TSTP Solution File: NUM705^4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM705^4 : 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.ofJVyPNNAG 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 12:43:38 EDT 2023
% Result : Theorem 92.80s 12.65s
% Output : Refutation 92.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM705^4 : TPTP v8.1.2. Released v7.1.0.
% 0.13/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.ofJVyPNNAG true
% 0.13/0.35 % Computer : n004.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 : Fri Aug 25 15:30:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in HO mode
% 0.21/0.67 % Total configuration time : 828
% 0.21/0.67 % Estimated wc time : 1656
% 0.21/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.75/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.75/0.75 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.75/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.35/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.35/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.35/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.35/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.35/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 92.80/12.65 % Solved by lams/40_b.comb.sh.
% 92.80/12.65 % done 329 iterations in 11.835s
% 92.80/12.65 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 92.80/12.65 % SZS output start Refutation
% 92.80/12.65 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
% 92.80/12.65 thf(n_one_type, type, n_one: ($i > $o) > $o).
% 92.80/12.65 thf('#sk2_type', type, '#sk2': $i).
% 92.80/12.65 thf('#sk1_type', type, '#sk1': $i > $o).
% 92.80/12.65 thf(one_type, type, one: $i > ($i > $o) > $o).
% 92.80/12.65 thf(nat_type, type, nat: $i).
% 92.80/12.65 thf(moreis_type, type, moreis: $i > $i > $o).
% 92.80/12.65 thf(lessis_type, type, lessis: $i > $i > $o).
% 92.80/12.65 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 92.80/12.65 thf(in_type, type, in: $i > $i > $o).
% 92.80/12.65 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 92.80/12.65 thf(n_lb_type, type, n_lb: ($i > $o) > $i > $o).
% 92.80/12.65 thf(n_is_type, type, n_is: $i > $i > $o).
% 92.80/12.65 thf(l_ec_type, type, l_ec: $o > $o > $o).
% 92.80/12.65 thf(imp_type, type, imp: $o > $o > $o).
% 92.80/12.65 thf('#sk3_type', type, '#sk3': $i).
% 92.80/12.65 thf(min_type, type, min: ($i > $o) > $i > $o).
% 92.80/12.65 thf(d_and_type, type, d_and: $o > $o > $o).
% 92.80/12.65 thf(lbprop_type, type, lbprop: ($i > $o) > $i > $i > $o).
% 92.80/12.65 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 92.80/12.65 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 92.80/12.65 thf(n_all_type, type, n_all: ($i > $o) > $o).
% 92.80/12.65 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 92.80/12.65 thf(l_or_type, type, l_or: $o > $o > $o).
% 92.80/12.65 thf(d_not_type, type, d_not: $o > $o).
% 92.80/12.65 thf(iii_type, type, iii: $i > $i > $o).
% 92.80/12.65 thf(amone_type, type, amone: $i > ($i > $o) > $o).
% 92.80/12.65 thf(e_is_type, type, e_is: $i > $i > $i > $o).
% 92.80/12.65 thf(all_type, type, all: $i > ($i > $o) > $o).
% 92.80/12.65 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 92.80/12.65 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 92.80/12.65 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 92.80/12.65 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 92.80/12.65 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 92.80/12.65 thf(satz27a, conjecture,
% 92.80/12.65 (![X0:( $i > $o )]: ( ( n_some @ X0 ) => ( n_one @ ( min @ X0 ) ) ))).
% 92.80/12.65 thf(zf_stmt_0, negated_conjecture,
% 92.80/12.65 (~( ![X0:( $i > $o )]: ( ( n_some @ X0 ) => ( n_one @ ( min @ X0 ) ) ) )),
% 92.80/12.65 inference('cnf.neg', [status(esa)], [satz27a])).
% 92.80/12.65 thf(zip_derived_cl261, plain,
% 92.80/12.65 (~ (((!!) @ (^[Y0 : $i > $o]: (((n_some @ Y0) => (n_one @ (min @ Y0)))))))),
% 92.80/12.65 inference('cnf', [status(esa)], [zf_stmt_0])).
% 92.80/12.65 thf(zip_derived_cl262, plain,
% 92.80/12.65 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ n_some)) @
% 92.80/12.65 ((('#B') @ n_one @ min))))))),
% 92.80/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl261])).
% 92.80/12.65 thf(zip_derived_cl265, plain,
% 92.80/12.65 (~ (((n_some @ '#sk1') => (n_one @ (min @ '#sk1'))))),
% 92.80/12.65 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl262])).
% 92.80/12.65 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 92.80/12.65 thf('0', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(def_l_ec, axiom,(( l_ec @ (X0)@ (X1)) = ((imp @ X0 @ (d_not @ X1))))).
% 92.80/12.65 thf('1', plain,
% 92.80/12.65 (![X1:$o,X0:$o]: ( ( l_ec @ X0 @ X1 ) = ( imp @ X0 @ ( d_not @ X1 ) ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(def_d_and, axiom,(( d_and @ (X0)@ (X1)) = ((d_not @ (l_ec @ X0 @ X1))))).
% 92.80/12.65 thf('2', plain,
% 92.80/12.65 (![X1:$o,X0:$o]: ( ( d_and @ X0 @ X1 ) = ( d_not @ ( l_ec @ X0 @ X1 ) ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(def_amone, axiom,(( amone @ (X0)@ (X1)) =
% 92.80/12.65 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ X0)) @
% 92.80/12.65 (^[Y0 : $i]:
% 92.80/12.65 (all_of @ (^[Y1 : $i]: (in @ Y1 @ X0)) @
% 92.80/12.65 (^[Y1 : $i]: (((X1 @ Y0) => (((X1 @ Y1) => (e_is @ X0 @ Y0 @ Y1)))))))))))).
% 92.80/12.65 thf('3', plain,
% 92.80/12.65 (![X1:( $i > $o ),X0:$i]:
% 92.80/12.65 ( ( amone @ X0 @ X1 ) =
% 92.80/12.65 ( all_of @
% 92.80/12.65 ( ^[V_1:$i]: ( in @ V_1 @ X0 ) ) @
% 92.80/12.65 ( ^[V_2:$i]:
% 92.80/12.65 ( all_of @
% 92.80/12.65 ( ^[V_3:$i]: ( in @ V_3 @ X0 ) ) @
% 92.80/12.65 ( ^[V_4:$i]:
% 92.80/12.65 ( ( X1 @ V_2 ) =>
% 92.80/12.65 ( ( X1 @ V_4 ) => ( e_is @ X0 @ V_2 @ V_4 ) ) ) ) ) ) ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(def_one, axiom,(( one @ (X0)@ (X1)) =
% 92.80/12.65 ((d_and @ (amone @ X0 @ X1) @ (l_some @ X0 @ X1))))).
% 92.80/12.65 thf('4', plain,
% 92.80/12.65 (![X1:( $i > $o ),X0:$i]:
% 92.80/12.65 ( ( one @ X0 @ X1 ) =
% 92.80/12.65 ( d_and @ ( amone @ X0 @ X1 ) @ ( l_some @ X0 @ X1 ) ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 92.80/12.65 thf('5', plain,
% 92.80/12.65 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(def_n_one, axiom,(( n_one @ (X0)) = ((one @ nat @ X0)))).
% 92.80/12.65 thf('6', plain, (![X0:( $i > $o )]: ( ( n_one @ X0 ) = ( one @ nat @ X0 ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(zip_derived_cl266, plain,
% 92.80/12.65 (~ (((l_some @ nat @ '#sk1') => (imp @
% 92.80/12.65 (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @
% 92.80/12.65 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ ('#B') @
% 92.80/12.65 ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 (e_is @ nat)))))))) @
% 92.80/12.65 (imp @ (l_some @ nat @ (min @ '#sk1')) @ ($false))) @
% 92.80/12.65 ($false))))),
% 92.80/12.65 inference('rw', [status(thm)],
% 92.80/12.65 [zip_derived_cl265, '0', '0', '1', '2', '3', '4', '5', '6'])).
% 92.80/12.65 thf(zip_derived_cl268, plain,
% 92.80/12.65 (~ (imp @
% 92.80/12.65 (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @
% 92.80/12.65 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 (e_is @ nat)))))))) @
% 92.80/12.65 (imp @ (l_some @ nat @ (min @ '#sk1')) @ ($false))) @
% 92.80/12.65 ($false))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl266])).
% 92.80/12.65 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 92.80/12.65 thf('7', plain,
% 92.80/12.65 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 92.80/12.65 inference('rw.lit', [status(esa)], [def_imp])).
% 92.80/12.65 thf(zip_derived_cl269, plain,
% 92.80/12.65 (~ (((imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @
% 92.80/12.65 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 (e_is @ nat)))))))) @
% 92.80/12.65 (imp @ (l_some @ nat @ (min @ '#sk1')) @ ($false))) => ($false)))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl268, '7'])).
% 92.80/12.65 thf(zip_derived_cl270, plain,
% 92.80/12.65 (~ (((~) @ (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @
% 92.80/12.65 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ ('#B') @
% 92.80/12.65 ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 (e_is @ nat)))))))) @
% 92.80/12.65 (imp @ (l_some @ nat @ (min @ '#sk1')) @ ($false)))))),
% 92.80/12.65 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl269])).
% 92.80/12.65 thf(zip_derived_cl271, plain,
% 92.80/12.65 ( (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @
% 92.80/12.65 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 (e_is @ nat)))))))) @
% 92.80/12.65 (imp @ (l_some @ nat @ (min @ '#sk1')) @ ($false)))),
% 92.80/12.65 inference('simplify nested equalities', [status(thm)],
% 92.80/12.65 [zip_derived_cl270])).
% 92.80/12.65 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 92.80/12.65 thf('8', plain,
% 92.80/12.65 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 92.80/12.65 inference('rw.lit', [status(esa)], [def_imp])).
% 92.80/12.65 thf(zip_derived_cl272, plain,
% 92.80/12.65 ( (((all_of @ ((('#C') @ in @ nat)) @
% 92.80/12.65 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 (e_is @ nat)))))))) =>
% 92.80/12.65 (imp @ (l_some @ nat @ (min @ '#sk1')) @ ($false))))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl271, '8'])).
% 92.80/12.65 thf(zip_derived_cl273, plain,
% 92.80/12.65 ((~ (all_of @ ((('#C') @ in @ nat)) @
% 92.80/12.65 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 (e_is @ nat))))))))
% 92.80/12.65 | (imp @ (l_some @ nat @ (min @ '#sk1')) @ ($false)))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl272])).
% 92.80/12.65 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 92.80/12.65 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 92.80/12.65 thf('9', plain,
% 92.80/12.65 (![X0:( $i > $o ),X1:( $i > $o )]:
% 92.80/12.65 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 92.80/12.65 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 92.80/12.65 inference('rw.lit', [status(esa)], [def_all_of])).
% 92.80/12.65 thf(zip_derived_cl274, plain,
% 92.80/12.65 ((~ (((!!) @ (^[Y0 : $i]:
% 92.80/12.65 (((is_of @ Y0 @ ((('#C') @ in @ nat))) =>
% 92.80/12.65 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ ('#B') @
% 92.80/12.65 ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 92.80/12.65 (min @ '#sk1'))))) @
% 92.80/12.65 (e_is @ nat))))) @
% 92.80/12.65 Y0)))))))
% 92.80/12.65 | (imp @ (l_some @ nat @ (min @ '#sk1')) @ ($false)))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl273, '9'])).
% 92.80/12.65 thf(zip_derived_cl275, plain,
% 92.80/12.65 ((~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 92.80/12.65 ((('#C') @ is_of @ ((('#C') @ in @ nat)))))) @
% 92.80/12.65 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ ('#B') @
% 92.80/12.65 ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 (e_is @ nat)))))))))))
% 92.80/12.65 | (imp @ (l_some @ nat @ (min @ '#sk1')) @ ($false)))),
% 92.80/12.65 inference('comb-normalize', [status(thm)], [zip_derived_cl274])).
% 92.80/12.65 thf(zip_derived_cl276, plain,
% 92.80/12.65 (( (((l_some @ nat @ (min @ '#sk1')) => ($false)))
% 92.80/12.65 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 92.80/12.65 ((('#C') @ is_of @ ((('#C') @ in @ nat)))))) @
% 92.80/12.65 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ ('#B') @
% 92.80/12.65 ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 92.80/12.65 (min @ '#sk1'))))) @
% 92.80/12.65 (e_is @ nat))))))))))))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl275, '8'])).
% 92.80/12.65 thf(zip_derived_cl277, plain,
% 92.80/12.65 (( (((~) @ (l_some @ nat @ (min @ '#sk1'))))
% 92.80/12.65 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 92.80/12.65 ((('#C') @ is_of @ ((('#C') @ in @ nat)))))) @
% 92.80/12.65 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ ('#B') @
% 92.80/12.65 ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 92.80/12.65 (min @ '#sk1'))))) @
% 92.80/12.65 (e_is @ nat))))))))))))),
% 92.80/12.65 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl276])).
% 92.80/12.65 thf(zip_derived_cl278, plain,
% 92.80/12.65 ((~ (l_some @ nat @ (min @ '#sk1'))
% 92.80/12.65 | ~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 92.80/12.65 ((('#C') @ is_of @ ((('#C') @ in @ nat)))))) @
% 92.80/12.65 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ ('#B') @
% 92.80/12.65 ((('#B') @ (=>) @ (min @ '#sk1'))))) @
% 92.80/12.65 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 92.80/12.65 (min @ '#sk1'))))) @
% 92.80/12.65 (e_is @ nat))))))))))))),
% 92.80/12.65 inference('simplify nested equalities', [status(thm)],
% 92.80/12.65 [zip_derived_cl277])).
% 92.80/12.65 thf(zip_derived_cl279, plain,
% 92.80/12.65 ((~ (((is_of @ '#sk2' @ ((('#C') @ in @ nat))) => (all_of @
% 92.80/12.65 ((('#C') @ in @ nat)) @
% 92.80/12.65 ((('#B') @ (((=>) @ (min @ '#sk1' @ '#sk2'))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ (=>) @ (min @ '#sk1'))) @
% 92.80/12.65 (e_is @ nat @ '#sk2'))))))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl278])).
% 92.80/12.65 thf(def_is_of, axiom,(( is_of @ (X1)@ (X0)) = ((X0 @ X1)))).
% 92.80/12.65 thf('10', plain,
% 92.80/12.65 (![X0:( $i > $o ),X1:$i]: ( ( is_of @ X1 @ X0 ) = ( X0 @ X1 ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(def_all, axiom,(( all @ (X0)@ (X1)) =
% 92.80/12.65 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ X0)) @ X1)))).
% 92.80/12.65 thf('11', plain,
% 92.80/12.65 (![X1:( $i > $o ),X0:$i]:
% 92.80/12.65 ( ( all @ X0 @ X1 ) = ( all_of @ ( ^[V_1:$i]: ( in @ V_1 @ X0 ) ) @ X1 ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(def_n_all, axiom,(( n_all @ (X0)) = ((all @ nat @ X0)))).
% 92.80/12.65 thf('12', plain,
% 92.80/12.65 (![X0:( $i > $o )]: ( ( n_all @ X0 ) = ( all @ nat @ X0 ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(def_n_lb, axiom,(( n_lb @ (X0)@ (X1)) = ((n_all @ (lbprop @ X0 @ X1))))).
% 92.80/12.65 thf('13', plain,
% 92.80/12.65 (![X1:$i,X0:( $i > $o )]:
% 92.80/12.65 ( ( n_lb @ X0 @ X1 ) = ( n_all @ ( lbprop @ X0 @ X1 ) ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(def_min, axiom,(( min @ (X0)@ (X1)) =
% 92.80/12.65 ((d_and @ (n_lb @ X0 @ X1) @ (X0 @ X1))))).
% 92.80/12.65 thf('14', plain,
% 92.80/12.65 (![X1:$i,X0:( $i > $o )]:
% 92.80/12.65 ( ( min @ X0 @ X1 ) = ( d_and @ ( n_lb @ X0 @ X1 ) @ ( X0 @ X1 ) ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(zip_derived_cl280, plain,
% 92.80/12.65 ((~ (((in @ '#sk2' @ nat) => (all_of @ ((('#C') @ in @ nat)) @
% 92.80/12.65 ((('#B') @ (((=>) @ (imp @
% 92.80/12.65 (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @
% 92.80/12.65 (lbprop @ '#sk1' @ '#sk2')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk2') @ ($false))) @
% 92.80/12.65 ($false)))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ (=>) @ (min @ '#sk1'))) @
% 92.80/12.65 (e_is @ nat @ '#sk2'))))))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('rw', [status(thm)],
% 92.80/12.65 [zip_derived_cl279, '10', '0', '0', '1', '2', '11', '12',
% 92.80/12.65 '13', '14'])).
% 92.80/12.65 thf(zip_derived_cl282, plain,
% 92.80/12.65 ((~ (all_of @ ((('#C') @ in @ nat)) @
% 92.80/12.65 ((('#B') @ (((=>) @ (imp @
% 92.80/12.65 (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @
% 92.80/12.65 (lbprop @ '#sk1' @ '#sk2')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk2') @ ($false))) @
% 92.80/12.65 ($false)))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ (=>) @ (min @ '#sk1'))) @
% 92.80/12.65 (e_is @ nat @ '#sk2'))))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl280])).
% 92.80/12.65 thf(zip_derived_cl283, plain,
% 92.80/12.65 ((~ (((!!) @ (^[Y0 : $i]:
% 92.80/12.65 (((is_of @ Y0 @ ((('#C') @ in @ nat))) =>
% 92.80/12.65 ((('#B') @ (((=>) @ (imp @
% 92.80/12.65 (imp @
% 92.80/12.65 (all_of @
% 92.80/12.65 ((('#C') @ in @ nat)) @
% 92.80/12.65 (lbprop @ '#sk1' @ '#sk2')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk2') @
% 92.80/12.65 ($false))) @
% 92.80/12.65 ($false)))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ (=>) @ (min @ '#sk1'))) @
% 92.80/12.65 (e_is @ nat @ '#sk2'))) @
% 92.80/12.65 Y0)))))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl282, '9'])).
% 92.80/12.65 thf(zip_derived_cl284, plain,
% 92.80/12.65 ((~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 92.80/12.65 ((('#C') @ is_of @ ((('#C') @ in @ nat)))))) @
% 92.80/12.65 ((('#B') @ (((=>) @ (imp @
% 92.80/12.65 (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @
% 92.80/12.65 (lbprop @ '#sk1' @ '#sk2')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk2') @ ($false))) @
% 92.80/12.65 ($false)))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ (=>) @ (min @ '#sk1'))) @
% 92.80/12.65 (e_is @ nat @ '#sk2')))))))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('comb-normalize', [status(thm)], [zip_derived_cl283])).
% 92.80/12.65 thf(zip_derived_cl285, plain,
% 92.80/12.65 ((~ (((is_of @ '#sk3' @ ((('#C') @ in @ nat))) =>
% 92.80/12.65 (((imp @
% 92.80/12.65 (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk2')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk2') @ ($false))) @
% 92.80/12.65 ($false)) =>
% 92.80/12.65 (((min @ '#sk1' @ '#sk3') => (e_is @ nat @ '#sk2' @ '#sk3')))))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl284])).
% 92.80/12.65 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))).
% 92.80/12.65 thf('15', plain,
% 92.80/12.65 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(zip_derived_cl286, plain,
% 92.80/12.65 ((~ (((in @ '#sk3' @ nat) =>
% 92.80/12.65 (((imp @
% 92.80/12.65 (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk2')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk2') @ ($false))) @
% 92.80/12.65 ($false)) =>
% 92.80/12.65 (((imp @
% 92.80/12.65 (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk3')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk3') @ ($false))) @
% 92.80/12.65 ($false)) => ((('#sk2') = ('#sk3')))))))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('rw', [status(thm)],
% 92.80/12.65 [zip_derived_cl285, '10', '0', '0', '1', '2', '11', '15',
% 92.80/12.65 '12', '13', '14'])).
% 92.80/12.65 thf(zip_derived_cl288, plain,
% 92.80/12.65 ((~ (((imp @
% 92.80/12.65 (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk2')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk2') @ ($false))) @
% 92.80/12.65 ($false)) =>
% 92.80/12.65 (((imp @
% 92.80/12.65 (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk3')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk3') @ ($false))) @
% 92.80/12.65 ($false)) => ((('#sk2') = ('#sk3')))))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl286])).
% 92.80/12.65 thf(zip_derived_cl289, plain,
% 92.80/12.65 (( (imp @
% 92.80/12.65 (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk2')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk2') @ ($false))) @
% 92.80/12.65 ($false))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl288])).
% 92.80/12.65 thf(zip_derived_cl291, plain,
% 92.80/12.65 (( (((imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk2')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk2') @ ($false))) => ($false)))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl289, '8'])).
% 92.80/12.65 thf(zip_derived_cl294, plain,
% 92.80/12.65 (( (((~) @ (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk2')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk2') @ ($false)))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl291])).
% 92.80/12.65 thf(zip_derived_cl295, plain,
% 92.80/12.65 ((~ (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk2')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk2') @ ($false)))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('simplify nested equalities', [status(thm)],
% 92.80/12.65 [zip_derived_cl294])).
% 92.80/12.65 thf(zip_derived_cl296, plain,
% 92.80/12.65 ((~ (((all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk2')) =>
% 92.80/12.65 (imp @ ('#sk1' @ '#sk2') @ ($false))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl295, '7'])).
% 92.80/12.65 thf(zip_derived_cl300, plain,
% 92.80/12.65 ((~ (imp @ ('#sk1' @ '#sk2') @ ($false))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl296])).
% 92.80/12.65 thf(zip_derived_cl305, plain,
% 92.80/12.65 ((~ ((('#sk1' @ '#sk2') => ($false))) | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl300, '7'])).
% 92.80/12.65 thf(zip_derived_cl310, plain,
% 92.80/12.65 ((~ (((~) @ ('#sk1' @ '#sk2'))) | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl305])).
% 92.80/12.65 thf(zip_derived_cl311, plain,
% 92.80/12.65 (( ('#sk1' @ '#sk2') | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('simplify nested equalities', [status(thm)],
% 92.80/12.65 [zip_derived_cl310])).
% 92.80/12.65 thf(satz27, axiom,
% 92.80/12.65 (![X0:( $i > $o )]: ( ( n_some @ X0 ) => ( n_some @ ( min @ X0 ) ) ))).
% 92.80/12.65 thf(zip_derived_cl259, plain,
% 92.80/12.65 ( (((!!) @ (^[Y0 : $i > $o]: (((n_some @ Y0) => (n_some @ (min @ Y0)))))))),
% 92.80/12.65 inference('cnf', [status(esa)], [satz27])).
% 92.80/12.65 thf(zip_derived_cl260, plain,
% 92.80/12.65 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ n_some)) @
% 92.80/12.65 ((('#B') @ n_some @ min))))))),
% 92.80/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl259])).
% 92.80/12.65 thf(zip_derived_cl419, plain,
% 92.80/12.65 (![X2 : $i > $o]: (((n_some @ X2) => (n_some @ (min @ X2))))),
% 92.80/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl260])).
% 92.80/12.65 thf(zip_derived_cl420, plain,
% 92.80/12.65 (![X2 : $i > $o]: (((l_some @ nat @ X2) => (l_some @ nat @ (min @ X2))))),
% 92.80/12.65 inference('rw', [status(thm)], [zip_derived_cl419, '5', '5'])).
% 92.80/12.65 thf(zip_derived_cl421, plain,
% 92.80/12.65 (![X2 : $i > $o]: (~ (l_some @ nat @ X2) | (l_some @ nat @ (min @ X2)))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl420])).
% 92.80/12.65 thf(zip_derived_cl2677, plain,
% 92.80/12.65 (( ('#sk1' @ '#sk2') | ~ (l_some @ nat @ '#sk1'))),
% 92.80/12.65 inference('sup+', [status(thm)], [zip_derived_cl311, zip_derived_cl421])).
% 92.80/12.65 thf(zip_derived_cl267, plain, ( (l_some @ nat @ '#sk1')),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl266])).
% 92.80/12.65 thf(zip_derived_cl2682, plain, ( ('#sk1' @ '#sk2')),
% 92.80/12.65 inference('demod', [status(thm)], [zip_derived_cl2677, zip_derived_cl267])).
% 92.80/12.65 thf(zip_derived_cl290, plain,
% 92.80/12.65 ((~ (((imp @
% 92.80/12.65 (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk3')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk3') @ ($false))) @
% 92.80/12.65 ($false)) => ((('#sk2') = ('#sk3')))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl288])).
% 92.80/12.65 thf(zip_derived_cl292, plain,
% 92.80/12.65 (( (imp @
% 92.80/12.65 (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk3')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk3') @ ($false))) @
% 92.80/12.65 ($false))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl290])).
% 92.80/12.65 thf(zip_derived_cl297, plain,
% 92.80/12.65 (( (((imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk3')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk3') @ ($false))) => ($false)))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl292, '8'])).
% 92.80/12.65 thf(zip_derived_cl301, plain,
% 92.80/12.65 (( (((~) @ (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk3')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk3') @ ($false)))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl297])).
% 92.80/12.65 thf(zip_derived_cl302, plain,
% 92.80/12.65 ((~ (imp @
% 92.80/12.65 (all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk3')) @
% 92.80/12.65 (imp @ ('#sk1' @ '#sk3') @ ($false)))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('simplify nested equalities', [status(thm)],
% 92.80/12.65 [zip_derived_cl301])).
% 92.80/12.65 thf(zip_derived_cl303, plain,
% 92.80/12.65 ((~ (((all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk3')) =>
% 92.80/12.65 (imp @ ('#sk1' @ '#sk3') @ ($false))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl302, '7'])).
% 92.80/12.65 thf(zip_derived_cl307, plain,
% 92.80/12.65 ((~ (imp @ ('#sk1' @ '#sk3') @ ($false))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl303])).
% 92.80/12.65 thf(zip_derived_cl313, plain,
% 92.80/12.65 ((~ ((('#sk1' @ '#sk3') => ($false))) | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl307, '7'])).
% 92.80/12.65 thf(zip_derived_cl318, plain,
% 92.80/12.65 ((~ (((~) @ ('#sk1' @ '#sk3'))) | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl313])).
% 92.80/12.65 thf(zip_derived_cl319, plain,
% 92.80/12.65 (( ('#sk1' @ '#sk3') | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('simplify nested equalities', [status(thm)],
% 92.80/12.65 [zip_derived_cl318])).
% 92.80/12.65 thf(zip_derived_cl421, plain,
% 92.80/12.65 (![X2 : $i > $o]: (~ (l_some @ nat @ X2) | (l_some @ nat @ (min @ X2)))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl420])).
% 92.80/12.65 thf(zip_derived_cl2678, plain,
% 92.80/12.65 (( ('#sk1' @ '#sk3') | ~ (l_some @ nat @ '#sk1'))),
% 92.80/12.65 inference('sup+', [status(thm)], [zip_derived_cl319, zip_derived_cl421])).
% 92.80/12.65 thf(zip_derived_cl267, plain, ( (l_some @ nat @ '#sk1')),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl266])).
% 92.80/12.65 thf(zip_derived_cl2683, plain, ( ('#sk1' @ '#sk3')),
% 92.80/12.65 inference('demod', [status(thm)], [zip_derived_cl2678, zip_derived_cl267])).
% 92.80/12.65 thf(zip_derived_cl287, plain,
% 92.80/12.65 (( (in @ '#sk3' @ nat) | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl286])).
% 92.80/12.65 thf(zip_derived_cl421, plain,
% 92.80/12.65 (![X2 : $i > $o]: (~ (l_some @ nat @ X2) | (l_some @ nat @ (min @ X2)))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl420])).
% 92.80/12.65 thf(zip_derived_cl2675, plain,
% 92.80/12.65 (( (in @ '#sk3' @ nat) | ~ (l_some @ nat @ '#sk1'))),
% 92.80/12.65 inference('sup+', [status(thm)], [zip_derived_cl287, zip_derived_cl421])).
% 92.80/12.65 thf(zip_derived_cl267, plain, ( (l_some @ nat @ '#sk1')),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl266])).
% 92.80/12.65 thf(zip_derived_cl2680, plain, ( (in @ '#sk3' @ nat)),
% 92.80/12.65 inference('demod', [status(thm)], [zip_derived_cl2675, zip_derived_cl267])).
% 92.80/12.65 thf(zip_derived_cl281, plain,
% 92.80/12.65 (( (in @ '#sk2' @ nat) | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl280])).
% 92.80/12.65 thf(zip_derived_cl421, plain,
% 92.80/12.65 (![X2 : $i > $o]: (~ (l_some @ nat @ X2) | (l_some @ nat @ (min @ X2)))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl420])).
% 92.80/12.65 thf(zip_derived_cl2674, plain,
% 92.80/12.65 (( (in @ '#sk2' @ nat) | ~ (l_some @ nat @ '#sk1'))),
% 92.80/12.65 inference('sup+', [status(thm)], [zip_derived_cl281, zip_derived_cl421])).
% 92.80/12.65 thf(zip_derived_cl267, plain, ( (l_some @ nat @ '#sk1')),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl266])).
% 92.80/12.65 thf(zip_derived_cl2679, plain, ( (in @ '#sk2' @ nat)),
% 92.80/12.65 inference('demod', [status(thm)], [zip_derived_cl2674, zip_derived_cl267])).
% 92.80/12.65 thf(zip_derived_cl293, plain,
% 92.80/12.65 ((~ ((('#sk2') = ('#sk3'))) | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl290])).
% 92.80/12.65 thf(zip_derived_cl298, plain,
% 92.80/12.65 (((('#sk2') != ('#sk3')) | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('simplify nested equalities', [status(thm)],
% 92.80/12.65 [zip_derived_cl293])).
% 92.80/12.65 thf(zip_derived_cl267, plain, ( (l_some @ nat @ '#sk1')),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl266])).
% 92.80/12.65 thf(zip_derived_cl306, plain,
% 92.80/12.65 (( (all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk3'))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl303])).
% 92.80/12.65 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 92.80/12.65 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 92.80/12.65 thf('16', plain,
% 92.80/12.65 (![X0:( $i > $o ),X1:( $i > $o )]:
% 92.80/12.65 ( ( all_of @ X0 @ X1 ) <=>
% 92.80/12.65 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 92.80/12.65 inference('rw.lit', [status(esa)], [def_all_of])).
% 92.80/12.65 thf(zip_derived_cl312, plain,
% 92.80/12.65 (( (((!!) @ (^[Y0 : $i]:
% 92.80/12.65 (((is_of @ Y0 @ ((('#C') @ in @ nat))) => (lbprop @
% 92.80/12.65 '#sk1' @ '#sk3' @ Y0))))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl306, '16'])).
% 92.80/12.65 thf(zip_derived_cl316, plain,
% 92.80/12.65 (( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 92.80/12.65 ((('#C') @ is_of @ ((('#C') @ in @ nat)))))) @
% 92.80/12.65 (lbprop @ '#sk1' @ '#sk3')))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('comb-normalize', [status(thm)], [zip_derived_cl312])).
% 92.80/12.65 thf(zip_derived_cl317, plain,
% 92.80/12.65 (![X2 : $i]:
% 92.80/12.65 ( (((is_of @ X2 @ ((('#C') @ in @ nat))) => (lbprop @ '#sk1' @
% 92.80/12.65 '#sk3' @ X2)))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl316])).
% 92.80/12.65 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 92.80/12.65 thf('17', plain,
% 92.80/12.65 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(def_n_is, axiom,(( n_is @ (X0)@ (X1)) = ((e_is @ nat @ X0 @ X1)))).
% 92.80/12.65 thf('18', plain,
% 92.80/12.65 (![X1:$i,X0:$i]: ( ( n_is @ X0 @ X1 ) = ( e_is @ nat @ X0 @ X1 ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))).
% 92.80/12.65 thf('19', plain,
% 92.80/12.65 (![X1:$i,X0:$i]:
% 92.80/12.65 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(def_lessis, axiom,(( lessis @ (X0)@ (X1)) =
% 92.80/12.65 ((l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1))))).
% 92.80/12.65 thf('20', plain,
% 92.80/12.65 (![X1:$i,X0:$i]:
% 92.80/12.65 ( ( lessis @ X0 @ X1 ) =
% 92.80/12.65 ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(def_lbprop, axiom,(( lbprop @ (X0)@ (X2)@ (X1)) =
% 92.80/12.65 ((imp @ (X0 @ X1) @ (lessis @ X2 @ X1))))).
% 92.80/12.65 thf('21', plain,
% 92.80/12.65 (![X2:$i,X0:( $i > $o ),X1:$i]:
% 92.80/12.65 ( ( lbprop @ X0 @ X2 @ X1 ) =
% 92.80/12.65 ( imp @ ( X0 @ X1 ) @ ( lessis @ X2 @ X1 ) ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(zip_derived_cl321, plain,
% 92.80/12.65 (![X2 : $i]:
% 92.80/12.65 ( (((in @ X2 @ nat) => (imp @ ('#sk1' @ X2) @
% 92.80/12.65 (imp @
% 92.80/12.65 (imp @ (l_some @ nat @ (diffprop @ X2 @ '#sk3')) @ ($false)) @
% 92.80/12.65 ((('#sk3') = (X2)))))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('rw', [status(thm)],
% 92.80/12.65 [zip_derived_cl317, '10', '0', '17', '15', '18', '5', '19',
% 92.80/12.65 '20', '21'])).
% 92.80/12.65 thf(zip_derived_cl322, plain,
% 92.80/12.65 (![X2 : $i]:
% 92.80/12.65 (~ (in @ X2 @ nat)
% 92.80/12.65 | (imp @ ('#sk1' @ X2) @
% 92.80/12.65 (imp @
% 92.80/12.65 (imp @ (l_some @ nat @ (diffprop @ X2 @ '#sk3')) @ ($false)) @
% 92.80/12.65 ((('#sk3') = (X2)))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl321])).
% 92.80/12.65 thf(zip_derived_cl324, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 ( ((('#sk1' @ X0) => (imp @
% 92.80/12.65 (imp @ (l_some @ nat @ (diffprop @ X0 @ '#sk3')) @ ($false)) @
% 92.80/12.65 ((('#sk3') = (X0))))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1'))
% 92.80/12.65 | ~ (in @ X0 @ nat))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl322, '8'])).
% 92.80/12.65 thf(zip_derived_cl326, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 (~ ('#sk1' @ X0)
% 92.80/12.65 | (imp @
% 92.80/12.65 (imp @ (l_some @ nat @ (diffprop @ X0 @ '#sk3')) @ ($false)) @
% 92.80/12.65 ((('#sk3') = (X0))))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl324])).
% 92.80/12.65 thf(zip_derived_cl328, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 ( (((imp @ (l_some @ nat @ (diffprop @ X0 @ '#sk3')) @ ($false)) =>
% 92.80/12.65 ((('#sk3') = (X0)))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1'))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ ('#sk1' @ X0))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl326, '8'])).
% 92.80/12.65 thf(zip_derived_cl331, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 (~ (imp @ (l_some @ nat @ (diffprop @ X0 @ '#sk3')) @ ($false))
% 92.80/12.65 | ((('#sk3') = (X0)))
% 92.80/12.65 | ~ ('#sk1' @ X0)
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl328])).
% 92.80/12.65 thf(zip_derived_cl334, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 (~ (imp @ (l_some @ nat @ (diffprop @ X0 @ '#sk3')) @ ($false))
% 92.80/12.65 | (('#sk3') = (X0))
% 92.80/12.65 | ~ ('#sk1' @ X0)
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('simplify nested equalities', [status(thm)],
% 92.80/12.65 [zip_derived_cl331])).
% 92.80/12.65 thf(zip_derived_cl335, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 (~ (((l_some @ nat @ (diffprop @ X0 @ '#sk3')) => ($false)))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1'))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ ('#sk1' @ X0)
% 92.80/12.65 | (('#sk3') = (X0)))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl334, '7'])).
% 92.80/12.65 thf(zip_derived_cl336, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 (~ (((~) @ (l_some @ nat @ (diffprop @ X0 @ '#sk3'))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1'))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ ('#sk1' @ X0)
% 92.80/12.65 | (('#sk3') = (X0)))),
% 92.80/12.65 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl335])).
% 92.80/12.65 thf(zip_derived_cl337, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 ( (l_some @ nat @ (diffprop @ X0 @ '#sk3'))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1'))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ ('#sk1' @ X0)
% 92.80/12.65 | (('#sk3') = (X0)))),
% 92.80/12.65 inference('simplify nested equalities', [status(thm)],
% 92.80/12.65 [zip_derived_cl336])).
% 92.80/12.65 thf(satz10c, axiom,
% 92.80/12.65 (all_of @
% 92.80/12.65 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @
% 92.80/12.65 ( ^[X0:$i]:
% 92.80/12.65 ( all_of @
% 92.80/12.65 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 92.80/12.65 ( ^[X1:$i]: ( ( moreis @ X0 @ X1 ) => ( d_not @ ( iii @ X0 @ X1 ) ) ) ) ) ))).
% 92.80/12.65 thf(zip_derived_cl143, plain,
% 92.80/12.65 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @
% 92.80/12.65 (^[Y0 : $i]:
% 92.80/12.65 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 92.80/12.65 (^[Y1 : $i]: (((moreis @ Y0 @ Y1) => (d_not @ (iii @ Y0 @ Y1))))))))),
% 92.80/12.65 inference('cnf', [status(esa)], [satz10c])).
% 92.80/12.65 thf(zip_derived_cl144, plain,
% 92.80/12.65 ( (all_of @ ((('#C') @ in @ nat)) @
% 92.80/12.65 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ ('#S') @
% 92.80/12.65 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @
% 92.80/12.65 ((('#B') @ ((('#B') @ d_not)) @ iii)))))))),
% 92.80/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl143])).
% 92.80/12.65 thf(zip_derived_cl701, plain,
% 92.80/12.65 ( (((!!) @ (^[Y0 : $i]:
% 92.80/12.65 (((is_of @ Y0 @ ((('#C') @ in @ nat))) =>
% 92.80/12.65 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ ('#S') @
% 92.80/12.65 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @
% 92.80/12.65 ((('#B') @ ((('#B') @ d_not)) @ iii)))) @
% 92.80/12.65 Y0)))))))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl144, '16'])).
% 92.80/12.65 thf(zip_derived_cl702, plain,
% 92.80/12.65 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 92.80/12.65 ((('#C') @ is_of @ ((('#C') @ in @ nat)))))) @
% 92.80/12.65 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ ('#S') @
% 92.80/12.65 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @
% 92.80/12.65 ((('#B') @ ((('#B') @ d_not)) @ iii))))))))))),
% 92.80/12.65 inference('comb-normalize', [status(thm)], [zip_derived_cl701])).
% 92.80/12.65 thf(zip_derived_cl703, plain,
% 92.80/12.65 (![X2 : $i]:
% 92.80/12.65 (((is_of @ X2 @ ((('#C') @ in @ nat))) => (all_of @
% 92.80/12.65 ((('#C') @ in @ nat)) @
% 92.80/12.65 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X2))) @
% 92.80/12.65 ((('#B') @ d_not @ (iii @ X2))))))))),
% 92.80/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl702])).
% 92.80/12.65 thf(zip_derived_cl704, plain,
% 92.80/12.65 (![X2 : $i]:
% 92.80/12.65 (((in @ X2 @ nat) => (all_of @ ((('#C') @ in @ nat)) @
% 92.80/12.65 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X2))) @
% 92.80/12.65 ((('#B') @ d_not @ (iii @ X2))))))))),
% 92.80/12.65 inference('rw', [status(thm)], [zip_derived_cl703, '10'])).
% 92.80/12.65 thf(zip_derived_cl705, plain,
% 92.80/12.65 (![X2 : $i]:
% 92.80/12.65 (~ (in @ X2 @ nat)
% 92.80/12.65 | (all_of @ ((('#C') @ in @ nat)) @
% 92.80/12.65 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X2))) @
% 92.80/12.65 ((('#B') @ d_not @ (iii @ X2)))))))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl704])).
% 92.80/12.65 thf(zip_derived_cl706, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 ( (((!!) @ (^[Y0 : $i]:
% 92.80/12.65 (((is_of @ Y0 @ ((('#C') @ in @ nat))) =>
% 92.80/12.65 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X0))) @
% 92.80/12.65 ((('#B') @ d_not @ (iii @ X0))) @ Y0)))))))
% 92.80/12.65 | ~ (in @ X0 @ nat))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl705, '16'])).
% 92.80/12.65 thf(zip_derived_cl707, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 92.80/12.65 ((('#C') @ is_of @ ((('#C') @ in @ nat)))))) @
% 92.80/12.65 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X0))) @
% 92.80/12.65 ((('#B') @ d_not @ (iii @ X0)))))))))
% 92.80/12.65 | ~ (in @ X0 @ nat))),
% 92.80/12.65 inference('comb-normalize', [status(thm)], [zip_derived_cl706])).
% 92.80/12.65 thf(zip_derived_cl708, plain,
% 92.80/12.65 (![X0 : $i, X2 : $i]:
% 92.80/12.65 ( (((is_of @ X2 @ ((('#C') @ in @ nat))) =>
% 92.80/12.65 (((moreis @ X0 @ X2) => (d_not @ (iii @ X0 @ X2))))))
% 92.80/12.65 | ~ (in @ X0 @ nat))),
% 92.80/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl707])).
% 92.80/12.65 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) =
% 92.80/12.65 ((n_some @ (diffprop @ X0 @ X1))))).
% 92.80/12.65 thf('22', plain,
% 92.80/12.65 (![X1:$i,X0:$i]:
% 92.80/12.65 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(def_moreis, axiom,(( moreis @ (X0)@ (X1)) =
% 92.80/12.65 ((l_or @ (d_29_ii @ X0 @ X1) @ (n_is @ X0 @ X1))))).
% 92.80/12.65 thf('23', plain,
% 92.80/12.65 (![X1:$i,X0:$i]:
% 92.80/12.65 ( ( moreis @ X0 @ X1 ) =
% 92.80/12.65 ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
% 92.80/12.65 define([status(thm)])).
% 92.80/12.65 thf(zip_derived_cl709, plain,
% 92.80/12.65 (![X0 : $i, X2 : $i]:
% 92.80/12.65 ( (((in @ X2 @ nat) =>
% 92.80/12.65 (((imp @
% 92.80/12.65 (imp @ (l_some @ nat @ (diffprop @ X0 @ X2)) @ ($false)) @
% 92.80/12.65 (((X0) = (X2)))) => (imp @
% 92.80/12.65 (l_some @ nat @ (diffprop @ X2 @ X0)) @ ($false))))))
% 92.80/12.65 | ~ (in @ X0 @ nat))),
% 92.80/12.65 inference('rw', [status(thm)],
% 92.80/12.65 [zip_derived_cl708, '10', '0', '0', '17', '15', '18', '5',
% 92.80/12.65 '5', '22', '19', '23'])).
% 92.80/12.65 thf(zip_derived_cl710, plain,
% 92.80/12.65 (![X0 : $i, X2 : $i]:
% 92.80/12.65 (~ (in @ X2 @ nat)
% 92.80/12.65 | (((imp @
% 92.80/12.65 (imp @ (l_some @ nat @ (diffprop @ X0 @ X2)) @ ($false)) @
% 92.80/12.65 (((X0) = (X2)))) => (imp @
% 92.80/12.65 (l_some @ nat @ (diffprop @ X2 @ X0)) @ ($false))))
% 92.80/12.65 | ~ (in @ X0 @ nat))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl709])).
% 92.80/12.65 thf(zip_derived_cl711, plain,
% 92.80/12.65 (![X0 : $i, X2 : $i]:
% 92.80/12.65 (~ (imp @ (imp @ (l_some @ nat @ (diffprop @ X0 @ X2)) @ ($false)) @
% 92.80/12.65 (((X0) = (X2))))
% 92.80/12.65 | (imp @ (l_some @ nat @ (diffprop @ X2 @ X0)) @ ($false))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ (in @ X2 @ nat))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl710])).
% 92.80/12.65 thf(zip_derived_cl712, plain,
% 92.80/12.65 (![X0 : $i, X1 : $i]:
% 92.80/12.65 (~ (((imp @ (l_some @ nat @ (diffprop @ X1 @ X0)) @ ($false)) =>
% 92.80/12.65 (((X1) = (X0)))))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ (in @ X1 @ nat)
% 92.80/12.65 | (imp @ (l_some @ nat @ (diffprop @ X0 @ X1)) @ ($false)))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl711, '7'])).
% 92.80/12.65 thf(zip_derived_cl713, plain,
% 92.80/12.65 (![X0 : $i, X1 : $i]:
% 92.80/12.65 ( (((l_some @ nat @ (diffprop @ X1 @ X0)) => ($false)))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ (in @ X1 @ nat)
% 92.80/12.65 | ~ (((imp @ (l_some @ nat @ (diffprop @ X0 @ X1)) @ ($false)) =>
% 92.80/12.65 (((X0) = (X1))))))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl712, '8'])).
% 92.80/12.65 thf(zip_derived_cl714, plain,
% 92.80/12.65 (![X0 : $i, X1 : $i]:
% 92.80/12.65 ( (((~) @ (l_some @ nat @ (diffprop @ X1 @ X0))))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ (in @ X1 @ nat)
% 92.80/12.65 | ~ (((imp @ (l_some @ nat @ (diffprop @ X0 @ X1)) @ ($false)) =>
% 92.80/12.65 (((X0) = (X1))))))),
% 92.80/12.65 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl713])).
% 92.80/12.65 thf(zip_derived_cl715, plain,
% 92.80/12.65 (![X0 : $i, X1 : $i]:
% 92.80/12.65 (~ (l_some @ nat @ (diffprop @ X1 @ X0))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ (in @ X1 @ nat)
% 92.80/12.65 | ~ (((imp @ (l_some @ nat @ (diffprop @ X0 @ X1)) @ ($false)) =>
% 92.80/12.65 (((X0) = (X1))))))),
% 92.80/12.65 inference('simplify nested equalities', [status(thm)],
% 92.80/12.65 [zip_derived_cl714])).
% 92.80/12.65 thf(zip_derived_cl716, plain,
% 92.80/12.65 (![X0 : $i, X1 : $i]:
% 92.80/12.65 ( (imp @ (l_some @ nat @ (diffprop @ X0 @ X1)) @ ($false))
% 92.80/12.65 | ~ (in @ X1 @ nat)
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ (l_some @ nat @ (diffprop @ X1 @ X0)))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl715])).
% 92.80/12.65 thf(zip_derived_cl718, plain,
% 92.80/12.65 (![X0 : $i, X1 : $i]:
% 92.80/12.65 ( (((l_some @ nat @ (diffprop @ X0 @ X1)) => ($false)))
% 92.80/12.65 | ~ (l_some @ nat @ (diffprop @ X1 @ X0))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ (in @ X1 @ nat))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl716, '8'])).
% 92.80/12.65 thf(zip_derived_cl720, plain,
% 92.80/12.65 (![X0 : $i, X1 : $i]:
% 92.80/12.65 ( (((~) @ (l_some @ nat @ (diffprop @ X0 @ X1))))
% 92.80/12.65 | ~ (l_some @ nat @ (diffprop @ X1 @ X0))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ (in @ X1 @ nat))),
% 92.80/12.65 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl718])).
% 92.80/12.65 thf(zip_derived_cl721, plain,
% 92.80/12.65 (![X0 : $i, X1 : $i]:
% 92.80/12.65 (~ (l_some @ nat @ (diffprop @ X0 @ X1))
% 92.80/12.65 | ~ (l_some @ nat @ (diffprop @ X1 @ X0))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ (in @ X1 @ nat))),
% 92.80/12.65 inference('simplify nested equalities', [status(thm)],
% 92.80/12.65 [zip_derived_cl720])).
% 92.80/12.65 thf(zip_derived_cl421, plain,
% 92.80/12.65 (![X2 : $i > $o]: (~ (l_some @ nat @ X2) | (l_some @ nat @ (min @ X2)))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl420])).
% 92.80/12.65 thf(zip_derived_cl299, plain,
% 92.80/12.65 (( (all_of @ ((('#C') @ in @ nat)) @ (lbprop @ '#sk1' @ '#sk2'))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl296])).
% 92.80/12.65 thf(zip_derived_cl304, plain,
% 92.80/12.65 (( (((!!) @ (^[Y0 : $i]:
% 92.80/12.65 (((is_of @ Y0 @ ((('#C') @ in @ nat))) => (lbprop @
% 92.80/12.65 '#sk1' @ '#sk2' @ Y0))))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl299, '16'])).
% 92.80/12.65 thf(zip_derived_cl308, plain,
% 92.80/12.65 (( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 92.80/12.65 ((('#C') @ is_of @ ((('#C') @ in @ nat)))))) @
% 92.80/12.65 (lbprop @ '#sk1' @ '#sk2')))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('comb-normalize', [status(thm)], [zip_derived_cl304])).
% 92.80/12.65 thf(zip_derived_cl309, plain,
% 92.80/12.65 (![X2 : $i]:
% 92.80/12.65 ( (((is_of @ X2 @ ((('#C') @ in @ nat))) => (lbprop @ '#sk1' @
% 92.80/12.65 '#sk2' @ X2)))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl308])).
% 92.80/12.65 thf(zip_derived_cl314, plain,
% 92.80/12.65 (![X2 : $i]:
% 92.80/12.65 ( (((in @ X2 @ nat) => (imp @ ('#sk1' @ X2) @
% 92.80/12.65 (imp @
% 92.80/12.65 (imp @ (l_some @ nat @ (diffprop @ X2 @ '#sk2')) @ ($false)) @
% 92.80/12.65 ((('#sk2') = (X2)))))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('rw', [status(thm)],
% 92.80/12.65 [zip_derived_cl309, '10', '0', '17', '15', '18', '5', '19',
% 92.80/12.65 '20', '21'])).
% 92.80/12.65 thf(zip_derived_cl315, plain,
% 92.80/12.65 (![X2 : $i]:
% 92.80/12.65 (~ (in @ X2 @ nat)
% 92.80/12.65 | (imp @ ('#sk1' @ X2) @
% 92.80/12.65 (imp @
% 92.80/12.65 (imp @ (l_some @ nat @ (diffprop @ X2 @ '#sk2')) @ ($false)) @
% 92.80/12.65 ((('#sk2') = (X2)))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl314])).
% 92.80/12.65 thf(zip_derived_cl320, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 ( ((('#sk1' @ X0) => (imp @
% 92.80/12.65 (imp @ (l_some @ nat @ (diffprop @ X0 @ '#sk2')) @ ($false)) @
% 92.80/12.65 ((('#sk2') = (X0))))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1'))
% 92.80/12.65 | ~ (in @ X0 @ nat))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl315, '8'])).
% 92.80/12.65 thf(zip_derived_cl323, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 (~ ('#sk1' @ X0)
% 92.80/12.65 | (imp @
% 92.80/12.65 (imp @ (l_some @ nat @ (diffprop @ X0 @ '#sk2')) @ ($false)) @
% 92.80/12.65 ((('#sk2') = (X0))))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl320])).
% 92.80/12.65 thf(zip_derived_cl325, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 ( (((imp @ (l_some @ nat @ (diffprop @ X0 @ '#sk2')) @ ($false)) =>
% 92.80/12.65 ((('#sk2') = (X0)))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1'))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ ('#sk1' @ X0))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl323, '8'])).
% 92.80/12.65 thf(zip_derived_cl327, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 (~ (imp @ (l_some @ nat @ (diffprop @ X0 @ '#sk2')) @ ($false))
% 92.80/12.65 | ((('#sk2') = (X0)))
% 92.80/12.65 | ~ ('#sk1' @ X0)
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl325])).
% 92.80/12.65 thf(zip_derived_cl329, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 (~ (imp @ (l_some @ nat @ (diffprop @ X0 @ '#sk2')) @ ($false))
% 92.80/12.65 | (('#sk2') = (X0))
% 92.80/12.65 | ~ ('#sk1' @ X0)
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1')))),
% 92.80/12.65 inference('simplify nested equalities', [status(thm)],
% 92.80/12.65 [zip_derived_cl327])).
% 92.80/12.65 thf(zip_derived_cl330, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 (~ (((l_some @ nat @ (diffprop @ X0 @ '#sk2')) => ($false)))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1'))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ ('#sk1' @ X0)
% 92.80/12.65 | (('#sk2') = (X0)))),
% 92.80/12.65 inference('rw_clause', [status(thm)], [zip_derived_cl329, '7'])).
% 92.80/12.65 thf(zip_derived_cl332, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 (~ (((~) @ (l_some @ nat @ (diffprop @ X0 @ '#sk2'))))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1'))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ ('#sk1' @ X0)
% 92.80/12.65 | (('#sk2') = (X0)))),
% 92.80/12.65 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl330])).
% 92.80/12.65 thf(zip_derived_cl333, plain,
% 92.80/12.65 (![X0 : $i]:
% 92.80/12.65 ( (l_some @ nat @ (diffprop @ X0 @ '#sk2'))
% 92.80/12.65 | ~ (l_some @ nat @ (min @ '#sk1'))
% 92.80/12.65 | ~ (in @ X0 @ nat)
% 92.80/12.65 | ~ ('#sk1' @ X0)
% 92.80/12.65 | (('#sk2') = (X0)))),
% 92.80/12.65 inference('simplify nested equalities', [status(thm)],
% 92.80/12.65 [zip_derived_cl332])).
% 92.80/12.65 thf(zip_derived_cl7661, plain, ($false),
% 92.80/12.65 inference('eprover', [status(thm)],
% 92.80/12.65 [zip_derived_cl2682, zip_derived_cl2683, zip_derived_cl2680,
% 92.80/12.65 zip_derived_cl2679, zip_derived_cl298, zip_derived_cl267,
% 92.80/12.65 zip_derived_cl337, zip_derived_cl721, zip_derived_cl421,
% 92.80/12.65 zip_derived_cl333])).
% 92.80/12.65
% 92.80/12.65 % SZS output end Refutation
% 92.80/12.65
% 92.80/12.65
% 92.80/12.65 % Terminating...
% 93.87/12.74 % Runner terminated.
% 93.87/12.75 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------