ omega @
% 22.97/3.54 ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.54 (diffprop @ X0 @ X2)))) @
% 22.97/3.54 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @ (n_pl @ X2))))))
% 22.97/3.54 | ~ (is_of @ X0 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 22.97/3.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl854])).
% 22.97/3.54 thf(zip_derived_cl856, plain,
% 22.97/3.54 (![X0 : $i, X1 : $i]:
% 22.97/3.54 ( (((!!) @ (^[Y0 : $i]:
% 22.97/3.54 (((is_of @ Y0 @
% 22.97/3.54 ((('#C') @ in @
% 22.97/3.54 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.54 ((('#B') @ (((=>) @ (l_some @
% 22.97/3.54 (d_Sep @ omega @
% 22.97/3.54 ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.54 (diffprop @ X0 @ X1)))) @
% 22.97/3.54 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @
% 22.97/3.54 (n_pl @ X1))) @
% 22.97/3.54 Y0)))))))
% 22.97/3.54 | ~ (is_of @ X0 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 22.97/3.54 | ~ (is_of @ X1 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 22.97/3.54 inference('rw_clause', [status(thm)], [zip_derived_cl855, '1'])).
% 22.97/3.54 thf(zip_derived_cl857, plain,
% 22.97/3.54 (![X0 : $i, X1 : $i]:
% 22.97/3.54 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 22.97/3.54 ((('#C') @ is_of @
% 22.97/3.54 ((('#C') @ in @
% 22.97/3.54 (d_Sep @ omega @
% 22.97/3.54 ((('#C') @ (!=) @ emptyset))))))))) @
% 22.97/3.54 ((('#B') @ (((=>) @ (l_some @
% 22.97/3.54 (d_Sep @ omega @
% 22.97/3.54 ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.54 (diffprop @ X0 @ X1)))) @
% 22.97/3.54 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @
% 22.97/3.54 (n_pl @ X1)))))))))
% 22.97/3.54 | ~ (is_of @ X0 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 22.97/3.54 | ~ (is_of @ X1 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 22.97/3.54 inference('comb-normalize', [status(thm)], [zip_derived_cl856])).
% 22.97/3.54 thf(zip_derived_cl858, plain,
% 22.97/3.54 (![X0 : $i, X1 : $i, X3 : $i]:
% 22.97/3.54 ( (((is_of @ X3 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.54 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.54 (diffprop @ X0 @ X1)) => (d_29_ii @ (n_pl @ X0 @ X3) @
% 22.97/3.54 (n_pl @ X1 @ X3))))))
% 22.97/3.54 | ~ (is_of @ X1 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 22.97/3.54 | ~ (is_of @ X0 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 22.97/3.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl857])).
% 22.97/3.54 thf(def_n_pl, axiom,(( n_pl @ (X0)@ (X1)) = ((ap @ (plus @ X0) @ X1)))).
% 22.97/3.54 thf('4', plain,
% 22.97/3.54 (![X1:$i,X0:$i]: ( ( n_pl @ X0 @ X1 ) = ( ap @ ( plus @ X0 ) @ X1 ) )),
% 22.97/3.54 define([status(thm)])).
% 22.97/3.54 thf(zip_derived_cl859, plain,
% 22.97/3.54 (![X0 : $i, X1 : $i, X3 : $i]:
% 22.97/3.54 ( (((is_of @ X3 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.54 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.54 (diffprop @ X0 @ X1)) => (l_some @
% 22.97/3.54 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.54 (diffprop @ (ap @ (plus @ X0) @ X3) @ (ap @ (plus @ X1) @ X3)))))))
% 22.97/3.54 | ~ (is_of @ X1 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 22.97/3.54 | ~ (is_of @ X0 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 22.97/3.54 inference('rw', [status(thm)],
% 22.97/3.54 [zip_derived_cl858, '0', '2', '4', '4', '3'])).
% 22.97/3.54 thf(zip_derived_cl860, plain,
% 22.97/3.54 (![X0 : $i, X1 : $i, X3 : $i]:
% 22.97/3.54 (~ (is_of @ X3 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 22.97/3.54 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.54 (diffprop @ X0 @ X1)) => (l_some @
% 22.97/3.54 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.54 (diffprop @ (ap @ (plus @ X0) @ X3) @ (ap @ (plus @ X1) @ X3)))))
% 22.97/3.54 | ~ (is_of @ X0 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 22.97/3.54 | ~ (is_of @ X1 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 22.97/3.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl859])).
% 22.97/3.54 thf(zip_derived_cl861, plain,
% 22.97/3.54 (![X0 : $i, X1 : $i, X3 : $i]:
% 22.97/3.54 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.54 (diffprop @ X0 @ X1))
% 22.97/3.54 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.54 (diffprop @ (ap @ (plus @ X0) @ X3) @ (ap @ (plus @ X1) @ X3)))
% 22.97/3.54 | ~ (is_of @ X1 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 22.97/3.54 | ~ (is_of @ X0 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 22.97/3.54 | ~ (is_of @ X3 @
% 22.97/3.54 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 22.97/3.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl860])).
% 22.97/3.54 thf(satz19h, conjecture,
% 22.97/3.54 (all_of @
% 22.97/3.54 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 22.97/3.54 ( ^[X0:$i]:
% 22.97/3.54 ( all_of @
% 22.97/3.54 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 22.97/3.54 ( ^[X1:$i]:
% 22.97/3.54 ( all_of @
% 22.97/3.54 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 22.97/3.54 ( ^[X2:$i]:
% 22.97/3.54 ( all_of @
% 22.97/3.54 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @
% 22.97/3.54 ( ^[X3:$i]:
% 22.97/3.54 ( ( n_is @ X0 @ X1 ) =>
% 22.97/3.54 ( ( d_29_ii @ X2 @ X3 ) =>
% 22.97/3.54 ( d_29_ii @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ))).
% 22.97/3.54 thf(zf_stmt_0, negated_conjecture,
% 22.97/3.54 (~( all_of @
% 22.97/3.54 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 22.97/3.54 ( ^[X0:$i]:
% 22.97/3.54 ( all_of @
% 22.97/3.54 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 22.97/3.54 ( ^[X1:$i]:
% 22.97/3.54 ( all_of @
% 22.97/3.54 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 22.97/3.54 ( ^[X2:$i]:
% 22.97/3.54 ( all_of @
% 22.97/3.54 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @
% 22.97/3.55 ( ^[X3:$i]:
% 22.97/3.55 ( ( n_is @ X0 @ X1 ) =>
% 22.97/3.55 ( ( d_29_ii @ X2 @ X3 ) =>
% 22.97/3.55 ( d_29_ii @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ) )),
% 22.97/3.55 inference('cnf.neg', [status(esa)], [satz19h])).
% 22.97/3.55 thf(zip_derived_cl110, plain,
% 22.97/3.55 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 22.97/3.55 (^[Y0 : $i]:
% 22.97/3.55 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 22.97/3.55 (^[Y1 : $i]:
% 22.97/3.55 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @
% 22.97/3.55 (^[Y2 : $i]:
% 22.97/3.55 (all_of @ (^[Y3 : $i]: (in @ Y3 @ nat)) @
% 22.97/3.55 (^[Y3 : $i]:
% 22.97/3.55 (((n_is @ Y0 @ Y1) =>
% 22.97/3.55 (((d_29_ii @ Y2 @ Y3) => (d_29_ii @
% 22.97/3.55 (n_pl @ Y2 @ Y0) @ (n_pl @ Y3 @ Y1))))))))))))))),
% 22.97/3.55 inference('cnf', [status(esa)], [zf_stmt_0])).
% 22.97/3.55 thf(zip_derived_cl111, plain,
% 22.97/3.55 (~ (all_of @ ((('#C') @ in @ nat)) @
% 22.97/3.55 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.55 ((('#B') @ ((('#B') @ ('#B'))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ ('#B'))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.55 ((('#B') @ ((('#B') @ (=>))) @
% 22.97/3.55 d_29_ii)))))))) @
% 22.97/3.55 ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ ('#C') @
% 22.97/3.55 ((('#B') @ ((('#B') @ ('#B'))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ d_29_ii)) @
% 22.97/3.55 ((('#C') @ n_pl)))))))))) @
% 22.97/3.55 ((('#C') @ n_pl)))))))))))))))),
% 22.97/3.55 inference('lams2combs', [status(thm)], [zip_derived_cl110])).
% 22.97/3.55 thf(zip_derived_cl765, plain,
% 22.97/3.55 (~ (all_of @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 22.97/3.55 ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @
% 22.97/3.55 ((('#C') @ (!=) @ emptyset)))))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @
% 22.97/3.55 ((('#C') @ (!=) @ emptyset)))))))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.55 ((('#B') @ ((('#B') @ ('#B'))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ ('#B'))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.55 ((('#B') @ ((('#B') @ (=>))) @
% 22.97/3.55 d_29_ii)))))))) @
% 22.97/3.55 ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ ('#C') @
% 22.97/3.55 ((('#B') @ ((('#B') @ ('#B'))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ d_29_ii)) @
% 22.97/3.55 ((('#C') @ n_pl)))))))))) @
% 22.97/3.55 ((('#C') @ n_pl)))))))))))))))),
% 22.97/3.55 inference('rw', [status(thm)], [zip_derived_cl111, '0'])).
% 22.97/3.55 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 22.97/3.55 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 22.97/3.55 thf('5', plain,
% 22.97/3.55 (![X0:( $i > $o ),X1:( $i > $o )]:
% 22.97/3.55 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 22.97/3.55 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 22.97/3.55 inference('rw.lit', [status(esa)], [def_all_of])).
% 22.97/3.55 thf(zip_derived_cl766, plain,
% 22.97/3.55 (~ (((!!) @ (^[Y0 : $i]:
% 22.97/3.55 (((is_of @ Y0 @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.55 ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @
% 22.97/3.55 ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @
% 22.97/3.55 ((('#C') @ (!=) @ emptyset)))))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @
% 22.97/3.55 omega @
% 22.97/3.55 ((('#C') @ (
% 22.97/3.55 !=) @
% 22.97/3.55 emptyset)))))))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.55 ((('#B') @ ((('#B') @ ('#B'))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ ('#B'))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (=>))) @
% 22.97/3.55 n_is)))))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 22.97/3.55 '#S') @
% 22.97/3.55 ((('#B') @ (
% 22.97/3.55 (('#B') @ (
% 22.97/3.55 =>))) @
% 22.97/3.55 d_29_ii)))))))) @
% 22.97/3.55 ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ ('#C') @
% 22.97/3.55 ((('#B') @ ((('#B') @ ('#B'))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ d_29_ii)) @
% 22.97/3.55 ((('#C') @ n_pl)))))))))) @
% 22.97/3.55 ((('#C') @ n_pl)))))))))))) @
% 22.97/3.55 Y0)))))))),
% 22.97/3.55 inference('rw_clause', [status(thm)], [zip_derived_cl765, '5'])).
% 22.97/3.55 thf(zip_derived_cl767, plain,
% 22.97/3.55 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 22.97/3.55 ((('#C') @ is_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @
% 22.97/3.55 ((('#C') @ (!=) @ emptyset))))))))) @
% 22.97/3.55 ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @
% 22.97/3.55 ((('#C') @ (!=) @ emptyset)))))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @
% 22.97/3.55 ((('#C') @ (
% 22.97/3.55 !=) @ emptyset)))))))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.55 ((('#B') @ ((('#B') @ ('#B'))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ ('#B'))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 22.97/3.55 '#S') @
% 22.97/3.55 ((('#B') @ (
% 22.97/3.55 (('#B') @ (=>))) @
% 22.97/3.55 d_29_ii)))))))) @
% 22.97/3.55 ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ ('#C') @
% 22.97/3.55 ((('#B') @ ((('#B') @ ('#B'))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ d_29_ii)) @
% 22.97/3.55 ((('#C') @ n_pl)))))))))) @
% 22.97/3.55 ((('#C') @ n_pl))))))))))))))))))),
% 22.97/3.55 inference('comb-normalize', [status(thm)], [zip_derived_cl766])).
% 22.97/3.55 thf(zip_derived_cl768, plain,
% 22.97/3.55 (~ (((is_of @ '#sk2' @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.55 (all_of @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 22.97/3.55 ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @
% 22.97/3.55 ((('#C') @ (!=) @ emptyset)))))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ (=>) @ (n_is @ '#sk2'))))))) @
% 22.97/3.55 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.55 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))) @
% 22.97/3.55 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ d_29_ii @
% 22.97/3.55 ((('#C') @ n_pl @ '#sk2')))))))) @
% 22.97/3.55 ((('#C') @ n_pl)))))))))))))))),
% 22.97/3.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl767])).
% 22.97/3.55 thf(zip_derived_cl770, plain,
% 22.97/3.55 (~ (all_of @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 22.97/3.55 ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @
% 22.97/3.55 ((('#C') @ (!=) @ emptyset)))))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ (=>) @ (n_is @ '#sk2'))))))) @
% 22.97/3.55 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.55 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))) @
% 22.97/3.55 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ d_29_ii @
% 22.97/3.55 ((('#C') @ n_pl @ '#sk2')))))))) @
% 22.97/3.55 ((('#C') @ n_pl)))))))))))))),
% 22.97/3.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl768])).
% 22.97/3.55 thf(zip_derived_cl771, plain,
% 22.97/3.55 (~ (((!!) @ (^[Y0 : $i]:
% 22.97/3.55 (((is_of @ Y0 @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.55 ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @
% 22.97/3.55 ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @
% 22.97/3.55 ((('#C') @ (!=) @ emptyset)))))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ (=>) @ (n_is @ '#sk2'))))))) @
% 22.97/3.55 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.55 ((('#B') @ ((('#B') @ (=>))) @
% 22.97/3.55 d_29_ii)))))) @
% 22.97/3.55 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ d_29_ii @
% 22.97/3.55 ((('#C') @ n_pl @
% 22.97/3.55 '#sk2')))))))) @
% 22.97/3.55 ((('#C') @ n_pl)))))))))) @
% 22.97/3.55 Y0)))))))),
% 22.97/3.55 inference('rw_clause', [status(thm)], [zip_derived_cl770, '5'])).
% 22.97/3.55 thf(zip_derived_cl772, plain,
% 22.97/3.55 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 22.97/3.55 ((('#C') @ is_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @
% 22.97/3.55 ((('#C') @ (!=) @ emptyset))))))))) @
% 22.97/3.55 ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @
% 22.97/3.55 ((('#C') @ (!=) @ emptyset)))))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ (=>) @ (n_is @ '#sk2'))))))) @
% 22.97/3.55 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.55 ((('#B') @ ((('#B') @ (=>))) @
% 22.97/3.55 d_29_ii)))))) @
% 22.97/3.55 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ d_29_ii @
% 22.97/3.55 ((('#C') @ n_pl @ '#sk2')))))))) @
% 22.97/3.55 ((('#C') @ n_pl))))))))))))))))),
% 22.97/3.55 inference('comb-normalize', [status(thm)], [zip_derived_cl771])).
% 22.97/3.55 thf(zip_derived_cl773, plain,
% 22.97/3.55 (~ (((is_of @ '#sk3' @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.55 (all_of @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 22.97/3.55 ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ '#sk2' @ '#sk3'))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.55 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 22.97/3.55 ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ d_29_ii @ ((('#C') @ n_pl @ '#sk2')))))) @
% 22.97/3.55 ((('#C') @ n_pl @ '#sk3')))))))))))))),
% 22.97/3.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl772])).
% 22.97/3.55 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))).
% 22.97/3.55 thf('6', plain,
% 22.97/3.55 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )),
% 22.97/3.55 define([status(thm)])).
% 22.97/3.55 thf(def_n_is, axiom,(( n_is @ (X0)@ (X1)) = ((e_is @ nat @ X0 @ X1)))).
% 22.97/3.55 thf('7', plain,
% 22.97/3.55 (![X1:$i,X0:$i]: ( ( n_is @ X0 @ X1 ) = ( e_is @ nat @ X0 @ X1 ) )),
% 22.97/3.55 define([status(thm)])).
% 22.97/3.55 thf(zip_derived_cl774, plain,
% 22.97/3.55 (~ (((is_of @ '#sk3' @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.55 (all_of @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 22.97/3.55 ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (((=>) @ ((('#sk2') = ('#sk3'))))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.55 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 22.97/3.55 ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ d_29_ii @ ((('#C') @ n_pl @ '#sk2')))))) @
% 22.97/3.55 ((('#C') @ n_pl @ '#sk3')))))))))))))),
% 22.97/3.55 inference('rw', [status(thm)], [zip_derived_cl773, '6', '0', '7'])).
% 22.97/3.55 thf(zip_derived_cl776, plain,
% 22.97/3.55 (~ (all_of @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 22.97/3.55 ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (((=>) @ ((('#sk2') = ('#sk3'))))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.55 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 22.97/3.55 ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ d_29_ii @ ((('#C') @ n_pl @ '#sk2')))))) @
% 22.97/3.55 ((('#C') @ n_pl @ '#sk3')))))))))))),
% 22.97/3.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl774])).
% 22.97/3.55 thf(zip_derived_cl777, plain,
% 22.97/3.55 (~ (((!!) @ (^[Y0 : $i]:
% 22.97/3.55 (((is_of @ Y0 @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.55 ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @
% 22.97/3.55 ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (((=>) @ ((('#sk2') = ('#sk3'))))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.55 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 22.97/3.55 ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ d_29_ii @
% 22.97/3.55 ((('#C') @ n_pl @ '#sk2')))))) @
% 22.97/3.55 ((('#C') @ n_pl @ '#sk3')))))))) @
% 22.97/3.55 Y0)))))))),
% 22.97/3.55 inference('rw_clause', [status(thm)], [zip_derived_cl776, '5'])).
% 22.97/3.55 thf(zip_derived_cl778, plain,
% 22.97/3.55 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 22.97/3.55 ((('#C') @ is_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @
% 22.97/3.55 ((('#C') @ (!=) @ emptyset))))))))) @
% 22.97/3.55 ((('#B') @ (all_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 22.97/3.55 ((('#B') @ ((('#B') @ (((=>) @ ((('#sk2') = ('#sk3'))))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ ('#S') @
% 22.97/3.55 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 22.97/3.55 ((('#C') @ ((('#B') @ ('#B') @
% 22.97/3.55 ((('#B') @ d_29_ii @
% 22.97/3.55 ((('#C') @ n_pl @ '#sk2')))))) @
% 22.97/3.55 ((('#C') @ n_pl @ '#sk3'))))))))))))))),
% 22.97/3.55 inference('comb-normalize', [status(thm)], [zip_derived_cl777])).
% 22.97/3.55 thf(zip_derived_cl779, plain,
% 22.97/3.55 (~ (((is_of @ '#sk4' @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.55 (all_of @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 22.97/3.55 ((('#B') @ (((=>) @ ((('#sk2') = ('#sk3'))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk4'))) @
% 22.97/3.55 ((('#B') @ (d_29_ii @ (n_pl @ '#sk4' @ '#sk2')) @
% 22.97/3.55 ((('#C') @ n_pl @ '#sk3')))))))))))),
% 22.97/3.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl778])).
% 22.97/3.55 thf(zip_derived_cl780, plain,
% 22.97/3.55 (~ (((is_of @ '#sk4' @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.55 (all_of @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 22.97/3.55 ((('#B') @ (((=>) @ ((('#sk2') = ('#sk3'))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk4'))) @
% 22.97/3.55 ((('#B') @ (d_29_ii @ (ap @ (plus @ '#sk4') @ '#sk2')) @
% 22.97/3.55 ((('#C') @ n_pl @ '#sk3')))))))))))),
% 22.97/3.55 inference('rw', [status(thm)], [zip_derived_cl779, '4'])).
% 22.97/3.55 thf(zip_derived_cl782, plain,
% 22.97/3.55 (~ (all_of @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 22.97/3.55 ((('#B') @ (((=>) @ ((('#sk2') = ('#sk3'))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk4'))) @
% 22.97/3.55 ((('#B') @ (d_29_ii @ (ap @ (plus @ '#sk4') @ '#sk2')) @
% 22.97/3.55 ((('#C') @ n_pl @ '#sk3')))))))))),
% 22.97/3.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl780])).
% 22.97/3.55 thf(zip_derived_cl783, plain,
% 22.97/3.55 (~ (((!!) @ (^[Y0 : $i]:
% 22.97/3.55 (((is_of @ Y0 @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.55 ((('#B') @ (((=>) @ ((('#sk2') = ('#sk3'))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk4'))) @
% 22.97/3.55 ((('#B') @ (d_29_ii @
% 22.97/3.55 (ap @ (plus @ '#sk4') @ '#sk2')) @
% 22.97/3.55 ((('#C') @ n_pl @ '#sk3')))))) @
% 22.97/3.55 Y0)))))))),
% 22.97/3.55 inference('rw_clause', [status(thm)], [zip_derived_cl782, '5'])).
% 22.97/3.55 thf(zip_derived_cl784, plain,
% 22.97/3.55 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 22.97/3.55 ((('#C') @ is_of @
% 22.97/3.55 ((('#C') @ in @
% 22.97/3.55 (d_Sep @ omega @
% 22.97/3.55 ((('#C') @ (!=) @ emptyset))))))))) @
% 22.97/3.55 ((('#B') @ (((=>) @ ((('#sk2') = ('#sk3'))))) @
% 22.97/3.55 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk4'))) @
% 22.97/3.55 ((('#B') @ (d_29_ii @ (ap @ (plus @ '#sk4') @ '#sk2')) @
% 22.97/3.55 ((('#C') @ n_pl @ '#sk3'))))))))))))),
% 22.97/3.55 inference('comb-normalize', [status(thm)], [zip_derived_cl783])).
% 22.97/3.55 thf(zip_derived_cl785, plain,
% 22.97/3.55 (~ (((is_of @ '#sk5' @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.55 ((((('#sk2') = ('#sk3'))) =>
% 22.97/3.55 (((d_29_ii @ '#sk4' @ '#sk5') => (d_29_ii @
% 22.97/3.55 (ap @ (plus @ '#sk4') @ '#sk2') @ (n_pl @ '#sk5' @ '#sk3'))))))))),
% 22.97/3.55 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl784])).
% 22.97/3.55 thf(zip_derived_cl786, plain,
% 22.97/3.55 (~ (((is_of @ '#sk5' @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 22.97/3.55 ((((('#sk2') = ('#sk3'))) =>
% 22.97/3.55 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.55 (diffprop @ '#sk4' @ '#sk5')) => (l_some @
% 22.97/3.55 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.55 (diffprop @ (ap @ (plus @ '#sk4') @ '#sk2') @
% 22.97/3.55 (ap @ (plus @ '#sk5') @ '#sk3')))))))))),
% 22.97/3.55 inference('rw', [status(thm)],
% 22.97/3.55 [zip_derived_cl785, '0', '2', '2', '4', '3', '3'])).
% 22.97/3.55 thf(zip_derived_cl788, plain,
% 22.97/3.55 (~ ((((('#sk2') = ('#sk3'))) =>
% 22.97/3.55 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.55 (diffprop @ '#sk4' @ '#sk5')) => (l_some @
% 22.97/3.55 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.55 (diffprop @ (ap @ (plus @ '#sk4') @ '#sk2') @
% 22.97/3.55 (ap @ (plus @ '#sk5') @ '#sk3')))))))),
% 22.97/3.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl786])).
% 22.97/3.55 thf(zip_derived_cl789, plain, ( ((('#sk2') = ('#sk3')))),
% 22.97/3.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl788])).
% 22.97/3.55 thf(zip_derived_cl791, plain, ((('#sk2') = ('#sk3'))),
% 22.97/3.55 inference('simplify nested equalities', [status(thm)],
% 22.97/3.55 [zip_derived_cl789])).
% 22.97/3.55 thf(zip_derived_cl790, plain,
% 22.97/3.55 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.55 (diffprop @ '#sk4' @ '#sk5')) => (l_some @
% 22.97/3.55 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.55 (diffprop @ (ap @ (plus @ '#sk4') @ '#sk2') @
% 22.97/3.55 (ap @ (plus @ '#sk5') @ '#sk3')))))),
% 22.97/3.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl788])).
% 22.97/3.55 thf(zip_derived_cl793, plain,
% 22.97/3.55 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.55 (diffprop @ (ap @ (plus @ '#sk4') @ '#sk2') @
% 22.97/3.55 (ap @ (plus @ '#sk5') @ '#sk3')))),
% 22.97/3.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl790])).
% 22.97/3.55 thf(zip_derived_cl1753, plain,
% 22.97/3.55 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.55 (diffprop @ (ap @ (plus @ '#sk4') @ '#sk2') @
% 22.97/3.55 (ap @ (plus @ '#sk5') @ '#sk2')))),
% 22.97/3.55 inference('sup-', [status(thm)], [zip_derived_cl791, zip_derived_cl793])).
% 22.97/3.55 thf(zip_derived_cl4072, plain,
% 22.97/3.55 ((~ (is_of @ '#sk2' @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 22.97/3.55 | ~ (is_of @ '#sk4' @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 22.97/3.55 | ~ (is_of @ '#sk5' @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 22.97/3.55 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.55 (diffprop @ '#sk4' @ '#sk5')))),
% 22.97/3.55 inference('sup-', [status(thm)], [zip_derived_cl861, zip_derived_cl1753])).
% 22.97/3.55 thf(zip_derived_cl769, plain,
% 22.97/3.55 ( (is_of @ '#sk2' @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 22.97/3.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl768])).
% 22.97/3.55 thf(zip_derived_cl781, plain,
% 22.97/3.55 ( (is_of @ '#sk4' @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 22.97/3.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl780])).
% 22.97/3.55 thf(zip_derived_cl787, plain,
% 22.97/3.55 ( (is_of @ '#sk5' @
% 22.97/3.55 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 22.97/3.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl786])).
% 22.97/3.55 thf(zip_derived_cl792, plain,
% 22.97/3.55 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 22.97/3.55 (diffprop @ '#sk4' @ '#sk5'))),
% 22.97/3.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl790])).
% 22.97/3.55 thf(zip_derived_cl4087, plain, ($false),
% 22.97/3.55 inference('demod', [status(thm)],
% 22.97/3.55 [zip_derived_cl4072, zip_derived_cl769, zip_derived_cl781,
% 22.97/3.55 zip_derived_cl787, zip_derived_cl792])).
% 22.97/3.55
% 22.97/3.55 % SZS output end Refutation
% 22.97/3.55
% 22.97/3.55
% 22.97/3.55 % Terminating...
% 23.55/3.57 % Runner terminated.
% 23.55/3.58 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------