%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM682^4 : 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.HodcRd0wER true
% Computer : n008.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 04:47:58 PM UTC 2025
% Result : Theorem 37.14s 8.02s
% Output : Refutation 37.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM682^4 : TPTP v9.2.0. Released v7.1.0.
% 0.03/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.HodcRd0wER true
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 1 16:48:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % Running in HO mode
% 0.50/0.63 % Total configuration time : 828
% 0.50/0.63 % Estimated wc time : 1656
% 0.50/0.63 % Estimated cpu time (8 cpus) : 207.0
% 0.51/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.52/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.52/0.79 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.52/0.79 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.52/0.81 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.52/0.82 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 37.14/8.02 % Solved by lams/40_b.comb.sh.
% 37.14/8.02 % done 394 iterations in 7.150s
% 37.14/8.02 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 37.14/8.02 % SZS output start Refutation
% 37.14/8.02 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
% 37.14/8.02 thf(nat_type, type, nat: $i).
% 37.14/8.02 thf('#sk3_type', type, '#sk3': $i).
% 37.14/8.02 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 37.14/8.02 thf(in_type, type, in: $i > $i > $o).
% 37.14/8.02 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 37.14/8.02 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 37.14/8.02 thf(ap_type, type, ap: $i > $i > $i).
% 37.14/8.02 thf(emptyset_type, type, emptyset: $i).
% 37.14/8.02 thf(omega_type, type, omega: $i).
% 37.14/8.02 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 37.14/8.02 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 37.14/8.02 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 37.14/8.02 thf('#sk2_type', type, '#sk2': $i).
% 37.14/8.02 thf('#sk4_type', type, '#sk4': $i).
% 37.14/8.02 thf(plus_type, type, plus: $i > $i).
% 37.14/8.02 thf(iii_type, type, iii: $i > $i > $o).
% 37.14/8.02 thf(n_pl_type, type, n_pl: $i > $i > $i).
% 37.14/8.02 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 37.14/8.02 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 37.14/8.02 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 37.14/8.02 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 37.14/8.02 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 37.14/8.02 thf(satz20c, conjecture,
% 37.14/8.02 (all_of @
% 37.14/8.02 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 37.14/8.02 ( ^[X0:$i]:
% 37.14/8.02 ( all_of @
% 37.14/8.02 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 37.14/8.02 ( ^[X1:$i]:
% 37.14/8.02 ( all_of @
% 37.14/8.02 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 37.14/8.02 ( ^[X2:$i]:
% 37.14/8.02 ( ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) =>
% 37.14/8.02 ( iii @ X0 @ X1 ) ) ) ) ) ) ))).
% 37.14/8.02 thf(zf_stmt_0, negated_conjecture,
% 37.14/8.02 (~( all_of @
% 37.14/8.02 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 37.14/8.02 ( ^[X0:$i]:
% 37.14/8.02 ( all_of @
% 37.14/8.02 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 37.14/8.02 ( ^[X1:$i]:
% 37.14/8.02 ( all_of @
% 37.14/8.02 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 37.14/8.02 ( ^[X2:$i]:
% 37.14/8.02 ( ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) =>
% 37.14/8.02 ( iii @ X0 @ X1 ) ) ) ) ) ) ) )),
% 37.14/8.02 inference('cnf.neg', [status(esa)], [satz20c])).
% 37.14/8.02 thf(zip_derived_cl124, plain,
% 37.14/8.02 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 37.14/8.02 (^[Y0 : $i]:
% 37.14/8.02 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 37.14/8.02 (^[Y1 : $i]:
% 37.14/8.02 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @
% 37.14/8.02 (^[Y2 : $i]:
% 37.14/8.02 (((iii @ (n_pl @ Y0 @ Y2) @ (n_pl @ Y1 @ Y2)) => (iii @
% 37.14/8.02 Y0 @ Y1)))))))))),
% 37.14/8.02 inference('cnf', [status(esa)], [zf_stmt_0])).
% 37.14/8.02 thf(zip_derived_cl125, plain,
% 37.14/8.02 (~ (all_of @ ((('#C') @ in @ nat)) @
% 37.14/8.02 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 37.14/8.02 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @
% 37.14/8.02 ((('#S') @ ((('#B') @ ('#S') @
% 37.14/8.02 ((('#B') @ ((('#B') @ ('#C'))) @
% 37.14/8.02 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 37.14/8.02 ((('#C') @ ((('#B') @ ('#B') @
% 37.14/8.02 ((('#B') @ ('#S') @
% 37.14/8.02 ((('#B') @ ((('#B') @ iii)) @
% 37.14/8.02 n_pl)))))) @
% 37.14/8.02 n_pl)))))))) @
% 37.14/8.02 iii)))))))),
% 37.14/8.02 inference('lams2combs', [status(thm)], [zip_derived_cl124])).
% 37.14/8.02 thf(def_nat, axiom,(( nat ) =
% 37.14/8.02 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))).
% 37.14/8.02 thf('0', plain,
% 37.14/8.02 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )),
% 37.14/8.02 define([status(thm)])).
% 37.14/8.02 thf(zip_derived_cl356, plain,
% 37.14/8.02 (~ (all_of @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 37.14/8.02 ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 37.14/8.02 ((('#B') @ ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @
% 37.14/8.02 ((('#C') @ (!=) @ emptyset)))))))) @
% 37.14/8.02 ((('#S') @ ((('#B') @ ('#S') @
% 37.14/8.02 ((('#B') @ ((('#B') @ ('#C'))) @
% 37.14/8.02 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 37.14/8.02 ((('#C') @ ((('#B') @ ('#B') @
% 37.14/8.02 ((('#B') @ ('#S') @
% 37.14/8.02 ((('#B') @ ((('#B') @ iii)) @
% 37.14/8.02 n_pl)))))) @
% 37.14/8.02 n_pl)))))))) @
% 37.14/8.02 iii)))))))),
% 37.14/8.02 inference('rw', [status(thm)], [zip_derived_cl125, '0'])).
% 37.14/8.02 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 37.14/8.02 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 37.14/8.02 thf('1', plain,
% 37.14/8.02 (![X0:( $i > $o ),X1:( $i > $o )]:
% 37.14/8.02 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 37.14/8.02 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 37.14/8.02 inference('rw.lit', [status(esa)], [def_all_of])).
% 37.14/8.02 thf(zip_derived_cl357, plain,
% 37.14/8.02 (~ (((!!) @ (^[Y0 : $i]:
% 37.14/8.02 (((is_of @ Y0 @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 37.14/8.02 ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @
% 37.14/8.02 ((('#C') @ (!=) @ emptyset)))))) @
% 37.14/8.02 ((('#B') @ ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @
% 37.14/8.02 ((('#C') @ (!=) @ emptyset)))))))) @
% 37.14/8.02 ((('#S') @ ((('#B') @ ('#S') @
% 37.14/8.02 ((('#B') @ ((('#B') @ ('#C'))) @
% 37.14/8.02 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 37.14/8.02 ((('#C') @ ((('#B') @ ('#B') @
% 37.14/8.02 ((('#B') @ ('#S') @
% 37.14/8.02 ((('#B') @ (
% 37.14/8.02 (('#B') @ iii)) @
% 37.14/8.02 n_pl)))))) @
% 37.14/8.02 n_pl)))))))) @
% 37.14/8.02 iii)))) @
% 37.14/8.02 Y0)))))))),
% 37.14/8.02 inference('rw_clause', [status(thm)], [zip_derived_cl356, '1'])).
% 37.14/8.02 thf(zip_derived_cl358, plain,
% 37.14/8.02 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 37.14/8.02 ((('#C') @ is_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @
% 37.14/8.02 ((('#C') @ (!=) @ emptyset))))))))) @
% 37.14/8.02 ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 37.14/8.02 ((('#B') @ ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @
% 37.14/8.02 ((('#C') @ (!=) @ emptyset)))))))) @
% 37.14/8.02 ((('#S') @ ((('#B') @ ('#S') @
% 37.14/8.02 ((('#B') @ ((('#B') @ ('#C'))) @
% 37.14/8.02 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 37.14/8.02 ((('#C') @ ((('#B') @ ('#B') @
% 37.14/8.02 ((('#B') @ ('#S') @
% 37.14/8.02 ((('#B') @ ((('#B') @ iii)) @
% 37.14/8.02 n_pl)))))) @
% 37.14/8.02 n_pl)))))))) @
% 37.14/8.02 iii))))))))))),
% 37.14/8.02 inference('comb-normalize', [status(thm)], [zip_derived_cl357])).
% 37.14/8.02 thf(zip_derived_cl359, plain,
% 37.14/8.02 (~ (((is_of @ '#sk2' @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 37.14/8.02 (all_of @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 37.14/8.02 ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 37.14/8.02 ((('#S') @ ((('#B') @ ('#C') @
% 37.14/8.02 ((('#B') @ ((('#B') @ (=>))) @
% 37.14/8.02 ((('#B') @ ((('#S') @ ((('#B') @ iii @
% 37.14/8.02 (n_pl @ '#sk2'))))) @
% 37.14/8.02 n_pl)))))) @
% 37.14/8.02 (iii @ '#sk2'))))))))),
% 37.14/8.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl358])).
% 37.14/8.02 thf(zip_derived_cl361, plain,
% 37.14/8.02 (~ (all_of @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 37.14/8.02 ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 37.14/8.02 ((('#S') @ ((('#B') @ ('#C') @
% 37.14/8.02 ((('#B') @ ((('#B') @ (=>))) @
% 37.14/8.02 ((('#B') @ ((('#S') @ ((('#B') @ iii @
% 37.14/8.02 (n_pl @ '#sk2'))))) @
% 37.14/8.02 n_pl)))))) @
% 37.14/8.02 (iii @ '#sk2'))))))),
% 37.14/8.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl359])).
% 37.14/8.02 thf(zip_derived_cl362, plain,
% 37.14/8.02 (~ (((!!) @ (^[Y0 : $i]:
% 37.14/8.02 (((is_of @ Y0 @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 37.14/8.02 ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @
% 37.14/8.02 ((('#C') @ (!=) @ emptyset)))))) @
% 37.14/8.02 ((('#S') @ ((('#B') @ ('#C') @
% 37.14/8.02 ((('#B') @ ((('#B') @ (=>))) @
% 37.14/8.02 ((('#B') @ ((('#S') @ ((('#B') @ iii @
% 37.14/8.02 (n_pl @ '#sk2'))))) @
% 37.14/8.02 n_pl)))))) @
% 37.14/8.02 (iii @ '#sk2'))) @
% 37.14/8.02 Y0)))))))),
% 37.14/8.02 inference('rw_clause', [status(thm)], [zip_derived_cl361, '1'])).
% 37.14/8.02 thf(zip_derived_cl363, plain,
% 37.14/8.02 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 37.14/8.02 ((('#C') @ is_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @
% 37.14/8.02 ((('#C') @ (!=) @ emptyset))))))))) @
% 37.14/8.02 ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 37.14/8.02 ((('#S') @ ((('#B') @ ('#C') @
% 37.14/8.02 ((('#B') @ ((('#B') @ (=>))) @
% 37.14/8.02 ((('#B') @ ((('#S') @ ((('#B') @ iii @
% 37.14/8.02 (n_pl @ '#sk2'))))) @
% 37.14/8.02 n_pl)))))) @
% 37.14/8.02 (iii @ '#sk2')))))))))),
% 37.14/8.02 inference('comb-normalize', [status(thm)], [zip_derived_cl362])).
% 37.14/8.02 thf(zip_derived_cl364, plain,
% 37.14/8.02 (~ (((is_of @ '#sk3' @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 37.14/8.02 (all_of @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 37.14/8.02 ((('#C') @ ((('#B') @ (=>) @
% 37.14/8.02 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @
% 37.14/8.02 (n_pl @ '#sk3'))))) @
% 37.14/8.02 (iii @ '#sk2' @ '#sk3'))))))),
% 37.14/8.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl363])).
% 37.14/8.02 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 37.14/8.02 thf('2', plain,
% 37.14/8.02 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 37.14/8.02 define([status(thm)])).
% 37.14/8.02 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))).
% 37.14/8.02 thf('3', plain,
% 37.14/8.02 (![X1:$i,X0:$i]:
% 37.14/8.02 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 37.14/8.02 define([status(thm)])).
% 37.14/8.02 thf(zip_derived_cl365, plain,
% 37.14/8.02 (~ (((is_of @ '#sk3' @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 37.14/8.02 (all_of @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 37.14/8.02 ((('#C') @ ((('#B') @ (=>) @
% 37.14/8.02 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @
% 37.14/8.02 (n_pl @ '#sk3'))))) @
% 37.14/8.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ '#sk3' @ '#sk2')))))))),
% 37.14/8.02 inference('rw', [status(thm)], [zip_derived_cl364, '0', '2', '3'])).
% 37.14/8.02 thf(zip_derived_cl367, plain,
% 37.14/8.02 (~ (all_of @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 37.14/8.02 ((('#C') @ ((('#B') @ (=>) @
% 37.14/8.02 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @
% 37.14/8.02 (n_pl @ '#sk3'))))) @
% 37.14/8.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ '#sk3' @ '#sk2')))))),
% 37.14/8.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl365])).
% 37.14/8.02 thf(zip_derived_cl368, plain,
% 37.14/8.02 (~ (((!!) @ (^[Y0 : $i]:
% 37.14/8.02 (((is_of @ Y0 @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 37.14/8.02 ((('#C') @ ((('#B') @ (=>) @
% 37.14/8.02 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @
% 37.14/8.02 (n_pl @ '#sk3'))))) @
% 37.14/8.02 (l_some @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ '#sk3' @ '#sk2')) @
% 37.14/8.02 Y0)))))))),
% 37.14/8.02 inference('rw_clause', [status(thm)], [zip_derived_cl367, '1'])).
% 37.14/8.02 thf(zip_derived_cl369, plain,
% 37.14/8.02 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 37.14/8.02 ((('#C') @ is_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @
% 37.14/8.02 ((('#C') @ (!=) @ emptyset))))))))) @
% 37.14/8.02 ((('#C') @ ((('#B') @ (=>) @
% 37.14/8.02 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @
% 37.14/8.02 (n_pl @ '#sk3'))))) @
% 37.14/8.02 (l_some @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ '#sk3' @ '#sk2'))))))))),
% 37.14/8.02 inference('comb-normalize', [status(thm)], [zip_derived_cl368])).
% 37.14/8.02 thf(zip_derived_cl370, plain,
% 37.14/8.02 (~ (((is_of @ '#sk4' @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 37.14/8.02 (((iii @ (n_pl @ '#sk2' @ '#sk4') @ (n_pl @ '#sk3' @ '#sk4')) =>
% 37.14/8.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ '#sk3' @ '#sk2'))))))),
% 37.14/8.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl369])).
% 37.14/8.02 thf(def_n_pl, axiom,(( n_pl @ (X0)@ (X1)) = ((ap @ (plus @ X0) @ X1)))).
% 37.14/8.02 thf('4', plain,
% 37.14/8.02 (![X1:$i,X0:$i]: ( ( n_pl @ X0 @ X1 ) = ( ap @ ( plus @ X0 ) @ X1 ) )),
% 37.14/8.02 define([status(thm)])).
% 37.14/8.02 thf(zip_derived_cl371, plain,
% 37.14/8.02 (~ (((is_of @ '#sk4' @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 37.14/8.02 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk4') @
% 37.14/8.02 (ap @ (plus @ '#sk2') @ '#sk4'))) =>
% 37.14/8.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ '#sk3' @ '#sk2'))))))),
% 37.14/8.02 inference('rw', [status(thm)],
% 37.14/8.02 [zip_derived_cl370, '0', '2', '4', '4', '3'])).
% 37.14/8.02 thf(zip_derived_cl373, plain,
% 37.14/8.02 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk4') @
% 37.14/8.02 (ap @ (plus @ '#sk2') @ '#sk4'))) =>
% 37.14/8.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ '#sk3' @ '#sk2'))))),
% 37.14/8.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl371])).
% 37.14/8.02 thf(zip_derived_cl375, plain,
% 37.14/8.02 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ '#sk3' @ '#sk2'))),
% 37.14/8.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl373])).
% 37.14/8.02 thf(zip_derived_cl374, plain,
% 37.14/8.02 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk4') @
% 37.14/8.02 (ap @ (plus @ '#sk2') @ '#sk4')))),
% 37.14/8.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl373])).
% 37.14/8.02 thf(satz20a, axiom,
% 37.14/8.02 (all_of @
% 37.14/8.02 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 37.14/8.02 ( ^[X0:$i]:
% 37.14/8.02 ( all_of @
% 37.14/8.02 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 37.14/8.02 ( ^[X1:$i]:
% 37.14/8.02 ( all_of @
% 37.14/8.02 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 37.14/8.02 ( ^[X2:$i]:
% 37.14/8.02 ( ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) =>
% 37.14/8.02 ( d_29_ii @ X0 @ X1 ) ) ) ) ) ) ))).
% 37.14/8.02 thf(zip_derived_cl120, plain,
% 37.14/8.02 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 37.14/8.02 (^[Y0 : $i]:
% 37.14/8.02 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 37.14/8.02 (^[Y1 : $i]:
% 37.14/8.02 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @
% 37.14/8.02 (^[Y2 : $i]:
% 37.14/8.02 (((d_29_ii @ (n_pl @ Y0 @ Y2) @ (n_pl @ Y1 @ Y2)) =>
% 37.14/8.02 (d_29_ii @ Y0 @ Y1)))))))))),
% 37.14/8.02 inference('cnf', [status(esa)], [satz20a])).
% 37.14/8.02 thf(zip_derived_cl121, plain,
% 37.14/8.02 ( (all_of @ ((('#C') @ in @ nat)) @
% 37.14/8.02 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 37.14/8.02 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @
% 37.14/8.02 ((('#S') @ ((('#B') @ ('#S') @
% 37.14/8.02 ((('#B') @ ((('#B') @ ('#C'))) @
% 37.14/8.02 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 37.14/8.02 ((('#C') @ ((('#B') @ ('#B') @
% 37.14/8.02 ((('#B') @ ('#S') @
% 37.14/8.02 ((('#B') @ ((('#B') @ d_29_ii)) @
% 37.14/8.02 n_pl)))))) @
% 37.14/8.02 n_pl)))))))) @
% 37.14/8.02 d_29_ii)))))))),
% 37.14/8.02 inference('lams2combs', [status(thm)], [zip_derived_cl120])).
% 37.14/8.02 thf(zip_derived_cl901, plain,
% 37.14/8.02 ( (all_of @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 37.14/8.02 ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 37.14/8.02 ((('#B') @ ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @
% 37.14/8.02 ((('#C') @ (!=) @ emptyset)))))))) @
% 37.14/8.02 ((('#S') @ ((('#B') @ ('#S') @
% 37.14/8.02 ((('#B') @ ((('#B') @ ('#C'))) @
% 37.14/8.02 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 37.14/8.02 ((('#C') @ ((('#B') @ ('#B') @
% 37.14/8.02 ((('#B') @ ('#S') @
% 37.14/8.02 ((('#B') @ ((('#B') @ d_29_ii)) @
% 37.14/8.02 n_pl)))))) @
% 37.14/8.02 n_pl)))))))) @
% 37.14/8.02 d_29_ii)))))))),
% 37.14/8.02 inference('rw', [status(thm)], [zip_derived_cl121, '0'])).
% 37.14/8.02 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 37.14/8.02 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 37.14/8.02 thf('5', plain,
% 37.14/8.02 (![X0:( $i > $o ),X1:( $i > $o )]:
% 37.14/8.02 ( ( all_of @ X0 @ X1 ) <=>
% 37.14/8.02 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 37.14/8.02 inference('rw.lit', [status(esa)], [def_all_of])).
% 37.14/8.02 thf(zip_derived_cl902, plain,
% 37.14/8.02 ( (((!!) @ (^[Y0 : $i]:
% 37.14/8.02 (((is_of @ Y0 @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 37.14/8.02 ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @
% 37.14/8.02 ((('#C') @ (!=) @ emptyset)))))) @
% 37.14/8.02 ((('#B') @ ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @
% 37.14/8.02 ((('#C') @ (!=) @ emptyset)))))))) @
% 37.14/8.02 ((('#S') @ ((('#B') @ ('#S') @
% 37.14/8.02 ((('#B') @ ((('#B') @ ('#C'))) @
% 37.14/8.02 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 37.14/8.02 ((('#C') @ ((('#B') @ ('#B') @
% 37.14/8.02 ((('#B') @ ('#S') @
% 37.14/8.02 ((('#B') @ ((
% 37.14/8.02 ('#B') @ d_29_ii)) @
% 37.14/8.02 n_pl)))))) @
% 37.14/8.02 n_pl)))))))) @
% 37.14/8.02 d_29_ii)))) @
% 37.14/8.02 Y0)))))))),
% 37.14/8.02 inference('rw_clause', [status(thm)], [zip_derived_cl901, '5'])).
% 37.14/8.02 thf(zip_derived_cl903, plain,
% 37.14/8.02 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 37.14/8.02 ((('#C') @ is_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 37.14/8.02 ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 37.14/8.02 ((('#B') @ ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @
% 37.14/8.02 ((('#C') @ (!=) @ emptyset)))))))) @
% 37.14/8.02 ((('#S') @ ((('#B') @ ('#S') @
% 37.14/8.02 ((('#B') @ ((('#B') @ ('#C'))) @
% 37.14/8.02 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 37.14/8.02 ((('#C') @ ((('#B') @ ('#B') @
% 37.14/8.02 ((('#B') @ ('#S') @
% 37.14/8.02 ((('#B') @ ((('#B') @ d_29_ii)) @
% 37.14/8.02 n_pl)))))) @
% 37.14/8.02 n_pl)))))))) @
% 37.14/8.02 d_29_ii))))))))))),
% 37.14/8.02 inference('comb-normalize', [status(thm)], [zip_derived_cl902])).
% 37.14/8.02 thf(zip_derived_cl904, plain,
% 37.14/8.02 (![X2 : $i]:
% 37.14/8.02 (((is_of @ X2 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 37.14/8.02 (all_of @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 37.14/8.02 ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 37.14/8.02 ((('#S') @ ((('#B') @ ('#C') @
% 37.14/8.02 ((('#B') @ ((('#B') @ (=>))) @
% 37.14/8.02 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @
% 37.14/8.02 (n_pl @ X2))))) @
% 37.14/8.02 n_pl)))))) @
% 37.14/8.02 (d_29_ii @ X2))))))))),
% 37.14/8.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl903])).
% 37.14/8.02 thf(zip_derived_cl905, plain,
% 37.14/8.02 (![X2 : $i]:
% 37.14/8.02 (~ (is_of @ X2 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 37.14/8.02 | (all_of @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 37.14/8.02 ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 37.14/8.02 ((('#S') @ ((('#B') @ ('#C') @
% 37.14/8.02 ((('#B') @ ((('#B') @ (=>))) @
% 37.14/8.02 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @
% 37.14/8.02 (n_pl @ X2))))) @
% 37.14/8.02 n_pl)))))) @
% 37.14/8.02 (d_29_ii @ X2)))))))),
% 37.14/8.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl904])).
% 37.14/8.02 thf(zip_derived_cl906, plain,
% 37.14/8.02 (![X0 : $i]:
% 37.14/8.02 ( (((!!) @ (^[Y0 : $i]:
% 37.14/8.02 (((is_of @ Y0 @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 37.14/8.02 ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @
% 37.14/8.02 ((('#C') @ (!=) @ emptyset)))))) @
% 37.14/8.02 ((('#S') @ ((('#B') @ ('#C') @
% 37.14/8.02 ((('#B') @ ((('#B') @ (=>))) @
% 37.14/8.02 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @
% 37.14/8.02 (n_pl @ X0))))) @
% 37.14/8.02 n_pl)))))) @
% 37.14/8.02 (d_29_ii @ X0))) @
% 37.14/8.02 Y0)))))))
% 37.14/8.02 | ~ (is_of @ X0 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 37.14/8.02 inference('rw_clause', [status(thm)], [zip_derived_cl905, '5'])).
% 37.14/8.02 thf(zip_derived_cl907, plain,
% 37.14/8.02 (![X0 : $i]:
% 37.14/8.02 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 37.14/8.02 ((('#C') @ is_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @
% 37.14/8.02 ((('#C') @ (!=) @ emptyset))))))))) @
% 37.14/8.02 ((('#B') @ (all_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @
% 37.14/8.02 ((('#C') @ (!=) @ emptyset)))))) @
% 37.14/8.02 ((('#S') @ ((('#B') @ ('#C') @
% 37.14/8.02 ((('#B') @ ((('#B') @ (=>))) @
% 37.14/8.02 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @
% 37.14/8.02 (n_pl @ X0))))) @
% 37.14/8.02 n_pl)))))) @
% 37.14/8.02 (d_29_ii @ X0)))))))))
% 37.14/8.02 | ~ (is_of @ X0 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 37.14/8.02 inference('comb-normalize', [status(thm)], [zip_derived_cl906])).
% 37.14/8.02 thf(zip_derived_cl908, plain,
% 37.14/8.02 (![X0 : $i, X2 : $i]:
% 37.14/8.02 ( (((is_of @ X2 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 37.14/8.02 (all_of @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 37.14/8.02 ((('#C') @ ((('#B') @ (=>) @
% 37.14/8.02 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @
% 37.14/8.02 (n_pl @ X2))))) @
% 37.14/8.02 (d_29_ii @ X0 @ X2))))))
% 37.14/8.02 | ~ (is_of @ X0 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 37.14/8.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl907])).
% 37.14/8.02 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) =
% 37.14/8.02 ((n_some @ (diffprop @ X0 @ X1))))).
% 37.14/8.02 thf('6', plain,
% 37.14/8.02 (![X1:$i,X0:$i]:
% 37.14/8.02 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 37.14/8.02 define([status(thm)])).
% 37.14/8.02 thf(zip_derived_cl909, plain,
% 37.14/8.02 (![X0 : $i, X2 : $i]:
% 37.14/8.02 ( (((is_of @ X2 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 37.14/8.02 (all_of @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 37.14/8.02 ((('#C') @ ((('#B') @ (=>) @
% 37.14/8.02 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @
% 37.14/8.02 (n_pl @ X2))))) @
% 37.14/8.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ X0 @ X2)))))))
% 37.14/8.02 | ~ (is_of @ X0 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 37.14/8.02 inference('rw', [status(thm)], [zip_derived_cl908, '0', '2', '6'])).
% 37.14/8.02 thf(zip_derived_cl910, plain,
% 37.14/8.02 (![X0 : $i, X2 : $i]:
% 37.14/8.02 (~ (is_of @ X2 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 37.14/8.02 | (all_of @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 37.14/8.02 ((('#C') @ ((('#B') @ (=>) @
% 37.14/8.02 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @
% 37.14/8.02 (n_pl @ X2))))) @
% 37.14/8.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ X0 @ X2)))))
% 37.14/8.02 | ~ (is_of @ X0 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 37.14/8.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl909])).
% 37.14/8.02 thf(zip_derived_cl911, plain,
% 37.14/8.02 (![X0 : $i, X1 : $i]:
% 37.14/8.02 ( (((!!) @ (^[Y0 : $i]:
% 37.14/8.02 (((is_of @ Y0 @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 37.14/8.02 ((('#C') @ ((('#B') @ (=>) @
% 37.14/8.02 ((('#S') @ ((('#B') @ d_29_ii @
% 37.14/8.02 (n_pl @ X0))) @
% 37.14/8.02 (n_pl @ X1))))) @
% 37.14/8.02 (l_some @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ X0 @ X1)) @
% 37.14/8.02 Y0)))))))
% 37.14/8.02 | ~ (is_of @ X0 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 37.14/8.02 | ~ (is_of @ X1 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 37.14/8.02 inference('rw_clause', [status(thm)], [zip_derived_cl910, '5'])).
% 37.14/8.02 thf(zip_derived_cl912, plain,
% 37.14/8.02 (![X0 : $i, X1 : $i]:
% 37.14/8.02 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 37.14/8.02 ((('#C') @ is_of @
% 37.14/8.02 ((('#C') @ in @
% 37.14/8.02 (d_Sep @ omega @
% 37.14/8.02 ((('#C') @ (!=) @ emptyset))))))))) @
% 37.14/8.02 ((('#C') @ ((('#B') @ (=>) @
% 37.14/8.02 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @
% 37.14/8.02 (n_pl @ X1))))) @
% 37.14/8.02 (l_some @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ X0 @ X1))))))))
% 37.14/8.02 | ~ (is_of @ X0 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 37.14/8.02 | ~ (is_of @ X1 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 37.14/8.02 inference('comb-normalize', [status(thm)], [zip_derived_cl911])).
% 37.14/8.02 thf(zip_derived_cl913, plain,
% 37.14/8.02 (![X0 : $i, X1 : $i, X3 : $i]:
% 37.14/8.02 ( (((is_of @ X3 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 37.14/8.02 (((d_29_ii @ (n_pl @ X0 @ X3) @ (n_pl @ X1 @ X3)) => (l_some @
% 37.14/8.02 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ X0 @ X1))))))
% 37.14/8.02 | ~ (is_of @ X1 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 37.14/8.02 | ~ (is_of @ X0 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 37.14/8.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl912])).
% 37.14/8.02 thf(zip_derived_cl914, plain,
% 37.14/8.02 (![X0 : $i, X1 : $i, X3 : $i]:
% 37.14/8.02 ( (((is_of @ X3 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 37.14/8.02 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ (ap @ (plus @ X0) @ X3) @ (ap @ (plus @ X1) @ X3))) =>
% 37.14/8.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ X0 @ X1))))))
% 37.14/8.02 | ~ (is_of @ X1 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 37.14/8.02 | ~ (is_of @ X0 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 37.14/8.02 inference('rw', [status(thm)],
% 37.14/8.02 [zip_derived_cl913, '0', '2', '4', '4', '6'])).
% 37.14/8.02 thf(zip_derived_cl915, plain,
% 37.14/8.02 (![X0 : $i, X1 : $i, X3 : $i]:
% 37.14/8.02 (~ (is_of @ X3 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 37.14/8.02 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ (ap @ (plus @ X0) @ X3) @ (ap @ (plus @ X1) @ X3))) =>
% 37.14/8.02 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ X0 @ X1))))
% 37.14/8.02 | ~ (is_of @ X0 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 37.14/8.02 | ~ (is_of @ X1 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 37.14/8.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl914])).
% 37.14/8.02 thf(zip_derived_cl916, plain,
% 37.14/8.02 (![X0 : $i, X1 : $i, X3 : $i]:
% 37.14/8.02 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ (ap @ (plus @ X0) @ X3) @ (ap @ (plus @ X1) @ X3)))
% 37.14/8.02 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ X0 @ X1))
% 37.14/8.02 | ~ (is_of @ X1 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 37.14/8.02 | ~ (is_of @ X0 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 37.14/8.02 | ~ (is_of @ X3 @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 37.14/8.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl915])).
% 37.14/8.02 thf(zip_derived_cl7064, plain,
% 37.14/8.02 ((~ (is_of @ '#sk4' @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 37.14/8.02 | ~ (is_of @ '#sk3' @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 37.14/8.02 | ~ (is_of @ '#sk2' @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 37.14/8.02 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ '#sk3' @ '#sk2')))),
% 37.14/8.02 inference('sup-', [status(thm)], [zip_derived_cl374, zip_derived_cl916])).
% 37.14/8.02 thf(zip_derived_cl372, plain,
% 37.14/8.02 ( (is_of @ '#sk4' @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 37.14/8.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl371])).
% 37.14/8.02 thf(zip_derived_cl366, plain,
% 37.14/8.02 ( (is_of @ '#sk3' @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 37.14/8.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl365])).
% 37.14/8.02 thf(zip_derived_cl360, plain,
% 37.14/8.02 ( (is_of @ '#sk2' @
% 37.14/8.02 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 37.14/8.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl359])).
% 37.14/8.02 thf(zip_derived_cl7080, plain,
% 37.14/8.02 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 37.14/8.02 (diffprop @ '#sk3' @ '#sk2'))),
% 37.14/8.02 inference('demod', [status(thm)],
% 37.14/8.02 [zip_derived_cl7064, zip_derived_cl372, zip_derived_cl366,
% 37.14/8.02 zip_derived_cl360])).
% 37.14/8.02 thf(zip_derived_cl7128, plain, ($false),
% 37.14/8.02 inference('demod', [status(thm)], [zip_derived_cl375, zip_derived_cl7080])).
% 37.14/8.02
% 37.14/8.02 % SZS output end Refutation
% 37.14/8.02
% 37.14/8.02
% 37.14/8.02 % Terminating...
% 37.92/8.29 % Runner terminated.
% 37.92/8.29 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------