%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM652^4 : 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.UVmVqVG0ZV true
% Computer : n027.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 04:47:49 PM UTC 2025
% Result : Theorem 9.88s 2.04s
% Output : Refutation 9.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : NUM652^4 : TPTP v9.2.0. Released v7.1.0.
% 0.06/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.UVmVqVG0ZV true
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 16:47:38 EDT 2025
% 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
% 0.13/0.36 % Running in HO mode
% 0.53/0.66 % Total configuration time : 828
% 0.53/0.66 % Estimated wc time : 1656
% 0.53/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.53/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.53/0.71 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.53/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.53/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.53/0.75 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.53/0.75 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.53/0.76 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.53/0.76 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.54/1.02 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 9.88/2.04 % Solved by lams/40_b.comb.sh.
% 9.88/2.04 % done 166 iterations in 1.204s
% 9.88/2.04 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 9.88/2.04 % SZS output start Refutation
% 9.88/2.04 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
% 9.88/2.04 thf('#sk2_type', type, '#sk2': $i).
% 9.88/2.04 thf(orec3_type, type, orec3: $o > $o > $o > $o).
% 9.88/2.04 thf(nat_type, type, nat: $i).
% 9.88/2.04 thf(moreis_type, type, moreis: $i > $i > $o).
% 9.88/2.04 thf(and3_type, type, and3: $o > $o > $o > $o).
% 9.88/2.04 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 9.88/2.04 thf(in_type, type, in: $i > $i > $o).
% 9.88/2.04 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 9.88/2.04 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 9.88/2.04 thf('#sk3_type', type, '#sk3': $i).
% 9.88/2.04 thf(emptyset_type, type, emptyset: $i).
% 9.88/2.04 thf(n_is_type, type, n_is: $i > $i > $o).
% 9.88/2.04 thf(l_ec_type, type, l_ec: $o > $o > $o).
% 9.88/2.04 thf(imp_type, type, imp: $o > $o > $o).
% 9.88/2.04 thf(ec3_type, type, ec3: $o > $o > $o > $o).
% 9.88/2.04 thf(d_and_type, type, d_and: $o > $o > $o).
% 9.88/2.04 thf(omega_type, type, omega: $i).
% 9.88/2.04 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 9.88/2.04 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 9.88/2.04 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 9.88/2.04 thf(l_or_type, type, l_or: $o > $o > $o).
% 9.88/2.04 thf(d_not_type, type, d_not: $o > $o).
% 9.88/2.04 thf(iii_type, type, iii: $i > $i > $o).
% 9.88/2.04 thf(or3_type, type, or3: $o > $o > $o > $o).
% 9.88/2.04 thf(e_is_type, type, e_is: $i > $i > $i > $o).
% 9.88/2.04 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 9.88/2.04 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 9.88/2.04 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 9.88/2.04 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 9.88/2.04 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 9.88/2.04 thf(satz10c, conjecture,
% 9.88/2.04 (all_of @
% 9.88/2.04 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 9.88/2.04 ( ^[X0:$i]:
% 9.88/2.04 ( all_of @
% 9.88/2.04 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 9.88/2.04 ( ^[X1:$i]: ( ( moreis @ X0 @ X1 ) => ( d_not @ ( iii @ X0 @ X1 ) ) ) ) ) ))).
% 9.88/2.04 thf(zf_stmt_0, negated_conjecture,
% 9.88/2.04 (~( all_of @
% 9.88/2.04 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 9.88/2.04 ( ^[X0:$i]:
% 9.88/2.04 ( all_of @
% 9.88/2.04 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 9.88/2.04 ( ^[X1:$i]:
% 9.88/2.04 ( ( moreis @ X0 @ X1 ) => ( d_not @ ( iii @ X0 @ X1 ) ) ) ) ) ) )),
% 9.88/2.04 inference('cnf.neg', [status(esa)], [satz10c])).
% 9.88/2.04 thf(zip_derived_cl93, plain,
% 9.88/2.04 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 9.88/2.04 (^[Y0 : $i]:
% 9.88/2.04 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 9.88/2.04 (^[Y1 : $i]: (((moreis @ Y0 @ Y1) => (d_not @ (iii @ Y0 @ Y1))))))))),
% 9.88/2.04 inference('cnf', [status(esa)], [zf_stmt_0])).
% 9.88/2.04 thf(zip_derived_cl94, plain,
% 9.88/2.04 (~ (all_of @ ((('#C') @ in @ nat)) @
% 9.88/2.04 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 9.88/2.04 ((('#S') @ ((('#B') @ ('#S') @
% 9.88/2.04 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @
% 9.88/2.04 ((('#B') @ ((('#B') @ d_not)) @ iii)))))))),
% 9.88/2.04 inference('lams2combs', [status(thm)], [zip_derived_cl93])).
% 9.88/2.04 thf(def_nat, axiom,(( nat ) =
% 9.88/2.04 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))).
% 9.88/2.04 thf('0', plain,
% 9.88/2.04 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )),
% 9.88/2.04 define([status(thm)])).
% 9.88/2.04 thf(zip_derived_cl161, plain,
% 9.88/2.04 (~ (all_of @
% 9.88/2.04 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 9.88/2.04 ((('#B') @ (all_of @
% 9.88/2.04 ((('#C') @ in @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 9.88/2.04 ((('#S') @ ((('#B') @ ('#S') @
% 9.88/2.04 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @
% 9.88/2.04 ((('#B') @ ((('#B') @ d_not)) @ iii)))))))),
% 9.88/2.04 inference('rw', [status(thm)], [zip_derived_cl94, '0'])).
% 9.88/2.04 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 9.88/2.04 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 9.88/2.04 thf('1', plain,
% 9.88/2.04 (![X0:( $i > $o ),X1:( $i > $o )]:
% 9.88/2.04 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 9.88/2.04 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 9.88/2.04 inference('rw.lit', [status(esa)], [def_all_of])).
% 9.88/2.04 thf(zip_derived_cl162, plain,
% 9.88/2.04 (~ (((!!) @ (^[Y0 : $i]:
% 9.88/2.04 (((is_of @ Y0 @
% 9.88/2.04 ((('#C') @ in @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 9.88/2.04 ((('#B') @ (all_of @
% 9.88/2.04 ((('#C') @ in @
% 9.88/2.04 (d_Sep @ omega @
% 9.88/2.04 ((('#C') @ (!=) @ emptyset)))))) @
% 9.88/2.04 ((('#S') @ ((('#B') @ ('#S') @
% 9.88/2.04 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @
% 9.88/2.04 ((('#B') @ ((('#B') @ d_not)) @ iii)))) @
% 9.88/2.04 Y0)))))))),
% 9.88/2.04 inference('rw_clause', [status(thm)], [zip_derived_cl161, '1'])).
% 9.88/2.04 thf(zip_derived_cl163, plain,
% 9.88/2.04 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 9.88/2.04 ((('#C') @ is_of @
% 9.88/2.04 ((('#C') @ in @
% 9.88/2.04 (d_Sep @ omega @
% 9.88/2.04 ((('#C') @ (!=) @ emptyset))))))))) @
% 9.88/2.04 ((('#B') @ (all_of @
% 9.88/2.04 ((('#C') @ in @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 9.88/2.04 ((('#S') @ ((('#B') @ ('#S') @
% 9.88/2.04 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @
% 9.88/2.04 ((('#B') @ ((('#B') @ d_not)) @ iii))))))))))),
% 9.88/2.04 inference('comb-normalize', [status(thm)], [zip_derived_cl162])).
% 9.88/2.04 thf(zip_derived_cl164, plain,
% 9.88/2.04 (~ (((is_of @ '#sk2' @
% 9.88/2.04 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 9.88/2.04 (all_of @
% 9.88/2.04 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 9.88/2.04 ((('#S') @ ((('#B') @ (=>) @ (moreis @ '#sk2'))) @
% 9.88/2.04 ((('#B') @ d_not @ (iii @ '#sk2'))))))))),
% 9.88/2.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl163])).
% 9.88/2.04 thf(def_is_of, axiom,(( is_of @ (X1)@ (X0)) = ((X0 @ X1)))).
% 9.88/2.04 thf('2', plain,
% 9.88/2.04 (![X0:( $i > $o ),X1:$i]: ( ( is_of @ X1 @ X0 ) = ( X0 @ X1 ) )),
% 9.88/2.04 define([status(thm)])).
% 9.88/2.04 thf(zip_derived_cl165, plain,
% 9.88/2.04 (~ (((in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 9.88/2.04 (all_of @
% 9.88/2.04 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 9.88/2.04 ((('#S') @ ((('#B') @ (=>) @ (moreis @ '#sk2'))) @
% 9.88/2.04 ((('#B') @ d_not @ (iii @ '#sk2'))))))))),
% 9.88/2.04 inference('rw', [status(thm)], [zip_derived_cl164, '2'])).
% 9.88/2.04 thf(zip_derived_cl167, plain,
% 9.88/2.04 (~ (all_of @
% 9.88/2.04 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 9.88/2.04 ((('#S') @ ((('#B') @ (=>) @ (moreis @ '#sk2'))) @
% 9.88/2.04 ((('#B') @ d_not @ (iii @ '#sk2'))))))),
% 9.88/2.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl165])).
% 9.88/2.04 thf(zip_derived_cl168, plain,
% 9.88/2.04 (~ (((!!) @ (^[Y0 : $i]:
% 9.88/2.04 (((is_of @ Y0 @
% 9.88/2.04 ((('#C') @ in @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 9.88/2.04 ((('#S') @ ((('#B') @ (=>) @ (moreis @ '#sk2'))) @
% 9.88/2.04 ((('#B') @ d_not @ (iii @ '#sk2'))) @ Y0)))))))),
% 9.88/2.04 inference('rw_clause', [status(thm)], [zip_derived_cl167, '1'])).
% 9.88/2.04 thf(zip_derived_cl169, plain,
% 9.88/2.04 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 9.88/2.04 ((('#C') @ is_of @
% 9.88/2.04 ((('#C') @ in @
% 9.88/2.04 (d_Sep @ omega @
% 9.88/2.04 ((('#C') @ (!=) @ emptyset))))))))) @
% 9.88/2.04 ((('#S') @ ((('#B') @ (=>) @ (moreis @ '#sk2'))) @
% 9.88/2.04 ((('#B') @ d_not @ (iii @ '#sk2')))))))))),
% 9.88/2.04 inference('comb-normalize', [status(thm)], [zip_derived_cl168])).
% 9.88/2.04 thf(zip_derived_cl170, plain,
% 9.88/2.04 (~ (((is_of @ '#sk3' @
% 9.88/2.04 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 9.88/2.04 (((moreis @ '#sk2' @ '#sk3') => (d_not @ (iii @ '#sk2' @ '#sk3'))))))),
% 9.88/2.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl169])).
% 9.88/2.04 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 9.88/2.04 thf('3', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 9.88/2.04 define([status(thm)])).
% 9.88/2.04 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 9.88/2.04 thf('4', plain,
% 9.88/2.04 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 9.88/2.04 define([status(thm)])).
% 9.88/2.04 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))).
% 9.88/2.04 thf('5', plain,
% 9.88/2.04 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )),
% 9.88/2.04 define([status(thm)])).
% 9.88/2.04 thf(def_n_is, axiom,(( n_is @ (X0)@ (X1)) = ((e_is @ nat @ X0 @ X1)))).
% 9.88/2.04 thf('6', plain,
% 9.88/2.04 (![X1:$i,X0:$i]: ( ( n_is @ X0 @ X1 ) = ( e_is @ nat @ X0 @ X1 ) )),
% 9.88/2.04 define([status(thm)])).
% 9.88/2.04 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 9.88/2.04 thf('7', plain,
% 9.88/2.04 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 9.88/2.04 define([status(thm)])).
% 9.88/2.04 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) =
% 9.88/2.04 ((n_some @ (diffprop @ X0 @ X1))))).
% 9.88/2.04 thf('8', plain,
% 9.88/2.04 (![X1:$i,X0:$i]:
% 9.88/2.04 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 9.88/2.04 define([status(thm)])).
% 9.88/2.04 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))).
% 9.88/2.04 thf('9', plain,
% 9.88/2.04 (![X1:$i,X0:$i]:
% 9.88/2.04 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 9.88/2.04 define([status(thm)])).
% 9.88/2.04 thf(def_moreis, axiom,(( moreis @ (X0)@ (X1)) =
% 9.88/2.04 ((l_or @ (d_29_ii @ X0 @ X1) @ (n_is @ X0 @ X1))))).
% 9.88/2.04 thf('10', plain,
% 9.88/2.04 (![X1:$i,X0:$i]:
% 9.88/2.04 ( ( moreis @ X0 @ X1 ) =
% 9.88/2.04 ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
% 9.88/2.04 define([status(thm)])).
% 9.88/2.04 thf(zip_derived_cl171, plain,
% 9.88/2.04 (~ (((in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 9.88/2.04 (((imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ '#sk2' @ '#sk3')) @
% 9.88/2.04 ($false)) @
% 9.88/2.04 ((('#sk2') = ('#sk3')))) => (imp @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ '#sk3' @ '#sk2')) @
% 9.88/2.04 ($false))))))),
% 9.88/2.04 inference('rw', [status(thm)],
% 9.88/2.04 [zip_derived_cl170, '2', '3', '3', '4', '5', '0', '6', '7',
% 9.88/2.04 '7', '8', '9', '10'])).
% 9.88/2.04 thf(zip_derived_cl173, plain,
% 9.88/2.04 (~ (((imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ '#sk2' @ '#sk3')) @
% 9.88/2.04 ($false)) @
% 9.88/2.04 ((('#sk2') = ('#sk3')))) => (imp @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ '#sk3' @ '#sk2')) @
% 9.88/2.04 ($false))))),
% 9.88/2.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl171])).
% 9.88/2.04 thf(zip_derived_cl174, plain,
% 9.88/2.04 ( (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ '#sk2' @ '#sk3')) @
% 9.88/2.04 ($false)) @
% 9.88/2.04 ((('#sk2') = ('#sk3'))))),
% 9.88/2.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])).
% 9.88/2.04 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 9.88/2.04 thf('11', plain,
% 9.88/2.04 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 9.88/2.04 inference('rw.lit', [status(esa)], [def_imp])).
% 9.88/2.04 thf(zip_derived_cl176, plain,
% 9.88/2.04 ( (((imp @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ '#sk2' @ '#sk3')) @
% 9.88/2.04 ($false)) => ((('#sk2') = ('#sk3')))))),
% 9.88/2.04 inference('rw_clause', [status(thm)], [zip_derived_cl174, '11'])).
% 9.88/2.04 thf(zip_derived_cl178, plain,
% 9.88/2.04 ((~ (imp @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ '#sk2' @ '#sk3')) @
% 9.88/2.04 ($false))
% 9.88/2.04 | ((('#sk2') = ('#sk3'))))),
% 9.88/2.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl176])).
% 9.88/2.04 thf(zip_derived_cl181, plain,
% 9.88/2.04 ((~ (imp @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ '#sk2' @ '#sk3')) @
% 9.88/2.04 ($false))
% 9.88/2.04 | (('#sk2') = ('#sk3')))),
% 9.88/2.04 inference('simplify nested equalities', [status(thm)],
% 9.88/2.04 [zip_derived_cl178])).
% 9.88/2.04 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 9.88/2.04 thf('12', plain,
% 9.88/2.04 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 9.88/2.04 inference('rw.lit', [status(esa)], [def_imp])).
% 9.88/2.04 thf(zip_derived_cl182, plain,
% 9.88/2.04 ((~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ '#sk2' @ '#sk3')) => ($false)))
% 9.88/2.04 | (('#sk2') = ('#sk3')))),
% 9.88/2.04 inference('rw_clause', [status(thm)], [zip_derived_cl181, '12'])).
% 9.88/2.04 thf(zip_derived_cl183, plain,
% 9.88/2.04 ((~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ '#sk2' @ '#sk3'))))
% 9.88/2.04 | (('#sk2') = ('#sk3')))),
% 9.88/2.04 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl182])).
% 9.88/2.04 thf(zip_derived_cl184, plain,
% 9.88/2.04 (( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ '#sk2' @ '#sk3'))
% 9.88/2.04 | (('#sk2') = ('#sk3')))),
% 9.88/2.04 inference('simplify nested equalities', [status(thm)],
% 9.88/2.04 [zip_derived_cl183])).
% 9.88/2.04 thf(satz10, axiom,
% 9.88/2.04 (all_of @
% 9.88/2.04 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 9.88/2.04 ( ^[X0:$i]:
% 9.88/2.04 ( all_of @
% 9.88/2.04 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 9.88/2.04 ( ^[X1:$i]:
% 9.88/2.04 ( orec3 @
% 9.88/2.04 ( n_is @ X0 @ X1 ) @ ( d_29_ii @ X0 @ X1 ) @ ( iii @ X0 @ X1 ) ) ) ) ))).
% 9.88/2.04 thf(zip_derived_cl79, plain,
% 9.88/2.04 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 9.88/2.04 (^[Y0 : $i]:
% 9.88/2.04 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 9.88/2.04 (^[Y1 : $i]:
% 9.88/2.04 (orec3 @ (n_is @ Y0 @ Y1) @ (d_29_ii @ Y0 @ Y1) @
% 9.88/2.04 (iii @ Y0 @ Y1))))))),
% 9.88/2.04 inference('cnf', [status(esa)], [satz10])).
% 9.88/2.04 thf(zip_derived_cl80, plain,
% 9.88/2.04 ( (all_of @ ((('#C') @ in @ nat)) @
% 9.88/2.04 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 9.88/2.04 ((('#S') @ ((('#B') @ ('#S') @
% 9.88/2.04 ((('#S') @ ((('#B') @ ('#S') @
% 9.88/2.04 ((('#B') @ ((('#B') @ orec3)) @ n_is)))) @
% 9.88/2.04 d_29_ii)))) @
% 9.88/2.04 iii)))))),
% 9.88/2.04 inference('lams2combs', [status(thm)], [zip_derived_cl79])).
% 9.88/2.04 thf(zip_derived_cl372, plain,
% 9.88/2.04 ( (all_of @
% 9.88/2.04 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 9.88/2.04 ((('#B') @ (all_of @
% 9.88/2.04 ((('#C') @ in @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 9.88/2.04 ((('#S') @ ((('#B') @ ('#S') @
% 9.88/2.04 ((('#S') @ ((('#B') @ ('#S') @
% 9.88/2.04 ((('#B') @ ((('#B') @ orec3)) @ n_is)))) @
% 9.88/2.04 d_29_ii)))) @
% 9.88/2.04 iii)))))),
% 9.88/2.04 inference('rw', [status(thm)], [zip_derived_cl80, '0'])).
% 9.88/2.04 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 9.88/2.04 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 9.88/2.04 thf('13', plain,
% 9.88/2.04 (![X0:( $i > $o ),X1:( $i > $o )]:
% 9.88/2.04 ( ( all_of @ X0 @ X1 ) <=>
% 9.88/2.04 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 9.88/2.04 inference('rw.lit', [status(esa)], [def_all_of])).
% 9.88/2.04 thf(zip_derived_cl373, plain,
% 9.88/2.04 ( (((!!) @ (^[Y0 : $i]:
% 9.88/2.04 (((is_of @ Y0 @
% 9.88/2.04 ((('#C') @ in @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 9.88/2.04 ((('#B') @ (all_of @
% 9.88/2.04 ((('#C') @ in @
% 9.88/2.04 (d_Sep @ omega @
% 9.88/2.04 ((('#C') @ (!=) @ emptyset)))))) @
% 9.88/2.04 ((('#S') @ ((('#B') @ ('#S') @
% 9.88/2.04 ((('#S') @ ((('#B') @ ('#S') @
% 9.88/2.04 ((('#B') @ ((('#B') @ orec3)) @
% 9.88/2.04 n_is)))) @
% 9.88/2.04 d_29_ii)))) @
% 9.88/2.04 iii)) @
% 9.88/2.04 Y0)))))))),
% 9.88/2.04 inference('rw_clause', [status(thm)], [zip_derived_cl372, '13'])).
% 9.88/2.04 thf(zip_derived_cl374, plain,
% 9.88/2.04 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 9.88/2.04 ((('#C') @ is_of @
% 9.88/2.04 ((('#C') @ in @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 9.88/2.04 ((('#B') @ (all_of @
% 9.88/2.04 ((('#C') @ in @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 9.88/2.04 ((('#S') @ ((('#B') @ ('#S') @
% 9.88/2.04 ((('#S') @ ((('#B') @ ('#S') @
% 9.88/2.04 ((('#B') @ ((('#B') @ orec3)) @
% 9.88/2.04 n_is)))) @
% 9.88/2.04 d_29_ii)))) @
% 9.88/2.04 iii))))))))),
% 9.88/2.04 inference('comb-normalize', [status(thm)], [zip_derived_cl373])).
% 9.88/2.04 thf(zip_derived_cl375, plain,
% 9.88/2.04 (![X2 : $i]:
% 9.88/2.04 (((is_of @ X2 @
% 9.88/2.04 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 9.88/2.04 (all_of @
% 9.88/2.04 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 9.88/2.04 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (n_is @ X2))) @
% 9.88/2.04 (d_29_ii @ X2))) @
% 9.88/2.04 (iii @ X2))))))),
% 9.88/2.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl374])).
% 9.88/2.04 thf(zip_derived_cl376, plain,
% 9.88/2.04 (![X2 : $i]:
% 9.88/2.04 (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 9.88/2.04 (all_of @
% 9.88/2.04 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 9.88/2.04 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (n_is @ X2))) @
% 9.88/2.04 (d_29_ii @ X2))) @
% 9.88/2.04 (iii @ X2))))))),
% 9.88/2.04 inference('rw', [status(thm)], [zip_derived_cl375, '2'])).
% 9.88/2.04 thf(zip_derived_cl377, plain,
% 9.88/2.04 (![X2 : $i]:
% 9.88/2.04 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.04 | (all_of @
% 9.88/2.04 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 9.88/2.04 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (n_is @ X2))) @
% 9.88/2.04 (d_29_ii @ X2))) @
% 9.88/2.04 (iii @ X2)))))),
% 9.88/2.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl376])).
% 9.88/2.04 thf(zip_derived_cl378, plain,
% 9.88/2.04 (![X0 : $i]:
% 9.88/2.04 ( (((!!) @ (^[Y0 : $i]:
% 9.88/2.04 (((is_of @ Y0 @
% 9.88/2.04 ((('#C') @ in @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 9.88/2.04 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (n_is @ X0))) @
% 9.88/2.04 (d_29_ii @ X0))) @
% 9.88/2.04 (iii @ X0) @ Y0)))))))
% 9.88/2.04 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.04 inference('rw_clause', [status(thm)], [zip_derived_cl377, '13'])).
% 9.88/2.04 thf(zip_derived_cl379, plain,
% 9.88/2.04 (![X0 : $i]:
% 9.88/2.04 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 9.88/2.04 ((('#C') @ is_of @
% 9.88/2.04 ((('#C') @ in @
% 9.88/2.04 (d_Sep @ omega @
% 9.88/2.04 ((('#C') @ (!=) @ emptyset))))))))) @
% 9.88/2.04 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (n_is @ X0))) @
% 9.88/2.04 (d_29_ii @ X0))) @
% 9.88/2.04 (iii @ X0)))))))
% 9.88/2.04 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.04 inference('comb-normalize', [status(thm)], [zip_derived_cl378])).
% 9.88/2.04 thf(zip_derived_cl380, plain,
% 9.88/2.04 (![X0 : $i, X2 : $i]:
% 9.88/2.04 ( (((is_of @ X2 @
% 9.88/2.04 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 9.88/2.04 (orec3 @ (n_is @ X0 @ X2) @ (d_29_ii @ X0 @ X2) @ (iii @ X0 @ X2))))
% 9.88/2.04 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl379])).
% 9.88/2.04 thf(def_l_ec, axiom,(( l_ec @ (X0)@ (X1)) = ((imp @ X0 @ (d_not @ X1))))).
% 9.88/2.04 thf('14', plain,
% 9.88/2.04 (![X1:$o,X0:$o]: ( ( l_ec @ X0 @ X1 ) = ( imp @ X0 @ ( d_not @ X1 ) ) )),
% 9.88/2.04 define([status(thm)])).
% 9.88/2.04 thf(def_d_and, axiom,(( d_and @ (X0)@ (X1)) = ((d_not @ (l_ec @ X0 @ X1))))).
% 9.88/2.04 thf('15', plain,
% 9.88/2.04 (![X1:$o,X0:$o]: ( ( d_and @ X0 @ X1 ) = ( d_not @ ( l_ec @ X0 @ X1 ) ) )),
% 9.88/2.04 define([status(thm)])).
% 9.88/2.04 thf(def_or3, axiom,(( or3 @ (X0)@ (X1)@ (X2)) =
% 9.88/2.04 ((l_or @ X0 @ (l_or @ X1 @ X2))))).
% 9.88/2.04 thf('16', plain,
% 9.88/2.04 (![X2:$o,X1:$o,X0:$o]:
% 9.88/2.04 ( ( or3 @ X0 @ X1 @ X2 ) = ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) )),
% 9.88/2.04 define([status(thm)])).
% 9.88/2.04 thf(def_and3, axiom,(( and3 @ (X0)@ (X1)@ (X2)) =
% 9.88/2.04 ((d_and @ X0 @ (d_and @ X1 @ X2))))).
% 9.88/2.04 thf('17', plain,
% 9.88/2.04 (![X2:$o,X1:$o,X0:$o]:
% 9.88/2.04 ( ( and3 @ X0 @ X1 @ X2 ) = ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) )),
% 9.88/2.04 define([status(thm)])).
% 9.88/2.04 thf(def_ec3, axiom,(( ec3 @ (X0)@ (X1)@ (X2)) =
% 9.88/2.04 ((and3 @ (l_ec @ X0 @ X1) @ (l_ec @ X1 @ X2) @ (l_ec @ X2 @ X0))))).
% 9.88/2.04 thf('18', plain,
% 9.88/2.04 (![X2:$o,X1:$o,X0:$o]:
% 9.88/2.04 ( ( ec3 @ X0 @ X1 @ X2 ) =
% 9.88/2.04 ( and3 @ ( l_ec @ X0 @ X1 ) @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X0 ) ) )),
% 9.88/2.04 define([status(thm)])).
% 9.88/2.04 thf(def_orec3, axiom,(( orec3 @ (X0)@ (X1)@ (X2)) =
% 9.88/2.04 ((d_and @ (or3 @ X0 @ X1 @ X2) @ (ec3 @ X0 @ X1 @ X2))))).
% 9.88/2.04 thf('19', plain,
% 9.88/2.04 (![X2:$o,X1:$o,X0:$o]:
% 9.88/2.04 ( ( orec3 @ X0 @ X1 @ X2 ) =
% 9.88/2.04 ( d_and @ ( or3 @ X0 @ X1 @ X2 ) @ ( ec3 @ X0 @ X1 @ X2 ) ) )),
% 9.88/2.04 define([status(thm)])).
% 9.88/2.04 thf(zip_derived_cl381, plain,
% 9.88/2.04 (![X0 : $i, X2 : $i]:
% 9.88/2.04 ( (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @ (imp @ (((X0) = (X2))) @ ($false)) @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X0 @ X2)) @
% 9.88/2.04 ($false)) @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X2 @ X0)))) @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @ (((X0) = (X2))) @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X0 @ X2)) @
% 9.88/2.04 ($false))) @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X0 @ X2)) @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X2 @ X0)) @
% 9.88/2.04 ($false))) @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X2 @ X0)) @
% 9.88/2.04 (imp @ (((X0) = (X2))) @ ($false))) @
% 9.88/2.04 ($false))) @
% 9.88/2.04 ($false)) @
% 9.88/2.04 ($false))) @
% 9.88/2.04 ($false)) @
% 9.88/2.04 ($false))) @
% 9.88/2.04 ($false))))
% 9.88/2.04 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.04 inference('rw', [status(thm)],
% 9.88/2.04 [zip_derived_cl380, '2', '3', '3', '3', '3', '3', '3', '3',
% 9.88/2.04 '3', '3', '14', '14', '14', '14', '14', '14', '15', '15',
% 9.88/2.04 '15', '4', '4', '16', '17', '18', '19', '5', '0', '6', '7',
% 9.88/2.04 '7', '8', '9'])).
% 9.88/2.04 thf(zip_derived_cl382, plain,
% 9.88/2.04 (![X0 : $i, X2 : $i]:
% 9.88/2.04 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.04 | (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @ (imp @ (((X0) = (X2))) @ ($false)) @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X0 @ X2)) @
% 9.88/2.04 ($false)) @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X2 @ X0)))) @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @ (((X0) = (X2))) @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X0 @ X2)) @
% 9.88/2.04 ($false))) @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X0 @ X2)) @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X2 @ X0)) @
% 9.88/2.04 ($false))) @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X2 @ X0)) @
% 9.88/2.04 (imp @ (((X0) = (X2))) @ ($false))) @
% 9.88/2.04 ($false))) @
% 9.88/2.04 ($false)) @
% 9.88/2.04 ($false))) @
% 9.88/2.04 ($false)) @
% 9.88/2.04 ($false))) @
% 9.88/2.04 ($false))
% 9.88/2.04 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl381])).
% 9.88/2.04 thf(zip_derived_cl383, plain,
% 9.88/2.04 (![X0 : $i, X1 : $i]:
% 9.88/2.04 ( (((imp @
% 9.88/2.04 (imp @ (imp @ (((X0) = (X1))) @ ($false)) @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X0 @ X1)) @
% 9.88/2.04 ($false)) @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X1 @ X0)))) @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @ (((X0) = (X1))) @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X0 @ X1)) @
% 9.88/2.04 ($false))) @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X0 @ X1)) @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X1 @ X0)) @
% 9.88/2.04 ($false))) @
% 9.88/2.04 (imp @
% 9.88/2.04 (imp @
% 9.88/2.04 (l_some @
% 9.88/2.04 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.04 (diffprop @ X1 @ X0)) @
% 9.88/2.04 (imp @ (((X0) = (X1))) @ ($false))) @
% 9.88/2.04 ($false))) @
% 9.88/2.04 ($false)) @
% 9.88/2.04 ($false))) @
% 9.88/2.04 ($false)) @
% 9.88/2.04 ($false))) =>
% 9.88/2.04 ($false)))
% 9.88/2.04 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.04 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.04 inference('rw_clause', [status(thm)], [zip_derived_cl382, '11'])).
% 9.88/2.04 thf(zip_derived_cl384, plain,
% 9.88/2.04 (![X0 : $i, X1 : $i]:
% 9.88/2.04 ( (((~) @ (imp @
% 9.88/2.04 (imp @ (imp @ (((X0) = (X1))) @ ($false)) @
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% 9.88/2.04 ($false)))))
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% 9.88/2.04 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
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% 9.88/2.04 thf(zip_derived_cl385, plain,
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% 9.88/2.04 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.04 inference('simplify nested equalities', [status(thm)],
% 9.88/2.04 [zip_derived_cl384])).
% 9.88/2.04 thf(zip_derived_cl386, plain,
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% 9.88/2.04 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.04 inference('rw_clause', [status(thm)], [zip_derived_cl385, '12'])).
% 9.88/2.04 thf(zip_derived_cl388, plain,
% 9.88/2.04 (![X0 : $i, X1 : $i]:
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% 9.88/2.04 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl386])).
% 9.88/2.04 thf(zip_derived_cl390, plain,
% 9.88/2.04 (![X0 : $i, X1 : $i]:
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% 9.88/2.04 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.04 inference('rw_clause', [status(thm)], [zip_derived_cl388, '12'])).
% 9.88/2.04 thf(zip_derived_cl392, plain,
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% 9.88/2.04 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
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% 9.88/2.04 thf(zip_derived_cl393, plain,
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% 9.88/2.04 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
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% 9.88/2.04 [zip_derived_cl392])).
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% 9.88/2.04 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.04 inference('rw_clause', [status(thm)], [zip_derived_cl393, '11'])).
% 9.88/2.04 thf(zip_derived_cl396, plain,
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% 9.88/2.04 thf(zip_derived_cl397, plain,
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% 9.88/2.04 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.04 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
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% 9.88/2.04 [zip_derived_cl396])).
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% 9.88/2.04 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
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% 9.88/2.04 thf(zip_derived_cl403, plain,
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% 9.88/2.05 (imp @ (((X1) = (X0))) @ ($false))) @
% 9.88/2.05 ($false))) @
% 9.88/2.05 ($false)) @
% 9.88/2.05 ($false))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl398])).
% 9.88/2.05 thf(zip_derived_cl406, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 (~ (((imp @
% 9.88/2.05 (imp @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1)) @
% 9.88/2.05 ($false))) @
% 9.88/2.05 (imp @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1)) @
% 9.88/2.05 (imp @ (((X1) = (X0))) @ ($false))) @
% 9.88/2.05 ($false))) @
% 9.88/2.05 ($false)) => ($false)))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('rw_clause', [status(thm)], [zip_derived_cl403, '12'])).
% 9.88/2.05 thf(zip_derived_cl409, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 (~ (((~) @ (imp @
% 9.88/2.05 (imp @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @
% 9.88/2.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @
% 9.88/2.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1)) @
% 9.88/2.05 ($false))) @
% 9.88/2.05 (imp @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @
% 9.88/2.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1)) @
% 9.88/2.05 (imp @ (((X1) = (X0))) @ ($false))) @
% 9.88/2.05 ($false))) @
% 9.88/2.05 ($false))))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl406])).
% 9.88/2.05 thf(zip_derived_cl410, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 ( (imp @
% 9.88/2.05 (imp @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1)) @
% 9.88/2.05 ($false))) @
% 9.88/2.05 (imp @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1)) @
% 9.88/2.05 (imp @ (((X1) = (X0))) @ ($false))) @
% 9.88/2.05 ($false))) @
% 9.88/2.05 ($false))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('simplify nested equalities', [status(thm)],
% 9.88/2.05 [zip_derived_cl409])).
% 9.88/2.05 thf(zip_derived_cl411, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 ( (((imp @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1)) @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) @
% 9.88/2.05 ($false))) @
% 9.88/2.05 (imp @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) @
% 9.88/2.05 (imp @ (((X0) = (X1))) @ ($false))) @
% 9.88/2.05 ($false))) =>
% 9.88/2.05 ($false)))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('rw_clause', [status(thm)], [zip_derived_cl410, '11'])).
% 9.88/2.05 thf(zip_derived_cl416, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 ( (((~) @ (imp @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @
% 9.88/2.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1)) @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @
% 9.88/2.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) @
% 9.88/2.05 ($false))) @
% 9.88/2.05 (imp @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @
% 9.88/2.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) @
% 9.88/2.05 (imp @ (((X0) = (X1))) @ ($false))) @
% 9.88/2.05 ($false)))))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl411])).
% 9.88/2.05 thf(zip_derived_cl417, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 (~ (imp @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1)) @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) @
% 9.88/2.05 ($false))) @
% 9.88/2.05 (imp @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) @
% 9.88/2.05 (imp @ (((X0) = (X1))) @ ($false))) @
% 9.88/2.05 ($false)))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('simplify nested equalities', [status(thm)],
% 9.88/2.05 [zip_derived_cl416])).
% 9.88/2.05 thf(zip_derived_cl418, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 (~ (((imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1)) @
% 9.88/2.05 ($false))) =>
% 9.88/2.05 (imp @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1)) @
% 9.88/2.05 (imp @ (((X1) = (X0))) @ ($false))) @
% 9.88/2.05 ($false))))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('rw_clause', [status(thm)], [zip_derived_cl417, '12'])).
% 9.88/2.05 thf(zip_derived_cl421, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 ( (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1)) @
% 9.88/2.05 ($false)))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl418])).
% 9.88/2.05 thf(zip_derived_cl423, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) => (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1)) @
% 9.88/2.05 ($false))))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('rw_clause', [status(thm)], [zip_derived_cl421, '11'])).
% 9.88/2.05 thf(zip_derived_cl425, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0))
% 9.88/2.05 | (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1)) @
% 9.88/2.05 ($false))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl423])).
% 9.88/2.05 thf(zip_derived_cl429, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1)) => ($false)))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)))),
% 9.88/2.05 inference('rw_clause', [status(thm)], [zip_derived_cl425, '11'])).
% 9.88/2.05 thf(zip_derived_cl431, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1))))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)))),
% 9.88/2.05 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl429])).
% 9.88/2.05 thf(zip_derived_cl432, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X0 @ X1))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)))),
% 9.88/2.05 inference('simplify nested equalities', [status(thm)],
% 9.88/2.05 [zip_derived_cl431])).
% 9.88/2.05 thf(zip_derived_cl2210, plain,
% 9.88/2.05 (((('#sk2') = ('#sk3'))
% 9.88/2.05 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ '#sk3' @ '#sk2'))
% 9.88/2.05 | ~ (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('sup-', [status(thm)], [zip_derived_cl184, zip_derived_cl432])).
% 9.88/2.05 thf(zip_derived_cl175, plain,
% 9.88/2.05 (~ (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ '#sk3' @ '#sk2')) @
% 9.88/2.05 ($false))),
% 9.88/2.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])).
% 9.88/2.05 thf(zip_derived_cl177, plain,
% 9.88/2.05 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ '#sk3' @ '#sk2')) => ($false)))),
% 9.88/2.05 inference('rw_clause', [status(thm)], [zip_derived_cl175, '12'])).
% 9.88/2.05 thf(zip_derived_cl179, plain,
% 9.88/2.05 (~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ '#sk3' @ '#sk2'))))),
% 9.88/2.05 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl177])).
% 9.88/2.05 thf(zip_derived_cl180, plain,
% 9.88/2.05 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ '#sk3' @ '#sk2'))),
% 9.88/2.05 inference('simplify nested equalities', [status(thm)],
% 9.88/2.05 [zip_derived_cl179])).
% 9.88/2.05 thf(zip_derived_cl172, plain,
% 9.88/2.05 ( (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 9.88/2.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl171])).
% 9.88/2.05 thf(zip_derived_cl166, plain,
% 9.88/2.05 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 9.88/2.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl165])).
% 9.88/2.05 thf(zip_derived_cl2231, plain, ((('#sk2') = ('#sk3'))),
% 9.88/2.05 inference('demod', [status(thm)],
% 9.88/2.05 [zip_derived_cl2210, zip_derived_cl180, zip_derived_cl172,
% 9.88/2.05 zip_derived_cl166])).
% 9.88/2.05 thf(zip_derived_cl180, plain,
% 9.88/2.05 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ '#sk3' @ '#sk2'))),
% 9.88/2.05 inference('simplify nested equalities', [status(thm)],
% 9.88/2.05 [zip_derived_cl179])).
% 9.88/2.05 thf(zip_derived_cl402, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 ( (imp @ (((X1) = (X0))) @
% 9.88/2.05 (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) @
% 9.88/2.05 ($false)))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl398])).
% 9.88/2.05 thf(zip_derived_cl405, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 ( (((((X1) = (X0))) => (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) @
% 9.88/2.05 ($false))))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('rw_clause', [status(thm)], [zip_derived_cl402, '11'])).
% 9.88/2.05 thf(zip_derived_cl408, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 (~ (((X1) = (X0)))
% 9.88/2.05 | (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) @
% 9.88/2.05 ($false))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl405])).
% 9.88/2.05 thf(zip_derived_cl414, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 (((X1) != (X0))
% 9.88/2.05 | (imp @
% 9.88/2.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) @
% 9.88/2.05 ($false))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('simplify nested equalities', [status(thm)],
% 9.88/2.05 [zip_derived_cl408])).
% 9.88/2.05 thf(zip_derived_cl415, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0)) => ($false)))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ((X1) != (X0)))),
% 9.88/2.05 inference('rw_clause', [status(thm)], [zip_derived_cl414, '11'])).
% 9.88/2.05 thf(zip_derived_cl419, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0))))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ((X1) != (X0)))),
% 9.88/2.05 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl415])).
% 9.88/2.05 thf(zip_derived_cl420, plain,
% 9.88/2.05 (![X0 : $i, X1 : $i]:
% 9.88/2.05 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 9.88/2.05 (diffprop @ X1 @ X0))
% 9.88/2.05 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ((X1) != (X0)))),
% 9.88/2.05 inference('simplify nested equalities', [status(thm)],
% 9.88/2.05 [zip_derived_cl419])).
% 9.88/2.05 thf(zip_derived_cl1906, plain,
% 9.88/2.05 (((('#sk3') != ('#sk2'))
% 9.88/2.05 | ~ (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
% 9.88/2.05 | ~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
% 9.88/2.05 inference('sup-', [status(thm)], [zip_derived_cl180, zip_derived_cl420])).
% 9.88/2.05 thf(zip_derived_cl172, plain,
% 9.88/2.05 ( (in @ '#sk3' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 9.88/2.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl171])).
% 9.88/2.05 thf(zip_derived_cl166, plain,
% 9.88/2.05 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
% 9.88/2.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl165])).
% 9.88/2.05 thf(zip_derived_cl1914, plain, ((('#sk3') != ('#sk2'))),
% 9.88/2.05 inference('demod', [status(thm)],
% 9.88/2.05 [zip_derived_cl1906, zip_derived_cl172, zip_derived_cl166])).
% 9.88/2.05 thf(zip_derived_cl2232, plain, ($false),
% 9.88/2.05 inference('simplify_reflect-', [status(thm)],
% 9.88/2.05 [zip_derived_cl2231, zip_derived_cl1914])).
% 9.88/2.05
% 9.88/2.05 % SZS output end Refutation
% 9.88/2.05
% 9.88/2.05
% 9.88/2.05 % Terminating...
% 10.92/2.17 % Runner terminated.
% 10.92/2.17 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------