%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM688^4 : TPTP v9.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.tL7RUq2MHN 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 04:48:00 PM UTC 2025
% Result : Theorem 56.32s 7.72s
% Output : Refutation 56.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM688^4 : TPTP v9.2.0. Released v7.1.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.tL7RUq2MHN true
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 1 16:25:23 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running portfolio for 300 s
% 0.14/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.34 % Number of cores: 8
% 0.14/0.34 % Python version: Python 3.6.8
% 0.14/0.34 % Running in HO mode
% 0.54/0.67 % Total configuration time : 828
% 0.54/0.67 % Estimated wc time : 1656
% 0.54/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.54/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.54/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.54/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.54/0.73 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 56.32/7.72 % Solved by lams/40_b.comb.sh.
% 56.32/7.72 % done 515 iterations in 6.904s
% 56.32/7.72 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 56.32/7.72 % SZS output start Refutation
% 56.32/7.72 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
% 56.32/7.72 thf(nat_type, type, nat: $i).
% 56.32/7.72 thf(moreis_type, type, moreis: $i > $i > $o).
% 56.32/7.72 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 56.32/7.72 thf(in_type, type, in: $i > $i > $o).
% 56.32/7.72 thf('#sk2_type', type, '#sk2': $i).
% 56.32/7.72 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 56.32/7.72 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 56.32/7.72 thf(ap_type, type, ap: $i > $i > $i).
% 56.32/7.72 thf('#sk4_type', type, '#sk4': $i).
% 56.32/7.72 thf(emptyset_type, type, emptyset: $i).
% 56.32/7.72 thf(n_is_type, type, n_is: $i > $i > $o).
% 56.32/7.72 thf(imp_type, type, imp: $o > $o > $o).
% 56.32/7.72 thf(omega_type, type, omega: $i).
% 56.32/7.72 thf('#sk5_type', type, '#sk5': $i).
% 56.32/7.72 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 56.32/7.72 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 56.32/7.72 thf('#sk3_type', type, '#sk3': $i).
% 56.32/7.72 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 56.32/7.72 thf(l_or_type, type, l_or: $o > $o > $o).
% 56.32/7.72 thf(d_not_type, type, d_not: $o > $o).
% 56.32/7.72 thf(plus_type, type, plus: $i > $i).
% 56.32/7.72 thf(n_pl_type, type, n_pl: $i > $i > $i).
% 56.32/7.72 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 56.32/7.72 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 56.32/7.72 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 56.32/7.72 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 56.32/7.72 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 56.32/7.72 thf(satz22b, conjecture,
% 56.32/7.72 (all_of @
% 56.32/7.72 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 56.32/7.72 ( ^[X0:$i]:
% 56.32/7.72 ( all_of @
% 56.32/7.72 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 56.32/7.72 ( ^[X1:$i]:
% 56.32/7.72 ( all_of @
% 56.32/7.72 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 56.32/7.72 ( ^[X2:$i]:
% 56.32/7.72 ( all_of @
% 56.32/7.72 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @
% 56.32/7.72 ( ^[X3:$i]:
% 56.32/7.72 ( ( d_29_ii @ X0 @ X1 ) =>
% 56.32/7.72 ( ( moreis @ X2 @ X3 ) =>
% 56.32/7.72 ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 56.32/7.72 thf(zf_stmt_0, negated_conjecture,
% 56.32/7.72 (~( all_of @
% 56.32/7.72 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 56.32/7.72 ( ^[X0:$i]:
% 56.32/7.72 ( all_of @
% 56.32/7.72 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 56.32/7.72 ( ^[X1:$i]:
% 56.32/7.72 ( all_of @
% 56.32/7.72 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 56.32/7.72 ( ^[X2:$i]:
% 56.32/7.72 ( all_of @
% 56.32/7.72 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @
% 56.32/7.72 ( ^[X3:$i]:
% 56.32/7.72 ( ( d_29_ii @ X0 @ X1 ) =>
% 56.32/7.72 ( ( moreis @ X2 @ X3 ) =>
% 56.32/7.72 ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) )),
% 56.32/7.72 inference('cnf.neg', [status(esa)], [satz22b])).
% 56.32/7.72 thf(zip_derived_cl144, plain,
% 56.32/7.72 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 56.32/7.72 (^[Y0 : $i]:
% 56.32/7.72 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 56.32/7.72 (^[Y1 : $i]:
% 56.32/7.72 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @
% 56.32/7.72 (^[Y2 : $i]:
% 56.32/7.72 (all_of @ (^[Y3 : $i]: (in @ Y3 @ nat)) @
% 56.32/7.72 (^[Y3 : $i]:
% 56.32/7.72 (((d_29_ii @ Y0 @ Y1) =>
% 56.32/7.72 (((moreis @ Y2 @ Y3) => (d_29_ii @
% 56.32/7.72 (n_pl @ Y0 @ Y2) @ (n_pl @ Y1 @ Y3))))))))))))))),
% 56.32/7.72 inference('cnf', [status(esa)], [zf_stmt_0])).
% 56.32/7.72 thf(zip_derived_cl145, plain,
% 56.32/7.72 (~ (all_of @ ((('#C') @ in @ nat)) @
% 56.32/7.72 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 moreis)))))))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#C') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ d_29_ii)) @ n_pl)))))))) @
% 56.32/7.72 n_pl)))))))))))))),
% 56.32/7.72 inference('lams2combs', [status(thm)], [zip_derived_cl144])).
% 56.32/7.72 thf(def_nat, axiom,(( nat ) =
% 56.32/7.72 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))).
% 56.32/7.72 thf('0', plain,
% 56.32/7.72 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )),
% 56.32/7.72 define([status(thm)])).
% 56.32/7.72 thf(zip_derived_cl763, plain,
% 56.32/7.72 (~ (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 moreis)))))))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#C') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ d_29_ii)) @ n_pl)))))))) @
% 56.32/7.72 n_pl)))))))))))))),
% 56.32/7.72 inference('rw', [status(thm)], [zip_derived_cl145, '0'])).
% 56.32/7.72 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 56.32/7.72 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 56.32/7.72 thf('1', plain,
% 56.32/7.72 (![X0:( $i > $o ),X1:( $i > $o )]:
% 56.32/7.72 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 56.32/7.72 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 56.32/7.72 inference('rw.lit', [status(esa)], [def_all_of])).
% 56.32/7.72 thf(zip_derived_cl764, plain,
% 56.32/7.72 (~ (((!!) @ (^[Y0 : $i]:
% 56.32/7.72 (((is_of @ Y0 @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @
% 56.32/7.72 omega @
% 56.32/7.72 ((('#C') @ (
% 56.32/7.72 !=) @
% 56.32/7.72 emptyset)))))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 56.32/7.72 '#S') @
% 56.32/7.72 ((('#B') @ (
% 56.32/7.72 (('#B') @ (
% 56.32/7.72 =>))) @
% 56.32/7.72 moreis)))))))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#C') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ d_29_ii)) @
% 56.32/7.72 n_pl)))))))) @
% 56.32/7.72 n_pl)))))))))) @
% 56.32/7.72 Y0)))))))),
% 56.32/7.72 inference('rw_clause', [status(thm)], [zip_derived_cl763, '1'])).
% 56.32/7.72 thf(zip_derived_cl765, plain,
% 56.32/7.72 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 56.32/7.72 ((('#C') @ is_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))))))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (
% 56.32/7.72 !=) @ emptyset)))))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 56.32/7.72 '#S') @
% 56.32/7.72 ((('#B') @ (
% 56.32/7.72 (('#B') @ (=>))) @
% 56.32/7.72 moreis)))))))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#C') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ d_29_ii)) @
% 56.32/7.72 n_pl)))))))) @
% 56.32/7.72 n_pl))))))))))))))))),
% 56.32/7.72 inference('comb-normalize', [status(thm)], [zip_derived_cl764])).
% 56.32/7.72 thf(zip_derived_cl766, plain,
% 56.32/7.72 (~ (((is_of @ '#sk2' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ (=>) @ (d_29_ii @ '#sk2'))))))) @
% 56.32/7.72 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ moreis)))))) @
% 56.32/7.72 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @ (n_pl @ '#sk2'))))))) @
% 56.32/7.72 n_pl)))))))))))))),
% 56.32/7.72 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl765])).
% 56.32/7.72 thf(zip_derived_cl768, plain,
% 56.32/7.72 (~ (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ (=>) @ (d_29_ii @ '#sk2'))))))) @
% 56.32/7.72 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ moreis)))))) @
% 56.32/7.72 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @ (n_pl @ '#sk2'))))))) @
% 56.32/7.72 n_pl)))))))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl766])).
% 56.32/7.72 thf(zip_derived_cl769, plain,
% 56.32/7.72 (~ (((!!) @ (^[Y0 : $i]:
% 56.32/7.72 (((is_of @ Y0 @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ (=>) @ (d_29_ii @ '#sk2'))))))) @
% 56.32/7.72 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 moreis)))))) @
% 56.32/7.72 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @
% 56.32/7.72 (n_pl @ '#sk2'))))))) @
% 56.32/7.72 n_pl)))))))) @
% 56.32/7.72 Y0)))))))),
% 56.32/7.72 inference('rw_clause', [status(thm)], [zip_derived_cl768, '1'])).
% 56.32/7.72 thf(zip_derived_cl770, plain,
% 56.32/7.72 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 56.32/7.72 ((('#C') @ is_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))))))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ (=>) @ (d_29_ii @ '#sk2'))))))) @
% 56.32/7.72 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 moreis)))))) @
% 56.32/7.72 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @
% 56.32/7.72 (n_pl @ '#sk2'))))))) @
% 56.32/7.72 n_pl))))))))))))))),
% 56.32/7.72 inference('comb-normalize', [status(thm)], [zip_derived_cl769])).
% 56.32/7.72 thf(zip_derived_cl771, plain,
% 56.32/7.72 (~ (((is_of @ '#sk3' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (((=>) @ (d_29_ii @ '#sk2' @ '#sk3'))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @ (n_pl @ '#sk2'))))) @
% 56.32/7.72 (n_pl @ '#sk3'))))))))))))),
% 56.32/7.72 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl770])).
% 56.32/7.72 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 56.32/7.72 thf('2', plain,
% 56.32/7.72 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 56.32/7.72 define([status(thm)])).
% 56.32/7.72 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) =
% 56.32/7.72 ((n_some @ (diffprop @ X0 @ X1))))).
% 56.32/7.72 thf('3', plain,
% 56.32/7.72 (![X1:$i,X0:$i]:
% 56.32/7.72 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 56.32/7.72 define([status(thm)])).
% 56.32/7.72 thf(zip_derived_cl772, plain,
% 56.32/7.72 (~ (((is_of @ '#sk3' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk2' @ '#sk3')))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @ (n_pl @ '#sk2'))))) @
% 56.32/7.72 (n_pl @ '#sk3'))))))))))))),
% 56.32/7.72 inference('rw', [status(thm)], [zip_derived_cl771, '0', '2', '3'])).
% 56.32/7.72 thf(zip_derived_cl774, plain,
% 56.32/7.72 (~ (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk2' @ '#sk3')))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @ (n_pl @ '#sk2'))))) @
% 56.32/7.72 (n_pl @ '#sk3'))))))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl772])).
% 56.32/7.72 thf(zip_derived_cl775, plain,
% 56.32/7.72 (~ (((!!) @ (^[Y0 : $i]:
% 56.32/7.72 (((is_of @ Y0 @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @
% 56.32/7.72 emptyset))) @
% 56.32/7.72 (diffprop @ '#sk2' @
% 56.32/7.72 '#sk3')))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @ (n_pl @ '#sk2'))))) @
% 56.32/7.72 (n_pl @ '#sk3'))))))) @
% 56.32/7.72 Y0)))))))),
% 56.32/7.72 inference('rw_clause', [status(thm)], [zip_derived_cl774, '1'])).
% 56.32/7.72 thf(zip_derived_cl776, plain,
% 56.32/7.72 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 56.32/7.72 ((('#C') @ is_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))))))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @
% 56.32/7.72 emptyset))) @
% 56.32/7.72 (diffprop @ '#sk2' @
% 56.32/7.72 '#sk3')))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @ (n_pl @ '#sk2'))))) @
% 56.32/7.72 (n_pl @ '#sk3')))))))))))))),
% 56.32/7.72 inference('comb-normalize', [status(thm)], [zip_derived_cl775])).
% 56.32/7.72 thf(zip_derived_cl777, plain,
% 56.32/7.72 (~ (((is_of @ '#sk4' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk2' @ '#sk3')))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ (=>) @ (moreis @ '#sk4'))) @
% 56.32/7.72 ((('#B') @ (d_29_ii @ (n_pl @ '#sk2' @ '#sk4')) @
% 56.32/7.72 (n_pl @ '#sk3'))))))))))),
% 56.32/7.72 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl776])).
% 56.32/7.72 thf(def_n_pl, axiom,(( n_pl @ (X0)@ (X1)) = ((ap @ (plus @ X0) @ X1)))).
% 56.32/7.72 thf('4', plain,
% 56.32/7.72 (![X1:$i,X0:$i]: ( ( n_pl @ X0 @ X1 ) = ( ap @ ( plus @ X0 ) @ X1 ) )),
% 56.32/7.72 define([status(thm)])).
% 56.32/7.72 thf(zip_derived_cl778, plain,
% 56.32/7.72 (~ (((is_of @ '#sk4' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk2' @ '#sk3')))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ (=>) @ (moreis @ '#sk4'))) @
% 56.32/7.72 ((('#B') @ (d_29_ii @ (ap @ (plus @ '#sk2') @ '#sk4')) @
% 56.32/7.72 (n_pl @ '#sk3'))))))))))),
% 56.32/7.72 inference('rw', [status(thm)], [zip_derived_cl777, '4'])).
% 56.32/7.72 thf(zip_derived_cl780, plain,
% 56.32/7.72 (~ (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk2' @ '#sk3')))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ (=>) @ (moreis @ '#sk4'))) @
% 56.32/7.72 ((('#B') @ (d_29_ii @ (ap @ (plus @ '#sk2') @ '#sk4')) @
% 56.32/7.72 (n_pl @ '#sk3'))))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl778])).
% 56.32/7.72 thf(zip_derived_cl781, plain,
% 56.32/7.72 (~ (((!!) @ (^[Y0 : $i]:
% 56.32/7.72 (((is_of @ Y0 @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk2' @ '#sk3')))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ (=>) @ (moreis @ '#sk4'))) @
% 56.32/7.72 ((('#B') @ (d_29_ii @
% 56.32/7.72 (ap @ (plus @ '#sk2') @ '#sk4')) @
% 56.32/7.72 (n_pl @ '#sk3'))))) @
% 56.32/7.72 Y0)))))))),
% 56.32/7.72 inference('rw_clause', [status(thm)], [zip_derived_cl780, '1'])).
% 56.32/7.72 thf(zip_derived_cl782, plain,
% 56.32/7.72 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 56.32/7.72 ((('#C') @ is_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))))))))) @
% 56.32/7.72 ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk2' @ '#sk3')))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ (=>) @ (moreis @ '#sk4'))) @
% 56.32/7.72 ((('#B') @ (d_29_ii @ (ap @ (plus @ '#sk2') @ '#sk4')) @
% 56.32/7.72 (n_pl @ '#sk3')))))))))))),
% 56.32/7.72 inference('comb-normalize', [status(thm)], [zip_derived_cl781])).
% 56.32/7.72 thf(zip_derived_cl783, plain,
% 56.32/7.72 (~ (((is_of @ '#sk5' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk2' @ '#sk3')) =>
% 56.32/7.72 (((moreis @ '#sk4' @ '#sk5') => (d_29_ii @
% 56.32/7.72 (ap @ (plus @ '#sk2') @ '#sk4') @ (n_pl @ '#sk3' @ '#sk5'))))))))),
% 56.32/7.72 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl782])).
% 56.32/7.72 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 56.32/7.72 thf('5', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 56.32/7.72 define([status(thm)])).
% 56.32/7.72 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 56.32/7.72 thf('6', plain,
% 56.32/7.72 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 56.32/7.72 define([status(thm)])).
% 56.32/7.72 thf(def_moreis, axiom,(( moreis @ (X0)@ (X1)) =
% 56.32/7.72 ((l_or @ (d_29_ii @ X0 @ X1) @ (n_is @ X0 @ X1))))).
% 56.32/7.72 thf('7', plain,
% 56.32/7.72 (![X1:$i,X0:$i]:
% 56.32/7.72 ( ( moreis @ X0 @ X1 ) =
% 56.32/7.72 ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
% 56.32/7.72 define([status(thm)])).
% 56.32/7.72 thf(zip_derived_cl784, plain,
% 56.32/7.72 (~ (((is_of @ '#sk5' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk2' @ '#sk3')) =>
% 56.32/7.72 (((imp @
% 56.32/7.72 (imp @
% 56.32/7.72 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk4' @ '#sk5')) @
% 56.32/7.72 ($false)) @
% 56.32/7.72 (n_is @ '#sk4' @ '#sk5')) => (l_some @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ (ap @ (plus @ '#sk2') @ '#sk4') @
% 56.32/7.72 (ap @ (plus @ '#sk3') @ '#sk5')))))))))),
% 56.32/7.72 inference('rw', [status(thm)],
% 56.32/7.72 [zip_derived_cl783, '5', '6', '0', '2', '2', '4', '3', '3', '7'])).
% 56.32/7.72 thf(zip_derived_cl786, plain,
% 56.32/7.72 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk2' @ '#sk3')) =>
% 56.32/7.72 (((imp @
% 56.32/7.72 (imp @
% 56.32/7.72 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk4' @ '#sk5')) @
% 56.32/7.72 ($false)) @
% 56.32/7.72 (n_is @ '#sk4' @ '#sk5')) => (l_some @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ (ap @ (plus @ '#sk2') @ '#sk4') @
% 56.32/7.72 (ap @ (plus @ '#sk3') @ '#sk5')))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl784])).
% 56.32/7.72 thf(zip_derived_cl788, plain,
% 56.32/7.72 (~ (((imp @
% 56.32/7.72 (imp @
% 56.32/7.72 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk4' @ '#sk5')) @
% 56.32/7.72 ($false)) @
% 56.32/7.72 (n_is @ '#sk4' @ '#sk5')) => (l_some @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ (ap @ (plus @ '#sk2') @ '#sk4') @
% 56.32/7.72 (ap @ (plus @ '#sk3') @ '#sk5')))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl786])).
% 56.32/7.72 thf(zip_derived_cl790, plain,
% 56.32/7.72 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ (ap @ (plus @ '#sk2') @ '#sk4') @
% 56.32/7.72 (ap @ (plus @ '#sk3') @ '#sk5')))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl788])).
% 56.32/7.72 thf(satz19h, axiom,
% 56.32/7.72 (all_of @
% 56.32/7.72 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 56.32/7.72 ( ^[X0:$i]:
% 56.32/7.72 ( all_of @
% 56.32/7.72 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 56.32/7.72 ( ^[X1:$i]:
% 56.32/7.72 ( all_of @
% 56.32/7.72 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 56.32/7.72 ( ^[X2:$i]:
% 56.32/7.72 ( all_of @
% 56.32/7.72 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @
% 56.32/7.72 ( ^[X3:$i]:
% 56.32/7.72 ( ( n_is @ X0 @ X1 ) =>
% 56.32/7.72 ( ( d_29_ii @ X2 @ X3 ) =>
% 56.32/7.72 ( d_29_ii @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ))).
% 56.32/7.72 thf(zip_derived_cl112, plain,
% 56.32/7.72 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 56.32/7.72 (^[Y0 : $i]:
% 56.32/7.72 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 56.32/7.72 (^[Y1 : $i]:
% 56.32/7.72 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @
% 56.32/7.72 (^[Y2 : $i]:
% 56.32/7.72 (all_of @ (^[Y3 : $i]: (in @ Y3 @ nat)) @
% 56.32/7.72 (^[Y3 : $i]:
% 56.32/7.72 (((n_is @ Y0 @ Y1) =>
% 56.32/7.72 (((d_29_ii @ Y2 @ Y3) => (d_29_ii @
% 56.32/7.72 (n_pl @ Y2 @ Y0) @ (n_pl @ Y3 @ Y1))))))))))))))),
% 56.32/7.72 inference('cnf', [status(esa)], [satz19h])).
% 56.32/7.72 thf(zip_derived_cl113, plain,
% 56.32/7.72 ( (all_of @ ((('#C') @ in @ nat)) @
% 56.32/7.72 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))))))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#C') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ d_29_ii)) @
% 56.32/7.72 ((('#C') @ n_pl)))))))))) @
% 56.32/7.72 ((('#C') @ n_pl)))))))))))))))),
% 56.32/7.72 inference('lams2combs', [status(thm)], [zip_derived_cl112])).
% 56.32/7.72 thf(zip_derived_cl1332, plain,
% 56.32/7.72 ( (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))))))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#C') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ d_29_ii)) @
% 56.32/7.72 ((('#C') @ n_pl)))))))))) @
% 56.32/7.72 ((('#C') @ n_pl)))))))))))))))),
% 56.32/7.72 inference('rw', [status(thm)], [zip_derived_cl113, '0'])).
% 56.32/7.72 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 56.32/7.72 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 56.32/7.72 thf('8', plain,
% 56.32/7.72 (![X0:( $i > $o ),X1:( $i > $o )]:
% 56.32/7.72 ( ( all_of @ X0 @ X1 ) <=>
% 56.32/7.72 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 56.32/7.72 inference('rw.lit', [status(esa)], [def_all_of])).
% 56.32/7.72 thf(zip_derived_cl1333, plain,
% 56.32/7.72 ( (((!!) @ (^[Y0 : $i]:
% 56.32/7.72 (((is_of @ Y0 @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (
% 56.32/7.72 !=) @ emptyset)))))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 n_is)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 56.32/7.72 '#S') @
% 56.32/7.72 ((('#B') @ (
% 56.32/7.72 (('#B') @ (
% 56.32/7.72 =>))) @
% 56.32/7.72 d_29_ii)))))))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#C') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ d_29_ii)) @
% 56.32/7.72 ((('#C') @ n_pl)))))))))) @
% 56.32/7.72 ((('#C') @ n_pl)))))))))))) @
% 56.32/7.72 Y0)))))))),
% 56.32/7.72 inference('rw_clause', [status(thm)], [zip_derived_cl1332, '8'])).
% 56.32/7.72 thf(zip_derived_cl1334, plain,
% 56.32/7.72 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 56.32/7.72 ((('#C') @ is_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (
% 56.32/7.72 !=) @ emptyset)))))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 56.32/7.72 '#S') @
% 56.32/7.72 ((('#B') @ (
% 56.32/7.72 (('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))))))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#C') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ d_29_ii)) @
% 56.32/7.72 ((('#C') @ n_pl)))))))))) @
% 56.32/7.72 ((('#C') @ n_pl))))))))))))))))))),
% 56.32/7.72 inference('comb-normalize', [status(thm)], [zip_derived_cl1333])).
% 56.32/7.72 thf(zip_derived_cl1335, plain,
% 56.32/7.72 (![X2 : $i]:
% 56.32/7.72 (((is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ (=>) @ (n_is @ X2))))))) @
% 56.32/7.72 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))))) @
% 56.32/7.72 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @
% 56.32/7.72 ((('#C') @ n_pl @ X2)))))))) @
% 56.32/7.72 ((('#C') @ n_pl)))))))))))))))),
% 56.32/7.72 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1334])).
% 56.32/7.72 thf(zip_derived_cl1336, plain,
% 56.32/7.72 (![X2 : $i]:
% 56.32/7.72 (~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ (=>) @ (n_is @ X2))))))) @
% 56.32/7.72 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))))) @
% 56.32/7.72 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @
% 56.32/7.72 ((('#C') @ n_pl @ X2)))))))) @
% 56.32/7.72 ((('#C') @ n_pl))))))))))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1335])).
% 56.32/7.72 thf(zip_derived_cl1337, plain,
% 56.32/7.72 (![X0 : $i]:
% 56.32/7.72 ( (((!!) @ (^[Y0 : $i]:
% 56.32/7.72 (((is_of @ Y0 @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ (=>) @ (n_is @ X0))))))) @
% 56.32/7.72 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (
% 56.32/7.72 =>))) @
% 56.32/7.72 d_29_ii)))))) @
% 56.32/7.72 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @
% 56.32/7.72 ((('#C') @ n_pl @ X0)))))))) @
% 56.32/7.72 ((('#C') @ n_pl)))))))))) @
% 56.32/7.72 Y0)))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('rw_clause', [status(thm)], [zip_derived_cl1336, '8'])).
% 56.32/7.72 thf(zip_derived_cl1338, plain,
% 56.32/7.72 (![X0 : $i]:
% 56.32/7.72 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 56.32/7.72 ((('#C') @ is_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))))))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ (=>) @ (n_is @ X0))))))) @
% 56.32/7.72 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))))) @
% 56.32/7.72 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @
% 56.32/7.72 ((('#C') @ n_pl @ X0)))))))) @
% 56.32/7.72 ((('#C') @ n_pl))))))))))))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('comb-normalize', [status(thm)], [zip_derived_cl1337])).
% 56.32/7.72 thf(zip_derived_cl1339, plain,
% 56.32/7.72 (![X0 : $i, X2 : $i]:
% 56.32/7.72 ( (((is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ X0 @ X2))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @ ((('#C') @ n_pl @ X0)))))) @
% 56.32/7.72 ((('#C') @ n_pl @ X2)))))))))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1338])).
% 56.32/7.72 thf(zip_derived_cl1340, plain,
% 56.32/7.72 (![X0 : $i, X2 : $i]:
% 56.32/7.72 (~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ X0 @ X2))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @ ((('#C') @ n_pl @ X0)))))) @
% 56.32/7.72 ((('#C') @ n_pl @ X2)))))))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1339])).
% 56.32/7.72 thf(zip_derived_cl1341, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i]:
% 56.32/7.72 ( (((!!) @ (^[Y0 : $i]:
% 56.32/7.72 (((is_of @ Y0 @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ X0 @ X1))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @
% 56.32/7.72 ((('#C') @ n_pl @ X0)))))) @
% 56.32/7.72 ((('#C') @ n_pl @ X1)))))))) @
% 56.32/7.72 Y0)))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('rw_clause', [status(thm)], [zip_derived_cl1340, '8'])).
% 56.32/7.72 thf(zip_derived_cl1342, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i]:
% 56.32/7.72 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 56.32/7.72 ((('#C') @ is_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))))))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ X0 @ X1))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @
% 56.32/7.72 ((('#C') @ n_pl @ X0)))))) @
% 56.32/7.72 ((('#C') @ n_pl @ X1))))))))))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('comb-normalize', [status(thm)], [zip_derived_cl1341])).
% 56.32/7.72 thf(zip_derived_cl1343, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X3 : $i]:
% 56.32/7.72 ( (((is_of @ X3 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (((=>) @ (n_is @ X0 @ X1))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X3))) @
% 56.32/7.72 ((('#B') @ (d_29_ii @ (n_pl @ X3 @ X0)) @
% 56.32/7.72 ((('#C') @ n_pl @ X1)))))))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1342])).
% 56.32/7.72 thf(zip_derived_cl1344, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X3 : $i]:
% 56.32/7.72 ( (((is_of @ X3 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (((=>) @ (n_is @ X0 @ X1))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X3))) @
% 56.32/7.72 ((('#B') @ (d_29_ii @ (ap @ (plus @ X3) @ X0)) @
% 56.32/7.72 ((('#C') @ n_pl @ X1)))))))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('rw', [status(thm)], [zip_derived_cl1343, '4'])).
% 56.32/7.72 thf(zip_derived_cl1345, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X3 : $i]:
% 56.32/7.72 (~ (is_of @ X3 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (((=>) @ (n_is @ X0 @ X1))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X3))) @
% 56.32/7.72 ((('#B') @ (d_29_ii @ (ap @ (plus @ X3) @ X0)) @
% 56.32/7.72 ((('#C') @ n_pl @ X1)))))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1344])).
% 56.32/7.72 thf(zip_derived_cl1346, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 56.32/7.72 ( (((!!) @ (^[Y0 : $i]:
% 56.32/7.72 (((is_of @ Y0 @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 ((('#B') @ (((=>) @ (n_is @ X1 @ X0))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X2))) @
% 56.32/7.72 ((('#B') @ (d_29_ii @ (ap @ (plus @ X2) @ X1)) @
% 56.32/7.72 ((('#C') @ n_pl @ X0)))))) @
% 56.32/7.72 Y0)))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('rw_clause', [status(thm)], [zip_derived_cl1345, '8'])).
% 56.32/7.72 thf(zip_derived_cl1347, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 56.32/7.72 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 56.32/7.72 ((('#C') @ is_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))))))))) @
% 56.32/7.72 ((('#B') @ (((=>) @ (n_is @ X1 @ X0))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X2))) @
% 56.32/7.72 ((('#B') @ (d_29_ii @ (ap @ (plus @ X2) @ X1)) @
% 56.32/7.72 ((('#C') @ n_pl @ X0))))))))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('comb-normalize', [status(thm)], [zip_derived_cl1346])).
% 56.32/7.72 thf(zip_derived_cl1348, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 56.32/7.72 ( (((is_of @ X4 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (((n_is @ X1 @ X0) =>
% 56.32/7.72 (((d_29_ii @ X2 @ X4) => (d_29_ii @ (ap @ (plus @ X2) @ X1) @
% 56.32/7.72 (n_pl @ X4 @ X0))))))))
% 56.32/7.72 | ~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1347])).
% 56.32/7.72 thf(zip_derived_cl1349, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 56.32/7.72 ( (((is_of @ X4 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (((n_is @ X1 @ X0) =>
% 56.32/7.72 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X2 @ X4)) => (l_some @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ (ap @ (plus @ X2) @ X1) @ (ap @ (plus @ X4) @ X0)))))))))
% 56.32/7.72 | ~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('rw', [status(thm)],
% 56.32/7.72 [zip_derived_cl1348, '0', '2', '2', '4', '3', '3'])).
% 56.32/7.72 thf(zip_derived_cl1350, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 56.32/7.72 (~ (is_of @ X4 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | (((n_is @ X1 @ X0) =>
% 56.32/7.72 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X2 @ X4)) => (l_some @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ (ap @ (plus @ X2) @ X1) @ (ap @ (plus @ X4) @ X0)))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1349])).
% 56.32/7.72 thf(zip_derived_cl1351, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 56.32/7.72 (~ (n_is @ X1 @ X0)
% 56.32/7.72 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X2 @ X4)) => (l_some @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ (ap @ (plus @ X2) @ X1) @ (ap @ (plus @ X4) @ X0)))))
% 56.32/7.72 | ~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X4 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1350])).
% 56.32/7.72 thf(zip_derived_cl1352, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 56.32/7.72 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X2 @ X4))
% 56.32/7.72 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ (ap @ (plus @ X2) @ X1) @ (ap @ (plus @ X4) @ X0)))
% 56.32/7.72 | ~ (is_of @ X4 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (n_is @ X1 @ X0))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1351])).
% 56.32/7.72 thf(zip_derived_cl9161, plain,
% 56.32/7.72 ((~ (n_is @ '#sk4' @ '#sk5')
% 56.32/7.72 | ~ (is_of @ '#sk2' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ '#sk4' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ '#sk5' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ '#sk3' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk2' @ '#sk3')))),
% 56.32/7.72 inference('sup+', [status(thm)], [zip_derived_cl790, zip_derived_cl1352])).
% 56.32/7.72 thf(zip_derived_cl790, plain,
% 56.32/7.72 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ (ap @ (plus @ '#sk2') @ '#sk4') @
% 56.32/7.72 (ap @ (plus @ '#sk3') @ '#sk5')))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl788])).
% 56.32/7.72 thf(satz21, axiom,
% 56.32/7.72 (all_of @
% 56.32/7.72 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 56.32/7.72 ( ^[X0:$i]:
% 56.32/7.72 ( all_of @
% 56.32/7.72 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 56.32/7.72 ( ^[X1:$i]:
% 56.32/7.72 ( all_of @
% 56.32/7.72 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 56.32/7.72 ( ^[X2:$i]:
% 56.32/7.72 ( all_of @
% 56.32/7.72 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @
% 56.32/7.72 ( ^[X3:$i]:
% 56.32/7.72 ( ( d_29_ii @ X0 @ X1 ) =>
% 56.32/7.72 ( ( d_29_ii @ X2 @ X3 ) =>
% 56.32/7.72 ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 56.32/7.72 thf(zip_derived_cl138, plain,
% 56.32/7.72 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 56.32/7.72 (^[Y0 : $i]:
% 56.32/7.72 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 56.32/7.72 (^[Y1 : $i]:
% 56.32/7.72 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @
% 56.32/7.72 (^[Y2 : $i]:
% 56.32/7.72 (all_of @ (^[Y3 : $i]: (in @ Y3 @ nat)) @
% 56.32/7.72 (^[Y3 : $i]:
% 56.32/7.72 (((d_29_ii @ Y0 @ Y1) =>
% 56.32/7.72 (((d_29_ii @ Y2 @ Y3) => (d_29_ii @
% 56.32/7.72 (n_pl @ Y0 @ Y2) @ (n_pl @ Y1 @ Y3))))))))))))))),
% 56.32/7.72 inference('cnf', [status(esa)], [satz21])).
% 56.32/7.72 thf(zip_derived_cl139, plain,
% 56.32/7.72 ( (all_of @ ((('#C') @ in @ nat)) @
% 56.32/7.72 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))))))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#C') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ d_29_ii)) @ n_pl)))))))) @
% 56.32/7.72 n_pl)))))))))))))),
% 56.32/7.72 inference('lams2combs', [status(thm)], [zip_derived_cl138])).
% 56.32/7.72 thf(zip_derived_cl1217, plain,
% 56.32/7.72 ( (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))))))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#C') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ d_29_ii)) @ n_pl)))))))) @
% 56.32/7.72 n_pl)))))))))))))),
% 56.32/7.72 inference('rw', [status(thm)], [zip_derived_cl139, '0'])).
% 56.32/7.72 thf(zip_derived_cl1218, plain,
% 56.32/7.72 ( (((!!) @ (^[Y0 : $i]:
% 56.32/7.72 (((is_of @ Y0 @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (
% 56.32/7.72 !=) @ emptyset)))))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 56.32/7.72 '#S') @
% 56.32/7.72 ((('#B') @ (
% 56.32/7.72 (('#B') @ (
% 56.32/7.72 =>))) @
% 56.32/7.72 d_29_ii)))))))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#C') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ d_29_ii)) @
% 56.32/7.72 n_pl)))))))) @
% 56.32/7.72 n_pl)))))))))) @
% 56.32/7.72 Y0)))))))),
% 56.32/7.72 inference('rw_clause', [status(thm)], [zip_derived_cl1217, '8'])).
% 56.32/7.72 thf(zip_derived_cl1219, plain,
% 56.32/7.72 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 56.32/7.72 ((('#C') @ is_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (
% 56.32/7.72 !=) @ emptyset)))))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 56.32/7.72 '#S') @
% 56.32/7.72 ((('#B') @ (
% 56.32/7.72 (('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))))))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#C') @
% 56.32/7.72 ((('#B') @ ((('#B') @ ('#B'))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ d_29_ii)) @
% 56.32/7.72 n_pl)))))))) @
% 56.32/7.72 n_pl))))))))))))))))),
% 56.32/7.72 inference('comb-normalize', [status(thm)], [zip_derived_cl1218])).
% 56.32/7.72 thf(zip_derived_cl1220, plain,
% 56.32/7.72 (![X2 : $i]:
% 56.32/7.72 (((is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ (=>) @ (d_29_ii @ X2))))))) @
% 56.32/7.72 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))))) @
% 56.32/7.72 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @ (n_pl @ X2))))))) @
% 56.32/7.72 n_pl)))))))))))))),
% 56.32/7.72 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1219])).
% 56.32/7.72 thf(zip_derived_cl1221, plain,
% 56.32/7.72 (![X2 : $i]:
% 56.32/7.72 (~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ (=>) @ (d_29_ii @ X2))))))) @
% 56.32/7.72 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))))) @
% 56.32/7.72 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @ (n_pl @ X2))))))) @
% 56.32/7.72 n_pl))))))))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1220])).
% 56.32/7.72 thf(zip_derived_cl1222, plain,
% 56.32/7.72 (![X0 : $i]:
% 56.32/7.72 ( (((!!) @ (^[Y0 : $i]:
% 56.32/7.72 (((is_of @ Y0 @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ (=>) @ (d_29_ii @ X0))))))) @
% 56.32/7.72 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (
% 56.32/7.72 =>))) @
% 56.32/7.72 d_29_ii)))))) @
% 56.32/7.72 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @
% 56.32/7.72 (n_pl @ X0))))))) @
% 56.32/7.72 n_pl)))))))) @
% 56.32/7.72 Y0)))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('rw_clause', [status(thm)], [zip_derived_cl1221, '8'])).
% 56.32/7.72 thf(zip_derived_cl1223, plain,
% 56.32/7.72 (![X0 : $i]:
% 56.32/7.72 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 56.32/7.72 ((('#C') @ is_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))))))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ (=>) @ (d_29_ii @ X0))))))) @
% 56.32/7.72 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))))) @
% 56.32/7.72 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @
% 56.32/7.72 (n_pl @ X0))))))) @
% 56.32/7.72 n_pl))))))))))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('comb-normalize', [status(thm)], [zip_derived_cl1222])).
% 56.32/7.72 thf(zip_derived_cl1224, plain,
% 56.32/7.72 (![X0 : $i, X2 : $i]:
% 56.32/7.72 ( (((is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (((=>) @ (d_29_ii @ X0 @ X2))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @ (n_pl @ X0))))) @
% 56.32/7.72 (n_pl @ X2))))))))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1223])).
% 56.32/7.72 thf(zip_derived_cl1225, plain,
% 56.32/7.72 (![X0 : $i, X2 : $i]:
% 56.32/7.72 ( (((is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X0 @ X2)))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @ (n_pl @ X0))))) @
% 56.32/7.72 (n_pl @ X2))))))))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('rw', [status(thm)], [zip_derived_cl1224, '0', '2', '3'])).
% 56.32/7.72 thf(zip_derived_cl1226, plain,
% 56.32/7.72 (![X0 : $i, X2 : $i]:
% 56.32/7.72 (~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X0 @ X2)))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @ (n_pl @ X0))))) @
% 56.32/7.72 (n_pl @ X2))))))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1225])).
% 56.32/7.72 thf(zip_derived_cl1227, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i]:
% 56.32/7.72 ( (((!!) @ (^[Y0 : $i]:
% 56.32/7.72 (((is_of @ Y0 @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (
% 56.32/7.72 !=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X0 @ X1)))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @
% 56.32/7.72 d_29_ii)))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @ (n_pl @ X0))))) @
% 56.32/7.72 (n_pl @ X1))))))) @
% 56.32/7.72 Y0)))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('rw_clause', [status(thm)], [zip_derived_cl1226, '8'])).
% 56.32/7.72 thf(zip_derived_cl1228, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i]:
% 56.32/7.72 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 56.32/7.72 ((('#C') @ is_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))))))))) @
% 56.32/7.72 ((('#B') @ (all_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset)))))) @
% 56.32/7.72 ((('#B') @ ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @
% 56.32/7.72 emptyset))) @
% 56.32/7.72 (diffprop @ X0 @ X1)))))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ ('#S') @
% 56.32/7.72 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @
% 56.32/7.72 ((('#C') @ ((('#B') @ ('#B') @
% 56.32/7.72 ((('#B') @ d_29_ii @ (n_pl @ X0))))) @
% 56.32/7.72 (n_pl @ X1)))))))))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('comb-normalize', [status(thm)], [zip_derived_cl1227])).
% 56.32/7.72 thf(zip_derived_cl1229, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X3 : $i]:
% 56.32/7.72 ( (((is_of @ X3 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X0 @ X1)))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X3))) @
% 56.32/7.72 ((('#B') @ (d_29_ii @ (n_pl @ X0 @ X3)) @ (n_pl @ X1))))))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1228])).
% 56.32/7.72 thf(zip_derived_cl1230, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X3 : $i]:
% 56.32/7.72 ( (((is_of @ X3 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X0 @ X1)))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X3))) @
% 56.32/7.72 ((('#B') @ (d_29_ii @ (ap @ (plus @ X0) @ X3)) @ (n_pl @ X1))))))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('rw', [status(thm)], [zip_derived_cl1229, '4'])).
% 56.32/7.72 thf(zip_derived_cl1231, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X3 : $i]:
% 56.32/7.72 (~ (is_of @ X3 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | (all_of @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 56.32/7.72 ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X0 @ X1)))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X3))) @
% 56.32/7.72 ((('#B') @ (d_29_ii @ (ap @ (plus @ X0) @ X3)) @ (n_pl @ X1))))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1230])).
% 56.32/7.72 thf(zip_derived_cl1232, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 56.32/7.72 ( (((!!) @ (^[Y0 : $i]:
% 56.32/7.72 (((is_of @ Y0 @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X1 @ X0)))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X2))) @
% 56.32/7.72 ((('#B') @ (d_29_ii @ (ap @ (plus @ X1) @ X2)) @
% 56.32/7.72 (n_pl @ X0))))) @
% 56.32/7.72 Y0)))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('rw_clause', [status(thm)], [zip_derived_cl1231, '8'])).
% 56.32/7.72 thf(zip_derived_cl1233, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 56.32/7.72 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 56.32/7.72 ((('#C') @ is_of @
% 56.32/7.72 ((('#C') @ in @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))))))))) @
% 56.32/7.72 ((('#B') @ (((=>) @ (l_some @
% 56.32/7.72 (d_Sep @ omega @
% 56.32/7.72 ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X1 @ X0)))) @
% 56.32/7.72 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X2))) @
% 56.32/7.72 ((('#B') @ (d_29_ii @ (ap @ (plus @ X1) @ X2)) @
% 56.32/7.72 (n_pl @ X0)))))))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('comb-normalize', [status(thm)], [zip_derived_cl1232])).
% 56.32/7.72 thf(zip_derived_cl1234, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 56.32/7.72 ( (((is_of @ X4 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X1 @ X0)) =>
% 56.32/7.72 (((d_29_ii @ X2 @ X4) => (d_29_ii @ (ap @ (plus @ X1) @ X2) @
% 56.32/7.72 (n_pl @ X0 @ X4))))))))
% 56.32/7.72 | ~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1233])).
% 56.32/7.72 thf(zip_derived_cl1235, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 56.32/7.72 ( (((is_of @ X4 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 56.32/7.72 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X1 @ X0)) =>
% 56.32/7.72 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X2 @ X4)) => (l_some @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ (ap @ (plus @ X1) @ X2) @ (ap @ (plus @ X0) @ X4)))))))))
% 56.32/7.72 | ~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('rw', [status(thm)],
% 56.32/7.72 [zip_derived_cl1234, '0', '2', '2', '4', '3', '3'])).
% 56.32/7.72 thf(zip_derived_cl1236, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 56.32/7.72 (~ (is_of @ X4 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X1 @ X0)) =>
% 56.32/7.72 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X2 @ X4)) => (l_some @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ (ap @ (plus @ X1) @ X2) @ (ap @ (plus @ X0) @ X4)))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1235])).
% 56.32/7.72 thf(zip_derived_cl1237, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 56.32/7.72 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X1 @ X0))
% 56.32/7.72 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X2 @ X4)) => (l_some @
% 56.32/7.72 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ (ap @ (plus @ X1) @ X2) @ (ap @ (plus @ X0) @ X4)))))
% 56.32/7.72 | ~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X4 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1236])).
% 56.32/7.72 thf(zip_derived_cl1238, plain,
% 56.32/7.72 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 56.32/7.72 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X2 @ X4))
% 56.32/7.72 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ (ap @ (plus @ X1) @ X2) @ (ap @ (plus @ X0) @ X4)))
% 56.32/7.72 | ~ (is_of @ X4 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X0 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X1 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ X2 @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ X1 @ X0)))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1237])).
% 56.32/7.72 thf(zip_derived_cl8714, plain,
% 56.32/7.72 ((~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk2' @ '#sk3'))
% 56.32/7.72 | ~ (is_of @ '#sk4' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ '#sk2' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ '#sk3' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (is_of @ '#sk5' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 56.32/7.72 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk4' @ '#sk5')))),
% 56.32/7.72 inference('sup+', [status(thm)], [zip_derived_cl790, zip_derived_cl1238])).
% 56.32/7.72 thf(zip_derived_cl787, plain,
% 56.32/7.72 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk2' @ '#sk3'))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl786])).
% 56.32/7.72 thf(zip_derived_cl779, plain,
% 56.32/7.72 ( (is_of @ '#sk4' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl778])).
% 56.32/7.72 thf(zip_derived_cl767, plain,
% 56.32/7.72 ( (is_of @ '#sk2' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl766])).
% 56.32/7.72 thf(zip_derived_cl773, plain,
% 56.32/7.72 ( (is_of @ '#sk3' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl772])).
% 56.32/7.72 thf(zip_derived_cl785, plain,
% 56.32/7.72 ( (is_of @ '#sk5' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl784])).
% 56.32/7.72 thf(zip_derived_cl8728, plain,
% 56.32/7.72 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk4' @ '#sk5'))),
% 56.32/7.72 inference('demod', [status(thm)],
% 56.32/7.72 [zip_derived_cl8714, zip_derived_cl787, zip_derived_cl779,
% 56.32/7.72 zip_derived_cl767, zip_derived_cl773, zip_derived_cl785])).
% 56.32/7.72 thf(zip_derived_cl789, plain,
% 56.32/7.72 ( (imp @
% 56.32/7.72 (imp @
% 56.32/7.72 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk4' @ '#sk5')) @
% 56.32/7.72 ($false)) @
% 56.32/7.72 (n_is @ '#sk4' @ '#sk5'))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl788])).
% 56.32/7.72 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 56.32/7.72 thf('9', plain,
% 56.32/7.72 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 56.32/7.72 inference('rw.lit', [status(esa)], [def_imp])).
% 56.32/7.72 thf(zip_derived_cl791, plain,
% 56.32/7.72 ( (((imp @
% 56.32/7.72 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk4' @ '#sk5')) @
% 56.32/7.72 ($false)) => (n_is @ '#sk4' @ '#sk5')))),
% 56.32/7.72 inference('rw_clause', [status(thm)], [zip_derived_cl789, '9'])).
% 56.32/7.72 thf(zip_derived_cl792, plain,
% 56.32/7.72 ((~ (imp @
% 56.32/7.72 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk4' @ '#sk5')) @
% 56.32/7.72 ($false))
% 56.32/7.72 | (n_is @ '#sk4' @ '#sk5'))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl791])).
% 56.32/7.72 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 56.32/7.72 thf('10', plain,
% 56.32/7.72 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 56.32/7.72 inference('rw.lit', [status(esa)], [def_imp])).
% 56.32/7.72 thf(zip_derived_cl793, plain,
% 56.32/7.72 ((~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk4' @ '#sk5')) => ($false)))
% 56.32/7.72 | (n_is @ '#sk4' @ '#sk5'))),
% 56.32/7.72 inference('rw_clause', [status(thm)], [zip_derived_cl792, '10'])).
% 56.32/7.72 thf(zip_derived_cl794, plain,
% 56.32/7.72 ((~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk4' @ '#sk5'))))
% 56.32/7.72 | (n_is @ '#sk4' @ '#sk5'))),
% 56.32/7.72 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl793])).
% 56.32/7.72 thf(zip_derived_cl795, plain,
% 56.32/7.72 (( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk4' @ '#sk5'))
% 56.32/7.72 | (n_is @ '#sk4' @ '#sk5'))),
% 56.32/7.72 inference('simplify nested equalities', [status(thm)],
% 56.32/7.72 [zip_derived_cl794])).
% 56.32/7.72 thf(zip_derived_cl8746, plain, ( (n_is @ '#sk4' @ '#sk5')),
% 56.32/7.72 inference('sup+', [status(thm)], [zip_derived_cl8728, zip_derived_cl795])).
% 56.32/7.72 thf(zip_derived_cl767, plain,
% 56.32/7.72 ( (is_of @ '#sk2' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl766])).
% 56.32/7.72 thf(zip_derived_cl779, plain,
% 56.32/7.72 ( (is_of @ '#sk4' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl778])).
% 56.32/7.72 thf(zip_derived_cl785, plain,
% 56.32/7.72 ( (is_of @ '#sk5' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl784])).
% 56.32/7.72 thf(zip_derived_cl773, plain,
% 56.32/7.72 ( (is_of @ '#sk3' @
% 56.32/7.72 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl772])).
% 56.32/7.72 thf(zip_derived_cl787, plain,
% 56.32/7.72 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 56.32/7.72 (diffprop @ '#sk2' @ '#sk3'))),
% 56.32/7.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl786])).
% 56.32/7.72 thf(zip_derived_cl9175, plain, ($false),
% 56.32/7.72 inference('demod', [status(thm)],
% 56.32/7.72 [zip_derived_cl9161, zip_derived_cl8746, zip_derived_cl767,
% 56.32/7.72 zip_derived_cl779, zip_derived_cl785, zip_derived_cl773,
% 56.32/7.72 zip_derived_cl787])).
% 56.32/7.72
% 56.32/7.72 % SZS output end Refutation
% 56.32/7.72
% 56.32/7.72
% 56.32/7.72 % Terminating...
% 56.37/7.82 % Runner terminated.
% 56.37/7.82 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------