%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM742^4 : TPTP v9.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.NwnIKkAARc true
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:48:11 PM UTC 2025
% Result : Theorem 73.53s 12.70s
% Output : Refutation 73.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM742^4 : TPTP v9.2.0. Released v7.1.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.NwnIKkAARc true
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 1 16:34:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.56/0.68 % Total configuration time : 828
% 0.56/0.68 % Estimated wc time : 1656
% 0.56/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.57/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.57/0.80 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.57/0.80 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 73.53/12.70 % Solved by lams/40_b.comb.sh.
% 73.53/12.70 % done 434 iterations in 11.769s
% 73.53/12.70 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 73.53/12.70 % SZS output start Refutation
% 73.53/12.70 thf(lessf_type, type, lessf: $i > $i > $o).
% 73.53/12.70 thf(nat_type, type, nat: $i).
% 73.53/12.70 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 73.53/12.70 thf(in_type, type, in: $i > $i > $o).
% 73.53/12.70 thf('#sk4_type', type, '#sk4': $i).
% 73.53/12.70 thf('#sk3_type', type, '#sk3': $i).
% 73.53/12.70 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 73.53/12.70 thf(lesseq_type, type, lesseq: $i > $i > $o).
% 73.53/12.70 thf(ap_type, type, ap: $i > $i > $i).
% 73.53/12.70 thf(n_is_type, type, n_is: $i > $i > $o).
% 73.53/12.70 thf(n_1t_type, type, n_1t: $i).
% 73.53/12.70 thf(imp_type, type, imp: $o > $o > $o).
% 73.53/12.70 thf(frac_type, type, frac: $i).
% 73.53/12.70 thf(n_2t_type, type, n_2t: $i).
% 73.53/12.70 thf(n_ts_type, type, n_ts: $i > $i > $i).
% 73.53/12.70 thf('#ty_enc5_type', type, '#ty_enc5': ($i > $i > $o) > $i > $i > $o).
% 73.53/12.70 thf(n_eq_type, type, n_eq: $i > $i > $o).
% 73.53/12.70 thf(pair1type_type, type, pair1type: $i > $i).
% 73.53/12.70 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 73.53/12.70 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 73.53/12.70 thf(num_type, type, num: $i > $i).
% 73.53/12.70 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 73.53/12.70 thf(l_or_type, type, l_or: $o > $o > $o).
% 73.53/12.70 thf(d_not_type, type, d_not: $o > $o).
% 73.53/12.70 thf(first1_type, type, first1: $i > $i > $i).
% 73.53/12.70 thf('#sk2_type', type, '#sk2': $i).
% 73.53/12.70 thf(den_type, type, den: $i > $i).
% 73.53/12.70 thf(iii_type, type, iii: $i > $i > $o).
% 73.53/12.70 thf(second1_type, type, second1: $i > $i > $i).
% 73.53/12.70 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 73.53/12.70 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 73.53/12.70 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 73.53/12.70 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 73.53/12.70 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 73.53/12.70 thf(satz37, axiom,
% 73.53/12.70 (all_of @
% 73.53/12.70 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ ( ^[X0:$i]: ( n_eq @ X0 @ X0 ) ))).
% 73.53/12.70 thf(zip_derived_cl238, plain,
% 73.53/12.70 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 73.53/12.70 (^[Y0 : $i]: (n_eq @ Y0 @ Y0)))),
% 73.53/12.70 inference('cnf', [status(esa)], [satz37])).
% 73.53/12.70 thf(zip_derived_cl239, plain,
% 73.53/12.70 ( (all_of @ ((('#C') @ in @ frac)) @ ((('#S') @ n_eq @ ('#I'))))),
% 73.53/12.70 inference('lams2combs', [status(thm)], [zip_derived_cl238])).
% 73.53/12.70 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))).
% 73.53/12.70 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])).
% 73.53/12.70 thf(zip_derived_cl321, plain,
% 73.53/12.70 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#S') @ n_eq @ ('#I'))))),
% 73.53/12.70 inference('rw', [status(thm)], [zip_derived_cl239, '0'])).
% 73.53/12.70 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 73.53/12.70 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 73.53/12.70 thf('1', plain,
% 73.53/12.70 (![X0:( $i > $o ),X1:( $i > $o )]:
% 73.53/12.70 ( ( all_of @ X0 @ X1 ) <=>
% 73.53/12.70 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 73.53/12.70 inference('rw.lit', [status(esa)], [def_all_of])).
% 73.53/12.70 thf(zip_derived_cl322, plain,
% 73.53/12.70 ( (((!!) @ (^[Y0 : $i]:
% 73.53/12.70 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.70 ((('#S') @ n_eq @ ('#I') @ Y0)))))))),
% 73.53/12.70 inference('rw_clause', [status(thm)], [zip_derived_cl321, '1'])).
% 73.53/12.70 thf(zip_derived_cl323, plain,
% 73.53/12.70 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.53/12.70 ((('#C') @ is_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))))))) @
% 73.53/12.70 ((('#S') @ n_eq @ ('#I')))))))),
% 73.53/12.70 inference('comb-normalize', [status(thm)], [zip_derived_cl322])).
% 73.53/12.70 thf(zip_derived_cl324, plain,
% 73.53/12.70 (![X2 : $i]:
% 73.53/12.70 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (n_eq @ X2 @
% 73.53/12.70 X2)))),
% 73.53/12.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl323])).
% 73.53/12.70 thf(def_first1, axiom,(( first1 @ (X1)@ (X0)) = ((ap @ X0 @ n_1t)))).
% 73.53/12.70 thf('2', plain,
% 73.53/12.70 (![X1:$i,X0:$i]: ( ( first1 @ X1 @ X0 ) = ( ap @ X0 @ n_1t ) )),
% 73.53/12.70 define([status(thm)])).
% 73.53/12.70 thf(def_second1, axiom,(( second1 @ (X1)@ (X0)) = ((ap @ X0 @ n_2t)))).
% 73.53/12.70 thf('3', plain,
% 73.53/12.70 (![X1:$i,X0:$i]: ( ( second1 @ X1 @ X0 ) = ( ap @ X0 @ n_2t ) )),
% 73.53/12.70 define([status(thm)])).
% 73.53/12.70 thf(def_num, axiom,(( num @ (X0)) = ((first1 @ nat @ X0)))).
% 73.53/12.70 thf('4', plain, (![X0:$i]: ( ( num @ X0 ) = ( first1 @ nat @ X0 ) )),
% 73.53/12.70 define([status(thm)])).
% 73.53/12.70 thf(def_den, axiom,(( den @ (X0)) = ((second1 @ nat @ X0)))).
% 73.53/12.70 thf('5', plain, (![X0:$i]: ( ( den @ X0 ) = ( second1 @ nat @ X0 ) )),
% 73.53/12.70 define([status(thm)])).
% 73.53/12.70 thf(def_n_eq, axiom,(( n_eq @ (X0)@ (X1)) =
% 73.53/12.70 ((n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 73.53/12.70 (n_ts @ (num @ X1) @ (den @ X0)))))).
% 73.53/12.70 thf('6', plain,
% 73.53/12.70 (![X1:$i,X0:$i]:
% 73.53/12.70 ( ( n_eq @ X0 @ X1 ) =
% 73.53/12.70 ( n_is @
% 73.53/12.70 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 73.53/12.70 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )),
% 73.53/12.70 define([status(thm)])).
% 73.53/12.70 thf(zip_derived_cl325, plain,
% 73.53/12.70 (![X2 : $i]:
% 73.53/12.70 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (n_is @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t)))))),
% 73.53/12.70 inference('rw', [status(thm)],
% 73.53/12.70 [zip_derived_cl324, '2', '3', '4', '5', '6'])).
% 73.53/12.70 thf(zip_derived_cl326, plain,
% 73.53/12.70 (![X2 : $i]:
% 73.53/12.70 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl325])).
% 73.53/12.70 thf(zip_derived_cl12084, plain,
% 73.53/12.70 (![X2 : $i]:
% 73.53/12.70 (~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 73.53/12.70 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t))))),
% 73.53/12.70 inference('remove_ty_args', [status(thm)], [zip_derived_cl326])).
% 73.53/12.70 thf(satz51a, conjecture,
% 73.53/12.70 (all_of @
% 73.53/12.70 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 73.53/12.70 ( ^[X0:$i]:
% 73.53/12.70 ( all_of @
% 73.53/12.70 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 73.53/12.70 ( ^[X1:$i]:
% 73.53/12.70 ( all_of @
% 73.53/12.70 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 73.53/12.70 ( ^[X2:$i]:
% 73.53/12.70 ( ( lesseq @ X0 @ X1 ) =>
% 73.53/12.70 ( ( lessf @ X1 @ X2 ) => ( lessf @ X0 @ X2 ) ) ) ) ) ) ) ))).
% 73.53/12.70 thf(zf_stmt_0, negated_conjecture,
% 73.53/12.70 (~( all_of @
% 73.53/12.70 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 73.53/12.70 ( ^[X0:$i]:
% 73.53/12.70 ( all_of @
% 73.53/12.70 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 73.53/12.70 ( ^[X1:$i]:
% 73.53/12.70 ( all_of @
% 73.53/12.70 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 73.53/12.70 ( ^[X2:$i]:
% 73.53/12.70 ( ( lesseq @ X0 @ X1 ) =>
% 73.53/12.70 ( ( lessf @ X1 @ X2 ) => ( lessf @ X0 @ X2 ) ) ) ) ) ) ) ) )),
% 73.53/12.70 inference('cnf.neg', [status(esa)], [satz51a])).
% 73.53/12.70 thf(zip_derived_cl292, plain,
% 73.53/12.70 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 73.53/12.70 (^[Y0 : $i]:
% 73.53/12.70 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 73.53/12.70 (^[Y1 : $i]:
% 73.53/12.70 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 73.53/12.70 (^[Y2 : $i]:
% 73.53/12.70 (((lesseq @ Y0 @ Y1) =>
% 73.53/12.70 (((lessf @ Y1 @ Y2) => (lessf @ Y0 @ Y2)))))))))))),
% 73.53/12.70 inference('cnf', [status(esa)], [zf_stmt_0])).
% 73.53/12.70 thf(zip_derived_cl293, plain,
% 73.53/12.70 (~ (all_of @ ((('#C') @ in @ frac)) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @
% 73.53/12.70 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @
% 73.53/12.70 lessf)))))))))),
% 73.53/12.70 inference('lams2combs', [status(thm)], [zip_derived_cl292])).
% 73.53/12.70 thf(zip_derived_cl449, plain,
% 73.53/12.70 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @
% 73.53/12.70 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @
% 73.53/12.70 lessf)))))))))),
% 73.53/12.70 inference('rw', [status(thm)], [zip_derived_cl293, '0'])).
% 73.53/12.70 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 73.53/12.70 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 73.53/12.70 thf('7', plain,
% 73.53/12.70 (![X0:( $i > $o ),X1:( $i > $o )]:
% 73.53/12.70 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 73.53/12.70 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 73.53/12.70 inference('rw.lit', [status(esa)], [def_all_of])).
% 73.53/12.70 thf(zip_derived_cl450, plain,
% 73.53/12.70 (~ (((!!) @ (^[Y0 : $i]:
% 73.53/12.70 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (all_of @
% 73.53/12.70 ((('#C') @ in @
% 73.53/12.70 (pair1type @ nat)))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @
% 73.53/12.70 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @
% 73.53/12.70 lessf)))))) @
% 73.53/12.70 lessf)))))) @
% 73.53/12.70 Y0)))))))),
% 73.53/12.70 inference('rw_clause', [status(thm)], [zip_derived_cl449, '7'])).
% 73.53/12.70 thf(zip_derived_cl451, plain,
% 73.53/12.70 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.53/12.70 ((('#C') @ is_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))))))) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (all_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat)))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @
% 73.53/12.70 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @
% 73.53/12.70 lessf)))))) @
% 73.53/12.70 lessf))))))))))))),
% 73.53/12.70 inference('comb-normalize', [status(thm)], [zip_derived_cl450])).
% 73.53/12.70 thf(zip_derived_cl452, plain,
% 73.53/12.70 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ (=>) @ (lesseq @ '#sk2'))))) @
% 73.53/12.70 ((('#C') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @
% 73.53/12.70 (lessf @ '#sk2'))))))))))),
% 73.53/12.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl451])).
% 73.53/12.70 thf(zip_derived_cl454, plain,
% 73.53/12.70 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ (=>) @ (lesseq @ '#sk2'))))) @
% 73.53/12.70 ((('#C') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @
% 73.53/12.70 (lessf @ '#sk2'))))))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl452])).
% 73.53/12.70 thf(zip_derived_cl455, plain,
% 73.53/12.70 (~ (((!!) @ (^[Y0 : $i]:
% 73.53/12.70 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ (=>) @ (lesseq @ '#sk2'))))) @
% 73.53/12.70 ((('#C') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @
% 73.53/12.70 (lessf @ '#sk2'))))) @
% 73.53/12.70 Y0)))))))),
% 73.53/12.70 inference('rw_clause', [status(thm)], [zip_derived_cl454, '7'])).
% 73.53/12.70 thf(zip_derived_cl456, plain,
% 73.53/12.70 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.53/12.70 ((('#C') @ is_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))))))) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ (=>) @ (lesseq @ '#sk2'))))) @
% 73.53/12.70 ((('#C') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @
% 73.53/12.70 (lessf @ '#sk2')))))))))))),
% 73.53/12.70 inference('comb-normalize', [status(thm)], [zip_derived_cl455])).
% 73.53/12.70 thf(zip_derived_cl457, plain,
% 73.53/12.70 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#B') @ (((=>) @ (lesseq @ '#sk2' @ '#sk3'))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ (=>) @ (lessf @ '#sk3'))) @ (lessf @ '#sk2'))))))))),
% 73.53/12.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl456])).
% 73.53/12.70 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 73.53/12.70 thf('8', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 73.53/12.70 define([status(thm)])).
% 73.53/12.70 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 73.53/12.70 thf('9', plain,
% 73.53/12.70 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 73.53/12.70 define([status(thm)])).
% 73.53/12.70 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 73.53/12.70 thf('10', plain,
% 73.53/12.70 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 73.53/12.70 define([status(thm)])).
% 73.53/12.70 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))).
% 73.53/12.70 thf('11', plain,
% 73.53/12.70 (![X1:$i,X0:$i]:
% 73.53/12.70 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 73.53/12.70 define([status(thm)])).
% 73.53/12.70 thf(def_lessf, axiom,(( lessf @ (X0)@ (X1)) =
% 73.53/12.70 ((iii @ (n_ts @ (num @ X0) @ (den @ X1)) @ (n_ts @ (num @ X1) @ (den @ X0)))))).
% 73.53/12.70 thf('12', plain,
% 73.53/12.70 (![X1:$i,X0:$i]:
% 73.53/12.70 ( ( lessf @ X0 @ X1 ) =
% 73.53/12.70 ( iii @
% 73.53/12.70 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 73.53/12.70 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )),
% 73.53/12.70 define([status(thm)])).
% 73.53/12.70 thf(def_lesseq, axiom,(( lesseq @ (X0)@ (X1)) =
% 73.53/12.70 ((l_or @ (lessf @ X0 @ X1) @ (n_eq @ X0 @ X1))))).
% 73.53/12.70 thf('13', plain,
% 73.53/12.70 (![X1:$i,X0:$i]:
% 73.53/12.70 ( ( lesseq @ X0 @ X1 ) =
% 73.53/12.70 ( l_or @ ( lessf @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )),
% 73.53/12.70 define([status(thm)])).
% 73.53/12.70 thf(zip_derived_cl458, plain,
% 73.53/12.70 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#B') @ (((=>) @ (imp @
% 73.53/12.70 (imp @
% 73.53/12.70 (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 73.53/12.70 (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 73.53/12.70 (ap @ '#sk3' @ n_2t)))) @
% 73.53/12.70 ($false)) @
% 73.53/12.70 (n_is @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 73.53/12.70 (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 73.53/12.70 (ap @ '#sk2' @ n_2t)))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ (=>) @ (lessf @ '#sk3'))) @ (lessf @ '#sk2'))))))))),
% 73.53/12.70 inference('rw', [status(thm)],
% 73.53/12.70 [zip_derived_cl457, '8', '9', '10', '11', '2', '2', '3', '3',
% 73.53/12.70 '4', '4', '5', '5', '6', '12', '13'])).
% 73.53/12.70 thf(zip_derived_cl460, plain,
% 73.53/12.70 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#B') @ (((=>) @ (imp @
% 73.53/12.70 (imp @
% 73.53/12.70 (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 73.53/12.70 (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 73.53/12.70 (ap @ '#sk3' @ n_2t)))) @
% 73.53/12.70 ($false)) @
% 73.53/12.70 (n_is @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 73.53/12.70 (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 73.53/12.70 (ap @ '#sk2' @ n_2t)))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ (=>) @ (lessf @ '#sk3'))) @ (lessf @ '#sk2'))))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl458])).
% 73.53/12.70 thf(zip_derived_cl461, plain,
% 73.53/12.70 (~ (((!!) @ (^[Y0 : $i]:
% 73.53/12.70 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.70 ((('#B') @ (((=>) @ (imp @
% 73.53/12.70 (imp @
% 73.53/12.70 (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 73.53/12.70 (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 73.53/12.70 (ap @ '#sk3' @ n_2t)))) @
% 73.53/12.70 ($false)) @
% 73.53/12.70 (n_is @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 73.53/12.70 (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 73.53/12.70 (ap @ '#sk2' @ n_2t)))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ (=>) @ (lessf @ '#sk3'))) @
% 73.53/12.70 (lessf @ '#sk2'))) @
% 73.53/12.70 Y0)))))))),
% 73.53/12.70 inference('rw_clause', [status(thm)], [zip_derived_cl460, '7'])).
% 73.53/12.70 thf(zip_derived_cl462, plain,
% 73.53/12.70 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.53/12.70 ((('#C') @ is_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))))))) @
% 73.53/12.70 ((('#B') @ (((=>) @ (imp @
% 73.53/12.70 (imp @
% 73.53/12.70 (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 73.53/12.70 (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 73.53/12.70 (ap @ '#sk3' @ n_2t)))) @
% 73.53/12.70 ($false)) @
% 73.53/12.70 (n_is @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 73.53/12.70 (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 73.53/12.70 (ap @ '#sk2' @ n_2t)))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ (=>) @ (lessf @ '#sk3'))) @
% 73.53/12.70 (lessf @ '#sk2')))))))))),
% 73.53/12.70 inference('comb-normalize', [status(thm)], [zip_derived_cl461])).
% 73.53/12.70 thf(zip_derived_cl463, plain,
% 73.53/12.70 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.70 (((imp @
% 73.53/12.70 (imp @
% 73.53/12.70 (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) @
% 73.53/12.70 ($false)) @
% 73.53/12.70 (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) =>
% 73.53/12.70 (((lessf @ '#sk3' @ '#sk4') => (lessf @ '#sk2' @ '#sk4')))))))),
% 73.53/12.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl462])).
% 73.53/12.70 thf(zip_derived_cl464, plain,
% 73.53/12.70 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.70 (((imp @
% 73.53/12.70 (imp @
% 73.53/12.70 (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) @
% 73.53/12.70 ($false)) @
% 73.53/12.70 (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) =>
% 73.53/12.70 (((l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) =>
% 73.53/12.70 (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))))))),
% 73.53/12.70 inference('rw', [status(thm)],
% 73.53/12.70 [zip_derived_cl463, '10', '10', '11', '11', '2', '2', '2',
% 73.53/12.70 '3', '3', '3', '4', '4', '4', '5', '5', '5', '12', '12'])).
% 73.53/12.70 thf(zip_derived_cl465, plain,
% 73.53/12.70 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl464])).
% 73.53/12.70 thf(zip_derived_cl12099, plain,
% 73.53/12.70 ( (is_of @ '#sk4' @ ('#ty_enc5' @ in @ (pair1type @ nat)))),
% 73.53/12.70 inference('remove_ty_args', [status(thm)], [zip_derived_cl465])).
% 73.53/12.70 thf(zip_derived_cl466, plain,
% 73.53/12.70 (~ (((imp @
% 73.53/12.70 (imp @
% 73.53/12.70 (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) @
% 73.53/12.70 ($false)) @
% 73.53/12.70 (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) =>
% 73.53/12.70 (((l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) =>
% 73.53/12.70 (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl464])).
% 73.53/12.70 thf(zip_derived_cl468, plain,
% 73.53/12.70 (~ (((l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) =>
% 73.53/12.70 (l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl466])).
% 73.53/12.70 thf(zip_derived_cl470, plain,
% 73.53/12.70 ( (l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl468])).
% 73.53/12.70 thf(zip_derived_cl459, plain,
% 73.53/12.70 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl458])).
% 73.53/12.70 thf(zip_derived_cl12098, plain,
% 73.53/12.70 ( (is_of @ '#sk3' @ ('#ty_enc5' @ in @ (pair1type @ nat)))),
% 73.53/12.70 inference('remove_ty_args', [status(thm)], [zip_derived_cl459])).
% 73.53/12.70 thf(zip_derived_cl453, plain,
% 73.53/12.70 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl452])).
% 73.53/12.70 thf(zip_derived_cl12097, plain,
% 73.53/12.70 ( (is_of @ '#sk2' @ ('#ty_enc5' @ in @ (pair1type @ nat)))),
% 73.53/12.70 inference('remove_ty_args', [status(thm)], [zip_derived_cl453])).
% 73.53/12.70 thf(zip_derived_cl467, plain,
% 73.53/12.70 ( (imp @
% 73.53/12.70 (imp @
% 73.53/12.70 (l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) @
% 73.53/12.70 ($false)) @
% 73.53/12.70 (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl466])).
% 73.53/12.70 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 73.53/12.70 thf('14', plain,
% 73.53/12.70 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 73.53/12.70 inference('rw.lit', [status(esa)], [def_imp])).
% 73.53/12.70 thf(zip_derived_cl469, plain,
% 73.53/12.70 ( (((imp @
% 73.53/12.70 (l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) @
% 73.53/12.70 ($false)) => (n_is @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))))),
% 73.53/12.70 inference('rw_clause', [status(thm)], [zip_derived_cl467, '14'])).
% 73.53/12.70 thf(zip_derived_cl472, plain,
% 73.53/12.70 ((~ (imp @
% 73.53/12.70 (l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) @
% 73.53/12.70 ($false))
% 73.53/12.70 | (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl469])).
% 73.53/12.70 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 73.53/12.70 thf('15', plain,
% 73.53/12.70 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 73.53/12.70 inference('rw.lit', [status(esa)], [def_imp])).
% 73.53/12.70 thf(zip_derived_cl473, plain,
% 73.53/12.70 ((~ (((l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) =>
% 73.53/12.70 ($false)))
% 73.53/12.70 | (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))),
% 73.53/12.70 inference('rw_clause', [status(thm)], [zip_derived_cl472, '15'])).
% 73.53/12.70 thf(zip_derived_cl474, plain,
% 73.53/12.70 ((~ (((~) @ (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t))))))
% 73.53/12.70 | (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))),
% 73.53/12.70 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl473])).
% 73.53/12.70 thf(zip_derived_cl475, plain,
% 73.53/12.70 (( (l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t))))
% 73.53/12.70 | (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))),
% 73.53/12.70 inference('simplify nested equalities', [status(thm)],
% 73.53/12.70 [zip_derived_cl474])).
% 73.53/12.70 thf(zip_derived_cl471, plain,
% 73.53/12.70 (~ (l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl468])).
% 73.53/12.70 thf(satz38, axiom,
% 73.53/12.70 (all_of @
% 73.53/12.70 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 73.53/12.70 ( ^[X0:$i]:
% 73.53/12.70 ( all_of @
% 73.53/12.70 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 73.53/12.70 ( ^[X1:$i]: ( ( n_eq @ X0 @ X1 ) => ( n_eq @ X1 @ X0 ) ) ) ) ))).
% 73.53/12.70 thf(zip_derived_cl240, plain,
% 73.53/12.70 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 73.53/12.70 (^[Y0 : $i]:
% 73.53/12.70 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 73.53/12.70 (^[Y1 : $i]: (((n_eq @ Y0 @ Y1) => (n_eq @ Y1 @ Y0)))))))),
% 73.53/12.70 inference('cnf', [status(esa)], [satz38])).
% 73.53/12.70 thf(zip_derived_cl241, plain,
% 73.53/12.70 ( (all_of @ ((('#C') @ in @ frac)) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#S') @ ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 73.53/12.70 ((('#C') @ n_eq)))))))),
% 73.53/12.70 inference('lams2combs', [status(thm)], [zip_derived_cl240])).
% 73.53/12.70 thf(zip_derived_cl549, plain,
% 73.53/12.70 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#S') @ ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 73.53/12.70 ((('#C') @ n_eq)))))))),
% 73.53/12.70 inference('rw', [status(thm)], [zip_derived_cl241, '0'])).
% 73.53/12.70 thf(zip_derived_cl550, plain,
% 73.53/12.70 ( (((!!) @ (^[Y0 : $i]:
% 73.53/12.70 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 73.53/12.70 ((('#C') @ n_eq)))) @
% 73.53/12.70 Y0)))))))),
% 73.53/12.70 inference('rw_clause', [status(thm)], [zip_derived_cl549, '1'])).
% 73.53/12.70 thf(zip_derived_cl551, plain,
% 73.53/12.70 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.53/12.70 ((('#C') @ is_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))))))) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 73.53/12.70 ((('#C') @ n_eq))))))))))),
% 73.53/12.70 inference('comb-normalize', [status(thm)], [zip_derived_cl550])).
% 73.53/12.70 thf(zip_derived_cl552, plain,
% 73.53/12.70 (![X2 : $i]:
% 73.53/12.70 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ ((('#C') @ n_eq @ X2)))))))),
% 73.53/12.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl551])).
% 73.53/12.70 thf(zip_derived_cl553, plain,
% 73.53/12.70 (![X2 : $i]:
% 73.53/12.70 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @
% 73.53/12.70 ((('#C') @ n_eq @ X2))))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl552])).
% 73.53/12.70 thf(zip_derived_cl554, plain,
% 73.53/12.70 (![X0 : $i]:
% 73.53/12.70 ( (((!!) @ (^[Y0 : $i]:
% 73.53/12.70 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.70 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @
% 73.53/12.70 ((('#C') @ n_eq @ X0)) @ Y0)))))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('rw_clause', [status(thm)], [zip_derived_cl553, '1'])).
% 73.53/12.70 thf(zip_derived_cl555, plain,
% 73.53/12.70 (![X0 : $i]:
% 73.53/12.70 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.53/12.70 ((('#C') @ is_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @
% 73.53/12.70 ((('#C') @ n_eq @ X0))))))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('comb-normalize', [status(thm)], [zip_derived_cl554])).
% 73.53/12.70 thf(zip_derived_cl556, plain,
% 73.53/12.70 (![X0 : $i, X2 : $i]:
% 73.53/12.70 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.70 (((n_eq @ X0 @ X2) => (n_eq @ X2 @ X0)))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl555])).
% 73.53/12.70 thf(zip_derived_cl557, plain,
% 73.53/12.70 (![X0 : $i, X2 : $i]:
% 73.53/12.70 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.70 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) => (n_is @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('rw', [status(thm)],
% 73.53/12.70 [zip_derived_cl556, '2', '2', '3', '3', '4', '4', '5', '5',
% 73.53/12.70 '6', '6'])).
% 73.53/12.70 thf(zip_derived_cl558, plain,
% 73.53/12.70 (![X0 : $i, X2 : $i]:
% 73.53/12.70 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) => (n_is @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl557])).
% 73.53/12.70 thf(zip_derived_cl559, plain,
% 73.53/12.70 (![X0 : $i, X2 : $i]:
% 73.53/12.70 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))
% 73.53/12.70 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl558])).
% 73.53/12.70 thf(zip_derived_cl12104, plain,
% 73.53/12.70 (![X0 : $i, X2 : $i]:
% 73.53/12.70 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))
% 73.53/12.70 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))
% 73.53/12.70 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 73.53/12.70 | ~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat))))),
% 73.53/12.70 inference('remove_ty_args', [status(thm)], [zip_derived_cl559])).
% 73.53/12.70 thf(satz45, axiom,
% 73.53/12.70 (all_of @
% 73.53/12.70 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 73.53/12.70 ( ^[X0:$i]:
% 73.53/12.70 ( all_of @
% 73.53/12.70 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 73.53/12.70 ( ^[X1:$i]:
% 73.53/12.70 ( all_of @
% 73.53/12.70 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 73.53/12.70 ( ^[X2:$i]:
% 73.53/12.70 ( all_of @
% 73.53/12.70 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 73.53/12.70 ( ^[X3:$i]:
% 73.53/12.70 ( ( lessf @ X0 @ X1 ) =>
% 73.53/12.70 ( ( n_eq @ X0 @ X2 ) =>
% 73.53/12.70 ( ( n_eq @ X1 @ X3 ) => ( lessf @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 73.53/12.70 thf(zip_derived_cl264, plain,
% 73.53/12.70 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 73.53/12.70 (^[Y0 : $i]:
% 73.53/12.70 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 73.53/12.70 (^[Y1 : $i]:
% 73.53/12.70 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 73.53/12.70 (^[Y2 : $i]:
% 73.53/12.70 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 73.53/12.70 (^[Y3 : $i]:
% 73.53/12.70 (((lessf @ Y0 @ Y1) =>
% 73.53/12.70 (((n_eq @ Y0 @ Y2) =>
% 73.53/12.70 (((n_eq @ Y1 @ Y3) => (lessf @ Y2 @ Y3)))))))))))))))),
% 73.53/12.70 inference('cnf', [status(esa)], [satz45])).
% 73.53/12.70 thf(zip_derived_cl265, plain,
% 73.53/12.70 ( (all_of @ ((('#C') @ in @ frac)) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @
% 73.53/12.70 ((('#C') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 73.53/12.70 ((('#C') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 73.53/12.70 lessf)))))))))))))),
% 73.53/12.70 inference('lams2combs', [status(thm)], [zip_derived_cl264])).
% 73.53/12.70 thf(zip_derived_cl2626, plain,
% 73.53/12.70 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 73.53/12.70 ((('#C') @ in @
% 73.53/12.70 (pair1type @ nat)))))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @
% 73.53/12.70 ((('#C') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 73.53/12.70 ((('#C') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 73.53/12.70 lessf)))))))))))))),
% 73.53/12.70 inference('rw', [status(thm)], [zip_derived_cl265, '0'])).
% 73.53/12.70 thf(zip_derived_cl2627, plain,
% 73.53/12.70 ( (((!!) @ (^[Y0 : $i]:
% 73.53/12.70 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (all_of @
% 73.53/12.70 ((('#C') @ in @
% 73.53/12.70 (pair1type @ nat)))))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 73.53/12.70 ((('#C') @ in @
% 73.53/12.70 (pair1type @ nat)))))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @
% 73.53/12.70 lessf)))))))) @
% 73.53/12.70 ((('#C') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @
% 73.53/12.70 n_eq)))))))) @
% 73.53/12.70 ((('#C') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @
% 73.53/12.70 n_eq)))))) @
% 73.53/12.70 lessf)))))))))) @
% 73.53/12.70 Y0)))))))),
% 73.53/12.70 inference('rw_clause', [status(thm)], [zip_derived_cl2626, '1'])).
% 73.53/12.70 thf(zip_derived_cl2628, plain,
% 73.53/12.70 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.53/12.70 ((('#C') @ is_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))))))) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (all_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat)))))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 73.53/12.70 ((('#C') @ in @
% 73.53/12.70 (pair1type @ nat)))))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @
% 73.53/12.70 ((('#C') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 73.53/12.70 ((('#C') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 73.53/12.70 lessf))))))))))))))))),
% 73.53/12.70 inference('comb-normalize', [status(thm)], [zip_derived_cl2627])).
% 73.53/12.70 thf(zip_derived_cl2629, plain,
% 73.53/12.70 (![X2 : $i]:
% 73.53/12.70 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (all_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat)))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ (=>) @ (lessf @ X2))))))) @
% 73.53/12.70 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ (=>) @ (n_eq @ X2))))))) @
% 73.53/12.70 ((('#C') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 73.53/12.70 lessf)))))))))))))),
% 73.53/12.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2628])).
% 73.53/12.70 thf(zip_derived_cl2630, plain,
% 73.53/12.70 (![X2 : $i]:
% 73.53/12.70 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (all_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat)))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ (=>) @ (lessf @ X2))))))) @
% 73.53/12.70 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ (=>) @ (n_eq @ X2))))))) @
% 73.53/12.70 ((('#C') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 73.53/12.70 lessf))))))))))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2629])).
% 73.53/12.70 thf(zip_derived_cl2631, plain,
% 73.53/12.70 (![X0 : $i]:
% 73.53/12.70 ( (((!!) @ (^[Y0 : $i]:
% 73.53/12.70 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.70 ((('#B') @ (all_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (all_of @
% 73.53/12.70 ((('#C') @ in @
% 73.53/12.70 (pair1type @ nat)))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ (=>) @ (lessf @ X0))))))) @
% 73.53/12.70 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ (=>) @
% 73.53/12.70 (n_eq @ X0))))))) @
% 73.53/12.70 ((('#C') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @
% 73.53/12.70 n_eq)))))) @
% 73.53/12.70 lessf)))))))) @
% 73.53/12.70 Y0)))))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('rw_clause', [status(thm)], [zip_derived_cl2630, '1'])).
% 73.53/12.70 thf(zip_derived_cl2632, plain,
% 73.53/12.70 (![X0 : $i]:
% 73.53/12.70 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.53/12.70 ((('#C') @ is_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))))))) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (all_of @
% 73.53/12.70 ((('#C') @ in @
% 73.53/12.70 (pair1type @ nat)))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ (=>) @ (lessf @ X0))))))) @
% 73.53/12.70 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ (=>) @
% 73.53/12.70 (n_eq @ X0))))))) @
% 73.53/12.70 ((('#C') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ ('#S') @
% 73.53/12.70 ((('#B') @ ((('#B') @ (=>))) @
% 73.53/12.70 n_eq)))))) @
% 73.53/12.70 lessf))))))))))))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('comb-normalize', [status(thm)], [zip_derived_cl2631])).
% 73.53/12.70 thf(zip_derived_cl2633, plain,
% 73.53/12.70 (![X0 : $i, X2 : $i]:
% 73.53/12.70 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (((=>) @ (lessf @ X0 @ X2))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 73.53/12.70 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @
% 73.53/12.70 lessf)))))))))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2632])).
% 73.53/12.70 thf(zip_derived_cl2634, plain,
% 73.53/12.70 (![X0 : $i, X2 : $i]:
% 73.53/12.70 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @
% 73.53/12.70 (ap @ X0 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X0 @ n_1t) @
% 73.53/12.70 (ap @ X2 @ n_2t)))))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 73.53/12.70 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @
% 73.53/12.70 lessf)))))))))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('rw', [status(thm)],
% 73.53/12.70 [zip_derived_cl2633, '10', '11', '2', '2', '3', '3', '4', '4',
% 73.53/12.70 '5', '5', '12'])).
% 73.53/12.70 thf(zip_derived_cl2635, plain,
% 73.53/12.70 (![X0 : $i, X2 : $i]:
% 73.53/12.70 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @
% 73.53/12.70 (ap @ X0 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X0 @ n_1t) @
% 73.53/12.70 (ap @ X2 @ n_2t)))))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 73.53/12.70 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @
% 73.53/12.70 lessf)))))))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2634])).
% 73.53/12.70 thf(zip_derived_cl2636, plain,
% 73.53/12.70 (![X0 : $i, X1 : $i]:
% 73.53/12.70 ( (((!!) @ (^[Y0 : $i]:
% 73.53/12.70 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.70 ((('#B') @ (all_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @
% 73.53/12.70 (ap @ X1 @ n_1t) @
% 73.53/12.70 (ap @ X0 @ n_2t)) @
% 73.53/12.70 (n_ts @
% 73.53/12.70 (ap @ X0 @ n_1t) @
% 73.53/12.70 (ap @ X1 @ n_2t)))))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 73.53/12.70 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 73.53/12.70 (n_eq @ X1))))) @
% 73.53/12.70 lessf)))))) @
% 73.53/12.70 Y0)))))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('rw_clause', [status(thm)], [zip_derived_cl2635, '1'])).
% 73.53/12.70 thf(zip_derived_cl2637, plain,
% 73.53/12.70 (![X0 : $i, X1 : $i]:
% 73.53/12.70 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.53/12.70 ((('#C') @ is_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))))))) @
% 73.53/12.70 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.70 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @
% 73.53/12.70 (ap @ X1 @ n_1t) @
% 73.53/12.70 (ap @ X0 @ n_2t)) @
% 73.53/12.70 (n_ts @
% 73.53/12.70 (ap @ X0 @ n_1t) @
% 73.53/12.70 (ap @ X1 @ n_2t)))))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.70 ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 73.53/12.70 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))))) @
% 73.53/12.70 lessf))))))))))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('comb-normalize', [status(thm)], [zip_derived_cl2636])).
% 73.53/12.70 thf(zip_derived_cl2638, plain,
% 73.53/12.70 (![X0 : $i, X1 : $i, X3 : $i]:
% 73.53/12.70 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#B') @ (((=>) @ (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) @
% 73.53/12.70 ((('#B') @ (((=>) @ (n_eq @ X0 @ X3))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (lessf @ X3))))))))))
% 73.53/12.70 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2637])).
% 73.53/12.70 thf(zip_derived_cl2639, plain,
% 73.53/12.70 (![X0 : $i, X1 : $i, X3 : $i]:
% 73.53/12.70 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#B') @ (((=>) @ (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) @
% 73.53/12.70 ((('#B') @ (((=>) @ (n_is @
% 73.53/12.70 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (lessf @ X3))))))))))
% 73.53/12.70 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('rw', [status(thm)],
% 73.53/12.70 [zip_derived_cl2638, '2', '2', '3', '3', '4', '4', '5', '5',
% 73.53/12.70 '6'])).
% 73.53/12.70 thf(zip_derived_cl2640, plain,
% 73.53/12.70 (![X0 : $i, X1 : $i, X3 : $i]:
% 73.53/12.70 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.70 ((('#B') @ (((=>) @ (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) @
% 73.53/12.70 ((('#B') @ (((=>) @ (n_is @
% 73.53/12.70 (n_ts @ (ap @ X0 @ n_1t) @
% 73.53/12.70 (ap @ X3 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X3 @ n_1t) @
% 73.53/12.70 (ap @ X0 @ n_2t))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (lessf @ X3))))))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2639])).
% 73.53/12.70 thf(zip_derived_cl2641, plain,
% 73.53/12.70 (![X0 : $i, X1 : $i, X2 : $i]:
% 73.53/12.70 ( (((!!) @ (^[Y0 : $i]:
% 73.53/12.70 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.70 ((('#B') @ (((=>) @ (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ X0 @ n_1t) @
% 73.53/12.70 (ap @ X1 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X1 @ n_1t) @
% 73.53/12.70 (ap @ X0 @ n_2t)))))) @
% 73.53/12.70 ((('#B') @ (((=>) @ (n_is @
% 73.53/12.70 (n_ts @ (ap @ X1 @ n_1t) @
% 73.53/12.70 (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @
% 73.53/12.70 (ap @ X1 @ n_2t))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @
% 73.53/12.70 (lessf @ X2))))) @
% 73.53/12.70 Y0)))))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('rw_clause', [status(thm)], [zip_derived_cl2640, '1'])).
% 73.53/12.70 thf(zip_derived_cl2642, plain,
% 73.53/12.70 (![X0 : $i, X1 : $i, X2 : $i]:
% 73.53/12.70 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.53/12.70 ((('#C') @ is_of @
% 73.53/12.70 ((('#C') @ in @ (pair1type @ nat))))))) @
% 73.53/12.70 ((('#B') @ (((=>) @ (l_some @ nat @
% 73.53/12.70 (diffprop @
% 73.53/12.70 (n_ts @ (ap @ X0 @ n_1t) @
% 73.53/12.70 (ap @ X1 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X1 @ n_1t) @
% 73.53/12.70 (ap @ X0 @ n_2t)))))) @
% 73.53/12.70 ((('#B') @ (((=>) @ (n_is @
% 73.53/12.70 (n_ts @ (ap @ X1 @ n_1t) @
% 73.53/12.70 (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @
% 73.53/12.70 (ap @ X1 @ n_2t))))) @
% 73.53/12.70 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @
% 73.53/12.70 (lessf @ X2)))))))))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('comb-normalize', [status(thm)], [zip_derived_cl2641])).
% 73.53/12.70 thf(zip_derived_cl2643, plain,
% 73.53/12.70 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 73.53/12.70 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.70 (((l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) =>
% 73.53/12.70 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) =>
% 73.53/12.70 (((n_eq @ X0 @ X4) => (lessf @ X2 @ X4)))))))))
% 73.53/12.70 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2642])).
% 73.53/12.70 thf(zip_derived_cl2644, plain,
% 73.53/12.70 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 73.53/12.70 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.70 (((l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) =>
% 73.53/12.70 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) =>
% 73.53/12.70 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @
% 73.53/12.70 nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t))))))))))))
% 73.53/12.70 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('rw', [status(thm)],
% 73.53/12.70 [zip_derived_cl2643, '10', '11', '2', '2', '2', '3', '3', '3',
% 73.53/12.70 '4', '4', '4', '5', '5', '5', '6', '12'])).
% 73.53/12.70 thf(zip_derived_cl2645, plain,
% 73.53/12.70 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 73.53/12.70 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | (((l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) =>
% 73.53/12.70 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) =>
% 73.53/12.70 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @
% 73.53/12.70 nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t))))))))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2644])).
% 73.53/12.70 thf(zip_derived_cl2646, plain,
% 73.53/12.70 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 73.53/12.70 (~ (l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))))
% 73.53/12.70 | (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) =>
% 73.53/12.70 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @
% 73.53/12.70 nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t))))))))
% 73.53/12.70 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2645])).
% 73.53/12.70 thf(zip_derived_cl2647, plain,
% 73.53/12.70 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 73.53/12.70 (~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t)))
% 73.53/12.70 | (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @
% 73.53/12.70 nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t))))))
% 73.53/12.70 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2646])).
% 73.53/12.70 thf(zip_derived_cl2648, plain,
% 73.53/12.70 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 73.53/12.70 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t)))
% 73.53/12.70 | (l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t))))
% 73.53/12.70 | ~ (l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))))
% 73.53/12.70 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.70 | ~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))))),
% 73.53/12.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2647])).
% 73.53/12.70 thf(zip_derived_cl12177, plain,
% 73.53/12.70 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 73.53/12.70 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t)))
% 73.53/12.70 | (l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t))))
% 73.53/12.70 | ~ (l_some @ nat @
% 73.53/12.70 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))))
% 73.53/12.70 | ~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 73.53/12.70 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 73.53/12.70 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 73.53/12.70 | ~ (is_of @ X4 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 73.53/12.70 | ~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 73.53/12.70 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))))),
% 73.53/12.70 inference('remove_ty_args', [status(thm)], [zip_derived_cl2648])).
% 73.53/12.70 thf(satz50, axiom,
% 73.53/12.70 (all_of @
% 73.53/12.70 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 73.53/12.70 ( ^[X0:$i]:
% 73.53/12.70 ( all_of @
% 73.53/12.70 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 73.53/12.70 ( ^[X1:$i]:
% 73.53/12.70 ( all_of @
% 73.53/12.70 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 73.53/12.71 ( ^[X2:$i]:
% 73.53/12.71 ( ( lessf @ X0 @ X1 ) =>
% 73.53/12.71 ( ( lessf @ X1 @ X2 ) => ( lessf @ X0 @ X2 ) ) ) ) ) ) ) ))).
% 73.53/12.71 thf(zip_derived_cl290, plain,
% 73.53/12.71 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 73.53/12.71 (^[Y0 : $i]:
% 73.53/12.71 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 73.53/12.71 (^[Y1 : $i]:
% 73.53/12.71 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 73.53/12.71 (^[Y2 : $i]:
% 73.53/12.71 (((lessf @ Y0 @ Y1) =>
% 73.53/12.71 (((lessf @ Y1 @ Y2) => (lessf @ Y0 @ Y2)))))))))))),
% 73.53/12.71 inference('cnf', [status(esa)], [satz50])).
% 73.53/12.71 thf(zip_derived_cl291, plain,
% 73.53/12.71 ( (all_of @ ((('#C') @ in @ frac)) @
% 73.53/12.71 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 73.53/12.71 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 73.53/12.71 ((('#S') @ ((('#B') @ ('#S') @
% 73.53/12.71 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.71 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @
% 73.53/12.71 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @
% 73.53/12.71 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @
% 73.53/12.71 lessf)))))))))),
% 73.53/12.71 inference('lams2combs', [status(thm)], [zip_derived_cl290])).
% 73.53/12.71 thf(zip_derived_cl1309, plain,
% 73.53/12.71 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.71 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.71 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 73.53/12.71 ((('#S') @ ((('#B') @ ('#S') @
% 73.53/12.71 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.71 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @
% 73.53/12.71 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @
% 73.53/12.71 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @
% 73.53/12.71 lessf)))))))))),
% 73.53/12.71 inference('rw', [status(thm)], [zip_derived_cl291, '0'])).
% 73.53/12.71 thf(zip_derived_cl1310, plain,
% 73.53/12.71 ( (((!!) @ (^[Y0 : $i]:
% 73.53/12.71 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.71 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.71 ((('#B') @ ((('#B') @ (all_of @
% 73.53/12.71 ((('#C') @ in @
% 73.53/12.71 (pair1type @ nat)))))) @
% 73.53/12.71 ((('#S') @ ((('#B') @ ('#S') @
% 73.53/12.71 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.71 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @
% 73.53/12.71 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @
% 73.53/12.71 ((('#B') @ ((('#B') @ (=>))) @
% 73.53/12.71 lessf)))))) @
% 73.53/12.71 lessf)))))) @
% 73.53/12.71 Y0)))))))),
% 73.53/12.71 inference('rw_clause', [status(thm)], [zip_derived_cl1309, '1'])).
% 73.53/12.71 thf(zip_derived_cl1311, plain,
% 73.53/12.71 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.53/12.71 ((('#C') @ is_of @
% 73.53/12.71 ((('#C') @ in @ (pair1type @ nat))))))) @
% 73.53/12.71 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.71 ((('#B') @ ((('#B') @ (all_of @
% 73.53/12.71 ((('#C') @ in @ (pair1type @ nat)))))) @
% 73.53/12.71 ((('#S') @ ((('#B') @ ('#S') @
% 73.53/12.71 ((('#B') @ ((('#B') @ ('#B'))) @
% 73.53/12.71 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @
% 73.53/12.71 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @
% 73.53/12.71 ((('#B') @ ((('#B') @ (=>))) @
% 73.53/12.71 lessf)))))) @
% 73.53/12.71 lessf))))))))))))),
% 73.53/12.71 inference('comb-normalize', [status(thm)], [zip_derived_cl1310])).
% 73.53/12.71 thf(zip_derived_cl1312, plain,
% 73.53/12.71 (![X2 : $i]:
% 73.53/12.71 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 73.53/12.71 ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.71 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.71 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (lessf @ X2))))) @
% 73.53/12.71 ((('#C') @ ((('#B') @ ('#S') @
% 73.53/12.71 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @
% 73.53/12.71 (lessf @ X2))))))))))),
% 73.53/12.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1311])).
% 73.53/12.71 thf(zip_derived_cl1313, plain,
% 73.53/12.71 (![X2 : $i]:
% 73.53/12.71 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.71 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.71 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.71 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (lessf @ X2))))) @
% 73.53/12.71 ((('#C') @ ((('#B') @ ('#S') @
% 73.53/12.71 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @
% 73.53/12.71 (lessf @ X2)))))))))),
% 73.53/12.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1312])).
% 73.53/12.71 thf(zip_derived_cl1314, plain,
% 73.53/12.71 (![X0 : $i]:
% 73.53/12.71 ( (((!!) @ (^[Y0 : $i]:
% 73.53/12.71 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.71 ((('#B') @ (all_of @
% 73.53/12.71 ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.71 ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.71 ((('#B') @ (=>) @ (lessf @ X0))))) @
% 73.53/12.71 ((('#C') @ ((('#B') @ ('#S') @
% 73.53/12.71 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @
% 73.53/12.71 (lessf @ X0))))) @
% 73.53/12.71 Y0)))))))
% 73.53/12.71 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.71 inference('rw_clause', [status(thm)], [zip_derived_cl1313, '1'])).
% 73.53/12.71 thf(zip_derived_cl1315, plain,
% 73.53/12.71 (![X0 : $i]:
% 73.53/12.71 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.53/12.71 ((('#C') @ is_of @
% 73.53/12.71 ((('#C') @ in @ (pair1type @ nat))))))) @
% 73.53/12.71 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 73.53/12.71 ((('#S') @ ((('#B') @ ('#B') @
% 73.53/12.71 ((('#B') @ (=>) @ (lessf @ X0))))) @
% 73.53/12.71 ((('#C') @ ((('#B') @ ('#S') @
% 73.53/12.71 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @
% 73.53/12.71 (lessf @ X0)))))))))))
% 73.53/12.71 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.71 inference('comb-normalize', [status(thm)], [zip_derived_cl1314])).
% 73.53/12.71 thf(zip_derived_cl1316, plain,
% 73.53/12.71 (![X0 : $i, X2 : $i]:
% 73.53/12.71 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 73.53/12.71 ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.71 ((('#B') @ (((=>) @ (lessf @ X0 @ X2))) @
% 73.53/12.71 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @ (lessf @ X0))))))))
% 73.53/12.71 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1315])).
% 73.53/12.71 thf(zip_derived_cl1317, plain,
% 73.53/12.71 (![X0 : $i, X2 : $i]:
% 73.53/12.71 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 73.53/12.71 ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.71 ((('#B') @ (((=>) @ (l_some @ nat @
% 73.53/12.71 (diffprop @
% 73.53/12.71 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))))) @
% 73.53/12.71 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @ (lessf @ X0))))))))
% 73.53/12.71 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.71 inference('rw', [status(thm)],
% 73.53/12.71 [zip_derived_cl1316, '10', '11', '2', '2', '3', '3', '4', '4',
% 73.53/12.71 '5', '5', '12'])).
% 73.53/12.71 thf(zip_derived_cl1318, plain,
% 73.53/12.71 (![X0 : $i, X2 : $i]:
% 73.53/12.71 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.71 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 73.53/12.71 ((('#B') @ (((=>) @ (l_some @ nat @
% 73.53/12.71 (diffprop @
% 73.53/12.71 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))))) @
% 73.53/12.71 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @ (lessf @ X0))))))
% 73.53/12.71 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1317])).
% 73.53/12.71 thf(zip_derived_cl1319, plain,
% 73.53/12.71 (![X0 : $i, X1 : $i]:
% 73.53/12.71 ( (((!!) @ (^[Y0 : $i]:
% 73.53/12.71 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.71 ((('#B') @ (((=>) @ (l_some @ nat @
% 73.53/12.71 (diffprop @
% 73.53/12.71 (n_ts @ (ap @ X1 @ n_1t) @
% 73.53/12.71 (ap @ X0 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X0 @ n_1t) @
% 73.53/12.71 (ap @ X1 @ n_2t)))))) @
% 73.53/12.71 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X1))) @
% 73.53/12.71 (lessf @ X0))) @
% 73.53/12.71 Y0)))))))
% 73.53/12.71 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.71 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.71 inference('rw_clause', [status(thm)], [zip_derived_cl1318, '1'])).
% 73.53/12.71 thf(zip_derived_cl1320, plain,
% 73.53/12.71 (![X0 : $i, X1 : $i]:
% 73.53/12.71 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.53/12.71 ((('#C') @ is_of @
% 73.53/12.71 ((('#C') @ in @ (pair1type @ nat))))))) @
% 73.53/12.71 ((('#B') @ (((=>) @ (l_some @ nat @
% 73.53/12.71 (diffprop @
% 73.53/12.71 (n_ts @ (ap @ X1 @ n_1t) @
% 73.53/12.71 (ap @ X0 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X0 @ n_1t) @
% 73.53/12.71 (ap @ X1 @ n_2t)))))) @
% 73.53/12.71 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X1))) @
% 73.53/12.71 (lessf @ X0)))))))))
% 73.53/12.71 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.71 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.71 inference('comb-normalize', [status(thm)], [zip_derived_cl1319])).
% 73.53/12.71 thf(zip_derived_cl1321, plain,
% 73.53/12.71 (![X0 : $i, X1 : $i, X3 : $i]:
% 73.53/12.71 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.71 (((l_some @ nat @
% 73.53/12.71 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) =>
% 73.53/12.71 (((lessf @ X1 @ X3) => (lessf @ X0 @ X3)))))))
% 73.53/12.71 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.71 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1320])).
% 73.53/12.71 thf(zip_derived_cl1322, plain,
% 73.53/12.71 (![X0 : $i, X1 : $i, X3 : $i]:
% 73.53/12.71 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 73.53/12.71 (((l_some @ nat @
% 73.53/12.71 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) =>
% 73.53/12.71 (((l_some @ nat @
% 73.53/12.71 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)))) =>
% 73.53/12.71 (l_some @ nat @
% 73.53/12.71 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t))))))))))
% 73.53/12.71 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.71 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.71 inference('rw', [status(thm)],
% 73.53/12.71 [zip_derived_cl1321, '10', '10', '11', '11', '2', '2', '2',
% 73.53/12.71 '3', '3', '3', '4', '4', '4', '5', '5', '5', '12', '12'])).
% 73.53/12.71 thf(zip_derived_cl1323, plain,
% 73.53/12.71 (![X0 : $i, X1 : $i, X3 : $i]:
% 73.53/12.71 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.71 | (((l_some @ nat @
% 73.53/12.71 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) =>
% 73.53/12.71 (((l_some @ nat @
% 73.53/12.71 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)))) =>
% 73.53/12.71 (l_some @ nat @
% 73.53/12.71 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t))))))))
% 73.53/12.71 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.71 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1322])).
% 73.53/12.71 thf(zip_derived_cl1324, plain,
% 73.53/12.71 (![X0 : $i, X1 : $i, X3 : $i]:
% 73.53/12.71 (~ (l_some @ nat @
% 73.53/12.71 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t))))
% 73.53/12.71 | (((l_some @ nat @
% 73.53/12.71 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)))) =>
% 73.53/12.71 (l_some @ nat @
% 73.53/12.71 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t))))))
% 73.53/12.71 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.71 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.71 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 73.53/12.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1323])).
% 73.53/12.71 thf(zip_derived_cl1325, plain,
% 73.53/12.71 (![X0 : $i, X1 : $i, X3 : $i]:
% 73.53/12.71 (~ (l_some @ nat @
% 73.53/12.71 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t))))
% 73.53/12.71 | (l_some @ nat @
% 73.53/12.71 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t))))
% 73.53/12.71 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.71 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.71 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 73.53/12.71 | ~ (l_some @ nat @
% 73.53/12.71 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))),
% 73.53/12.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1324])).
% 73.53/12.71 thf(zip_derived_cl12140, plain,
% 73.53/12.71 (![X0 : $i, X1 : $i, X3 : $i]:
% 73.53/12.71 (~ (l_some @ nat @
% 73.53/12.71 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t))))
% 73.53/12.71 | (l_some @ nat @
% 73.53/12.71 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t))))
% 73.53/12.71 | ~ (is_of @ X3 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 73.53/12.71 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 73.53/12.71 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 73.53/12.71 | ~ (l_some @ nat @
% 73.53/12.71 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 73.53/12.71 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))),
% 73.53/12.71 inference('remove_ty_args', [status(thm)], [zip_derived_cl1325])).
% 73.53/12.71 thf(zip_derived_cl12203, plain, ($false),
% 73.53/12.71 inference('eprover', [status(thm)],
% 73.53/12.71 [zip_derived_cl12084, zip_derived_cl12099, zip_derived_cl470,
% 73.53/12.71 zip_derived_cl12098, zip_derived_cl12097, zip_derived_cl475,
% 73.53/12.71 zip_derived_cl471, zip_derived_cl12104, zip_derived_cl12177,
% 73.53/12.71 zip_derived_cl12140])).
% 73.53/12.71
% 73.53/12.71 % SZS output end Refutation
% 73.53/12.71
% 73.53/12.71
% 73.87/12.73 % Terminating...
% 74.31/12.91 % Runner terminated.
% 74.31/12.92 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------