TSTP Solution File: NUM689^4 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM689^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.1ppegdWWGA true
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 12:43:28 EDT 2023
% Result : Theorem 54.44s 7.48s
% Output : Refutation 54.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM689^4 : TPTP v8.1.2. Released v7.1.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.1ppegdWWGA true
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 15:18:12 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.55/0.65 % Total configuration time : 828
% 0.55/0.65 % Estimated wc time : 1656
% 0.55/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.56/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.56/0.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 54.44/7.48 % Solved by lams/40_b.comb.sh.
% 54.44/7.48 % done 491 iterations in 6.639s
% 54.44/7.48 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 54.44/7.48 % SZS output start Refutation
% 54.44/7.48 thf('#sk5_type', type, '#sk5': $i).
% 54.44/7.48 thf(nat_type, type, nat: $i).
% 54.44/7.48 thf(lessis_type, type, lessis: $i > $i > $o).
% 54.44/7.48 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 54.44/7.48 thf(in_type, type, in: $i > $i > $o).
% 54.44/7.48 thf('#sk2_type', type, '#sk2': $i).
% 54.44/7.48 thf('#sk4_type', type, '#sk4': $i).
% 54.44/7.48 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 54.44/7.48 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 54.44/7.48 thf(ap_type, type, ap: $i > $i > $i).
% 54.44/7.48 thf(emptyset_type, type, emptyset: $i).
% 54.44/7.48 thf(n_is_type, type, n_is: $i > $i > $o).
% 54.44/7.48 thf(imp_type, type, imp: $o > $o > $o).
% 54.44/7.48 thf(omega_type, type, omega: $i).
% 54.44/7.48 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 54.44/7.48 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 54.44/7.48 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 54.44/7.48 thf(l_or_type, type, l_or: $o > $o > $o).
% 54.44/7.48 thf(d_not_type, type, d_not: $o > $o).
% 54.44/7.48 thf('#sk3_type', type, '#sk3': $i).
% 54.44/7.48 thf(plus_type, type, plus: $i > $i).
% 54.44/7.48 thf(iii_type, type, iii: $i > $i > $o).
% 54.44/7.48 thf(n_pl_type, type, n_pl: $i > $i > $i).
% 54.44/7.48 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 54.44/7.48 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 54.44/7.48 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 54.44/7.48 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 54.44/7.48 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 54.44/7.48 thf(satz22c, conjecture,
% 54.44/7.48 (all_of @
% 54.44/7.48 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 54.44/7.48 ( ^[X0:$i]:
% 54.44/7.48 ( all_of @
% 54.44/7.48 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 54.44/7.48 ( ^[X1:$i]:
% 54.44/7.48 ( all_of @
% 54.44/7.48 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 54.44/7.48 ( ^[X2:$i]:
% 54.44/7.48 ( all_of @
% 54.44/7.48 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @
% 54.44/7.48 ( ^[X3:$i]:
% 54.44/7.48 ( ( lessis @ X0 @ X1 ) =>
% 54.44/7.48 ( ( iii @ X2 @ X3 ) =>
% 54.44/7.48 ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 54.44/7.48 thf(zf_stmt_0, negated_conjecture,
% 54.44/7.48 (~( all_of @
% 54.44/7.48 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 54.44/7.48 ( ^[X0:$i]:
% 54.44/7.48 ( all_of @
% 54.44/7.48 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 54.44/7.48 ( ^[X1:$i]:
% 54.44/7.48 ( all_of @
% 54.44/7.48 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 54.44/7.48 ( ^[X2:$i]:
% 54.44/7.48 ( all_of @
% 54.44/7.48 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @
% 54.44/7.48 ( ^[X3:$i]:
% 54.44/7.48 ( ( lessis @ X0 @ X1 ) =>
% 54.44/7.48 ( ( iii @ X2 @ X3 ) =>
% 54.44/7.48 ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) )),
% 54.44/7.48 inference('cnf.neg', [status(esa)], [satz22c])).
% 54.44/7.48 thf(zip_derived_cl146, plain,
% 54.44/7.48 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 54.44/7.48 (^[Y0 : $i]:
% 54.44/7.48 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 54.44/7.48 (^[Y1 : $i]:
% 54.44/7.48 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @
% 54.44/7.48 (^[Y2 : $i]:
% 54.44/7.48 (all_of @ (^[Y3 : $i]: (in @ Y3 @ nat)) @
% 54.44/7.48 (^[Y3 : $i]:
% 54.44/7.48 (((lessis @ Y0 @ Y1) =>
% 54.44/7.48 (((iii @ Y2 @ Y3) => (iii @ (n_pl @ Y0 @ Y2) @
% 54.44/7.48 (n_pl @ Y1 @ Y3))))))))))))))),
% 54.44/7.48 inference('cnf', [status(esa)], [zf_stmt_0])).
% 54.44/7.48 thf(zip_derived_cl147, plain,
% 54.44/7.48 (~ (all_of @ ((('#C') @ in @ nat)) @
% 54.44/7.48 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @ lessis)))))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @
% 54.44/7.48 iii)))))))) @
% 54.44/7.48 ((('#C') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ ('#C') @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))))) @
% 54.44/7.48 n_pl)))))))))))))),
% 54.44/7.48 inference('lams2combs', [status(thm)], [zip_derived_cl146])).
% 54.44/7.48 thf(def_nat, axiom,(( nat ) =
% 54.44/7.48 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))).
% 54.44/7.48 thf('0', plain,
% 54.44/7.48 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )),
% 54.44/7.48 define([status(thm)])).
% 54.44/7.48 thf(zip_derived_cl765, plain,
% 54.44/7.48 (~ (all_of @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.44/7.48 ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset)))))))))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @ lessis)))))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @
% 54.44/7.48 iii)))))))) @
% 54.44/7.48 ((('#C') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ ('#C') @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))))) @
% 54.44/7.48 n_pl)))))))))))))),
% 54.44/7.48 inference('rw', [status(thm)], [zip_derived_cl147, '0'])).
% 54.44/7.48 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 54.44/7.48 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 54.44/7.48 thf('1', plain,
% 54.44/7.48 (![X0:( $i > $o ),X1:( $i > $o )]:
% 54.44/7.48 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 54.44/7.48 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 54.44/7.48 inference('rw.lit', [status(esa)], [def_all_of])).
% 54.44/7.48 thf(zip_derived_cl766, plain,
% 54.44/7.48 (~ (((!!) @ (^[Y0 : $i]:
% 54.44/7.48 (((is_of @ Y0 @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.44/7.48 ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset)))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @
% 54.44/7.48 omega @
% 54.44/7.48 ((('#C') @ (
% 54.44/7.48 !=) @
% 54.44/7.48 emptyset)))))))))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @
% 54.44/7.48 lessis)))))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 54.44/7.48 '#S') @
% 54.44/7.48 ((('#B') @ (
% 54.44/7.48 (('#B') @ (
% 54.44/7.48 =>))) @
% 54.44/7.48 iii)))))))) @
% 54.44/7.48 ((('#C') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ ('#C') @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ iii)) @
% 54.44/7.48 n_pl)))))))) @
% 54.44/7.48 n_pl)))))))))) @
% 54.44/7.48 Y0)))))))),
% 54.44/7.48 inference('rw_clause', [status(thm)], [zip_derived_cl765, '1'])).
% 54.44/7.48 thf(zip_derived_cl767, plain,
% 54.44/7.48 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 54.44/7.48 ((('#C') @ is_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset))))))))) @
% 54.44/7.48 ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (
% 54.44/7.48 !=) @ emptyset)))))))))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @
% 54.44/7.48 lessis)))))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 54.44/7.48 '#S') @
% 54.44/7.48 ((('#B') @ (
% 54.44/7.48 (('#B') @ (=>))) @
% 54.44/7.48 iii)))))))) @
% 54.44/7.48 ((('#C') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ ('#C') @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ iii)) @
% 54.44/7.48 n_pl)))))))) @
% 54.44/7.48 n_pl))))))))))))))))),
% 54.44/7.48 inference('comb-normalize', [status(thm)], [zip_derived_cl766])).
% 54.44/7.48 thf(zip_derived_cl768, plain,
% 54.44/7.48 (~ (((is_of @ '#sk2' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.44/7.48 (all_of @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.44/7.48 ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ (=>) @ (lessis @ '#sk2'))))))) @
% 54.44/7.48 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @ iii)))))) @
% 54.44/7.48 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ iii @ (n_pl @ '#sk2'))))))) @
% 54.44/7.48 n_pl)))))))))))))),
% 54.44/7.48 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl767])).
% 54.44/7.48 thf(zip_derived_cl770, plain,
% 54.44/7.48 (~ (all_of @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.44/7.48 ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ (=>) @ (lessis @ '#sk2'))))))) @
% 54.44/7.48 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @ iii)))))) @
% 54.44/7.48 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ iii @ (n_pl @ '#sk2'))))))) @
% 54.44/7.48 n_pl)))))))))))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl768])).
% 54.44/7.48 thf(zip_derived_cl771, plain,
% 54.44/7.48 (~ (((!!) @ (^[Y0 : $i]:
% 54.44/7.48 (((is_of @ Y0 @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.44/7.48 ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset)))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ (=>) @ (lessis @ '#sk2'))))))) @
% 54.44/7.48 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @
% 54.44/7.48 iii)))))) @
% 54.44/7.48 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ iii @
% 54.44/7.48 (n_pl @ '#sk2'))))))) @
% 54.44/7.48 n_pl)))))))) @
% 54.44/7.48 Y0)))))))),
% 54.44/7.48 inference('rw_clause', [status(thm)], [zip_derived_cl770, '1'])).
% 54.44/7.48 thf(zip_derived_cl772, plain,
% 54.44/7.48 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 54.44/7.48 ((('#C') @ is_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset))))))))) @
% 54.44/7.48 ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset)))))))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ (=>) @ (lessis @ '#sk2'))))))) @
% 54.44/7.48 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @
% 54.44/7.48 iii)))))) @
% 54.44/7.48 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ iii @
% 54.44/7.48 (n_pl @ '#sk2'))))))) @
% 54.44/7.48 n_pl))))))))))))))),
% 54.44/7.48 inference('comb-normalize', [status(thm)], [zip_derived_cl771])).
% 54.44/7.48 thf(zip_derived_cl773, plain,
% 54.44/7.48 (~ (((is_of @ '#sk3' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.44/7.48 (all_of @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.44/7.48 ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (((=>) @ (lessis @ '#sk2' @ '#sk3'))))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @
% 54.44/7.48 ((('#C') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ iii @ (n_pl @ '#sk2'))))) @
% 54.44/7.48 (n_pl @ '#sk3'))))))))))))),
% 54.44/7.48 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl772])).
% 54.44/7.48 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 54.44/7.48 thf('2', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 54.44/7.48 define([status(thm)])).
% 54.44/7.48 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 54.44/7.48 thf('3', plain,
% 54.44/7.48 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 54.44/7.48 define([status(thm)])).
% 54.44/7.48 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 54.44/7.48 thf('4', plain,
% 54.44/7.48 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 54.44/7.48 define([status(thm)])).
% 54.44/7.48 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))).
% 54.44/7.48 thf('5', plain,
% 54.44/7.48 (![X1:$i,X0:$i]:
% 54.44/7.48 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 54.44/7.48 define([status(thm)])).
% 54.44/7.48 thf(def_lessis, axiom,(( lessis @ (X0)@ (X1)) =
% 54.44/7.48 ((l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1))))).
% 54.44/7.48 thf('6', plain,
% 54.44/7.48 (![X1:$i,X0:$i]:
% 54.44/7.48 ( ( lessis @ X0 @ X1 ) =
% 54.44/7.48 ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
% 54.44/7.48 define([status(thm)])).
% 54.44/7.48 thf(zip_derived_cl774, plain,
% 54.44/7.48 (~ (((is_of @ '#sk3' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.44/7.48 (all_of @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.44/7.48 ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 54.44/7.48 (imp @
% 54.44/7.48 (l_some @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2')) @
% 54.44/7.48 ($false)) @
% 54.44/7.48 (n_is @ '#sk2' @ '#sk3')))))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @
% 54.44/7.48 ((('#C') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ iii @ (n_pl @ '#sk2'))))) @
% 54.44/7.48 (n_pl @ '#sk3'))))))))))))),
% 54.44/7.48 inference('rw', [status(thm)],
% 54.44/7.48 [zip_derived_cl773, '2', '3', '0', '4', '5', '6'])).
% 54.44/7.48 thf(zip_derived_cl776, plain,
% 54.44/7.48 (~ (all_of @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.44/7.48 ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 54.44/7.48 (imp @
% 54.44/7.48 (l_some @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2')) @
% 54.44/7.48 ($false)) @
% 54.44/7.48 (n_is @ '#sk2' @ '#sk3')))))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @
% 54.44/7.48 ((('#C') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ iii @ (n_pl @ '#sk2'))))) @
% 54.44/7.48 (n_pl @ '#sk3'))))))))))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl774])).
% 54.44/7.48 thf(zip_derived_cl777, plain,
% 54.44/7.48 (~ (((!!) @ (^[Y0 : $i]:
% 54.44/7.48 (((is_of @ Y0 @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.44/7.48 ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset)))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 54.44/7.48 (imp @
% 54.44/7.48 (l_some @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (
% 54.44/7.48 !=) @ emptyset))) @
% 54.44/7.48 (diffprop @
% 54.44/7.48 '#sk3' @ '#sk2')) @
% 54.44/7.48 ($false)) @
% 54.44/7.48 (n_is @ '#sk2' @
% 54.44/7.48 '#sk3')))))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @
% 54.44/7.48 ((('#C') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ iii @ (n_pl @ '#sk2'))))) @
% 54.44/7.48 (n_pl @ '#sk3'))))))) @
% 54.44/7.48 Y0)))))))),
% 54.44/7.48 inference('rw_clause', [status(thm)], [zip_derived_cl776, '1'])).
% 54.44/7.48 thf(zip_derived_cl778, plain,
% 54.44/7.48 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 54.44/7.48 ((('#C') @ is_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset))))))))) @
% 54.44/7.48 ((('#B') @ (all_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 54.44/7.48 (imp @
% 54.44/7.48 (l_some @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @
% 54.44/7.48 emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @
% 54.44/7.48 '#sk2')) @
% 54.44/7.48 ($false)) @
% 54.44/7.48 (n_is @ '#sk2' @ '#sk3')))))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @
% 54.44/7.48 ((('#C') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ iii @ (n_pl @ '#sk2'))))) @
% 54.44/7.48 (n_pl @ '#sk3')))))))))))))),
% 54.44/7.48 inference('comb-normalize', [status(thm)], [zip_derived_cl777])).
% 54.44/7.48 thf(zip_derived_cl779, plain,
% 54.44/7.48 (~ (((is_of @ '#sk4' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.44/7.48 (all_of @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.44/7.48 ((('#B') @ (((=>) @ (imp @
% 54.44/7.48 (imp @
% 54.44/7.48 (l_some @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2')) @
% 54.44/7.48 ($false)) @
% 54.44/7.48 (n_is @ '#sk2' @ '#sk3')))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ (=>) @ (iii @ '#sk4'))) @
% 54.44/7.48 ((('#B') @ (iii @ (n_pl @ '#sk2' @ '#sk4')) @ (n_pl @ '#sk3'))))))))))),
% 54.44/7.48 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl778])).
% 54.44/7.48 thf(def_n_pl, axiom,(( n_pl @ (X0)@ (X1)) = ((ap @ (plus @ X0) @ X1)))).
% 54.44/7.48 thf('7', plain,
% 54.44/7.48 (![X1:$i,X0:$i]: ( ( n_pl @ X0 @ X1 ) = ( ap @ ( plus @ X0 ) @ X1 ) )),
% 54.44/7.48 define([status(thm)])).
% 54.44/7.48 thf(zip_derived_cl780, plain,
% 54.44/7.48 (~ (((is_of @ '#sk4' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.44/7.48 (all_of @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.44/7.48 ((('#B') @ (((=>) @ (imp @
% 54.44/7.48 (imp @
% 54.44/7.48 (l_some @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2')) @
% 54.44/7.48 ($false)) @
% 54.44/7.48 (n_is @ '#sk2' @ '#sk3')))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ (=>) @ (iii @ '#sk4'))) @
% 54.44/7.48 ((('#B') @ (iii @ (ap @ (plus @ '#sk2') @ '#sk4')) @
% 54.44/7.48 (n_pl @ '#sk3'))))))))))),
% 54.44/7.48 inference('rw', [status(thm)], [zip_derived_cl779, '7'])).
% 54.44/7.48 thf(zip_derived_cl782, plain,
% 54.44/7.48 (~ (all_of @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 54.44/7.48 ((('#B') @ (((=>) @ (imp @
% 54.44/7.48 (imp @
% 54.44/7.48 (l_some @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2')) @
% 54.44/7.48 ($false)) @
% 54.44/7.48 (n_is @ '#sk2' @ '#sk3')))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ (=>) @ (iii @ '#sk4'))) @
% 54.44/7.48 ((('#B') @ (iii @ (ap @ (plus @ '#sk2') @ '#sk4')) @
% 54.44/7.48 (n_pl @ '#sk3'))))))))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl780])).
% 54.44/7.48 thf(zip_derived_cl783, plain,
% 54.44/7.48 (~ (((!!) @ (^[Y0 : $i]:
% 54.44/7.48 (((is_of @ Y0 @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.44/7.48 ((('#B') @ (((=>) @ (imp @
% 54.44/7.48 (imp @
% 54.44/7.48 (l_some @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2')) @
% 54.44/7.48 ($false)) @
% 54.44/7.48 (n_is @ '#sk2' @ '#sk3')))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ (=>) @ (iii @ '#sk4'))) @
% 54.44/7.48 ((('#B') @ (iii @ (ap @ (plus @ '#sk2') @ '#sk4')) @
% 54.44/7.48 (n_pl @ '#sk3'))))) @
% 54.44/7.48 Y0)))))))),
% 54.44/7.48 inference('rw_clause', [status(thm)], [zip_derived_cl782, '1'])).
% 54.44/7.48 thf(zip_derived_cl784, plain,
% 54.44/7.48 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 54.44/7.48 ((('#C') @ is_of @
% 54.44/7.48 ((('#C') @ in @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset))))))))) @
% 54.44/7.48 ((('#B') @ (((=>) @ (imp @
% 54.44/7.48 (imp @
% 54.44/7.48 (l_some @
% 54.44/7.48 (d_Sep @ omega @
% 54.44/7.48 ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2')) @
% 54.44/7.48 ($false)) @
% 54.44/7.48 (n_is @ '#sk2' @ '#sk3')))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ (=>) @ (iii @ '#sk4'))) @
% 54.44/7.48 ((('#B') @ (iii @ (ap @ (plus @ '#sk2') @ '#sk4')) @
% 54.44/7.48 (n_pl @ '#sk3')))))))))))),
% 54.44/7.48 inference('comb-normalize', [status(thm)], [zip_derived_cl783])).
% 54.44/7.48 thf(zip_derived_cl785, plain,
% 54.44/7.48 (~ (((is_of @ '#sk5' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.44/7.48 (((imp @
% 54.44/7.48 (imp @
% 54.44/7.48 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2')) @
% 54.44/7.48 ($false)) @
% 54.44/7.48 (n_is @ '#sk2' @ '#sk3')) =>
% 54.44/7.48 (((iii @ '#sk4' @ '#sk5') => (iii @
% 54.44/7.48 (ap @ (plus @ '#sk2') @ '#sk4') @ (n_pl @ '#sk3' @ '#sk5'))))))))),
% 54.44/7.48 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl784])).
% 54.44/7.48 thf(zip_derived_cl786, plain,
% 54.44/7.48 (~ (((is_of @ '#sk5' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 54.44/7.48 (((imp @
% 54.44/7.48 (imp @
% 54.44/7.48 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2')) @
% 54.44/7.48 ($false)) @
% 54.44/7.48 (n_is @ '#sk2' @ '#sk3')) =>
% 54.44/7.48 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk5' @ '#sk4')) => (l_some @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk5') @
% 54.44/7.48 (ap @ (plus @ '#sk2') @ '#sk4')))))))))),
% 54.44/7.48 inference('rw', [status(thm)],
% 54.44/7.48 [zip_derived_cl785, '0', '4', '4', '7', '5', '5'])).
% 54.44/7.48 thf(zip_derived_cl788, plain,
% 54.44/7.48 (~ (((imp @
% 54.44/7.48 (imp @
% 54.44/7.48 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2')) @
% 54.44/7.48 ($false)) @
% 54.44/7.48 (n_is @ '#sk2' @ '#sk3')) =>
% 54.44/7.48 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk5' @ '#sk4')) => (l_some @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk5') @
% 54.44/7.48 (ap @ (plus @ '#sk2') @ '#sk4')))))))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl786])).
% 54.44/7.48 thf(zip_derived_cl790, plain,
% 54.44/7.48 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk5' @ '#sk4')) => (l_some @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk5') @
% 54.44/7.48 (ap @ (plus @ '#sk2') @ '#sk4')))))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl788])).
% 54.44/7.48 thf(zip_derived_cl793, plain,
% 54.44/7.48 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk5') @
% 54.44/7.48 (ap @ (plus @ '#sk2') @ '#sk4')))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl790])).
% 54.44/7.48 thf(satz19j, axiom,
% 54.44/7.48 (all_of @
% 54.44/7.48 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 54.44/7.48 ( ^[X0:$i]:
% 54.44/7.48 ( all_of @
% 54.44/7.48 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 54.44/7.48 ( ^[X1:$i]:
% 54.44/7.48 ( all_of @
% 54.44/7.48 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 54.44/7.48 ( ^[X2:$i]:
% 54.44/7.48 ( all_of @
% 54.44/7.48 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @
% 54.44/7.48 ( ^[X3:$i]:
% 54.44/7.48 ( ( n_is @ X0 @ X1 ) =>
% 54.44/7.48 ( ( iii @ X2 @ X3 ) =>
% 54.44/7.48 ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 54.44/7.48 thf(zip_derived_cl114, plain,
% 54.44/7.48 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 54.44/7.48 (^[Y0 : $i]:
% 54.44/7.48 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 54.44/7.48 (^[Y1 : $i]:
% 54.44/7.48 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @
% 54.44/7.48 (^[Y2 : $i]:
% 54.44/7.48 (all_of @ (^[Y3 : $i]: (in @ Y3 @ nat)) @
% 54.44/7.48 (^[Y3 : $i]:
% 54.44/7.48 (((n_is @ Y0 @ Y1) =>
% 54.44/7.48 (((iii @ Y2 @ Y3) => (iii @ (n_pl @ Y0 @ Y2) @
% 54.44/7.48 (n_pl @ Y1 @ Y3))))))))))))))),
% 54.44/7.48 inference('cnf', [status(esa)], [satz19j])).
% 54.44/7.48 thf(zip_derived_cl115, plain,
% 54.44/7.48 ( (all_of @ ((('#C') @ in @ nat)) @
% 54.44/7.48 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @
% 54.44/7.48 iii)))))))) @
% 54.44/7.48 ((('#C') @ ((('#B') @ ('#B') @
% 54.44/7.48 ((('#B') @ ('#C') @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))))) @
% 54.44/7.48 n_pl)))))))))))))),
% 54.44/7.48 inference('lams2combs', [status(thm)], [zip_derived_cl114])).
% 54.44/7.48 thf(zip_derived_cl1240, plain,
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% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
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% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
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% 54.44/7.48 ((('#B') @ ('#C') @
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% 54.44/7.48 n_pl)))))))))))))),
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% 54.44/7.48 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
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% 54.44/7.48 ( ( all_of @ X0 @ X1 ) <=>
% 54.44/7.48 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
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% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
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% 54.44/7.48 ((('#B') @ (
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% 54.44/7.48 ((('#B') @ ('#C') @
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% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
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% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
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% 54.44/7.48 ((('#S') @ ((('#B') @ ('#B') @
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% 54.44/7.48 thf(zip_derived_cl1244, plain,
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% 54.44/7.48 | (all_of @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
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% 54.44/7.48 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
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% 54.44/7.48 Y0)))))))
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% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.44/7.48 inference('rw_clause', [status(thm)], [zip_derived_cl1244, '8'])).
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% 54.44/7.48 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
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% 54.44/7.48 n_pl))))))))))))))
% 54.44/7.48 | ~ (is_of @ X0 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.44/7.48 inference('comb-normalize', [status(thm)], [zip_derived_cl1245])).
% 54.44/7.48 thf(zip_derived_cl1247, plain,
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% 54.44/7.48 (n_pl @ X2))))))))))))
% 54.44/7.48 | ~ (is_of @ X0 @
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% 54.44/7.48 thf(zip_derived_cl1248, plain,
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% 54.44/7.48 | (all_of @
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% 54.44/7.48 (n_pl @ X2))))))))))
% 54.44/7.48 | ~ (is_of @ X0 @
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% 54.44/7.48 (n_pl @ X1))))))) @
% 54.44/7.48 Y0)))))))
% 54.44/7.48 | ~ (is_of @ X0 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X1 @
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% 54.44/7.48 ((('#B') @ iii @ (n_pl @ X0))))) @
% 54.44/7.48 (n_pl @ X1)))))))))))))
% 54.44/7.48 | ~ (is_of @ X0 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X1 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.44/7.48 inference('comb-normalize', [status(thm)], [zip_derived_cl1249])).
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% 54.44/7.48 ((('#B') @ (((=>) @ (n_is @ X0 @ X1))) @
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% 54.44/7.48 ((('#B') @ (iii @ (n_pl @ X0 @ X3)) @ (n_pl @ X1))))))))))
% 54.44/7.48 | ~ (is_of @ X1 @
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% 54.44/7.48 | ~ (is_of @ X0 @
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% 54.44/7.48 ((('#B') @ (iii @ (ap @ (plus @ X0) @ X3)) @ (n_pl @ X1))))))))))
% 54.44/7.48 | ~ (is_of @ X1 @
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% 54.44/7.48 ((('#B') @ (iii @ (ap @ (plus @ X0) @ X3)) @ (n_pl @ X1))))))))
% 54.44/7.48 | ~ (is_of @ X0 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X1 @
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% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1252])).
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% 54.44/7.48 ((('#B') @ (((=>) @ (n_is @ X1 @ X0))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ (=>) @ (iii @ X2))) @
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% 54.44/7.48 (n_pl @ X0))))) @
% 54.44/7.48 Y0)))))))
% 54.44/7.48 | ~ (is_of @ X0 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X1 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X2 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.44/7.48 inference('rw_clause', [status(thm)], [zip_derived_cl1253, '8'])).
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% 54.44/7.48 ((('#B') @ (((=>) @ (n_is @ X1 @ X0))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ (=>) @ (iii @ X2))) @
% 54.44/7.48 ((('#B') @ (iii @ (ap @ (plus @ X1) @ X2)) @
% 54.44/7.48 (n_pl @ X0)))))))))))
% 54.44/7.48 | ~ (is_of @ X0 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X1 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X2 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.44/7.48 inference('comb-normalize', [status(thm)], [zip_derived_cl1254])).
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% 54.44/7.48 (n_pl @ X0 @ X4))))))))
% 54.44/7.48 | ~ (is_of @ X2 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X1 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X0 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
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% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ (ap @ (plus @ X0) @ X4) @ (ap @ (plus @ X1) @ X2)))))))))
% 54.44/7.48 | ~ (is_of @ X2 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X1 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X0 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.44/7.48 inference('rw', [status(thm)],
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% 54.44/7.48 (diffprop @ X4 @ X2)) => (l_some @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ (ap @ (plus @ X0) @ X4) @ (ap @ (plus @ X1) @ X2)))))))
% 54.44/7.48 | ~ (is_of @ X0 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X1 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X2 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1257])).
% 54.44/7.48 thf(zip_derived_cl1259, plain,
% 54.44/7.48 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 54.44/7.48 (~ (n_is @ X1 @ X0)
% 54.44/7.48 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ X4 @ X2)) => (l_some @
% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ (ap @ (plus @ X0) @ X4) @ (ap @ (plus @ X1) @ X2)))))
% 54.44/7.48 | ~ (is_of @ X2 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X1 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X0 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X4 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1258])).
% 54.44/7.48 thf(zip_derived_cl1260, plain,
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% 54.44/7.48 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ X4 @ X2))
% 54.44/7.48 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ (ap @ (plus @ X0) @ X4) @ (ap @ (plus @ X1) @ X2)))
% 54.44/7.48 | ~ (is_of @ X4 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X0 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X1 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X2 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (n_is @ X1 @ X0))),
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% 54.44/7.48 thf(zip_derived_cl8986, plain,
% 54.44/7.48 ((~ (n_is @ '#sk2' @ '#sk3')
% 54.44/7.48 | ~ (is_of @ '#sk4' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ '#sk2' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ '#sk3' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ '#sk5' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk5' @ '#sk4')))),
% 54.44/7.48 inference('sup+', [status(thm)], [zip_derived_cl793, zip_derived_cl1260])).
% 54.44/7.48 thf(zip_derived_cl793, plain,
% 54.44/7.48 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk5') @
% 54.44/7.48 (ap @ (plus @ '#sk2') @ '#sk4')))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl790])).
% 54.44/7.48 thf(satz21a, axiom,
% 54.44/7.48 (all_of @
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% 54.44/7.48 ( ^[X0:$i]:
% 54.44/7.48 ( all_of @
% 54.44/7.48 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 54.44/7.48 ( ^[X1:$i]:
% 54.44/7.48 ( all_of @
% 54.44/7.48 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @
% 54.44/7.48 ( ^[X2:$i]:
% 54.44/7.48 ( all_of @
% 54.44/7.48 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @
% 54.44/7.48 ( ^[X3:$i]:
% 54.44/7.48 ( ( iii @ X0 @ X1 ) =>
% 54.44/7.48 ( ( iii @ X2 @ X3 ) =>
% 54.44/7.48 ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
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% 54.44/7.48 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 54.44/7.48 (^[Y0 : $i]:
% 54.44/7.48 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 54.44/7.48 (^[Y1 : $i]:
% 54.44/7.48 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @
% 54.44/7.48 (^[Y2 : $i]:
% 54.44/7.48 (all_of @ (^[Y3 : $i]: (in @ Y3 @ nat)) @
% 54.44/7.48 (^[Y3 : $i]:
% 54.44/7.48 (((iii @ Y0 @ Y1) =>
% 54.44/7.48 (((iii @ Y2 @ Y3) => (iii @ (n_pl @ Y0 @ Y2) @
% 54.44/7.48 (n_pl @ Y1 @ Y3))))))))))))))),
% 54.44/7.48 inference('cnf', [status(esa)], [satz21a])).
% 54.44/7.48 thf(zip_derived_cl141, plain,
% 54.44/7.48 ( (all_of @ ((('#C') @ in @ nat)) @
% 54.44/7.48 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))))) @
% 54.44/7.48 ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ('#B'))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @ iii)))))))) @
% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 54.44/7.48 ((('#B') @ ((('#B') @ (=>))) @
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% 54.44/7.48 ((('#C') @ ((('#B') @ ('#B') @
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% 54.44/7.48 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))))) @
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% 54.44/7.48 inference('lams2combs', [status(thm)], [zip_derived_cl140])).
% 54.44/7.48 thf(zip_derived_cl1218, plain,
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% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
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% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
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% 54.44/7.48 ((('#C') @ ((('#B') @ ('#B') @
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% 54.44/7.48 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))))) @
% 54.44/7.48 n_pl)))))))))))))),
% 54.44/7.48 inference('rw', [status(thm)], [zip_derived_cl141, '0'])).
% 54.44/7.48 thf(zip_derived_cl1219, plain,
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% 54.44/7.48 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
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% 54.44/7.48 thf(zip_derived_cl1220, plain,
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% 54.44/7.48 thf(zip_derived_cl1223, plain,
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% 54.44/7.48 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ (ap @ (plus @ X0) @ X4) @ (ap @ (plus @ X1) @ X2)))))
% 54.44/7.48 | ~ (is_of @ X2 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X1 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X0 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X4 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1237])).
% 54.44/7.48 thf(zip_derived_cl1239, plain,
% 54.44/7.48 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 54.44/7.48 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ X4 @ X2))
% 54.44/7.48 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ (ap @ (plus @ X0) @ X4) @ (ap @ (plus @ X1) @ X2)))
% 54.44/7.48 | ~ (is_of @ X4 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X0 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X1 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ X2 @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ X0 @ X1)))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1238])).
% 54.44/7.48 thf(zip_derived_cl8741, plain,
% 54.44/7.48 ((~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2'))
% 54.44/7.48 | ~ (is_of @ '#sk4' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ '#sk2' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ '#sk3' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (is_of @ '#sk5' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 54.44/7.48 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk5' @ '#sk4')))),
% 54.44/7.48 inference('sup+', [status(thm)], [zip_derived_cl793, zip_derived_cl1239])).
% 54.44/7.48 thf(zip_derived_cl781, plain,
% 54.44/7.48 ( (is_of @ '#sk4' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl780])).
% 54.44/7.48 thf(zip_derived_cl769, plain,
% 54.44/7.48 ( (is_of @ '#sk2' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl768])).
% 54.44/7.48 thf(zip_derived_cl775, plain,
% 54.44/7.48 ( (is_of @ '#sk3' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl774])).
% 54.44/7.48 thf(zip_derived_cl787, plain,
% 54.44/7.48 ( (is_of @ '#sk5' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl786])).
% 54.44/7.48 thf(zip_derived_cl792, plain,
% 54.44/7.48 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk5' @ '#sk4'))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl790])).
% 54.44/7.48 thf(zip_derived_cl8755, plain,
% 54.44/7.48 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2'))),
% 54.44/7.48 inference('demod', [status(thm)],
% 54.44/7.48 [zip_derived_cl8741, zip_derived_cl781, zip_derived_cl769,
% 54.44/7.48 zip_derived_cl775, zip_derived_cl787, zip_derived_cl792])).
% 54.44/7.48 thf(zip_derived_cl789, plain,
% 54.44/7.48 ( (imp @
% 54.44/7.48 (imp @
% 54.44/7.48 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2')) @
% 54.44/7.48 ($false)) @
% 54.44/7.48 (n_is @ '#sk2' @ '#sk3'))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl788])).
% 54.44/7.48 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 54.44/7.48 thf('9', plain,
% 54.44/7.48 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 54.44/7.48 inference('rw.lit', [status(esa)], [def_imp])).
% 54.44/7.48 thf(zip_derived_cl791, plain,
% 54.44/7.48 ( (((imp @
% 54.44/7.48 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2')) @
% 54.44/7.48 ($false)) => (n_is @ '#sk2' @ '#sk3')))),
% 54.44/7.48 inference('rw_clause', [status(thm)], [zip_derived_cl789, '9'])).
% 54.44/7.48 thf(zip_derived_cl794, plain,
% 54.44/7.48 ((~ (imp @
% 54.44/7.48 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2')) @
% 54.44/7.48 ($false))
% 54.44/7.48 | (n_is @ '#sk2' @ '#sk3'))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl791])).
% 54.44/7.48 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 54.44/7.48 thf('10', plain,
% 54.44/7.48 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 54.44/7.48 inference('rw.lit', [status(esa)], [def_imp])).
% 54.44/7.48 thf(zip_derived_cl795, plain,
% 54.44/7.48 ((~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2')) => ($false)))
% 54.44/7.48 | (n_is @ '#sk2' @ '#sk3'))),
% 54.44/7.48 inference('rw_clause', [status(thm)], [zip_derived_cl794, '10'])).
% 54.44/7.48 thf(zip_derived_cl796, plain,
% 54.44/7.48 ((~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2'))))
% 54.44/7.48 | (n_is @ '#sk2' @ '#sk3'))),
% 54.44/7.48 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl795])).
% 54.44/7.48 thf(zip_derived_cl797, plain,
% 54.44/7.48 (( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk3' @ '#sk2'))
% 54.44/7.48 | (n_is @ '#sk2' @ '#sk3'))),
% 54.44/7.48 inference('simplify nested equalities', [status(thm)],
% 54.44/7.48 [zip_derived_cl796])).
% 54.44/7.48 thf(zip_derived_cl8773, plain, ( (n_is @ '#sk2' @ '#sk3')),
% 54.44/7.48 inference('sup+', [status(thm)], [zip_derived_cl8755, zip_derived_cl797])).
% 54.44/7.48 thf(zip_derived_cl781, plain,
% 54.44/7.48 ( (is_of @ '#sk4' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl780])).
% 54.44/7.48 thf(zip_derived_cl769, plain,
% 54.44/7.48 ( (is_of @ '#sk2' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl768])).
% 54.44/7.48 thf(zip_derived_cl775, plain,
% 54.44/7.48 ( (is_of @ '#sk3' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl774])).
% 54.44/7.48 thf(zip_derived_cl787, plain,
% 54.44/7.48 ( (is_of @ '#sk5' @
% 54.44/7.48 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl786])).
% 54.44/7.48 thf(zip_derived_cl792, plain,
% 54.44/7.48 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 54.44/7.48 (diffprop @ '#sk5' @ '#sk4'))),
% 54.44/7.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl790])).
% 54.44/7.48 thf(zip_derived_cl9000, plain, ($false),
% 54.44/7.48 inference('demod', [status(thm)],
% 54.44/7.48 [zip_derived_cl8986, zip_derived_cl8773, zip_derived_cl781,
% 54.44/7.48 zip_derived_cl769, zip_derived_cl775, zip_derived_cl787,
% 54.44/7.48 zip_derived_cl792])).
% 54.44/7.48
% 54.44/7.48 % SZS output end Refutation
% 54.44/7.48
% 54.44/7.48
% 54.44/7.48 % Terminating...
% 55.09/7.61 % Runner terminated.
% 55.09/7.61 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------