TSTP Solution File: NUM703^4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM703^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.szbs5V2Hw7 true
% Computer : n004.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 12:43:36 EDT 2023
% Result : Theorem 38.10s 5.49s
% Output : Refutation 38.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM703^4 : TPTP v8.1.2. Released v7.1.0.
% 0.08/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.szbs5V2Hw7 true
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 17:07:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in HO mode
% 0.42/0.67 % Total configuration time : 828
% 0.42/0.67 % Estimated wc time : 1656
% 0.42/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.42/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.42/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.42/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.42/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 38.10/5.49 % Solved by lams/40_b.comb.sh.
% 38.10/5.49 % done 252 iterations in 4.674s
% 38.10/5.49 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 38.10/5.49 % SZS output start Refutation
% 38.10/5.49 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
% 38.10/5.49 thf('#sk3_type', type, '#sk3': $i).
% 38.10/5.49 thf(nat_type, type, nat: $i).
% 38.10/5.49 thf(moreis_type, type, moreis: $i > $i > $o).
% 38.10/5.49 thf(lessis_type, type, lessis: $i > $i > $o).
% 38.10/5.49 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 38.10/5.49 thf(in_type, type, in: $i > $i > $o).
% 38.10/5.49 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 38.10/5.49 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 38.10/5.49 thf(emptyset_type, type, emptyset: $i).
% 38.10/5.49 thf(d_Sing_type, type, d_Sing: $i > $i).
% 38.10/5.49 thf(n_is_type, type, n_is: $i > $i > $o).
% 38.10/5.49 thf(imp_type, type, imp: $o > $o > $o).
% 38.10/5.49 thf(omega_type, type, omega: $i).
% 38.10/5.49 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 38.10/5.49 thf('#sk2_type', type, '#sk2': $i).
% 38.10/5.49 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 38.10/5.49 thf(binunion_type, type, binunion: $i > $i > $i).
% 38.10/5.49 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 38.10/5.49 thf(l_or_type, type, l_or: $o > $o > $o).
% 38.10/5.49 thf(ordsucc_type, type, ordsucc: $i > $i).
% 38.10/5.49 thf(d_not_type, type, d_not: $o > $o).
% 38.10/5.49 thf(iii_type, type, iii: $i > $i > $o).
% 38.10/5.49 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 38.10/5.49 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 38.10/5.49 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 38.10/5.49 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 38.10/5.49 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 38.10/5.49 thf(satz26c, conjecture,
% 38.10/5.49 (all_of @
% 38.10/5.49 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 38.10/5.49 ( ^[X0:$i]:
% 38.10/5.49 ( all_of @
% 38.10/5.49 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 38.10/5.49 ( ^[X1:$i]:
% 38.10/5.49 ( ( d_29_ii @ ( ordsucc @ X1 ) @ X0 ) => ( moreis @ X1 @ X0 ) ) ) ) ))).
% 38.10/5.49 thf(zf_stmt_0, negated_conjecture,
% 38.10/5.49 (~( all_of @
% 38.10/5.49 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 38.10/5.49 ( ^[X0:$i]:
% 38.10/5.49 ( all_of @
% 38.10/5.49 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 38.10/5.49 ( ^[X1:$i]:
% 38.10/5.49 ( ( d_29_ii @ ( ordsucc @ X1 ) @ X0 ) => ( moreis @ X1 @ X0 ) ) ) ) ) )),
% 38.10/5.49 inference('cnf.neg', [status(esa)], [satz26c])).
% 38.10/5.49 thf(zip_derived_cl183, plain,
% 38.10/5.49 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 38.10/5.49 (^[Y0 : $i]:
% 38.10/5.49 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 38.10/5.49 (^[Y1 : $i]:
% 38.10/5.49 (((d_29_ii @ (ordsucc @ Y1) @ Y0) => (moreis @ Y1 @ Y0)))))))),
% 38.10/5.49 inference('cnf', [status(esa)], [zf_stmt_0])).
% 38.10/5.49 thf(zip_derived_cl184, plain,
% 38.10/5.49 (~ (all_of @ ((('#C') @ in @ nat)) @
% 38.10/5.49 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ ('#S') @
% 38.10/5.49 ((('#B') @ ((('#B') @ (=>))) @
% 38.10/5.49 ((('#C') @ ((('#B') @ d_29_ii @ ordsucc)))))))) @
% 38.10/5.49 ((('#C') @ moreis)))))))),
% 38.10/5.49 inference('lams2combs', [status(thm)], [zip_derived_cl183])).
% 38.10/5.49 thf(def_nat, axiom,(( nat ) =
% 38.10/5.49 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))).
% 38.10/5.49 thf('0', plain,
% 38.10/5.49 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )),
% 38.10/5.49 define([status(thm)])).
% 38.10/5.49 thf(zip_derived_cl276, plain,
% 38.10/5.49 (~ (all_of @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 38.10/5.49 ((('#B') @ (all_of @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ ('#S') @
% 38.10/5.49 ((('#B') @ ((('#B') @ (=>))) @
% 38.10/5.49 ((('#C') @ ((('#B') @ d_29_ii @ ordsucc)))))))) @
% 38.10/5.49 ((('#C') @ moreis)))))))),
% 38.10/5.49 inference('rw', [status(thm)], [zip_derived_cl184, '0'])).
% 38.10/5.49 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 38.10/5.49 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 38.10/5.49 thf('1', plain,
% 38.10/5.49 (![X0:( $i > $o ),X1:( $i > $o )]:
% 38.10/5.49 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 38.10/5.49 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 38.10/5.49 inference('rw.lit', [status(esa)], [def_all_of])).
% 38.10/5.49 thf(zip_derived_cl277, plain,
% 38.10/5.49 (~ (((!!) @ (^[Y0 : $i]:
% 38.10/5.49 (((is_of @ Y0 @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 38.10/5.49 ((('#B') @ (all_of @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @
% 38.10/5.49 ((('#C') @ (!=) @ emptyset)))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ ('#S') @
% 38.10/5.49 ((('#B') @ ((('#B') @ (=>))) @
% 38.10/5.49 ((('#C') @ ((('#B') @ d_29_ii @ ordsucc)))))))) @
% 38.10/5.49 ((('#C') @ moreis)))) @
% 38.10/5.49 Y0)))))))),
% 38.10/5.49 inference('rw_clause', [status(thm)], [zip_derived_cl276, '1'])).
% 38.10/5.49 thf(zip_derived_cl278, plain,
% 38.10/5.49 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 38.10/5.49 ((('#C') @ is_of @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @
% 38.10/5.49 ((('#C') @ (!=) @ emptyset))))))))) @
% 38.10/5.49 ((('#B') @ (all_of @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ ('#S') @
% 38.10/5.49 ((('#B') @ ((('#B') @ (=>))) @
% 38.10/5.49 ((('#C') @ ((('#B') @ d_29_ii @ ordsucc)))))))) @
% 38.10/5.49 ((('#C') @ moreis))))))))))),
% 38.10/5.49 inference('comb-normalize', [status(thm)], [zip_derived_cl277])).
% 38.10/5.49 thf(zip_derived_cl279, plain,
% 38.10/5.49 (~ (((is_of @ '#sk2' @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 38.10/5.49 (all_of @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ (=>) @
% 38.10/5.49 ((('#C') @ ((('#B') @ d_29_ii @ ordsucc)) @ '#sk2')))) @
% 38.10/5.49 ((('#C') @ moreis @ '#sk2')))))))),
% 38.10/5.49 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl278])).
% 38.10/5.49 thf(zip_derived_cl281, plain,
% 38.10/5.49 (~ (all_of @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ (=>) @
% 38.10/5.49 ((('#C') @ ((('#B') @ d_29_ii @ ordsucc)) @ '#sk2')))) @
% 38.10/5.49 ((('#C') @ moreis @ '#sk2')))))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl279])).
% 38.10/5.49 thf(zip_derived_cl282, plain,
% 38.10/5.49 (~ (((!!) @ (^[Y0 : $i]:
% 38.10/5.49 (((is_of @ Y0 @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 38.10/5.49 ((('#S') @ ((('#B') @ (=>) @
% 38.10/5.49 ((('#C') @ ((('#B') @ d_29_ii @ ordsucc)) @
% 38.10/5.49 '#sk2')))) @
% 38.10/5.49 ((('#C') @ moreis @ '#sk2')) @ Y0)))))))),
% 38.10/5.49 inference('rw_clause', [status(thm)], [zip_derived_cl281, '1'])).
% 38.10/5.49 thf(zip_derived_cl283, plain,
% 38.10/5.49 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 38.10/5.49 ((('#C') @ is_of @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @
% 38.10/5.49 ((('#C') @ (!=) @ emptyset))))))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ (=>) @
% 38.10/5.49 ((('#C') @ ((('#B') @ d_29_ii @ ordsucc)) @
% 38.10/5.49 '#sk2')))) @
% 38.10/5.49 ((('#C') @ moreis @ '#sk2'))))))))),
% 38.10/5.49 inference('comb-normalize', [status(thm)], [zip_derived_cl282])).
% 38.10/5.49 thf(zip_derived_cl284, plain,
% 38.10/5.49 (~ (((is_of @ '#sk3' @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 38.10/5.49 (((d_29_ii @ (ordsucc @ '#sk3') @ '#sk2') => (moreis @ '#sk3' @
% 38.10/5.49 '#sk2')))))),
% 38.10/5.49 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl283])).
% 38.10/5.49 thf(def_ordsucc, axiom,(( ordsucc @ (X0)) =
% 38.10/5.49 ((binunion @ X0 @ (d_Sing @ X0))))).
% 38.10/5.49 thf('2', plain,
% 38.10/5.49 (![X0:$i]: ( ( ordsucc @ X0 ) = ( binunion @ X0 @ ( d_Sing @ X0 ) ) )),
% 38.10/5.49 define([status(thm)])).
% 38.10/5.49 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 38.10/5.49 thf('3', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 38.10/5.49 define([status(thm)])).
% 38.10/5.49 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 38.10/5.49 thf('4', plain,
% 38.10/5.49 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 38.10/5.49 define([status(thm)])).
% 38.10/5.49 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 38.10/5.49 thf('5', plain,
% 38.10/5.49 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 38.10/5.49 define([status(thm)])).
% 38.10/5.49 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) =
% 38.10/5.49 ((n_some @ (diffprop @ X0 @ X1))))).
% 38.10/5.49 thf('6', plain,
% 38.10/5.49 (![X1:$i,X0:$i]:
% 38.10/5.49 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 38.10/5.49 define([status(thm)])).
% 38.10/5.49 thf(def_moreis, axiom,(( moreis @ (X0)@ (X1)) =
% 38.10/5.49 ((l_or @ (d_29_ii @ X0 @ X1) @ (n_is @ X0 @ X1))))).
% 38.10/5.49 thf('7', plain,
% 38.10/5.49 (![X1:$i,X0:$i]:
% 38.10/5.49 ( ( moreis @ X0 @ X1 ) =
% 38.10/5.49 ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
% 38.10/5.49 define([status(thm)])).
% 38.10/5.49 thf(zip_derived_cl285, plain,
% 38.10/5.49 (~ (((is_of @ '#sk3' @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 38.10/5.49 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')) @ '#sk2')) =>
% 38.10/5.49 (imp @
% 38.10/5.49 (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ '#sk3' @ '#sk2')) @
% 38.10/5.49 ($false)) @
% 38.10/5.49 (n_is @ '#sk3' @ '#sk2'))))))),
% 38.10/5.49 inference('rw', [status(thm)],
% 38.10/5.49 [zip_derived_cl284, '2', '3', '4', '0', '5', '5', '6', '6', '7'])).
% 38.10/5.49 thf(zip_derived_cl287, plain,
% 38.10/5.49 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')) @ '#sk2')) =>
% 38.10/5.49 (imp @
% 38.10/5.49 (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ '#sk3' @ '#sk2')) @
% 38.10/5.49 ($false)) @
% 38.10/5.49 (n_is @ '#sk3' @ '#sk2'))))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl285])).
% 38.10/5.49 thf(zip_derived_cl289, plain,
% 38.10/5.49 (~ (imp @
% 38.10/5.49 (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ '#sk3' @ '#sk2')) @
% 38.10/5.49 ($false)) @
% 38.10/5.49 (n_is @ '#sk3' @ '#sk2'))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl287])).
% 38.10/5.49 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 38.10/5.49 thf('8', plain,
% 38.10/5.49 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 38.10/5.49 inference('rw.lit', [status(esa)], [def_imp])).
% 38.10/5.49 thf(zip_derived_cl290, plain,
% 38.10/5.49 (~ (((imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ '#sk3' @ '#sk2')) @
% 38.10/5.49 ($false)) => (n_is @ '#sk3' @ '#sk2')))),
% 38.10/5.49 inference('rw_clause', [status(thm)], [zip_derived_cl289, '8'])).
% 38.10/5.49 thf(zip_derived_cl291, plain,
% 38.10/5.49 ( (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ '#sk3' @ '#sk2')) @
% 38.10/5.49 ($false))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl290])).
% 38.10/5.49 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 38.10/5.49 thf('9', plain,
% 38.10/5.49 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 38.10/5.49 inference('rw.lit', [status(esa)], [def_imp])).
% 38.10/5.49 thf(zip_derived_cl293, plain,
% 38.10/5.49 ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ '#sk3' @ '#sk2')) => ($false)))),
% 38.10/5.49 inference('rw_clause', [status(thm)], [zip_derived_cl291, '9'])).
% 38.10/5.49 thf(zip_derived_cl294, plain,
% 38.10/5.49 ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ '#sk3' @ '#sk2'))))),
% 38.10/5.49 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl293])).
% 38.10/5.49 thf(zip_derived_cl295, plain,
% 38.10/5.49 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ '#sk3' @ '#sk2'))),
% 38.10/5.49 inference('simplify nested equalities', [status(thm)],
% 38.10/5.49 [zip_derived_cl294])).
% 38.10/5.49 thf(zip_derived_cl288, plain,
% 38.10/5.49 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ (binunion @ '#sk3' @ (d_Sing @ '#sk3')) @ '#sk2'))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl287])).
% 38.10/5.49 thf(satz26a, axiom,
% 38.10/5.49 (all_of @
% 38.10/5.49 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 38.10/5.49 ( ^[X0:$i]:
% 38.10/5.49 ( all_of @
% 38.10/5.49 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 38.10/5.49 ( ^[X1:$i]:
% 38.10/5.49 ( ( iii @ X1 @ ( ordsucc @ X0 ) ) => ( lessis @ X1 @ X0 ) ) ) ) ))).
% 38.10/5.49 thf(zip_derived_cl179, plain,
% 38.10/5.49 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 38.10/5.49 (^[Y0 : $i]:
% 38.10/5.49 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 38.10/5.49 (^[Y1 : $i]: (((iii @ Y1 @ (ordsucc @ Y0)) => (lessis @ Y1 @ Y0)))))))),
% 38.10/5.49 inference('cnf', [status(esa)], [satz26a])).
% 38.10/5.49 thf(zip_derived_cl180, plain,
% 38.10/5.49 ( (all_of @ ((('#C') @ in @ nat)) @
% 38.10/5.49 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ ('#S') @
% 38.10/5.49 ((('#B') @ ((('#B') @ (=>))) @
% 38.10/5.49 ((('#B') @ ((('#C') @ iii)) @ ordsucc)))))) @
% 38.10/5.49 ((('#C') @ lessis)))))))),
% 38.10/5.49 inference('lams2combs', [status(thm)], [zip_derived_cl179])).
% 38.10/5.49 thf(zip_derived_cl636, plain,
% 38.10/5.49 ( (all_of @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 38.10/5.49 ((('#B') @ (all_of @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ ('#S') @
% 38.10/5.49 ((('#B') @ ((('#B') @ (=>))) @
% 38.10/5.49 ((('#B') @ ((('#C') @ iii)) @ ordsucc)))))) @
% 38.10/5.49 ((('#C') @ lessis)))))))),
% 38.10/5.49 inference('rw', [status(thm)], [zip_derived_cl180, '0'])).
% 38.10/5.49 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 38.10/5.49 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 38.10/5.49 thf('10', plain,
% 38.10/5.49 (![X0:( $i > $o ),X1:( $i > $o )]:
% 38.10/5.49 ( ( all_of @ X0 @ X1 ) <=>
% 38.10/5.49 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 38.10/5.49 inference('rw.lit', [status(esa)], [def_all_of])).
% 38.10/5.49 thf(zip_derived_cl637, plain,
% 38.10/5.49 ( (((!!) @ (^[Y0 : $i]:
% 38.10/5.49 (((is_of @ Y0 @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 38.10/5.49 ((('#B') @ (all_of @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @
% 38.10/5.49 ((('#C') @ (!=) @ emptyset)))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ ('#S') @
% 38.10/5.49 ((('#B') @ ((('#B') @ (=>))) @
% 38.10/5.49 ((('#B') @ ((('#C') @ iii)) @ ordsucc)))))) @
% 38.10/5.49 ((('#C') @ lessis)))) @
% 38.10/5.49 Y0)))))))),
% 38.10/5.49 inference('rw_clause', [status(thm)], [zip_derived_cl636, '10'])).
% 38.10/5.49 thf(zip_derived_cl638, plain,
% 38.10/5.49 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 38.10/5.49 ((('#C') @ is_of @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 38.10/5.49 ((('#B') @ (all_of @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ ('#S') @
% 38.10/5.49 ((('#B') @ ((('#B') @ (=>))) @
% 38.10/5.49 ((('#B') @ ((('#C') @ iii)) @ ordsucc)))))) @
% 38.10/5.49 ((('#C') @ lessis))))))))))),
% 38.10/5.49 inference('comb-normalize', [status(thm)], [zip_derived_cl637])).
% 38.10/5.49 thf(zip_derived_cl639, plain,
% 38.10/5.49 (![X2 : $i]:
% 38.10/5.49 (((is_of @ X2 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 38.10/5.49 (all_of @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ iii @ (ordsucc @ X2))))) @
% 38.10/5.49 ((('#C') @ lessis @ X2)))))))),
% 38.10/5.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl638])).
% 38.10/5.49 thf(zip_derived_cl640, plain,
% 38.10/5.49 (![X2 : $i]:
% 38.10/5.49 (((is_of @ X2 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 38.10/5.49 (all_of @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ (=>) @
% 38.10/5.49 ((('#C') @ iii @ (binunion @ X2 @ (d_Sing @ X2)))))) @
% 38.10/5.49 ((('#C') @ lessis @ X2)))))))),
% 38.10/5.49 inference('rw', [status(thm)], [zip_derived_cl639, '2'])).
% 38.10/5.49 thf(zip_derived_cl641, plain,
% 38.10/5.49 (![X2 : $i]:
% 38.10/5.49 (~ (is_of @ X2 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | (all_of @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ (=>) @
% 38.10/5.49 ((('#C') @ iii @ (binunion @ X2 @ (d_Sing @ X2)))))) @
% 38.10/5.49 ((('#C') @ lessis @ X2))))))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl640])).
% 38.10/5.49 thf(zip_derived_cl642, plain,
% 38.10/5.49 (![X0 : $i]:
% 38.10/5.49 ( (((!!) @ (^[Y0 : $i]:
% 38.10/5.49 (((is_of @ Y0 @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 38.10/5.49 ((('#S') @ ((('#B') @ (=>) @
% 38.10/5.49 ((('#C') @ iii @
% 38.10/5.49 (binunion @ X0 @ (d_Sing @ X0)))))) @
% 38.10/5.49 ((('#C') @ lessis @ X0)) @ Y0)))))))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('rw_clause', [status(thm)], [zip_derived_cl641, '10'])).
% 38.10/5.49 thf(zip_derived_cl643, plain,
% 38.10/5.49 (![X0 : $i]:
% 38.10/5.49 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 38.10/5.49 ((('#C') @ is_of @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @
% 38.10/5.49 ((('#C') @ (!=) @ emptyset))))))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ (=>) @
% 38.10/5.49 ((('#C') @ iii @
% 38.10/5.49 (binunion @ X0 @ (d_Sing @ X0)))))) @
% 38.10/5.49 ((('#C') @ lessis @ X0))))))))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('comb-normalize', [status(thm)], [zip_derived_cl642])).
% 38.10/5.49 thf(zip_derived_cl644, plain,
% 38.10/5.49 (![X0 : $i, X2 : $i]:
% 38.10/5.49 ( (((is_of @ X2 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 38.10/5.49 (((iii @ X2 @ (binunion @ X0 @ (d_Sing @ X0))) => (lessis @ X2 @
% 38.10/5.49 X0)))))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl643])).
% 38.10/5.49 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))).
% 38.10/5.49 thf('11', plain,
% 38.10/5.49 (![X1:$i,X0:$i]:
% 38.10/5.49 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 38.10/5.49 define([status(thm)])).
% 38.10/5.49 thf(def_lessis, axiom,(( lessis @ (X0)@ (X1)) =
% 38.10/5.49 ((l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1))))).
% 38.10/5.49 thf('12', plain,
% 38.10/5.49 (![X1:$i,X0:$i]:
% 38.10/5.49 ( ( lessis @ X0 @ X1 ) =
% 38.10/5.49 ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
% 38.10/5.49 define([status(thm)])).
% 38.10/5.49 thf(zip_derived_cl645, plain,
% 38.10/5.49 (![X0 : $i, X2 : $i]:
% 38.10/5.49 ( (((is_of @ X2 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 38.10/5.49 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ (binunion @ X0 @ (d_Sing @ X0)) @ X2)) => (imp @
% 38.10/5.49 (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X0 @ X2)) @
% 38.10/5.49 ($false)) @
% 38.10/5.49 (n_is @ X2 @ X0))))))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('rw', [status(thm)],
% 38.10/5.49 [zip_derived_cl644, '3', '4', '0', '5', '5', '11', '11', '12'])).
% 38.10/5.49 thf(zip_derived_cl646, plain,
% 38.10/5.49 (![X0 : $i, X2 : $i]:
% 38.10/5.49 (~ (is_of @ X2 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ (binunion @ X0 @ (d_Sing @ X0)) @ X2)) => (imp @
% 38.10/5.49 (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X0 @ X2)) @
% 38.10/5.49 ($false)) @
% 38.10/5.49 (n_is @ X2 @ X0))))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl645])).
% 38.10/5.49 thf(zip_derived_cl647, plain,
% 38.10/5.49 (![X0 : $i, X2 : $i]:
% 38.10/5.49 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ (binunion @ X0 @ (d_Sing @ X0)) @ X2))
% 38.10/5.49 | (imp @
% 38.10/5.49 (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X0 @ X2)) @
% 38.10/5.49 ($false)) @
% 38.10/5.49 (n_is @ X2 @ X0))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ X2 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl646])).
% 38.10/5.49 thf(zip_derived_cl648, plain,
% 38.10/5.49 (![X0 : $i, X1 : $i]:
% 38.10/5.49 ( (((imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X1 @ X0)) @
% 38.10/5.49 ($false)) => (n_is @ X0 @ X1)))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ X1 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ (binunion @ X1 @ (d_Sing @ X1)) @ X0)))),
% 38.10/5.49 inference('rw_clause', [status(thm)], [zip_derived_cl647, '9'])).
% 38.10/5.49 thf(zip_derived_cl649, plain,
% 38.10/5.49 (![X0 : $i, X1 : $i]:
% 38.10/5.49 (~ (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X1 @ X0)) @
% 38.10/5.49 ($false))
% 38.10/5.49 | (n_is @ X0 @ X1)
% 38.10/5.49 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ (binunion @ X1 @ (d_Sing @ X1)) @ X0))
% 38.10/5.49 | ~ (is_of @ X1 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl648])).
% 38.10/5.49 thf(zip_derived_cl650, plain,
% 38.10/5.49 (![X0 : $i, X1 : $i]:
% 38.10/5.49 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X1 @ X0)) => ($false)))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ X1 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ (binunion @ X1 @ (d_Sing @ X1)) @ X0))
% 38.10/5.49 | (n_is @ X0 @ X1))),
% 38.10/5.49 inference('rw_clause', [status(thm)], [zip_derived_cl649, '8'])).
% 38.10/5.49 thf(zip_derived_cl651, plain,
% 38.10/5.49 (![X0 : $i, X1 : $i]:
% 38.10/5.49 (~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X1 @ X0))))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ X1 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ (binunion @ X1 @ (d_Sing @ X1)) @ X0))
% 38.10/5.49 | (n_is @ X0 @ X1))),
% 38.10/5.49 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl650])).
% 38.10/5.49 thf(zip_derived_cl652, plain,
% 38.10/5.49 (![X0 : $i, X1 : $i]:
% 38.10/5.49 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X1 @ X0))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ X1 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ (binunion @ X1 @ (d_Sing @ X1)) @ X0))
% 38.10/5.49 | (n_is @ X0 @ X1))),
% 38.10/5.49 inference('simplify nested equalities', [status(thm)],
% 38.10/5.49 [zip_derived_cl651])).
% 38.10/5.49 thf(zip_derived_cl3897, plain,
% 38.10/5.49 (( (n_is @ '#sk2' @ '#sk3')
% 38.10/5.49 | ~ (is_of @ '#sk3' @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ '#sk2' @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ '#sk3' @ '#sk2')))),
% 38.10/5.49 inference('sup-', [status(thm)], [zip_derived_cl288, zip_derived_cl652])).
% 38.10/5.49 thf(zip_derived_cl295, plain,
% 38.10/5.49 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ '#sk3' @ '#sk2'))),
% 38.10/5.49 inference('simplify nested equalities', [status(thm)],
% 38.10/5.49 [zip_derived_cl294])).
% 38.10/5.49 thf(satz14, axiom,
% 38.10/5.49 (all_of @
% 38.10/5.49 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 38.10/5.49 ( ^[X0:$i]:
% 38.10/5.49 ( all_of @
% 38.10/5.49 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 38.10/5.49 ( ^[X1:$i]: ( ( lessis @ X0 @ X1 ) => ( moreis @ X1 @ X0 ) ) ) ) ))).
% 38.10/5.49 thf(zip_derived_cl67, plain,
% 38.10/5.49 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 38.10/5.49 (^[Y0 : $i]:
% 38.10/5.49 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 38.10/5.49 (^[Y1 : $i]: (((lessis @ Y0 @ Y1) => (moreis @ Y1 @ Y0)))))))),
% 38.10/5.49 inference('cnf', [status(esa)], [satz14])).
% 38.10/5.49 thf(zip_derived_cl68, plain,
% 38.10/5.49 ( (all_of @ ((('#C') @ in @ nat)) @
% 38.10/5.49 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ ('#S') @
% 38.10/5.49 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @
% 38.10/5.49 ((('#C') @ moreis)))))))),
% 38.10/5.49 inference('lams2combs', [status(thm)], [zip_derived_cl67])).
% 38.10/5.49 thf(zip_derived_cl418, plain,
% 38.10/5.49 ( (all_of @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 38.10/5.49 ((('#B') @ (all_of @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ ('#S') @
% 38.10/5.49 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @
% 38.10/5.49 ((('#C') @ moreis)))))))),
% 38.10/5.49 inference('rw', [status(thm)], [zip_derived_cl68, '0'])).
% 38.10/5.49 thf(zip_derived_cl419, plain,
% 38.10/5.49 ( (((!!) @ (^[Y0 : $i]:
% 38.10/5.49 (((is_of @ Y0 @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 38.10/5.49 ((('#B') @ (all_of @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @
% 38.10/5.49 ((('#C') @ (!=) @ emptyset)))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ ('#S') @
% 38.10/5.49 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @
% 38.10/5.49 ((('#C') @ moreis)))) @
% 38.10/5.49 Y0)))))))),
% 38.10/5.49 inference('rw_clause', [status(thm)], [zip_derived_cl418, '10'])).
% 38.10/5.49 thf(zip_derived_cl420, plain,
% 38.10/5.49 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 38.10/5.49 ((('#C') @ is_of @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @
% 38.10/5.49 ((('#B') @ (all_of @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ ('#S') @
% 38.10/5.49 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @
% 38.10/5.49 ((('#C') @ moreis))))))))))),
% 38.10/5.49 inference('comb-normalize', [status(thm)], [zip_derived_cl419])).
% 38.10/5.49 thf(zip_derived_cl421, plain,
% 38.10/5.49 (![X2 : $i]:
% 38.10/5.49 (((is_of @ X2 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 38.10/5.49 (all_of @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ (=>) @ (lessis @ X2))) @
% 38.10/5.49 ((('#C') @ moreis @ X2)))))))),
% 38.10/5.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl420])).
% 38.10/5.49 thf(zip_derived_cl422, plain,
% 38.10/5.49 (![X2 : $i]:
% 38.10/5.49 (~ (is_of @ X2 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | (all_of @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ (=>) @ (lessis @ X2))) @
% 38.10/5.49 ((('#C') @ moreis @ X2))))))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl421])).
% 38.10/5.49 thf(zip_derived_cl423, plain,
% 38.10/5.49 (![X0 : $i]:
% 38.10/5.49 ( (((!!) @ (^[Y0 : $i]:
% 38.10/5.49 (((is_of @ Y0 @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 38.10/5.49 ((('#S') @ ((('#B') @ (=>) @ (lessis @ X0))) @
% 38.10/5.49 ((('#C') @ moreis @ X0)) @ Y0)))))))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('rw_clause', [status(thm)], [zip_derived_cl422, '10'])).
% 38.10/5.49 thf(zip_derived_cl424, plain,
% 38.10/5.49 (![X0 : $i]:
% 38.10/5.49 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 38.10/5.49 ((('#C') @ is_of @
% 38.10/5.49 ((('#C') @ in @
% 38.10/5.49 (d_Sep @ omega @
% 38.10/5.49 ((('#C') @ (!=) @ emptyset))))))))) @
% 38.10/5.49 ((('#S') @ ((('#B') @ (=>) @ (lessis @ X0))) @
% 38.10/5.49 ((('#C') @ moreis @ X0))))))))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('comb-normalize', [status(thm)], [zip_derived_cl423])).
% 38.10/5.49 thf(zip_derived_cl425, plain,
% 38.10/5.49 (![X0 : $i, X2 : $i]:
% 38.10/5.49 ( (((is_of @ X2 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 38.10/5.49 (((lessis @ X0 @ X2) => (moreis @ X2 @ X0)))))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl424])).
% 38.10/5.49 thf(zip_derived_cl426, plain,
% 38.10/5.49 (![X0 : $i, X2 : $i]:
% 38.10/5.49 ( (((is_of @ X2 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 38.10/5.49 (((imp @
% 38.10/5.49 (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X2 @ X0)) @
% 38.10/5.49 ($false)) @
% 38.10/5.49 (n_is @ X0 @ X2)) => (imp @
% 38.10/5.49 (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X2 @ X0)) @
% 38.10/5.49 ($false)) @
% 38.10/5.49 (n_is @ X2 @ X0))))))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('rw', [status(thm)],
% 38.10/5.49 [zip_derived_cl425, '3', '4', '4', '0', '5', '6', '11', '7',
% 38.10/5.49 '12'])).
% 38.10/5.49 thf(zip_derived_cl427, plain,
% 38.10/5.49 (![X0 : $i, X2 : $i]:
% 38.10/5.49 (~ (is_of @ X2 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | (((imp @
% 38.10/5.49 (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X2 @ X0)) @
% 38.10/5.49 ($false)) @
% 38.10/5.49 (n_is @ X0 @ X2)) => (imp @
% 38.10/5.49 (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X2 @ X0)) @
% 38.10/5.49 ($false)) @
% 38.10/5.49 (n_is @ X2 @ X0))))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl426])).
% 38.10/5.49 thf(zip_derived_cl428, plain,
% 38.10/5.49 (![X0 : $i, X2 : $i]:
% 38.10/5.49 (~ (imp @
% 38.10/5.49 (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X2 @ X0)) @
% 38.10/5.49 ($false)) @
% 38.10/5.49 (n_is @ X0 @ X2))
% 38.10/5.49 | (imp @
% 38.10/5.49 (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X2 @ X0)) @
% 38.10/5.49 ($false)) @
% 38.10/5.49 (n_is @ X2 @ X0))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ X2 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl427])).
% 38.10/5.49 thf(zip_derived_cl429, plain,
% 38.10/5.49 (![X0 : $i, X1 : $i]:
% 38.10/5.49 (~ (((imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X0 @ X1)) @
% 38.10/5.49 ($false)) => (n_is @ X1 @ X0)))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ X1 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | (imp @
% 38.10/5.49 (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X0 @ X1)) @
% 38.10/5.49 ($false)) @
% 38.10/5.49 (n_is @ X0 @ X1)))),
% 38.10/5.49 inference('rw_clause', [status(thm)], [zip_derived_cl428, '8'])).
% 38.10/5.49 thf(zip_derived_cl430, plain,
% 38.10/5.49 (![X0 : $i, X1 : $i]:
% 38.10/5.49 ( (((imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X1 @ X0)) @
% 38.10/5.49 ($false)) => (n_is @ X1 @ X0)))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ X1 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (((imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X1 @ X0)) @
% 38.10/5.49 ($false)) => (n_is @ X0 @ X1))))),
% 38.10/5.49 inference('rw_clause', [status(thm)], [zip_derived_cl429, '9'])).
% 38.10/5.49 thf(zip_derived_cl431, plain,
% 38.10/5.49 (![X0 : $i, X1 : $i]:
% 38.10/5.49 (~ (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X1 @ X0)) @
% 38.10/5.49 ($false))
% 38.10/5.49 | (n_is @ X1 @ X0)
% 38.10/5.49 | ~ (((imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X1 @ X0)) @
% 38.10/5.49 ($false)) => (n_is @ X0 @ X1)))
% 38.10/5.49 | ~ (is_of @ X1 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl430])).
% 38.10/5.49 thf(zip_derived_cl432, plain,
% 38.10/5.49 (![X0 : $i, X1 : $i]:
% 38.10/5.49 (~ (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X1 @ X0)) @
% 38.10/5.49 ($false))
% 38.10/5.49 | (n_is @ X1 @ X0)
% 38.10/5.49 | ~ ((($true) => (n_is @ X0 @ X1)))
% 38.10/5.49 | ~ (is_of @ X1 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('local_rewriting', [status(thm)], [zip_derived_cl431])).
% 38.10/5.49 thf(zip_derived_cl433, plain,
% 38.10/5.49 (![X0 : $i, X1 : $i]:
% 38.10/5.49 (~ (imp @
% 38.10/5.49 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X1 @ X0)) @
% 38.10/5.49 ($false))
% 38.10/5.49 | (n_is @ X1 @ X0)
% 38.10/5.49 | ~ (n_is @ X0 @ X1)
% 38.10/5.49 | ~ (is_of @ X1 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl432])).
% 38.10/5.49 thf(zip_derived_cl434, plain,
% 38.10/5.49 (![X0 : $i, X1 : $i]:
% 38.10/5.49 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X1 @ X0)) => ($false)))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ X1 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (n_is @ X0 @ X1)
% 38.10/5.49 | (n_is @ X1 @ X0))),
% 38.10/5.49 inference('rw_clause', [status(thm)], [zip_derived_cl433, '8'])).
% 38.10/5.49 thf(zip_derived_cl435, plain,
% 38.10/5.49 (![X0 : $i, X1 : $i]:
% 38.10/5.49 (~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X1 @ X0))))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ X1 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (n_is @ X0 @ X1)
% 38.10/5.49 | (n_is @ X1 @ X0))),
% 38.10/5.49 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl434])).
% 38.10/5.49 thf(zip_derived_cl436, plain,
% 38.10/5.49 (![X0 : $i, X1 : $i]:
% 38.10/5.49 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ X1 @ X0))
% 38.10/5.49 | ~ (is_of @ X0 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ X1 @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (n_is @ X0 @ X1)
% 38.10/5.49 | (n_is @ X1 @ X0))),
% 38.10/5.49 inference('simplify nested equalities', [status(thm)],
% 38.10/5.49 [zip_derived_cl435])).
% 38.10/5.49 thf(zip_derived_cl2867, plain,
% 38.10/5.49 (( (n_is @ '#sk3' @ '#sk2')
% 38.10/5.49 | ~ (n_is @ '#sk2' @ '#sk3')
% 38.10/5.49 | ~ (is_of @ '#sk3' @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 38.10/5.49 | ~ (is_of @ '#sk2' @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 38.10/5.49 inference('sup+', [status(thm)], [zip_derived_cl295, zip_derived_cl436])).
% 38.10/5.49 thf(zip_derived_cl292, plain, (~ (n_is @ '#sk3' @ '#sk2')),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl290])).
% 38.10/5.49 thf(zip_derived_cl286, plain,
% 38.10/5.49 ( (is_of @ '#sk3' @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl285])).
% 38.10/5.49 thf(zip_derived_cl280, plain,
% 38.10/5.49 ( (is_of @ '#sk2' @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl279])).
% 38.10/5.49 thf(zip_derived_cl2870, plain, (~ (n_is @ '#sk2' @ '#sk3')),
% 38.10/5.49 inference('demod', [status(thm)],
% 38.10/5.49 [zip_derived_cl2867, zip_derived_cl292, zip_derived_cl286,
% 38.10/5.49 zip_derived_cl280])).
% 38.10/5.49 thf(zip_derived_cl286, plain,
% 38.10/5.49 ( (is_of @ '#sk3' @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl285])).
% 38.10/5.49 thf(zip_derived_cl280, plain,
% 38.10/5.49 ( (is_of @ '#sk2' @
% 38.10/5.49 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 38.10/5.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl279])).
% 38.10/5.49 thf(zip_derived_cl3913, plain,
% 38.10/5.49 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 38.10/5.49 (diffprop @ '#sk3' @ '#sk2'))),
% 38.10/5.49 inference('demod', [status(thm)],
% 38.10/5.49 [zip_derived_cl3897, zip_derived_cl2870, zip_derived_cl286,
% 38.10/5.49 zip_derived_cl280])).
% 38.10/5.49 thf(zip_derived_cl3927, plain, ($false),
% 38.10/5.49 inference('demod', [status(thm)], [zip_derived_cl295, zip_derived_cl3913])).
% 38.10/5.49
% 38.10/5.49 % SZS output end Refutation
% 38.10/5.49
% 38.10/5.49
% 38.10/5.49 % Terminating...
% 38.59/5.58 % Runner terminated.
% 38.59/5.59 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------