%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM738^4 : 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.zVdRYHdMlK true
% Computer : n003.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 04:48:10 PM UTC 2025
% Result : Theorem 76.89s 13.34s
% Output : Refutation 76.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM738^4 : TPTP v9.2.0. Released v7.1.0.
% 0.03/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.zVdRYHdMlK true
% 0.15/0.35 % Computer : n003.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Oct 1 16:43:23 EDT 2025
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.35 % Number of cores: 8
% 0.15/0.35 % Python version: Python 3.6.8
% 0.15/0.35 % Running in HO mode
% 0.58/0.69 % Total configuration time : 828
% 0.58/0.69 % Estimated wc time : 1656
% 0.58/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.60/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.60/0.79 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.60/0.79 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.60/0.80 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.60/0.81 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.60/0.82 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.60/0.84 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.61/0.87 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 76.89/13.34 % Solved by lams/40_b.comb.sh.
% 76.89/13.34 % done 423 iterations in 12.437s
% 76.89/13.34 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 76.89/13.34 % SZS output start Refutation
% 76.89/13.34 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
% 76.89/13.34 thf(n_1_type, type, n_1: $i).
% 76.89/13.34 thf(lessf_type, type, lessf: $i > $i > $o).
% 76.89/13.34 thf(nat_type, type, nat: $i).
% 76.89/13.34 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 76.89/13.34 thf(in_type, type, in: $i > $i > $o).
% 76.89/13.34 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 76.89/13.34 thf('#ty_enc6_type', type, '#ty_enc6': ($i > $i > $o) > $i > $i > $o).
% 76.89/13.34 thf('#sk2_type', type, '#sk2': $i).
% 76.89/13.34 thf(n_2_type, type, n_2: $i).
% 76.89/13.34 thf(ap_type, type, ap: $i > $i > $i).
% 76.89/13.34 thf('#sk3_type', type, '#sk3': $i).
% 76.89/13.34 thf(emptyset_type, type, emptyset: $i).
% 76.89/13.34 thf(n_is_type, type, n_is: $i > $i > $o).
% 76.89/13.34 thf(n_1t_type, type, n_1t: $i).
% 76.89/13.34 thf(frac_type, type, frac: $i).
% 76.89/13.34 thf(n_2t_type, type, n_2t: $i).
% 76.89/13.34 thf(n_ts_type, type, n_ts: $i > $i > $i).
% 76.89/13.34 thf(n_eq_type, type, n_eq: $i > $i > $o).
% 76.89/13.34 thf(pair1type_type, type, pair1type: $i > $i).
% 76.89/13.34 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 76.89/13.34 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 76.89/13.34 thf(num_type, type, num: $i > $i).
% 76.89/13.34 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 76.89/13.34 thf(ordsucc_type, type, ordsucc: $i > $i).
% 76.89/13.34 thf(moref_type, type, moref: $i > $i > $o).
% 76.89/13.34 thf(outn_type, type, outn: $i > $i > $i).
% 76.89/13.34 thf(first1_type, type, first1: $i > $i > $i).
% 76.89/13.34 thf(den_type, type, den: $i > $i).
% 76.89/13.34 thf('#sk5_type', type, '#sk5': $i).
% 76.89/13.34 thf('#sk4_type', type, '#sk4': $i).
% 76.89/13.34 thf(iii_type, type, iii: $i > $i > $o).
% 76.89/13.34 thf(second1_type, type, second1: $i > $i > $i).
% 76.89/13.34 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 76.89/13.34 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 76.89/13.34 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 76.89/13.34 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 76.89/13.34 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 76.89/13.34 thf(satz45, conjecture,
% 76.89/13.34 (all_of @
% 76.89/13.34 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 76.89/13.34 ( ^[X0:$i]:
% 76.89/13.34 ( all_of @
% 76.89/13.34 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 76.89/13.34 ( ^[X1:$i]:
% 76.89/13.34 ( all_of @
% 76.89/13.34 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 76.89/13.34 ( ^[X2:$i]:
% 76.89/13.34 ( all_of @
% 76.89/13.34 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 76.89/13.34 ( ^[X3:$i]:
% 76.89/13.34 ( ( lessf @ X0 @ X1 ) =>
% 76.89/13.34 ( ( n_eq @ X0 @ X2 ) =>
% 76.89/13.34 ( ( n_eq @ X1 @ X3 ) => ( lessf @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 76.89/13.34 thf(zf_stmt_0, negated_conjecture,
% 76.89/13.34 (~( all_of @
% 76.89/13.34 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 76.89/13.34 ( ^[X0:$i]:
% 76.89/13.34 ( all_of @
% 76.89/13.34 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 76.89/13.34 ( ^[X1:$i]:
% 76.89/13.34 ( all_of @
% 76.89/13.34 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 76.89/13.34 ( ^[X2:$i]:
% 76.89/13.34 ( all_of @
% 76.89/13.34 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 76.89/13.34 ( ^[X3:$i]:
% 76.89/13.34 ( ( lessf @ X0 @ X1 ) =>
% 76.89/13.34 ( ( n_eq @ X0 @ X2 ) =>
% 76.89/13.34 ( ( n_eq @ X1 @ X3 ) => ( lessf @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) )),
% 76.89/13.34 inference('cnf.neg', [status(esa)], [satz45])).
% 76.89/13.34 thf(zip_derived_cl283, plain,
% 76.89/13.34 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 76.89/13.34 (^[Y0 : $i]:
% 76.89/13.34 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 76.89/13.34 (^[Y1 : $i]:
% 76.89/13.34 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 76.89/13.34 (^[Y2 : $i]:
% 76.89/13.34 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 76.89/13.34 (^[Y3 : $i]:
% 76.89/13.34 (((lessf @ Y0 @ Y1) =>
% 76.89/13.34 (((n_eq @ Y0 @ Y2) =>
% 76.89/13.34 (((n_eq @ Y1 @ Y3) => (lessf @ Y2 @ Y3)))))))))))))))),
% 76.89/13.34 inference('cnf', [status(esa)], [zf_stmt_0])).
% 76.89/13.34 thf(zip_derived_cl284, plain,
% 76.89/13.34 (~ (all_of @ ((('#C') @ in @ frac)) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 76.89/13.34 lessf)))))))))))))),
% 76.89/13.34 inference('lams2combs', [status(thm)], [zip_derived_cl283])).
% 76.89/13.34 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))).
% 76.89/13.34 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])).
% 76.89/13.34 thf(zip_derived_cl1195, plain,
% 76.89/13.34 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @
% 76.89/13.34 (pair1type @ nat)))))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 76.89/13.34 lessf)))))))))))))),
% 76.89/13.34 inference('rw', [status(thm)], [zip_derived_cl284, '0'])).
% 76.89/13.34 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 76.89/13.34 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 76.89/13.34 thf('1', plain,
% 76.89/13.34 (![X0:( $i > $o ),X1:( $i > $o )]:
% 76.89/13.34 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 76.89/13.34 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 76.89/13.34 inference('rw.lit', [status(esa)], [def_all_of])).
% 76.89/13.34 thf(zip_derived_cl1196, plain,
% 76.89/13.34 (~ (((!!) @ (^[Y0 : $i]:
% 76.89/13.34 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @
% 76.89/13.34 (pair1type @ nat)))))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @
% 76.89/13.34 (pair1type @ nat)))))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @
% 76.89/13.34 lessf)))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @
% 76.89/13.34 n_eq)))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @
% 76.89/13.34 n_eq)))))) @
% 76.89/13.34 lessf)))))))))) @
% 76.89/13.34 Y0)))))))),
% 76.89/13.34 inference('rw_clause', [status(thm)], [zip_derived_cl1195, '1'])).
% 76.89/13.34 thf(zip_derived_cl1197, plain,
% 76.89/13.34 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 76.89/13.34 ((('#C') @ is_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))))))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat)))))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @
% 76.89/13.34 (pair1type @ nat)))))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @
% 76.89/13.34 n_eq)))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @
% 76.89/13.34 n_eq)))))) @
% 76.89/13.34 lessf))))))))))))))))),
% 76.89/13.34 inference('comb-normalize', [status(thm)], [zip_derived_cl1196])).
% 76.89/13.34 thf(zip_derived_cl1198, plain,
% 76.89/13.34 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat)))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (lessf @ '#sk2'))))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 76.89/13.34 lessf)))))))))))))),
% 76.89/13.34 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1197])).
% 76.89/13.34 thf(zip_derived_cl1200, plain,
% 76.89/13.34 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (lessf @ '#sk2'))))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 76.89/13.34 lessf)))))))))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1198])).
% 76.89/13.34 thf(zip_derived_cl1201, plain,
% 76.89/13.34 (~ (((!!) @ (^[Y0 : $i]:
% 76.89/13.34 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @
% 76.89/13.34 (pair1type @ nat)))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (lessf @ '#sk2'))))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @
% 76.89/13.34 (n_eq @ '#sk2'))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @
% 76.89/13.34 n_eq)))))) @
% 76.89/13.34 lessf)))))))) @
% 76.89/13.34 Y0)))))))),
% 76.89/13.34 inference('rw_clause', [status(thm)], [zip_derived_cl1200, '1'])).
% 76.89/13.34 thf(zip_derived_cl1202, plain,
% 76.89/13.34 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 76.89/13.34 ((('#C') @ is_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))))))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat)))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (lessf @ '#sk2'))))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @
% 76.89/13.34 (n_eq @ '#sk2'))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 76.89/13.34 lessf))))))))))))))),
% 76.89/13.34 inference('comb-normalize', [status(thm)], [zip_derived_cl1201])).
% 76.89/13.34 thf(zip_derived_cl1203, plain,
% 76.89/13.34 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (((=>) @ (lessf @ '#sk2' @ '#sk3'))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))))) @
% 76.89/13.34 lessf)))))))))))),
% 76.89/13.34 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1202])).
% 76.89/13.34 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 76.89/13.34 thf('2', plain,
% 76.89/13.34 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 76.89/13.34 define([status(thm)])).
% 76.89/13.34 thf(def_n_1, axiom,(( n_1 ) = ((ordsucc @ emptyset)))).
% 76.89/13.34 thf('3', plain, (( n_1 ) = ( ordsucc @ emptyset )), define([status(thm)])).
% 76.89/13.34 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))).
% 76.89/13.34 thf('4', plain,
% 76.89/13.34 (![X1:$i,X0:$i]:
% 76.89/13.34 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 76.89/13.34 define([status(thm)])).
% 76.89/13.34 thf(def_n_1t, axiom,(( n_1t ) = ((outn @ n_2 @ n_1)))).
% 76.89/13.34 thf('5', plain, (( n_1t ) = ( outn @ n_2 @ n_1 )), define([status(thm)])).
% 76.89/13.34 thf(def_n_2t, axiom,(( n_2t ) = ((outn @ n_2 @ n_2)))).
% 76.89/13.34 thf('6', plain, (( n_2t ) = ( outn @ n_2 @ n_2 )), define([status(thm)])).
% 76.89/13.34 thf(def_first1, axiom,(( first1 @ (X1)@ (X0)) = ((ap @ X0 @ n_1t)))).
% 76.89/13.34 thf('7', plain,
% 76.89/13.34 (![X1:$i,X0:$i]: ( ( first1 @ X1 @ X0 ) = ( ap @ X0 @ n_1t ) )),
% 76.89/13.34 define([status(thm)])).
% 76.89/13.34 thf(def_second1, axiom,(( second1 @ (X1)@ (X0)) = ((ap @ X0 @ n_2t)))).
% 76.89/13.34 thf('8', plain,
% 76.89/13.34 (![X1:$i,X0:$i]: ( ( second1 @ X1 @ X0 ) = ( ap @ X0 @ n_2t ) )),
% 76.89/13.34 define([status(thm)])).
% 76.89/13.34 thf(def_num, axiom,(( num @ (X0)) = ((first1 @ nat @ X0)))).
% 76.89/13.34 thf('9', plain, (![X0:$i]: ( ( num @ X0 ) = ( first1 @ nat @ X0 ) )),
% 76.89/13.34 define([status(thm)])).
% 76.89/13.34 thf(def_den, axiom,(( den @ (X0)) = ((second1 @ nat @ X0)))).
% 76.89/13.34 thf('10', plain, (![X0:$i]: ( ( den @ X0 ) = ( second1 @ nat @ X0 ) )),
% 76.89/13.34 define([status(thm)])).
% 76.89/13.34 thf(def_lessf, axiom,(( lessf @ (X0)@ (X1)) =
% 76.89/13.34 ((iii @ (n_ts @ (num @ X0) @ (den @ X1)) @ (n_ts @ (num @ X1) @ (den @ X0)))))).
% 76.89/13.34 thf('11', plain,
% 76.89/13.34 (![X1:$i,X0:$i]:
% 76.89/13.34 ( ( lessf @ X0 @ X1 ) =
% 76.89/13.34 ( iii @
% 76.89/13.34 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 76.89/13.34 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )),
% 76.89/13.34 define([status(thm)])).
% 76.89/13.34 thf(zip_derived_cl1204, plain,
% 76.89/13.34 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk3' @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @
% 76.89/13.34 (outn @ n_2 @ n_2))))))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))))) @
% 76.89/13.34 lessf)))))))))))),
% 76.89/13.34 inference('rw', [status(thm)],
% 76.89/13.34 [zip_derived_cl1203, '2', '3', '4', '5', '6', '7', '7', '8',
% 76.89/13.34 '8', '9', '9', '10', '10', '11'])).
% 76.89/13.34 thf(zip_derived_cl1206, plain,
% 76.89/13.34 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk3' @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @ (outn @ n_2 @ n_2))))))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))))) @
% 76.89/13.34 lessf)))))))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1204])).
% 76.89/13.34 thf(zip_derived_cl1207, plain,
% 76.89/13.34 (~ (((!!) @ (^[Y0 : $i]:
% 76.89/13.34 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk3' @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @
% 76.89/13.34 emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @
% 76.89/13.34 emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @
% 76.89/13.34 (outn @ n_2 @ n_2))))))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 76.89/13.34 (n_eq @ '#sk3'))))) @
% 76.89/13.34 lessf)))))) @
% 76.89/13.34 Y0)))))))),
% 76.89/13.34 inference('rw_clause', [status(thm)], [zip_derived_cl1206, '1'])).
% 76.89/13.34 thf(zip_derived_cl1208, plain,
% 76.89/13.34 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 76.89/13.34 ((('#C') @ is_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))))))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk3' @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @
% 76.89/13.34 (outn @ n_2 @ n_2))))))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 76.89/13.34 (n_eq @ '#sk3'))))) @
% 76.89/13.34 lessf))))))))))))),
% 76.89/13.34 inference('comb-normalize', [status(thm)], [zip_derived_cl1207])).
% 76.89/13.34 thf(zip_derived_cl1209, plain,
% 76.89/13.34 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk3' @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @ (outn @ n_2 @ n_2))))))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (n_eq @ '#sk2' @ '#sk4'))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @
% 76.89/13.34 (lessf @ '#sk4'))))))))))),
% 76.89/13.34 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1208])).
% 76.89/13.34 thf(def_n_eq, axiom,(( n_eq @ (X0)@ (X1)) =
% 76.89/13.34 ((n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 76.89/13.34 (n_ts @ (num @ X1) @ (den @ X0)))))).
% 76.89/13.34 thf('12', plain,
% 76.89/13.34 (![X1:$i,X0:$i]:
% 76.89/13.34 ( ( n_eq @ X0 @ X1 ) =
% 76.89/13.34 ( n_is @
% 76.89/13.34 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 76.89/13.34 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )),
% 76.89/13.34 define([status(thm)])).
% 76.89/13.34 thf(zip_derived_cl1210, plain,
% 76.89/13.34 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk3' @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @ (outn @ n_2 @ n_2))))))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (n_is @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk4' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk4' @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2)))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @
% 76.89/13.34 (lessf @ '#sk4'))))))))))),
% 76.89/13.34 inference('rw', [status(thm)],
% 76.89/13.34 [zip_derived_cl1209, '3', '5', '6', '7', '7', '8', '8', '9',
% 76.89/13.34 '9', '10', '10', '12'])).
% 76.89/13.34 thf(zip_derived_cl1211, plain,
% 76.89/13.34 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1210])).
% 76.89/13.34 thf(zip_derived_cl10505, plain,
% 76.89/13.34 ( (is_of @ '#sk4' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 76.89/13.34 inference('remove_ty_args', [status(thm)], [zip_derived_cl1211])).
% 76.89/13.34 thf(zip_derived_cl1212, plain,
% 76.89/13.34 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk3' @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @ (outn @ n_2 @ n_2))))))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (n_is @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk4' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk4' @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2)))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @ (lessf @ '#sk4'))))))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1210])).
% 76.89/13.34 thf(zip_derived_cl1213, plain,
% 76.89/13.34 (~ (((!!) @ (^[Y0 : $i]:
% 76.89/13.34 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 76.89/13.34 ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk3' @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @ (outn @ n_2 @ n_2))))))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (n_is @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk4' @
% 76.89/13.34 (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk4' @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @ n_2)))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @
% 76.89/13.34 (lessf @ '#sk4'))))) @
% 76.89/13.34 Y0)))))))),
% 76.89/13.34 inference('rw_clause', [status(thm)], [zip_derived_cl1212, '1'])).
% 76.89/13.34 thf(zip_derived_cl1214, plain,
% 76.89/13.34 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 76.89/13.34 ((('#C') @ is_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))))))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk3' @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @ (outn @ n_2 @ n_2))))))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (n_is @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk2' @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk4' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk4' @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2)))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @
% 76.89/13.34 (lessf @ '#sk4')))))))))))),
% 76.89/13.34 inference('comb-normalize', [status(thm)], [zip_derived_cl1213])).
% 76.89/13.34 thf(zip_derived_cl1215, plain,
% 76.89/13.34 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 76.89/13.34 (((l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ '#sk3' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk2' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @ (outn @ n_2 @ n_2))))) =>
% 76.89/13.34 (((n_is @
% 76.89/13.34 (n_ts @ (ap @ '#sk2' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk4' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk4' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2)))) =>
% 76.89/13.34 (((n_eq @ '#sk3' @ '#sk5') => (lessf @ '#sk4' @ '#sk5')))))))))),
% 76.89/13.34 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1214])).
% 76.89/13.34 thf(zip_derived_cl1216, plain,
% 76.89/13.34 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 76.89/13.34 (((l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ '#sk3' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk2' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @ (outn @ n_2 @ n_2))))) =>
% 76.89/13.34 (((n_is @
% 76.89/13.34 (n_ts @ (ap @ '#sk2' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk4' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk4' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2)))) =>
% 76.89/13.34 (((n_is @
% 76.89/13.34 (n_ts @ (ap @ '#sk3' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk5' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk5' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @ (outn @ n_2 @ n_2)))) =>
% 76.89/13.34 (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk5' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk4' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ '#sk4' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk5' @ (outn @ n_2 @ n_2)))))))))))))),
% 76.89/13.34 inference('rw', [status(thm)],
% 76.89/13.34 [zip_derived_cl1215, '2', '3', '4', '5', '6', '7', '7', '7',
% 76.89/13.34 '8', '8', '8', '9', '9', '9', '10', '10', '10', '12', '11'])).
% 76.89/13.34 thf(zip_derived_cl1217, plain,
% 76.89/13.34 ( (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1216])).
% 76.89/13.34 thf(zip_derived_cl10506, plain,
% 76.89/13.34 ( (is_of @ '#sk5' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 76.89/13.34 inference('remove_ty_args', [status(thm)], [zip_derived_cl1217])).
% 76.89/13.34 thf(zip_derived_cl1218, plain,
% 76.89/13.34 (~ (((l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ '#sk3' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk2' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @ (outn @ n_2 @ n_2))))) =>
% 76.89/13.34 (((n_is @
% 76.89/13.34 (n_ts @ (ap @ '#sk2' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk4' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk4' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2)))) =>
% 76.89/13.34 (((n_is @
% 76.89/13.34 (n_ts @ (ap @ '#sk3' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk5' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk5' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @ (outn @ n_2 @ n_2)))) =>
% 76.89/13.34 (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ '#sk5' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk4' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk4' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk5' @ (outn @ n_2 @ n_2)))))))))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1216])).
% 76.89/13.34 thf(zip_derived_cl1220, plain,
% 76.89/13.34 (~ (((n_is @
% 76.89/13.34 (n_ts @ (ap @ '#sk2' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk4' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk4' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2)))) =>
% 76.89/13.34 (((n_is @
% 76.89/13.34 (n_ts @ (ap @ '#sk3' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk5' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk5' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @ (outn @ n_2 @ n_2)))) =>
% 76.89/13.34 (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ '#sk5' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk4' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk4' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk5' @ (outn @ n_2 @ n_2)))))))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1218])).
% 76.89/13.34 thf(zip_derived_cl1221, plain,
% 76.89/13.34 ( (n_is @
% 76.89/13.34 (n_ts @ (ap @ '#sk2' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk4' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk4' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1220])).
% 76.89/13.34 thf(zip_derived_cl1222, plain,
% 76.89/13.34 (~ (((n_is @
% 76.89/13.34 (n_ts @ (ap @ '#sk3' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk5' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk5' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @ (outn @ n_2 @ n_2)))) =>
% 76.89/13.34 (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ '#sk5' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk4' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk4' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk5' @ (outn @ n_2 @ n_2)))))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1220])).
% 76.89/13.34 thf(zip_derived_cl1223, plain,
% 76.89/13.34 ( (n_is @
% 76.89/13.34 (n_ts @ (ap @ '#sk3' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk5' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk5' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @ (outn @ n_2 @ n_2))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1222])).
% 76.89/13.34 thf(zip_derived_cl1199, plain,
% 76.89/13.34 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1198])).
% 76.89/13.34 thf(zip_derived_cl10503, plain,
% 76.89/13.34 ( (is_of @ '#sk2' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 76.89/13.34 inference('remove_ty_args', [status(thm)], [zip_derived_cl1199])).
% 76.89/13.34 thf(zip_derived_cl1205, plain,
% 76.89/13.34 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1204])).
% 76.89/13.34 thf(zip_derived_cl10504, plain,
% 76.89/13.34 ( (is_of @ '#sk3' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 76.89/13.34 inference('remove_ty_args', [status(thm)], [zip_derived_cl1205])).
% 76.89/13.34 thf(zip_derived_cl1219, plain,
% 76.89/13.34 ( (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ '#sk3' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk2' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk2' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk3' @ (outn @ n_2 @ n_2)))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1218])).
% 76.89/13.34 thf(zip_derived_cl1224, plain,
% 76.89/13.34 (~ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ '#sk5' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk4' @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ '#sk4' @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ '#sk5' @ (outn @ n_2 @ n_2)))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1222])).
% 76.89/13.34 thf(satz44, axiom,
% 76.89/13.34 (all_of @
% 76.89/13.34 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 76.89/13.34 ( ^[X0:$i]:
% 76.89/13.34 ( all_of @
% 76.89/13.34 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 76.89/13.34 ( ^[X1:$i]:
% 76.89/13.34 ( all_of @
% 76.89/13.34 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 76.89/13.34 ( ^[X2:$i]:
% 76.89/13.34 ( all_of @
% 76.89/13.34 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 76.89/13.34 ( ^[X3:$i]:
% 76.89/13.34 ( ( moref @ X0 @ X1 ) =>
% 76.89/13.34 ( ( n_eq @ X0 @ X2 ) =>
% 76.89/13.34 ( ( n_eq @ X1 @ X3 ) => ( moref @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 76.89/13.34 thf(zip_derived_cl281, plain,
% 76.89/13.34 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 76.89/13.34 (^[Y0 : $i]:
% 76.89/13.34 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 76.89/13.34 (^[Y1 : $i]:
% 76.89/13.34 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 76.89/13.34 (^[Y2 : $i]:
% 76.89/13.34 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 76.89/13.34 (^[Y3 : $i]:
% 76.89/13.34 (((moref @ Y0 @ Y1) =>
% 76.89/13.34 (((n_eq @ Y0 @ Y2) =>
% 76.89/13.34 (((n_eq @ Y1 @ Y3) => (moref @ Y2 @ Y3)))))))))))))))),
% 76.89/13.34 inference('cnf', [status(esa)], [satz44])).
% 76.89/13.34 thf(zip_derived_cl282, plain,
% 76.89/13.34 ( (all_of @ ((('#C') @ in @ frac)) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 76.89/13.34 moref)))))))))))))),
% 76.89/13.34 inference('lams2combs', [status(thm)], [zip_derived_cl281])).
% 76.89/13.34 thf(zip_derived_cl2495, plain,
% 76.89/13.34 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @
% 76.89/13.34 (pair1type @ nat)))))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 76.89/13.34 moref)))))))))))))),
% 76.89/13.34 inference('rw', [status(thm)], [zip_derived_cl282, '0'])).
% 76.89/13.34 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 76.89/13.34 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 76.89/13.34 thf('13', plain,
% 76.89/13.34 (![X0:( $i > $o ),X1:( $i > $o )]:
% 76.89/13.34 ( ( all_of @ X0 @ X1 ) <=>
% 76.89/13.34 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 76.89/13.34 inference('rw.lit', [status(esa)], [def_all_of])).
% 76.89/13.34 thf(zip_derived_cl2496, plain,
% 76.89/13.34 ( (((!!) @ (^[Y0 : $i]:
% 76.89/13.34 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @
% 76.89/13.34 (pair1type @ nat)))))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @
% 76.89/13.34 (pair1type @ nat)))))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @
% 76.89/13.34 moref)))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @
% 76.89/13.34 n_eq)))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @
% 76.89/13.34 n_eq)))))) @
% 76.89/13.34 moref)))))))))) @
% 76.89/13.34 Y0)))))))),
% 76.89/13.34 inference('rw_clause', [status(thm)], [zip_derived_cl2495, '13'])).
% 76.89/13.34 thf(zip_derived_cl2497, plain,
% 76.89/13.34 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 76.89/13.34 ((('#C') @ is_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))))))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat)))))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @
% 76.89/13.34 (pair1type @ nat)))))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ ('#B'))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 76.89/13.34 moref))))))))))))))))),
% 76.89/13.34 inference('comb-normalize', [status(thm)], [zip_derived_cl2496])).
% 76.89/13.34 thf(zip_derived_cl2498, plain,
% 76.89/13.34 (![X2 : $i]:
% 76.89/13.34 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat)))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (moref @ X2))))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (n_eq @ X2))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 76.89/13.34 moref)))))))))))))),
% 76.89/13.34 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2497])).
% 76.89/13.34 thf(zip_derived_cl2499, plain,
% 76.89/13.34 (![X2 : $i]:
% 76.89/13.34 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat)))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (moref @ X2))))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (n_eq @ X2))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 76.89/13.34 moref))))))))))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2498])).
% 76.89/13.34 thf(zip_derived_cl2500, plain,
% 76.89/13.34 (![X0 : $i]:
% 76.89/13.34 ( (((!!) @ (^[Y0 : $i]:
% 76.89/13.34 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 76.89/13.34 ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @
% 76.89/13.34 (pair1type @ nat)))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (moref @ X0))))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @
% 76.89/13.34 (n_eq @ X0))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @
% 76.89/13.34 n_eq)))))) @
% 76.89/13.34 moref)))))))) @
% 76.89/13.34 Y0)))))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 76.89/13.34 inference('rw_clause', [status(thm)], [zip_derived_cl2499, '13'])).
% 76.89/13.34 thf(zip_derived_cl2501, plain,
% 76.89/13.34 (![X0 : $i]:
% 76.89/13.34 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 76.89/13.34 ((('#C') @ is_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))))))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @
% 76.89/13.34 (pair1type @ nat)))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (moref @ X0))))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @
% 76.89/13.34 (n_eq @ X0))))))) @
% 76.89/13.34 ((('#C') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ ('#S') @
% 76.89/13.34 ((('#B') @ ((('#B') @ (=>))) @
% 76.89/13.34 n_eq)))))) @
% 76.89/13.34 moref))))))))))))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 76.89/13.34 inference('comb-normalize', [status(thm)], [zip_derived_cl2500])).
% 76.89/13.34 thf(zip_derived_cl2502, plain,
% 76.89/13.34 (![X0 : $i, X2 : $i]:
% 76.89/13.34 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X2))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @
% 76.89/13.34 moref)))))))))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 76.89/13.34 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2501])).
% 76.89/13.34 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) =
% 76.89/13.34 ((n_some @ (diffprop @ X0 @ X1))))).
% 76.89/13.34 thf('14', plain,
% 76.89/13.34 (![X1:$i,X0:$i]:
% 76.89/13.34 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 76.89/13.34 define([status(thm)])).
% 76.89/13.34 thf(def_moref, axiom,(( moref @ (X0)@ (X1)) =
% 76.89/13.34 ((d_29_ii @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 76.89/13.34 (n_ts @ (num @ X1) @ (den @ X0)))))).
% 76.89/13.34 thf('15', plain,
% 76.89/13.34 (![X1:$i,X0:$i]:
% 76.89/13.34 ( ( moref @ X0 @ X1 ) =
% 76.89/13.34 ( d_29_ii @
% 76.89/13.34 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 76.89/13.34 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )),
% 76.89/13.34 define([status(thm)])).
% 76.89/13.34 thf(zip_derived_cl2503, plain,
% 76.89/13.34 (![X0 : $i, X2 : $i]:
% 76.89/13.34 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X0 @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X2 @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2))))))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @
% 76.89/13.34 moref)))))))))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 76.89/13.34 inference('rw', [status(thm)],
% 76.89/13.34 [zip_derived_cl2502, '2', '3', '14', '5', '6', '7', '7', '8',
% 76.89/13.34 '8', '9', '9', '10', '10', '15'])).
% 76.89/13.34 thf(zip_derived_cl2504, plain,
% 76.89/13.34 (![X0 : $i, X2 : $i]:
% 76.89/13.34 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X0 @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X2 @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2))))))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @
% 76.89/13.34 moref)))))))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2503])).
% 76.89/13.34 thf(zip_derived_cl2505, plain,
% 76.89/13.34 (![X0 : $i, X1 : $i]:
% 76.89/13.34 ( (((!!) @ (^[Y0 : $i]:
% 76.89/13.34 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 76.89/13.34 ((('#B') @ (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X0 @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @
% 76.89/13.34 emptyset))) @
% 76.89/13.34 (ap @ X1 @
% 76.89/13.34 (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X1 @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @
% 76.89/13.34 emptyset))) @
% 76.89/13.34 (ap @ X0 @
% 76.89/13.34 (outn @ n_2 @ n_2))))))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 76.89/13.34 (n_eq @ X1))))) @
% 76.89/13.34 moref)))))) @
% 76.89/13.34 Y0)))))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 76.89/13.34 inference('rw_clause', [status(thm)], [zip_derived_cl2504, '13'])).
% 76.89/13.34 thf(zip_derived_cl2506, plain,
% 76.89/13.34 (![X0 : $i, X1 : $i]:
% 76.89/13.34 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 76.89/13.34 ((('#C') @ is_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))))))) @
% 76.89/13.34 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 76.89/13.34 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X0 @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @
% 76.89/13.34 (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X1 @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @
% 76.89/13.34 (outn @ n_2 @ n_2))))))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ ('#B') @
% 76.89/13.34 ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 76.89/13.34 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))))) @
% 76.89/13.34 moref))))))))))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 76.89/13.34 inference('comb-normalize', [status(thm)], [zip_derived_cl2505])).
% 76.89/13.34 thf(zip_derived_cl2507, plain,
% 76.89/13.34 (![X0 : $i, X1 : $i, X3 : $i]:
% 76.89/13.34 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X0 @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X1 @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2))))))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (n_eq @ X0 @ X3))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (moref @ X3))))))))))
% 76.89/13.34 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 76.89/13.34 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2506])).
% 76.89/13.34 thf(zip_derived_cl2508, plain,
% 76.89/13.34 (![X0 : $i, X1 : $i, X3 : $i]:
% 76.89/13.34 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X0 @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X1 @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2))))))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (n_is @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X0 @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X3 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X3 @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2)))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (moref @ X3))))))))))
% 76.89/13.34 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 76.89/13.34 inference('rw', [status(thm)],
% 76.89/13.34 [zip_derived_cl2507, '3', '5', '6', '7', '7', '8', '8', '9',
% 76.89/13.34 '9', '10', '10', '12'])).
% 76.89/13.34 thf(zip_derived_cl2509, plain,
% 76.89/13.34 (![X0 : $i, X1 : $i, X3 : $i]:
% 76.89/13.34 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X0 @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X1 @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2))))))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (n_is @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X0 @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X3 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X3 @
% 76.89/13.34 (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2)))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (moref @ X3))))))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2508])).
% 76.89/13.34 thf(zip_derived_cl2510, plain,
% 76.89/13.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 76.89/13.34 ( (((!!) @ (^[Y0 : $i]:
% 76.89/13.34 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 76.89/13.34 ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X1 @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X0 @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2))))))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (n_is @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X1 @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X2 @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2)))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @
% 76.89/13.34 (moref @ X2))))) @
% 76.89/13.34 Y0)))))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 76.89/13.34 inference('rw_clause', [status(thm)], [zip_derived_cl2509, '13'])).
% 76.89/13.34 thf(zip_derived_cl2511, plain,
% 76.89/13.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 76.89/13.34 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 76.89/13.34 ((('#C') @ is_of @
% 76.89/13.34 ((('#C') @ in @ (pair1type @ nat))))))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X1 @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X0 @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2))))))) @
% 76.89/13.34 ((('#B') @ (((=>) @ (n_is @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X1 @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @
% 76.89/13.34 (ap @ X2 @
% 76.89/13.34 (outn @ n_2 @
% 76.89/13.34 (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2)))))) @
% 76.89/13.34 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @
% 76.89/13.34 (moref @ X2)))))))))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 76.89/13.34 inference('comb-normalize', [status(thm)], [zip_derived_cl2510])).
% 76.89/13.34 thf(zip_derived_cl2512, plain,
% 76.89/13.34 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 76.89/13.34 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 76.89/13.34 (((l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ X1 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X0 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2))))) =>
% 76.89/13.34 (((n_is @
% 76.89/13.34 (n_ts @ (ap @ X1 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X2 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2)))) =>
% 76.89/13.34 (((n_eq @ X0 @ X4) => (moref @ X2 @ X4)))))))))
% 76.89/13.34 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 76.89/13.34 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2511])).
% 76.89/13.34 thf(zip_derived_cl2513, plain,
% 76.89/13.34 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 76.89/13.34 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 76.89/13.34 (((l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ X1 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X0 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2))))) =>
% 76.89/13.34 (((n_is @
% 76.89/13.34 (n_ts @ (ap @ X1 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X2 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2)))) =>
% 76.89/13.34 (((n_is @
% 76.89/13.34 (n_ts @ (ap @ X0 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X4 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X4 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2)))) =>
% 76.89/13.34 (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ X2 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X4 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X4 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2)))))))))))))
% 76.89/13.34 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 76.89/13.34 inference('rw', [status(thm)],
% 76.89/13.34 [zip_derived_cl2512, '2', '3', '14', '5', '6', '7', '7', '7',
% 76.89/13.34 '8', '8', '8', '9', '9', '9', '10', '10', '10', '12', '15'])).
% 76.89/13.34 thf(zip_derived_cl2514, plain,
% 76.89/13.34 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 76.89/13.34 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | (((l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ X1 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X0 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2))))) =>
% 76.89/13.34 (((n_is @
% 76.89/13.34 (n_ts @ (ap @ X1 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X2 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2)))) =>
% 76.89/13.34 (((n_is @
% 76.89/13.34 (n_ts @ (ap @ X0 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X4 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X4 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2)))) =>
% 76.89/13.34 (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ X2 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X4 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X4 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2)))))))))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2513])).
% 76.89/13.34 thf(zip_derived_cl2515, plain,
% 76.89/13.34 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 76.89/13.34 (~ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ X1 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X0 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2)))))
% 76.89/13.34 | (((n_is @
% 76.89/13.34 (n_ts @ (ap @ X1 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X2 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2)))) =>
% 76.89/13.34 (((n_is @
% 76.89/13.34 (n_ts @ (ap @ X0 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X4 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X4 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2)))) =>
% 76.89/13.34 (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ X2 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X4 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X4 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2)))))))))
% 76.89/13.34 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2514])).
% 76.89/13.34 thf(zip_derived_cl2516, plain,
% 76.89/13.34 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 76.89/13.34 (~ (n_is @
% 76.89/13.34 (n_ts @ (ap @ X1 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X2 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2))))
% 76.89/13.34 | (((n_is @
% 76.89/13.34 (n_ts @ (ap @ X0 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X4 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X4 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2)))) =>
% 76.89/13.34 (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ X2 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X4 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X4 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2)))))))
% 76.89/13.34 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ X1 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X0 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2))))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2515])).
% 76.89/13.34 thf(zip_derived_cl2517, plain,
% 76.89/13.34 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 76.89/13.34 (~ (n_is @
% 76.89/13.34 (n_ts @ (ap @ X0 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X4 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X4 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2))))
% 76.89/13.34 | (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ X2 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X4 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X4 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2)))))
% 76.89/13.34 | ~ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ X1 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X0 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2)))))
% 76.89/13.34 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 76.89/13.34 | ~ (n_is @
% 76.89/13.34 (n_ts @ (ap @ X1 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X2 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2)))))),
% 76.89/13.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2516])).
% 76.89/13.34 thf(zip_derived_cl10541, plain,
% 76.89/13.34 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 76.89/13.34 (~ (n_is @
% 76.89/13.34 (n_ts @ (ap @ X0 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X4 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X4 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2))))
% 76.89/13.34 | (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ X2 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X4 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X4 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2)))))
% 76.89/13.34 | ~ (l_some @ nat @
% 76.89/13.34 (diffprop @
% 76.89/13.34 (n_ts @ (ap @ X1 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X0 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X0 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2)))))
% 76.89/13.34 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 76.89/13.34 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 76.89/13.34 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 76.89/13.34 | ~ (is_of @ X4 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 76.89/13.34 | ~ (n_is @
% 76.89/13.34 (n_ts @ (ap @ X1 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X2 @ (outn @ n_2 @ n_2))) @
% 76.89/13.34 (n_ts @ (ap @ X2 @ (outn @ n_2 @ (ordsucc @ emptyset))) @
% 76.89/13.34 (ap @ X1 @ (outn @ n_2 @ n_2)))))),
% 76.89/13.34 inference('remove_ty_args', [status(thm)], [zip_derived_cl2517])).
% 76.89/13.34 thf(zip_derived_cl10551, plain, ($false),
% 76.89/13.34 inference('eprover', [status(thm)],
% 76.89/13.34 [zip_derived_cl10505, zip_derived_cl10506, zip_derived_cl1221,
% 76.89/13.34 zip_derived_cl1223, zip_derived_cl10503, zip_derived_cl10504,
% 76.89/13.34 zip_derived_cl1219, zip_derived_cl1224, zip_derived_cl10541])).
% 76.89/13.34
% 76.89/13.34 % SZS output end Refutation
% 76.89/13.34
% 76.89/13.34
% 76.89/13.34 % Terminating...
% 77.32/13.51 % Runner terminated.
% 77.32/13.53 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------