%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM739^4 : TPTP v9.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.jubkIlKvNG true
% Computer : n023.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 97.21s 13.02s
% Output : Refutation 97.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM739^4 : TPTP v9.2.0. Released v7.1.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.jubkIlKvNG true
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 16:16:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.58/0.67 % Total configuration time : 828
% 0.58/0.67 % Estimated wc time : 1656
% 0.58/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.61/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.61/0.77 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.61/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.61/0.80 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.61/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.61/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.61/0.80 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.61/0.84 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 97.21/13.02 % Solved by lams/40_b.comb.sh.
% 97.21/13.02 % done 310 iterations in 12.100s
% 97.21/13.02 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 97.21/13.02 % SZS output start Refutation
% 97.21/13.02 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
% 97.21/13.02 thf('#sk5_type', type, '#sk5': $i).
% 97.21/13.02 thf('#ty_enc6_type', type, '#ty_enc6': ($i > $i > $o) > $i > $i > $o).
% 97.21/13.02 thf(moreq_type, type, moreq: $i > $i > $o).
% 97.21/13.02 thf(nat_type, type, nat: $i).
% 97.21/13.02 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 97.21/13.02 thf(in_type, type, in: $i > $i > $o).
% 97.21/13.02 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 97.21/13.02 thf(ap_type, type, ap: $i > $i > $i).
% 97.21/13.02 thf('#sk4_type', type, '#sk4': $i).
% 97.21/13.02 thf(n_is_type, type, n_is: $i > $i > $o).
% 97.21/13.02 thf(n_1t_type, type, n_1t: $i).
% 97.21/13.02 thf(imp_type, type, imp: $o > $o > $o).
% 97.21/13.02 thf(frac_type, type, frac: $i).
% 97.21/13.02 thf('#sk2_type', type, '#sk2': $i).
% 97.21/13.02 thf(n_2t_type, type, n_2t: $i).
% 97.21/13.02 thf(n_ts_type, type, n_ts: $i > $i > $i).
% 97.21/13.02 thf(n_eq_type, type, n_eq: $i > $i > $o).
% 97.21/13.02 thf(pair1type_type, type, pair1type: $i > $i).
% 97.21/13.02 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 97.21/13.02 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 97.21/13.02 thf(num_type, type, num: $i > $i).
% 97.21/13.02 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 97.21/13.02 thf(l_or_type, type, l_or: $o > $o > $o).
% 97.21/13.02 thf(moref_type, type, moref: $i > $i > $o).
% 97.21/13.02 thf(d_not_type, type, d_not: $o > $o).
% 97.21/13.02 thf(first1_type, type, first1: $i > $i > $i).
% 97.21/13.02 thf(den_type, type, den: $i > $i).
% 97.21/13.02 thf('#sk3_type', type, '#sk3': $i).
% 97.21/13.02 thf(second1_type, type, second1: $i > $i > $i).
% 97.21/13.02 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 97.21/13.02 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 97.21/13.02 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 97.21/13.02 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 97.21/13.02 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 97.21/13.02 thf(satz46, conjecture,
% 97.21/13.02 (all_of @
% 97.21/13.02 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 97.21/13.02 ( ^[X0:$i]:
% 97.21/13.02 ( all_of @
% 97.21/13.02 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 97.21/13.02 ( ^[X1:$i]:
% 97.21/13.02 ( all_of @
% 97.21/13.02 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 97.21/13.02 ( ^[X2:$i]:
% 97.21/13.02 ( all_of @
% 97.21/13.02 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 97.21/13.02 ( ^[X3:$i]:
% 97.21/13.02 ( ( moreq @ X0 @ X1 ) =>
% 97.21/13.02 ( ( n_eq @ X0 @ X2 ) =>
% 97.21/13.02 ( ( n_eq @ X1 @ X3 ) => ( moreq @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 97.21/13.02 thf(zf_stmt_0, negated_conjecture,
% 97.21/13.02 (~( all_of @
% 97.21/13.02 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 97.21/13.02 ( ^[X0:$i]:
% 97.21/13.02 ( all_of @
% 97.21/13.02 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 97.21/13.02 ( ^[X1:$i]:
% 97.21/13.02 ( all_of @
% 97.21/13.02 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 97.21/13.02 ( ^[X2:$i]:
% 97.21/13.02 ( all_of @
% 97.21/13.02 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 97.21/13.02 ( ^[X3:$i]:
% 97.21/13.02 ( ( moreq @ X0 @ X1 ) =>
% 97.21/13.02 ( ( n_eq @ X0 @ X2 ) =>
% 97.21/13.02 ( ( n_eq @ X1 @ X3 ) => ( moreq @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) )),
% 97.21/13.02 inference('cnf.neg', [status(esa)], [satz46])).
% 97.21/13.02 thf(zip_derived_cl282, plain,
% 97.21/13.02 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 97.21/13.02 (^[Y0 : $i]:
% 97.21/13.02 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 97.21/13.02 (^[Y1 : $i]:
% 97.21/13.02 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 97.21/13.02 (^[Y2 : $i]:
% 97.21/13.02 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 97.21/13.02 (^[Y3 : $i]:
% 97.21/13.02 (((moreq @ Y0 @ Y1) =>
% 97.21/13.02 (((n_eq @ Y0 @ Y2) =>
% 97.21/13.02 (((n_eq @ Y1 @ Y3) => (moreq @ Y2 @ Y3)))))))))))))))),
% 97.21/13.02 inference('cnf', [status(esa)], [zf_stmt_0])).
% 97.21/13.02 thf(zip_derived_cl283, plain,
% 97.21/13.02 (~ (all_of @ ((('#C') @ in @ frac)) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.21/13.02 moreq)))))))))))))),
% 97.21/13.02 inference('lams2combs', [status(thm)], [zip_derived_cl282])).
% 97.21/13.02 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))).
% 97.21/13.02 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])).
% 97.21/13.02 thf(zip_derived_cl1290, plain,
% 97.21/13.02 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @
% 97.21/13.02 (pair1type @ nat)))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.21/13.02 moreq)))))))))))))),
% 97.21/13.02 inference('rw', [status(thm)], [zip_derived_cl283, '0'])).
% 97.21/13.02 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 97.21/13.02 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 97.21/13.02 thf('1', plain,
% 97.21/13.02 (![X0:( $i > $o ),X1:( $i > $o )]:
% 97.21/13.02 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 97.21/13.02 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 97.21/13.02 inference('rw.lit', [status(esa)], [def_all_of])).
% 97.21/13.02 thf(zip_derived_cl1291, plain,
% 97.21/13.02 (~ (((!!) @ (^[Y0 : $i]:
% 97.21/13.02 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @
% 97.21/13.02 (pair1type @ nat)))))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @
% 97.21/13.02 (pair1type @ nat)))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @
% 97.21/13.02 moreq)))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @
% 97.21/13.02 n_eq)))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @
% 97.21/13.02 n_eq)))))) @
% 97.21/13.02 moreq)))))))))) @
% 97.21/13.02 Y0)))))))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl1290, '1'])).
% 97.21/13.02 thf(zip_derived_cl1292, plain,
% 97.21/13.02 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.21/13.02 ((('#C') @ is_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @
% 97.21/13.02 (pair1type @ nat)))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @
% 97.21/13.02 n_eq)))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @
% 97.21/13.02 n_eq)))))) @
% 97.21/13.02 moreq))))))))))))))))),
% 97.21/13.02 inference('comb-normalize', [status(thm)], [zip_derived_cl1291])).
% 97.21/13.02 thf(zip_derived_cl1293, plain,
% 97.21/13.02 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.21/13.02 moreq)))))))))))))),
% 97.21/13.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1292])).
% 97.21/13.02 thf(zip_derived_cl1295, plain,
% 97.21/13.02 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.21/13.02 moreq)))))))))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1293])).
% 97.21/13.02 thf(zip_derived_cl1296, plain,
% 97.21/13.02 (~ (((!!) @ (^[Y0 : $i]:
% 97.21/13.02 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @
% 97.21/13.02 (pair1type @ nat)))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @
% 97.21/13.02 (n_eq @ '#sk2'))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @
% 97.21/13.02 n_eq)))))) @
% 97.21/13.02 moreq)))))))) @
% 97.21/13.02 Y0)))))))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl1295, '1'])).
% 97.21/13.02 thf(zip_derived_cl1297, plain,
% 97.21/13.02 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.21/13.02 ((('#C') @ is_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @
% 97.21/13.02 (n_eq @ '#sk2'))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.21/13.02 moreq))))))))))))))),
% 97.21/13.02 inference('comb-normalize', [status(thm)], [zip_derived_cl1296])).
% 97.21/13.02 thf(zip_derived_cl1298, plain,
% 97.21/13.02 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (((=>) @ (moreq @ '#sk2' @ '#sk3'))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))))) @
% 97.21/13.02 moreq)))))))))))),
% 97.21/13.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1297])).
% 97.21/13.02 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 97.21/13.02 thf('2', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 97.21/13.02 define([status(thm)])).
% 97.21/13.02 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 97.21/13.02 thf('3', plain,
% 97.21/13.02 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 97.21/13.02 define([status(thm)])).
% 97.21/13.02 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 97.21/13.02 thf('4', plain,
% 97.21/13.02 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 97.21/13.02 define([status(thm)])).
% 97.21/13.02 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) =
% 97.21/13.02 ((n_some @ (diffprop @ X0 @ X1))))).
% 97.21/13.02 thf('5', plain,
% 97.21/13.02 (![X1:$i,X0:$i]:
% 97.21/13.02 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 97.21/13.02 define([status(thm)])).
% 97.21/13.02 thf(def_first1, axiom,(( first1 @ (X1)@ (X0)) = ((ap @ X0 @ n_1t)))).
% 97.21/13.02 thf('6', plain,
% 97.21/13.02 (![X1:$i,X0:$i]: ( ( first1 @ X1 @ X0 ) = ( ap @ X0 @ n_1t ) )),
% 97.21/13.02 define([status(thm)])).
% 97.21/13.02 thf(def_second1, axiom,(( second1 @ (X1)@ (X0)) = ((ap @ X0 @ n_2t)))).
% 97.21/13.02 thf('7', plain,
% 97.21/13.02 (![X1:$i,X0:$i]: ( ( second1 @ X1 @ X0 ) = ( ap @ X0 @ n_2t ) )),
% 97.21/13.02 define([status(thm)])).
% 97.21/13.02 thf(def_num, axiom,(( num @ (X0)) = ((first1 @ nat @ X0)))).
% 97.21/13.02 thf('8', plain, (![X0:$i]: ( ( num @ X0 ) = ( first1 @ nat @ X0 ) )),
% 97.21/13.02 define([status(thm)])).
% 97.21/13.02 thf(def_den, axiom,(( den @ (X0)) = ((second1 @ nat @ X0)))).
% 97.21/13.02 thf('9', plain, (![X0:$i]: ( ( den @ X0 ) = ( second1 @ nat @ X0 ) )),
% 97.21/13.02 define([status(thm)])).
% 97.21/13.02 thf(def_n_eq, axiom,(( n_eq @ (X0)@ (X1)) =
% 97.21/13.02 ((n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 97.21/13.02 (n_ts @ (num @ X1) @ (den @ X0)))))).
% 97.21/13.02 thf('10', plain,
% 97.21/13.02 (![X1:$i,X0:$i]:
% 97.21/13.02 ( ( n_eq @ X0 @ X1 ) =
% 97.21/13.02 ( n_is @
% 97.21/13.02 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 97.21/13.02 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )),
% 97.21/13.02 define([status(thm)])).
% 97.21/13.02 thf(def_moref, axiom,(( moref @ (X0)@ (X1)) =
% 97.21/13.02 ((d_29_ii @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 97.21/13.02 (n_ts @ (num @ X1) @ (den @ X0)))))).
% 97.21/13.02 thf('11', plain,
% 97.21/13.02 (![X1:$i,X0:$i]:
% 97.21/13.02 ( ( moref @ X0 @ X1 ) =
% 97.21/13.02 ( d_29_ii @
% 97.21/13.02 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 97.21/13.02 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )),
% 97.21/13.02 define([status(thm)])).
% 97.21/13.02 thf(def_moreq, axiom,(( moreq @ (X0)@ (X1)) =
% 97.21/13.02 ((l_or @ (moref @ X0 @ X1) @ (n_eq @ X0 @ X1))))).
% 97.21/13.02 thf('12', plain,
% 97.21/13.02 (![X1:$i,X0:$i]:
% 97.21/13.02 ( ( moreq @ X0 @ X1 ) =
% 97.21/13.02 ( l_or @ ( moref @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )),
% 97.21/13.02 define([status(thm)])).
% 97.21/13.02 thf(zip_derived_cl1299, plain,
% 97.21/13.02 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))))) @
% 97.21/13.02 moreq)))))))))))),
% 97.21/13.02 inference('rw', [status(thm)],
% 97.21/13.02 [zip_derived_cl1298, '2', '3', '4', '5', '6', '6', '7', '7',
% 97.21/13.02 '8', '8', '9', '9', '10', '11', '12'])).
% 97.21/13.02 thf(zip_derived_cl1301, plain,
% 97.21/13.02 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))))) @
% 97.21/13.02 moreq)))))))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1299])).
% 97.21/13.02 thf(zip_derived_cl1302, plain,
% 97.21/13.02 (~ (((!!) @ (^[Y0 : $i]:
% 97.21/13.02 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @
% 97.21/13.02 (ap @ '#sk2' @
% 97.21/13.02 n_1t) @
% 97.21/13.02 (ap @ '#sk3' @
% 97.21/13.02 n_2t)) @
% 97.21/13.02 (n_ts @
% 97.21/13.02 (ap @ '#sk3' @
% 97.21/13.02 n_1t) @
% 97.21/13.02 (ap @ '#sk2' @
% 97.21/13.02 n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @
% 97.21/13.02 (n_ts @
% 97.21/13.02 (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @
% 97.21/13.02 (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 97.21/13.02 (n_eq @ '#sk3'))))) @
% 97.21/13.02 moreq)))))) @
% 97.21/13.02 Y0)))))))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl1301, '1'])).
% 97.21/13.02 thf(zip_derived_cl1303, plain,
% 97.21/13.02 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.21/13.02 ((('#C') @ is_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @
% 97.21/13.02 (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @
% 97.21/13.02 (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @
% 97.21/13.02 (n_ts @
% 97.21/13.02 (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @
% 97.21/13.02 (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 97.21/13.02 (n_eq @ '#sk3'))))) @
% 97.21/13.02 moreq))))))))))))),
% 97.21/13.02 inference('comb-normalize', [status(thm)], [zip_derived_cl1302])).
% 97.21/13.02 thf(zip_derived_cl1304, plain,
% 97.21/13.02 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (n_eq @ '#sk2' @ '#sk4'))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @
% 97.21/13.02 (moreq @ '#sk4'))))))))))),
% 97.21/13.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1303])).
% 97.21/13.02 thf(zip_derived_cl1305, plain,
% 97.21/13.02 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (n_is @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk4' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @
% 97.21/13.02 (moreq @ '#sk4'))))))))))),
% 97.21/13.02 inference('rw', [status(thm)],
% 97.21/13.02 [zip_derived_cl1304, '6', '6', '7', '7', '8', '8', '9', '9',
% 97.21/13.02 '10'])).
% 97.21/13.02 thf(zip_derived_cl1307, plain,
% 97.21/13.02 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (n_is @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk4' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @ (moreq @ '#sk4'))))))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1305])).
% 97.21/13.02 thf(zip_derived_cl1308, plain,
% 97.21/13.02 (~ (((!!) @ (^[Y0 : $i]:
% 97.21/13.02 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 ((('#B') @ (((=>) @ (imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (n_is @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk4' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @
% 97.21/13.02 (moreq @ '#sk4'))))) @
% 97.21/13.02 Y0)))))))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl1307, '1'])).
% 97.21/13.02 thf(zip_derived_cl1309, plain,
% 97.21/13.02 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.21/13.02 ((('#C') @ is_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t)))))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (n_is @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @
% 97.21/13.02 (ap @ '#sk4' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @
% 97.21/13.02 (ap @ '#sk2' @ n_2t))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @
% 97.21/13.02 (moreq @ '#sk4')))))))))))),
% 97.21/13.02 inference('comb-normalize', [status(thm)], [zip_derived_cl1308])).
% 97.21/13.02 thf(zip_derived_cl1310, plain,
% 97.21/13.02 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 (((imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) =>
% 97.21/13.02 (((n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t))) =>
% 97.21/13.02 (((n_eq @ '#sk3' @ '#sk5') => (moreq @ '#sk4' @ '#sk5')))))))))),
% 97.21/13.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1309])).
% 97.21/13.02 thf(zip_derived_cl1311, plain,
% 97.21/13.02 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 (((imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) =>
% 97.21/13.02 (((n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t))) =>
% 97.21/13.02 (((n_is @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t))) =>
% 97.21/13.02 (imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))))))))),
% 97.21/13.02 inference('rw', [status(thm)],
% 97.21/13.02 [zip_derived_cl1310, '2', '3', '4', '5', '6', '6', '6', '7',
% 97.21/13.02 '7', '7', '8', '8', '8', '9', '9', '9', '10', '10', '11', '12'])).
% 97.21/13.02 thf(zip_derived_cl1313, plain,
% 97.21/13.02 (~ (((imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) =>
% 97.21/13.02 (((n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t))) =>
% 97.21/13.02 (((n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t))) => (imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1311])).
% 97.21/13.02 thf(zip_derived_cl1315, plain,
% 97.21/13.02 (~ (((n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t))) =>
% 97.21/13.02 (((n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t))) => (imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1313])).
% 97.21/13.02 thf(zip_derived_cl1318, plain,
% 97.21/13.02 (~ (((n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t))) => (imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1315])).
% 97.21/13.02 thf(zip_derived_cl1321, plain,
% 97.21/13.02 (~ (imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1318])).
% 97.21/13.02 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 97.21/13.02 thf('13', plain,
% 97.21/13.02 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 97.21/13.02 inference('rw.lit', [status(esa)], [def_imp])).
% 97.21/13.02 thf(zip_derived_cl1323, plain,
% 97.21/13.02 (~ (((imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @
% 97.21/13.02 ($false)) => (n_is @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl1321, '13'])).
% 97.21/13.02 thf(zip_derived_cl1327, plain,
% 97.21/13.02 (~ (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1323])).
% 97.21/13.02 thf(satz38, axiom,
% 97.21/13.02 (all_of @
% 97.21/13.02 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 97.21/13.02 ( ^[X0:$i]:
% 97.21/13.02 ( all_of @
% 97.21/13.02 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 97.21/13.02 ( ^[X1:$i]: ( ( n_eq @ X0 @ X1 ) => ( n_eq @ X1 @ X0 ) ) ) ) ))).
% 97.21/13.02 thf(zip_derived_cl240, plain,
% 97.21/13.02 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 97.21/13.02 (^[Y0 : $i]:
% 97.21/13.02 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 97.21/13.02 (^[Y1 : $i]: (((n_eq @ Y0 @ Y1) => (n_eq @ Y1 @ Y0)))))))),
% 97.21/13.02 inference('cnf', [status(esa)], [satz38])).
% 97.21/13.02 thf(zip_derived_cl241, plain,
% 97.21/13.02 ( (all_of @ ((('#C') @ in @ frac)) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#S') @ ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 97.21/13.02 ((('#C') @ n_eq)))))))),
% 97.21/13.02 inference('lams2combs', [status(thm)], [zip_derived_cl240])).
% 97.21/13.02 thf(zip_derived_cl483, plain,
% 97.21/13.02 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#S') @ ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 97.21/13.02 ((('#C') @ n_eq)))))))),
% 97.21/13.02 inference('rw', [status(thm)], [zip_derived_cl241, '0'])).
% 97.21/13.02 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 97.21/13.02 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 97.21/13.02 thf('14', plain,
% 97.21/13.02 (![X0:( $i > $o ),X1:( $i > $o )]:
% 97.21/13.02 ( ( all_of @ X0 @ X1 ) <=>
% 97.21/13.02 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 97.21/13.02 inference('rw.lit', [status(esa)], [def_all_of])).
% 97.21/13.02 thf(zip_derived_cl484, plain,
% 97.21/13.02 ( (((!!) @ (^[Y0 : $i]:
% 97.21/13.02 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 97.21/13.02 ((('#C') @ n_eq)))) @
% 97.21/13.02 Y0)))))))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl483, '14'])).
% 97.21/13.02 thf(zip_derived_cl485, plain,
% 97.21/13.02 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.21/13.02 ((('#C') @ is_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 97.21/13.02 ((('#C') @ n_eq))))))))))),
% 97.21/13.02 inference('comb-normalize', [status(thm)], [zip_derived_cl484])).
% 97.21/13.02 thf(zip_derived_cl486, plain,
% 97.21/13.02 (![X2 : $i]:
% 97.21/13.02 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ ((('#C') @ n_eq @ X2)))))))),
% 97.21/13.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl485])).
% 97.21/13.02 thf(zip_derived_cl487, plain,
% 97.21/13.02 (![X2 : $i]:
% 97.21/13.02 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @
% 97.21/13.02 ((('#C') @ n_eq @ X2))))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl486])).
% 97.21/13.02 thf(zip_derived_cl488, plain,
% 97.21/13.02 (![X0 : $i]:
% 97.21/13.02 ( (((!!) @ (^[Y0 : $i]:
% 97.21/13.02 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @
% 97.21/13.02 ((('#C') @ n_eq @ X0)) @ Y0)))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl487, '14'])).
% 97.21/13.02 thf(zip_derived_cl489, plain,
% 97.21/13.02 (![X0 : $i]:
% 97.21/13.02 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.21/13.02 ((('#C') @ is_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @
% 97.21/13.02 ((('#C') @ n_eq @ X0))))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('comb-normalize', [status(thm)], [zip_derived_cl488])).
% 97.21/13.02 thf(zip_derived_cl490, plain,
% 97.21/13.02 (![X0 : $i, X2 : $i]:
% 97.21/13.02 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 (((n_eq @ X0 @ X2) => (n_eq @ X2 @ X0)))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl489])).
% 97.21/13.02 thf(zip_derived_cl491, plain,
% 97.21/13.02 (![X0 : $i, X2 : $i]:
% 97.21/13.02 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) => (n_is @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('rw', [status(thm)],
% 97.21/13.02 [zip_derived_cl490, '6', '6', '7', '7', '8', '8', '9', '9',
% 97.21/13.02 '10', '10'])).
% 97.21/13.02 thf(zip_derived_cl492, plain,
% 97.21/13.02 (![X0 : $i, X2 : $i]:
% 97.21/13.02 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) => (n_is @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl491])).
% 97.21/13.02 thf(zip_derived_cl493, plain,
% 97.21/13.02 (![X0 : $i, X2 : $i]:
% 97.21/13.02 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))
% 97.21/13.02 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl492])).
% 97.21/13.02 thf(zip_derived_cl4119, plain,
% 97.21/13.02 ((~ (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (n_is @ (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t))))),
% 97.21/13.02 inference('sup+', [status(thm)], [zip_derived_cl1327, zip_derived_cl493])).
% 97.21/13.02 thf(zip_derived_cl1306, plain,
% 97.21/13.02 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1305])).
% 97.21/13.02 thf(zip_derived_cl1312, plain,
% 97.21/13.02 ( (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1311])).
% 97.21/13.02 thf(zip_derived_cl4152, plain,
% 97.21/13.02 (~ (n_is @ (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)))),
% 97.21/13.02 inference('demod', [status(thm)],
% 97.21/13.02 [zip_derived_cl4119, zip_derived_cl1306, zip_derived_cl1312])).
% 97.21/13.02 thf(zip_derived_cl1320, plain,
% 97.21/13.02 ( (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t)))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1318])).
% 97.21/13.02 thf(zip_derived_cl493, plain,
% 97.21/13.02 (![X0 : $i, X2 : $i]:
% 97.21/13.02 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))
% 97.21/13.02 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl492])).
% 97.21/13.02 thf(zip_derived_cl4085, plain,
% 97.21/13.02 ((~ (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | (n_is @ (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t))))),
% 97.21/13.02 inference('sup-', [status(thm)], [zip_derived_cl1320, zip_derived_cl493])).
% 97.21/13.02 thf(zip_derived_cl1312, plain,
% 97.21/13.02 ( (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1311])).
% 97.21/13.02 thf(zip_derived_cl1300, plain,
% 97.21/13.02 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1299])).
% 97.21/13.02 thf(zip_derived_cl4150, plain,
% 97.21/13.02 ( (n_is @ (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)))),
% 97.21/13.02 inference('demod', [status(thm)],
% 97.21/13.02 [zip_derived_cl4085, zip_derived_cl1312, zip_derived_cl1300])).
% 97.21/13.02 thf(zip_derived_cl1312, plain,
% 97.21/13.02 ( (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1311])).
% 97.21/13.02 thf(zip_derived_cl7221, plain,
% 97.21/13.02 ( (is_of @ '#sk5' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 97.21/13.02 inference('remove_ty_args', [status(thm)], [zip_derived_cl1312])).
% 97.21/13.02 thf(zip_derived_cl1320, plain,
% 97.21/13.02 ( (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t)))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1318])).
% 97.21/13.02 thf(zip_derived_cl1317, plain,
% 97.21/13.02 ( (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1315])).
% 97.21/13.02 thf(zip_derived_cl1306, plain,
% 97.21/13.02 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1305])).
% 97.21/13.02 thf(zip_derived_cl7220, plain,
% 97.21/13.02 ( (is_of @ '#sk4' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 97.21/13.02 inference('remove_ty_args', [status(thm)], [zip_derived_cl1306])).
% 97.21/13.02 thf(zip_derived_cl1317, plain,
% 97.21/13.02 ( (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1315])).
% 97.21/13.02 thf(zip_derived_cl493, plain,
% 97.21/13.02 (![X0 : $i, X2 : $i]:
% 97.21/13.02 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))
% 97.21/13.02 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl492])).
% 97.21/13.02 thf(zip_derived_cl4084, plain,
% 97.21/13.02 ((~ (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t))))),
% 97.21/13.02 inference('sup-', [status(thm)], [zip_derived_cl1317, zip_derived_cl493])).
% 97.21/13.02 thf(zip_derived_cl1306, plain,
% 97.21/13.02 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1305])).
% 97.21/13.02 thf(zip_derived_cl1294, plain,
% 97.21/13.02 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1293])).
% 97.21/13.02 thf(zip_derived_cl4149, plain,
% 97.21/13.02 ( (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)))),
% 97.21/13.02 inference('demod', [status(thm)],
% 97.21/13.02 [zip_derived_cl4084, zip_derived_cl1306, zip_derived_cl1294])).
% 97.21/13.02 thf(zip_derived_cl493, plain,
% 97.21/13.02 (![X0 : $i, X2 : $i]:
% 97.21/13.02 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))
% 97.21/13.02 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl492])).
% 97.21/13.02 thf(zip_derived_cl7178, plain,
% 97.21/13.02 (![X0 : $i, X2 : $i]:
% 97.21/13.02 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))
% 97.21/13.02 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))
% 97.21/13.02 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.21/13.02 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat))))),
% 97.21/13.02 inference('remove_ty_args', [status(thm)], [zip_derived_cl493])).
% 97.21/13.02 thf(zip_derived_cl1300, plain,
% 97.21/13.02 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1299])).
% 97.21/13.02 thf(zip_derived_cl7219, plain,
% 97.21/13.02 ( (is_of @ '#sk3' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 97.21/13.02 inference('remove_ty_args', [status(thm)], [zip_derived_cl1300])).
% 97.21/13.02 thf(zip_derived_cl1294, plain,
% 97.21/13.02 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1293])).
% 97.21/13.02 thf(zip_derived_cl7218, plain,
% 97.21/13.02 ( (is_of @ '#sk2' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 97.21/13.02 inference('remove_ty_args', [status(thm)], [zip_derived_cl1294])).
% 97.21/13.02 thf(zip_derived_cl1314, plain,
% 97.21/13.02 ( (imp @
% 97.21/13.02 (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @
% 97.21/13.02 ($false)) @
% 97.21/13.02 (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1313])).
% 97.21/13.02 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 97.21/13.02 thf('15', plain,
% 97.21/13.02 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 97.21/13.02 inference('rw.lit', [status(esa)], [def_imp])).
% 97.21/13.02 thf(zip_derived_cl1316, plain,
% 97.21/13.02 ( (((imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @
% 97.21/13.02 ($false)) => (n_is @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl1314, '15'])).
% 97.21/13.02 thf(zip_derived_cl1319, plain,
% 97.21/13.02 ((~ (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @
% 97.21/13.02 ($false))
% 97.21/13.02 | (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1316])).
% 97.21/13.02 thf(zip_derived_cl1322, plain,
% 97.21/13.02 ((~ (((l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) =>
% 97.21/13.02 ($false)))
% 97.21/13.02 | (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl1319, '13'])).
% 97.21/13.02 thf(zip_derived_cl1324, plain,
% 97.21/13.02 ((~ (((~) @ (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))))
% 97.21/13.02 | (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))),
% 97.21/13.02 inference('simplify boolean subterms', [status(thm)],
% 97.21/13.02 [zip_derived_cl1322])).
% 97.21/13.02 thf(zip_derived_cl1325, plain,
% 97.21/13.02 (( (l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))
% 97.21/13.02 | (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))),
% 97.21/13.02 inference('simplify nested equalities', [status(thm)],
% 97.21/13.02 [zip_derived_cl1324])).
% 97.21/13.02 thf(zip_derived_cl1326, plain,
% 97.21/13.02 ( (imp @
% 97.21/13.02 (l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @
% 97.21/13.02 ($false))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1323])).
% 97.21/13.02 thf(zip_derived_cl1328, plain,
% 97.21/13.02 ( (((l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) =>
% 97.21/13.02 ($false)))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl1326, '15'])).
% 97.21/13.02 thf(zip_derived_cl1329, plain,
% 97.21/13.02 ( (((~) @ (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))),
% 97.21/13.02 inference('simplify boolean subterms', [status(thm)],
% 97.21/13.02 [zip_derived_cl1328])).
% 97.21/13.02 thf(zip_derived_cl1330, plain,
% 97.21/13.02 (~ (l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))),
% 97.21/13.02 inference('simplify nested equalities', [status(thm)],
% 97.21/13.02 [zip_derived_cl1329])).
% 97.21/13.02 thf(satz39, axiom,
% 97.21/13.02 (all_of @
% 97.21/13.02 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 97.21/13.02 ( ^[X0:$i]:
% 97.21/13.02 ( all_of @
% 97.21/13.02 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 97.21/13.02 ( ^[X1:$i]:
% 97.21/13.02 ( all_of @
% 97.21/13.02 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 97.21/13.02 ( ^[X2:$i]:
% 97.21/13.02 ( ( n_eq @ X0 @ X1 ) =>
% 97.21/13.02 ( ( n_eq @ X1 @ X2 ) => ( n_eq @ X0 @ X2 ) ) ) ) ) ) ) ))).
% 97.21/13.02 thf(zip_derived_cl242, plain,
% 97.21/13.02 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 97.21/13.02 (^[Y0 : $i]:
% 97.21/13.02 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 97.21/13.02 (^[Y1 : $i]:
% 97.21/13.02 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 97.21/13.02 (^[Y2 : $i]:
% 97.21/13.02 (((n_eq @ Y0 @ Y1) =>
% 97.21/13.02 (((n_eq @ Y1 @ Y2) => (n_eq @ Y0 @ Y2)))))))))))),
% 97.21/13.02 inference('cnf', [status(esa)], [satz39])).
% 97.21/13.02 thf(zip_derived_cl243, plain,
% 97.21/13.02 ( (all_of @ ((('#C') @ in @ frac)) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.21/13.02 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.21/13.02 n_eq)))))))))),
% 97.21/13.02 inference('lams2combs', [status(thm)], [zip_derived_cl242])).
% 97.21/13.02 thf(zip_derived_cl1154, plain,
% 97.21/13.02 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.21/13.02 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.21/13.02 n_eq)))))))))),
% 97.21/13.02 inference('rw', [status(thm)], [zip_derived_cl243, '0'])).
% 97.21/13.02 thf(zip_derived_cl1155, plain,
% 97.21/13.02 ( (((!!) @ (^[Y0 : $i]:
% 97.21/13.02 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @
% 97.21/13.02 (pair1type @ nat)))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.21/13.02 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @
% 97.21/13.02 n_eq)))))) @
% 97.21/13.02 n_eq)))))) @
% 97.21/13.02 Y0)))))))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl1154, '14'])).
% 97.21/13.02 thf(zip_derived_cl1156, plain,
% 97.21/13.02 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.21/13.02 ((('#C') @ is_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.21/13.02 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @
% 97.21/13.02 n_eq)))))) @
% 97.21/13.02 n_eq))))))))))))),
% 97.21/13.02 inference('comb-normalize', [status(thm)], [zip_derived_cl1155])).
% 97.21/13.02 thf(zip_derived_cl1157, plain,
% 97.21/13.02 (![X2 : $i]:
% 97.21/13.02 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 97.21/13.02 (n_eq @ X2))))))))))),
% 97.21/13.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1156])).
% 97.21/13.02 thf(zip_derived_cl1158, plain,
% 97.21/13.02 (![X2 : $i]:
% 97.21/13.02 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 97.21/13.02 (n_eq @ X2)))))))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1157])).
% 97.21/13.02 thf(zip_derived_cl1159, plain,
% 97.21/13.02 (![X0 : $i]:
% 97.21/13.02 ( (((!!) @ (^[Y0 : $i]:
% 97.21/13.02 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 97.21/13.02 (n_eq @ X0))))) @
% 97.21/13.02 Y0)))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl1158, '14'])).
% 97.21/13.02 thf(zip_derived_cl1160, plain,
% 97.21/13.02 (![X0 : $i]:
% 97.21/13.02 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.21/13.02 ((('#C') @ is_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 97.21/13.02 (n_eq @ X0)))))))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('comb-normalize', [status(thm)], [zip_derived_cl1159])).
% 97.21/13.02 thf(zip_derived_cl1161, plain,
% 97.21/13.02 (![X0 : $i, X2 : $i]:
% 97.21/13.02 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ (n_eq @ X0))))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1160])).
% 97.21/13.02 thf(zip_derived_cl1162, plain,
% 97.21/13.02 (![X0 : $i, X2 : $i]:
% 97.21/13.02 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (n_is @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ (n_eq @ X0))))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('rw', [status(thm)],
% 97.21/13.02 [zip_derived_cl1161, '6', '6', '7', '7', '8', '8', '9', '9',
% 97.21/13.02 '10'])).
% 97.21/13.02 thf(zip_derived_cl1163, plain,
% 97.21/13.02 (![X0 : $i, X2 : $i]:
% 97.21/13.02 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (n_is @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ (n_eq @ X0))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1162])).
% 97.21/13.02 thf(zip_derived_cl1164, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i]:
% 97.21/13.02 ( (((!!) @ (^[Y0 : $i]:
% 97.21/13.02 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 ((('#B') @ (((=>) @ (n_is @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @
% 97.21/13.02 (ap @ X1 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X1 @ n_1t) @
% 97.21/13.02 (ap @ X0 @ n_2t))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @
% 97.21/13.02 (n_eq @ X0))) @
% 97.21/13.02 Y0)))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl1163, '14'])).
% 97.21/13.02 thf(zip_derived_cl1165, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i]:
% 97.21/13.02 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.21/13.02 ((('#C') @ is_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (n_is @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @
% 97.21/13.02 (ap @ X1 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X1 @ n_1t) @
% 97.21/13.02 (ap @ X0 @ n_2t))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @
% 97.21/13.02 (n_eq @ X0)))))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('comb-normalize', [status(thm)], [zip_derived_cl1164])).
% 97.21/13.02 thf(zip_derived_cl1166, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.21/13.02 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))) =>
% 97.21/13.02 (((n_eq @ X1 @ X3) => (n_eq @ X0 @ X3)))))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1165])).
% 97.21/13.02 thf(zip_derived_cl1167, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.21/13.02 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))) =>
% 97.21/13.02 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t))) => (n_is @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)))))))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('rw', [status(thm)],
% 97.21/13.02 [zip_derived_cl1166, '6', '6', '6', '7', '7', '7', '8', '8',
% 97.21/13.02 '8', '9', '9', '9', '10', '10'])).
% 97.21/13.02 thf(zip_derived_cl1168, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.21/13.02 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))) =>
% 97.21/13.02 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t))) => (n_is @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1167])).
% 97.21/13.02 thf(zip_derived_cl1169, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.21/13.02 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))
% 97.21/13.02 | (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t))) => (n_is @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1168])).
% 97.21/13.02 thf(zip_derived_cl1170, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.21/13.02 (~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)))
% 97.21/13.02 | (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)))
% 97.21/13.02 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1169])).
% 97.21/13.02 thf(zip_derived_cl7211, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.21/13.02 (~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)))
% 97.21/13.02 | (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)))
% 97.21/13.02 | ~ (is_of @ X3 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.21/13.02 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.21/13.02 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.21/13.02 | ~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))))),
% 97.21/13.02 inference('remove_ty_args', [status(thm)], [zip_derived_cl1170])).
% 97.21/13.02 thf(satz44, axiom,
% 97.21/13.02 (all_of @
% 97.21/13.02 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 97.21/13.02 ( ^[X0:$i]:
% 97.21/13.02 ( all_of @
% 97.21/13.02 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 97.21/13.02 ( ^[X1:$i]:
% 97.21/13.02 ( all_of @
% 97.21/13.02 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 97.21/13.02 ( ^[X2:$i]:
% 97.21/13.02 ( all_of @
% 97.21/13.02 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 97.21/13.02 ( ^[X3:$i]:
% 97.21/13.02 ( ( moref @ X0 @ X1 ) =>
% 97.21/13.02 ( ( n_eq @ X0 @ X2 ) =>
% 97.21/13.02 ( ( n_eq @ X1 @ X3 ) => ( moref @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 97.21/13.02 thf(zip_derived_cl262, plain,
% 97.21/13.02 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 97.21/13.02 (^[Y0 : $i]:
% 97.21/13.02 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 97.21/13.02 (^[Y1 : $i]:
% 97.21/13.02 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 97.21/13.02 (^[Y2 : $i]:
% 97.21/13.02 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 97.21/13.02 (^[Y3 : $i]:
% 97.21/13.02 (((moref @ Y0 @ Y1) =>
% 97.21/13.02 (((n_eq @ Y0 @ Y2) =>
% 97.21/13.02 (((n_eq @ Y1 @ Y3) => (moref @ Y2 @ Y3)))))))))))))))),
% 97.21/13.02 inference('cnf', [status(esa)], [satz44])).
% 97.21/13.02 thf(zip_derived_cl263, plain,
% 97.21/13.02 ( (all_of @ ((('#C') @ in @ frac)) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.21/13.02 moref)))))))))))))),
% 97.21/13.02 inference('lams2combs', [status(thm)], [zip_derived_cl262])).
% 97.21/13.02 thf(zip_derived_cl2579, plain,
% 97.21/13.02 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @
% 97.21/13.02 (pair1type @ nat)))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.21/13.02 moref)))))))))))))),
% 97.21/13.02 inference('rw', [status(thm)], [zip_derived_cl263, '0'])).
% 97.21/13.02 thf(zip_derived_cl2580, plain,
% 97.21/13.02 ( (((!!) @ (^[Y0 : $i]:
% 97.21/13.02 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @
% 97.21/13.02 (pair1type @ nat)))))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @
% 97.21/13.02 (pair1type @ nat)))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @
% 97.21/13.02 moref)))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @
% 97.21/13.02 n_eq)))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @
% 97.21/13.02 n_eq)))))) @
% 97.21/13.02 moref)))))))))) @
% 97.21/13.02 Y0)))))))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl2579, '14'])).
% 97.21/13.02 thf(zip_derived_cl2581, plain,
% 97.21/13.02 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.21/13.02 ((('#C') @ is_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @
% 97.21/13.02 (pair1type @ nat)))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.21/13.02 moref))))))))))))))))),
% 97.21/13.02 inference('comb-normalize', [status(thm)], [zip_derived_cl2580])).
% 97.21/13.02 thf(zip_derived_cl2582, plain,
% 97.21/13.02 (![X2 : $i]:
% 97.21/13.02 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (moref @ X2))))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (n_eq @ X2))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.21/13.02 moref)))))))))))))),
% 97.21/13.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2581])).
% 97.21/13.02 thf(zip_derived_cl2583, plain,
% 97.21/13.02 (![X2 : $i]:
% 97.21/13.02 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (moref @ X2))))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (n_eq @ X2))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.21/13.02 moref))))))))))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2582])).
% 97.21/13.02 thf(zip_derived_cl2584, plain,
% 97.21/13.02 (![X0 : $i]:
% 97.21/13.02 ( (((!!) @ (^[Y0 : $i]:
% 97.21/13.02 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @
% 97.21/13.02 (pair1type @ nat)))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (moref @ X0))))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @
% 97.21/13.02 (n_eq @ X0))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @
% 97.21/13.02 n_eq)))))) @
% 97.21/13.02 moref)))))))) @
% 97.21/13.02 Y0)))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl2583, '14'])).
% 97.21/13.02 thf(zip_derived_cl2585, plain,
% 97.21/13.02 (![X0 : $i]:
% 97.21/13.02 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.21/13.02 ((('#C') @ is_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @
% 97.21/13.02 (pair1type @ nat)))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (moref @ X0))))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @
% 97.21/13.02 (n_eq @ X0))))))) @
% 97.21/13.02 ((('#C') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ ('#S') @
% 97.21/13.02 ((('#B') @ ((('#B') @ (=>))) @
% 97.21/13.02 n_eq)))))) @
% 97.21/13.02 moref))))))))))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('comb-normalize', [status(thm)], [zip_derived_cl2584])).
% 97.21/13.02 thf(zip_derived_cl2586, plain,
% 97.21/13.02 (![X0 : $i, X2 : $i]:
% 97.21/13.02 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X2))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @
% 97.21/13.02 moref)))))))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2585])).
% 97.21/13.02 thf(zip_derived_cl2587, plain,
% 97.21/13.02 (![X0 : $i, X2 : $i]:
% 97.21/13.02 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @
% 97.21/13.02 (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @
% 97.21/13.02 (ap @ X0 @ n_2t)))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @
% 97.21/13.02 moref)))))))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('rw', [status(thm)],
% 97.21/13.02 [zip_derived_cl2586, '4', '5', '6', '6', '7', '7', '8', '8',
% 97.21/13.02 '9', '9', '11'])).
% 97.21/13.02 thf(zip_derived_cl2588, plain,
% 97.21/13.02 (![X0 : $i, X2 : $i]:
% 97.21/13.02 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @
% 97.21/13.02 (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @
% 97.21/13.02 (ap @ X0 @ n_2t)))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @
% 97.21/13.02 moref)))))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2587])).
% 97.21/13.02 thf(zip_derived_cl2589, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i]:
% 97.21/13.02 ( (((!!) @ (^[Y0 : $i]:
% 97.21/13.02 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 ((('#B') @ (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @
% 97.21/13.02 (ap @ X0 @ n_1t) @
% 97.21/13.02 (ap @ X1 @ n_2t)) @
% 97.21/13.02 (n_ts @
% 97.21/13.02 (ap @ X1 @ n_1t) @
% 97.21/13.02 (ap @ X0 @ n_2t)))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 97.21/13.02 (n_eq @ X1))))) @
% 97.21/13.02 moref)))))) @
% 97.21/13.02 Y0)))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl2588, '14'])).
% 97.21/13.02 thf(zip_derived_cl2590, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i]:
% 97.21/13.02 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.21/13.02 ((('#C') @ is_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.21/13.02 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.21/13.02 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @
% 97.21/13.02 (ap @ X0 @ n_1t) @
% 97.21/13.02 (ap @ X1 @ n_2t)) @
% 97.21/13.02 (n_ts @
% 97.21/13.02 (ap @ X1 @ n_1t) @
% 97.21/13.02 (ap @ X0 @ n_2t)))))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ ('#B') @
% 97.21/13.02 ((('#B') @ (=>) @ (n_eq @ X0))))) @
% 97.21/13.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))))) @
% 97.21/13.02 moref))))))))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('comb-normalize', [status(thm)], [zip_derived_cl2589])).
% 97.21/13.02 thf(zip_derived_cl2591, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.21/13.02 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (n_eq @ X0 @ X3))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (moref @ X3))))))))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2590])).
% 97.21/13.02 thf(zip_derived_cl2592, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.21/13.02 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (n_is @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (moref @ X3))))))))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('rw', [status(thm)],
% 97.21/13.02 [zip_derived_cl2591, '6', '6', '7', '7', '8', '8', '9', '9',
% 97.21/13.02 '10'])).
% 97.21/13.02 thf(zip_derived_cl2593, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.21/13.02 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (n_is @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @
% 97.21/13.02 (ap @ X3 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X3 @ n_1t) @
% 97.21/13.02 (ap @ X0 @ n_2t))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (moref @ X3))))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2592])).
% 97.21/13.02 thf(zip_derived_cl2594, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 97.21/13.02 ( (((!!) @ (^[Y0 : $i]:
% 97.21/13.02 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 ((('#B') @ (((=>) @ (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ X1 @ n_1t) @
% 97.21/13.02 (ap @ X0 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @
% 97.21/13.02 (ap @ X1 @ n_2t)))))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (n_is @
% 97.21/13.02 (n_ts @ (ap @ X1 @ n_1t) @
% 97.21/13.02 (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @
% 97.21/13.02 (ap @ X1 @ n_2t))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @
% 97.21/13.02 (moref @ X2))))) @
% 97.21/13.02 Y0)))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('rw_clause', [status(thm)], [zip_derived_cl2593, '14'])).
% 97.21/13.02 thf(zip_derived_cl2595, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X2 : $i]:
% 97.21/13.02 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.21/13.02 ((('#C') @ is_of @
% 97.21/13.02 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (l_some @ nat @
% 97.21/13.02 (diffprop @
% 97.21/13.02 (n_ts @ (ap @ X1 @ n_1t) @
% 97.21/13.02 (ap @ X0 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @
% 97.21/13.02 (ap @ X1 @ n_2t)))))) @
% 97.21/13.02 ((('#B') @ (((=>) @ (n_is @
% 97.21/13.02 (n_ts @ (ap @ X1 @ n_1t) @
% 97.21/13.02 (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @
% 97.21/13.02 (ap @ X1 @ n_2t))))) @
% 97.21/13.02 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @
% 97.21/13.02 (moref @ X2)))))))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('comb-normalize', [status(thm)], [zip_derived_cl2594])).
% 97.21/13.02 thf(zip_derived_cl2596, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.21/13.02 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 (((l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) =>
% 97.21/13.02 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) =>
% 97.21/13.02 (((n_eq @ X0 @ X4) => (moref @ X2 @ X4)))))))))
% 97.21/13.02 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2595])).
% 97.21/13.02 thf(zip_derived_cl2597, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.21/13.02 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.21/13.02 (((l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) =>
% 97.21/13.02 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) =>
% 97.21/13.02 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @
% 97.21/13.02 nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t))))))))))))
% 97.21/13.02 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('rw', [status(thm)],
% 97.21/13.02 [zip_derived_cl2596, '4', '5', '6', '6', '6', '7', '7', '7',
% 97.21/13.02 '8', '8', '8', '9', '9', '9', '10', '11'])).
% 97.21/13.02 thf(zip_derived_cl2598, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.21/13.02 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | (((l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) =>
% 97.21/13.02 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) =>
% 97.21/13.02 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @
% 97.21/13.02 nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t))))))))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2597])).
% 97.21/13.02 thf(zip_derived_cl2599, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.21/13.02 (~ (l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t))))
% 97.21/13.02 | (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) =>
% 97.21/13.02 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @
% 97.21/13.02 nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t))))))))
% 97.21/13.02 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2598])).
% 97.21/13.02 thf(zip_derived_cl2600, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.21/13.02 (~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t)))
% 97.21/13.02 | (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @
% 97.21/13.02 nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t))))))
% 97.21/13.02 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2599])).
% 97.21/13.02 thf(zip_derived_cl2601, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.21/13.02 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t)))
% 97.21/13.02 | (l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t))))
% 97.21/13.02 | ~ (l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t))))
% 97.21/13.02 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.21/13.02 | ~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))))),
% 97.21/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2600])).
% 97.21/13.02 thf(zip_derived_cl7255, plain,
% 97.21/13.02 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.21/13.02 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t)))
% 97.21/13.02 | (l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t))))
% 97.21/13.02 | ~ (l_some @ nat @
% 97.21/13.02 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t))))
% 97.21/13.02 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.21/13.02 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.21/13.02 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.21/13.02 | ~ (is_of @ X4 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.21/13.02 | ~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @
% 97.21/13.02 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))))),
% 97.21/13.02 inference('remove_ty_args', [status(thm)], [zip_derived_cl2601])).
% 97.21/13.02 thf(zip_derived_cl7277, plain, ($false),
% 97.21/13.02 inference('eprover', [status(thm)],
% 97.21/13.02 [zip_derived_cl4152, zip_derived_cl4150, zip_derived_cl7221,
% 97.21/13.02 zip_derived_cl1320, zip_derived_cl1317, zip_derived_cl7220,
% 97.21/13.02 zip_derived_cl4149, zip_derived_cl7178, zip_derived_cl7219,
% 97.21/13.02 zip_derived_cl7218, zip_derived_cl1325, zip_derived_cl1330,
% 97.21/13.02 zip_derived_cl7211, zip_derived_cl7255])).
% 97.21/13.02
% 97.21/13.02 % SZS output end Refutation
% 97.21/13.02
% 97.21/13.02
% 97.21/13.02 % Terminating...
% 97.82/13.16 % Runner terminated.
% 97.82/13.17 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------