%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM761^4 : TPTP v9.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.fDVfzDu4Ni true
% Computer : n016.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 04:48:16 PM UTC 2025
% Result : Theorem 97.28s 12.83s
% Output : Refutation 97.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM761^4 : TPTP v9.2.0. Released v7.1.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.fDVfzDu4Ni true
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 16:38:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.53/0.63 % Total configuration time : 828
% 0.53/0.63 % Estimated wc time : 1656
% 0.53/0.63 % Estimated cpu time (8 cpus) : 207.0
% 0.53/0.67 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.53/0.70 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.53/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.53/0.72 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.53/0.73 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.53/0.73 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.53/0.73 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.53/0.75 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 97.28/12.83 % Solved by lams/40_b.comb.sh.
% 97.28/12.83 % done 706 iterations in 12.018s
% 97.28/12.83 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 97.28/12.83 % SZS output start Refutation
% 97.28/12.83 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
% 97.28/12.83 thf('#sk2_type', type, '#sk2': $i).
% 97.28/12.83 thf(moreq_type, type, moreq: $i > $i > $o).
% 97.28/12.83 thf(lessf_type, type, lessf: $i > $i > $o).
% 97.28/12.83 thf(nat_type, type, nat: $i).
% 97.28/12.83 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 97.28/12.83 thf(in_type, type, in: $i > $i > $o).
% 97.28/12.83 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 97.28/12.83 thf(n_pf_type, type, n_pf: $i > $i > $i).
% 97.28/12.83 thf(n_fr_type, type, n_fr: $i > $i > $i).
% 97.28/12.83 thf('#sk3_type', type, '#sk3': $i).
% 97.28/12.83 thf(imp_type, type, imp: $o > $o > $o).
% 97.28/12.83 thf(frac_type, type, frac: $i).
% 97.28/12.83 thf('#sk5_type', type, '#sk5': $i).
% 97.28/12.83 thf('#ty_enc6_type', type, '#ty_enc6': ($i > $i > $o) > $i > $i > $o).
% 97.28/12.83 thf(n_ts_type, type, n_ts: $i > $i > $i).
% 97.28/12.83 thf(n_eq_type, type, n_eq: $i > $i > $o).
% 97.28/12.83 thf(pair1type_type, type, pair1type: $i > $i).
% 97.28/12.83 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 97.28/12.83 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 97.28/12.83 thf('#sk4_type', type, '#sk4': $i).
% 97.28/12.83 thf(num_type, type, num: $i > $i).
% 97.28/12.83 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 97.28/12.83 thf(l_or_type, type, l_or: $o > $o > $o).
% 97.28/12.83 thf(moref_type, type, moref: $i > $i > $o).
% 97.28/12.83 thf(d_not_type, type, d_not: $o > $o).
% 97.28/12.83 thf(den_type, type, den: $i > $i).
% 97.28/12.83 thf(n_pl_type, type, n_pl: $i > $i > $i).
% 97.28/12.83 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 97.28/12.83 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 97.28/12.83 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 97.28/12.83 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 97.28/12.83 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 97.28/12.83 thf(satz42, axiom,
% 97.28/12.83 (all_of @
% 97.28/12.83 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 97.28/12.83 ( ^[X0:$i]:
% 97.28/12.83 ( all_of @
% 97.28/12.83 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 97.28/12.83 ( ^[X1:$i]: ( ( moref @ X0 @ X1 ) => ( lessf @ X1 @ X0 ) ) ) ) ))).
% 97.28/12.83 thf(zip_derived_cl260, plain,
% 97.28/12.83 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 97.28/12.83 (^[Y0 : $i]:
% 97.28/12.83 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 97.28/12.83 (^[Y1 : $i]: (((moref @ Y0 @ Y1) => (lessf @ Y1 @ Y0)))))))),
% 97.28/12.83 inference('cnf', [status(esa)], [satz42])).
% 97.28/12.83 thf(zip_derived_cl261, plain,
% 97.28/12.83 ( (all_of @ ((('#C') @ in @ frac)) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ lessf)))))))),
% 97.28/12.83 inference('lams2combs', [status(thm)], [zip_derived_cl260])).
% 97.28/12.83 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))).
% 97.28/12.83 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])).
% 97.28/12.83 thf(zip_derived_cl558, plain,
% 97.28/12.83 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ lessf)))))))),
% 97.28/12.83 inference('rw', [status(thm)], [zip_derived_cl261, '0'])).
% 97.28/12.83 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 97.28/12.83 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 97.28/12.83 thf('1', plain,
% 97.28/12.83 (![X0:( $i > $o ),X1:( $i > $o )]:
% 97.28/12.83 ( ( all_of @ X0 @ X1 ) <=>
% 97.28/12.83 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 97.28/12.83 inference('rw.lit', [status(esa)], [def_all_of])).
% 97.28/12.83 thf(zip_derived_cl559, plain,
% 97.28/12.83 ( (((!!) @ (^[Y0 : $i]:
% 97.28/12.83 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ lessf)))) @
% 97.28/12.83 Y0)))))))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl558, '1'])).
% 97.28/12.83 thf(zip_derived_cl560, plain,
% 97.28/12.83 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.28/12.83 ((('#C') @ is_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ lessf))))))))))),
% 97.28/12.83 inference('comb-normalize', [status(thm)], [zip_derived_cl559])).
% 97.28/12.83 thf(zip_derived_cl561, plain,
% 97.28/12.83 (![X2 : $i]:
% 97.28/12.83 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @
% 97.28/12.83 ((('#C') @ lessf @ X2)))))))),
% 97.28/12.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl560])).
% 97.28/12.83 thf(zip_derived_cl562, plain,
% 97.28/12.83 (![X2 : $i]:
% 97.28/12.83 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @
% 97.28/12.83 ((('#C') @ lessf @ X2))))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl561])).
% 97.28/12.83 thf(zip_derived_cl563, plain,
% 97.28/12.83 (![X0 : $i]:
% 97.28/12.83 ( (((!!) @ (^[Y0 : $i]:
% 97.28/12.83 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ X0))) @
% 97.28/12.83 ((('#C') @ lessf @ X0)) @ Y0)))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl562, '1'])).
% 97.28/12.83 thf(zip_derived_cl564, plain,
% 97.28/12.83 (![X0 : $i]:
% 97.28/12.83 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.28/12.83 ((('#C') @ is_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ X0))) @
% 97.28/12.83 ((('#C') @ lessf @ X0))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('comb-normalize', [status(thm)], [zip_derived_cl563])).
% 97.28/12.83 thf(zip_derived_cl565, plain,
% 97.28/12.83 (![X0 : $i, X2 : $i]:
% 97.28/12.83 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 (((moref @ X0 @ X2) => (lessf @ X2 @ X0)))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl564])).
% 97.28/12.83 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 97.28/12.83 thf('2', plain,
% 97.28/12.83 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 97.28/12.83 define([status(thm)])).
% 97.28/12.83 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) =
% 97.28/12.83 ((n_some @ (diffprop @ X0 @ X1))))).
% 97.28/12.83 thf('3', plain,
% 97.28/12.83 (![X1:$i,X0:$i]:
% 97.28/12.83 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 97.28/12.83 define([status(thm)])).
% 97.28/12.83 thf(def_moref, axiom,(( moref @ (X0)@ (X1)) =
% 97.28/12.83 ((d_29_ii @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 97.28/12.83 (n_ts @ (num @ X1) @ (den @ X0)))))).
% 97.28/12.83 thf('4', plain,
% 97.28/12.83 (![X1:$i,X0:$i]:
% 97.28/12.83 ( ( moref @ X0 @ X1 ) =
% 97.28/12.83 ( d_29_ii @
% 97.28/12.83 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 97.28/12.83 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )),
% 97.28/12.83 define([status(thm)])).
% 97.28/12.83 thf(zip_derived_cl566, plain,
% 97.28/12.83 (![X0 : $i, X2 : $i]:
% 97.28/12.83 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 (((l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X0) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X0)))) =>
% 97.28/12.83 (lessf @ X2 @ X0)))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('rw', [status(thm)], [zip_derived_cl565, '2', '3', '4'])).
% 97.28/12.83 thf(zip_derived_cl567, plain,
% 97.28/12.83 (![X0 : $i, X2 : $i]:
% 97.28/12.83 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | (((l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X0) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X0)))) =>
% 97.28/12.83 (lessf @ X2 @ X0)))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl566])).
% 97.28/12.83 thf(zip_derived_cl568, plain,
% 97.28/12.83 (![X0 : $i, X2 : $i]:
% 97.28/12.83 (~ (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X0) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X0))))
% 97.28/12.83 | (lessf @ X2 @ X0)
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl567])).
% 97.28/12.83 thf(satz65a, conjecture,
% 97.28/12.83 (all_of @
% 97.28/12.83 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 97.28/12.83 ( ^[X0:$i]:
% 97.28/12.83 ( all_of @
% 97.28/12.83 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 97.28/12.83 ( ^[X1:$i]:
% 97.28/12.83 ( all_of @
% 97.28/12.83 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 97.28/12.83 ( ^[X2:$i]:
% 97.28/12.83 ( all_of @
% 97.28/12.83 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 97.28/12.83 ( ^[X3:$i]:
% 97.28/12.83 ( ( moreq @ X0 @ X1 ) =>
% 97.28/12.83 ( ( moref @ X2 @ X3 ) =>
% 97.28/12.83 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 97.28/12.83 thf(zf_stmt_0, negated_conjecture,
% 97.28/12.83 (~( all_of @
% 97.28/12.83 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 97.28/12.83 ( ^[X0:$i]:
% 97.28/12.83 ( all_of @
% 97.28/12.83 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 97.28/12.83 ( ^[X1:$i]:
% 97.28/12.83 ( all_of @
% 97.28/12.83 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 97.28/12.83 ( ^[X2:$i]:
% 97.28/12.83 ( all_of @
% 97.28/12.83 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 97.28/12.83 ( ^[X3:$i]:
% 97.28/12.83 ( ( moreq @ X0 @ X1 ) =>
% 97.28/12.83 ( ( moref @ X2 @ X3 ) =>
% 97.28/12.83 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) )),
% 97.28/12.83 inference('cnf.neg', [status(esa)], [satz65a])).
% 97.28/12.83 thf(zip_derived_cl356, plain,
% 97.28/12.83 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 97.28/12.83 (^[Y0 : $i]:
% 97.28/12.83 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 97.28/12.83 (^[Y1 : $i]:
% 97.28/12.83 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 97.28/12.83 (^[Y2 : $i]:
% 97.28/12.83 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 97.28/12.83 (^[Y3 : $i]:
% 97.28/12.83 (((moreq @ Y0 @ Y1) =>
% 97.28/12.83 (((moref @ Y2 @ Y3) => (moref @ (n_pf @ Y0 @ Y2) @
% 97.28/12.83 (n_pf @ Y1 @ Y3))))))))))))))),
% 97.28/12.83 inference('cnf', [status(esa)], [zf_stmt_0])).
% 97.28/12.83 thf(zip_derived_cl357, plain,
% 97.28/12.83 (~ (all_of @ ((('#C') @ in @ frac)) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @
% 97.28/12.83 moref)))))))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#C') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @
% 97.28/12.83 n_pf)))))))))))))),
% 97.28/12.83 inference('lams2combs', [status(thm)], [zip_derived_cl356])).
% 97.28/12.83 thf(zip_derived_cl1341, plain,
% 97.28/12.83 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @
% 97.28/12.83 moref)))))))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#C') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @
% 97.28/12.83 n_pf)))))))))))))),
% 97.28/12.83 inference('rw', [status(thm)], [zip_derived_cl357, '0'])).
% 97.28/12.83 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 97.28/12.83 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 97.28/12.83 thf('5', plain,
% 97.28/12.83 (![X0:( $i > $o ),X1:( $i > $o )]:
% 97.28/12.83 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 97.28/12.83 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 97.28/12.83 inference('rw.lit', [status(esa)], [def_all_of])).
% 97.28/12.83 thf(zip_derived_cl1342, plain,
% 97.28/12.83 (~ (((!!) @ (^[Y0 : $i]:
% 97.28/12.83 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @
% 97.28/12.83 moreq)))))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 97.28/12.83 '#S') @
% 97.28/12.83 ((('#B') @ (
% 97.28/12.83 (('#B') @ (
% 97.28/12.83 =>))) @
% 97.28/12.83 moref)))))))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#C') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ moref)) @
% 97.28/12.83 n_pf)))))))) @
% 97.28/12.83 n_pf)))))))))) @
% 97.28/12.83 Y0)))))))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl1341, '5'])).
% 97.28/12.83 thf(zip_derived_cl1343, plain,
% 97.28/12.83 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.28/12.83 ((('#C') @ is_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 97.28/12.83 '#S') @
% 97.28/12.83 ((('#B') @ (
% 97.28/12.83 (('#B') @ (=>))) @
% 97.28/12.83 moref)))))))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#C') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ moref)) @
% 97.28/12.83 n_pf)))))))) @
% 97.28/12.83 n_pf))))))))))))))))),
% 97.28/12.83 inference('comb-normalize', [status(thm)], [zip_derived_cl1342])).
% 97.28/12.83 thf(zip_derived_cl1344, plain,
% 97.28/12.83 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @
% 97.28/12.83 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @
% 97.28/12.83 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ '#sk2'))))))) @
% 97.28/12.83 n_pf)))))))))))))),
% 97.28/12.83 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1343])).
% 97.28/12.83 thf(zip_derived_cl1346, plain,
% 97.28/12.83 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @
% 97.28/12.83 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @
% 97.28/12.83 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ '#sk2'))))))) @
% 97.28/12.83 n_pf)))))))))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1344])).
% 97.28/12.83 thf(zip_derived_cl1347, plain,
% 97.28/12.83 (~ (((!!) @ (^[Y0 : $i]:
% 97.28/12.83 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @
% 97.28/12.83 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @
% 97.28/12.83 moref)))))) @
% 97.28/12.83 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @
% 97.28/12.83 (n_pf @ '#sk2'))))))) @
% 97.28/12.83 n_pf)))))))) @
% 97.28/12.83 Y0)))))))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl1346, '5'])).
% 97.28/12.83 thf(zip_derived_cl1348, plain,
% 97.28/12.83 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.28/12.83 ((('#C') @ is_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @
% 97.28/12.83 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @
% 97.28/12.83 moref)))))) @
% 97.28/12.83 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @
% 97.28/12.83 (n_pf @ '#sk2'))))))) @
% 97.28/12.83 n_pf))))))))))))))),
% 97.28/12.83 inference('comb-normalize', [status(thm)], [zip_derived_cl1347])).
% 97.28/12.83 thf(zip_derived_cl1349, plain,
% 97.28/12.83 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (((=>) @ (moreq @ '#sk2' @ '#sk3'))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @
% 97.28/12.83 (n_pf @ '#sk3'))))))))))))),
% 97.28/12.83 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1348])).
% 97.28/12.83 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 97.28/12.83 thf('6', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 97.28/12.83 define([status(thm)])).
% 97.28/12.83 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 97.28/12.83 thf('7', plain,
% 97.28/12.83 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 97.28/12.83 define([status(thm)])).
% 97.28/12.83 thf(def_moreq, axiom,(( moreq @ (X0)@ (X1)) =
% 97.28/12.83 ((l_or @ (moref @ X0 @ X1) @ (n_eq @ X0 @ X1))))).
% 97.28/12.83 thf('8', plain,
% 97.28/12.83 (![X1:$i,X0:$i]:
% 97.28/12.83 ( ( moreq @ X0 @ X1 ) =
% 97.28/12.83 ( l_or @ ( moref @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )),
% 97.28/12.83 define([status(thm)])).
% 97.28/12.83 thf(zip_derived_cl1350, plain,
% 97.28/12.83 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 97.28/12.83 (imp @
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @ (num @ '#sk2') @
% 97.28/12.83 (den @ '#sk3')) @
% 97.28/12.83 (n_ts @ (num @ '#sk3') @
% 97.28/12.83 (den @ '#sk2')))) @
% 97.28/12.83 ($false)) @
% 97.28/12.83 (n_eq @ '#sk2' @ '#sk3')))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @
% 97.28/12.83 (n_pf @ '#sk3'))))))))))))),
% 97.28/12.83 inference('rw', [status(thm)],
% 97.28/12.83 [zip_derived_cl1349, '6', '7', '2', '3', '4', '8'])).
% 97.28/12.83 thf(zip_derived_cl1352, plain,
% 97.28/12.83 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 97.28/12.83 (imp @
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @ (num @ '#sk2') @
% 97.28/12.83 (den @ '#sk3')) @
% 97.28/12.83 (n_ts @ (num @ '#sk3') @
% 97.28/12.83 (den @ '#sk2')))) @
% 97.28/12.83 ($false)) @
% 97.28/12.83 (n_eq @ '#sk2' @ '#sk3')))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @
% 97.28/12.83 (n_pf @ '#sk3'))))))))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1350])).
% 97.28/12.83 thf(zip_derived_cl1353, plain,
% 97.28/12.83 (~ (((!!) @ (^[Y0 : $i]:
% 97.28/12.83 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 97.28/12.83 (imp @
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @ '#sk2') @
% 97.28/12.83 (den @ '#sk3')) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @ '#sk3') @
% 97.28/12.83 (den @ '#sk2')))) @
% 97.28/12.83 ($false)) @
% 97.28/12.83 (n_eq @ '#sk2' @
% 97.28/12.83 '#sk3')))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @
% 97.28/12.83 (n_pf @ '#sk3'))))))) @
% 97.28/12.83 Y0)))))))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl1352, '5'])).
% 97.28/12.83 thf(zip_derived_cl1354, plain,
% 97.28/12.83 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.28/12.83 ((('#C') @ is_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 97.28/12.83 (imp @
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @ '#sk2') @
% 97.28/12.83 (den @ '#sk3')) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @ '#sk3') @
% 97.28/12.83 (den @ '#sk2')))) @
% 97.28/12.83 ($false)) @
% 97.28/12.83 (n_eq @ '#sk2' @ '#sk3')))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @
% 97.28/12.83 (n_pf @ '#sk3')))))))))))))),
% 97.28/12.83 inference('comb-normalize', [status(thm)], [zip_derived_cl1353])).
% 97.28/12.83 thf(zip_derived_cl1355, plain,
% 97.28/12.83 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (((=>) @ (imp @
% 97.28/12.83 (imp @
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.28/12.83 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @
% 97.28/12.83 ($false)) @
% 97.28/12.83 (n_eq @ '#sk2' @ '#sk3')))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ '#sk4'))) @
% 97.28/12.83 ((('#B') @ (moref @ (n_pf @ '#sk2' @ '#sk4')) @ (n_pf @ '#sk3'))))))))))),
% 97.28/12.83 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1354])).
% 97.28/12.83 thf(def_n_pf, axiom,(( n_pf @ (X0)@ (X1)) =
% 97.28/12.83 ((n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 97.28/12.83 (n_ts @ (num @ X1) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X1)))))).
% 97.28/12.83 thf('9', plain,
% 97.28/12.83 (![X1:$i,X0:$i]:
% 97.28/12.83 ( ( n_pf @ X0 @ X1 ) =
% 97.28/12.83 ( n_fr @
% 97.28/12.83 ( n_pl @
% 97.28/12.83 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 97.28/12.83 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) @
% 97.28/12.83 ( n_ts @ ( den @ X0 ) @ ( den @ X1 ) ) ) )),
% 97.28/12.83 define([status(thm)])).
% 97.28/12.83 thf(zip_derived_cl1356, plain,
% 97.28/12.83 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (((=>) @ (imp @
% 97.28/12.83 (imp @
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.28/12.83 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @
% 97.28/12.83 ($false)) @
% 97.28/12.83 (n_eq @ '#sk2' @ '#sk3')))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ '#sk4'))) @
% 97.28/12.83 ((('#B') @ (moref @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.28/12.83 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 97.28/12.83 (n_pf @ '#sk3'))))))))))),
% 97.28/12.83 inference('rw', [status(thm)], [zip_derived_cl1355, '9'])).
% 97.28/12.83 thf(zip_derived_cl1358, plain,
% 97.28/12.83 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (((=>) @ (imp @
% 97.28/12.83 (imp @
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.28/12.83 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @
% 97.28/12.83 ($false)) @
% 97.28/12.83 (n_eq @ '#sk2' @ '#sk3')))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ '#sk4'))) @
% 97.28/12.83 ((('#B') @ (moref @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.28/12.83 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 97.28/12.83 (n_pf @ '#sk3'))))))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1356])).
% 97.28/12.83 thf(zip_derived_cl1359, plain,
% 97.28/12.83 (~ (((!!) @ (^[Y0 : $i]:
% 97.28/12.83 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 ((('#B') @ (((=>) @ (imp @
% 97.28/12.83 (imp @
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @ (num @ '#sk2') @
% 97.28/12.83 (den @ '#sk3')) @
% 97.28/12.83 (n_ts @ (num @ '#sk3') @
% 97.28/12.83 (den @ '#sk2')))) @
% 97.28/12.83 ($false)) @
% 97.28/12.83 (n_eq @ '#sk2' @ '#sk3')))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ '#sk4'))) @
% 97.28/12.83 ((('#B') @ (moref @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @
% 97.28/12.83 (n_ts @ (num @ '#sk2') @
% 97.28/12.83 (den @ '#sk4')) @
% 97.28/12.83 (n_ts @ (num @ '#sk4') @
% 97.28/12.83 (den @ '#sk2'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 97.28/12.83 (n_pf @ '#sk3'))))) @
% 97.28/12.83 Y0)))))))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl1358, '5'])).
% 97.28/12.83 thf(zip_derived_cl1360, plain,
% 97.28/12.83 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.28/12.83 ((('#C') @ is_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.28/12.83 ((('#B') @ (((=>) @ (imp @
% 97.28/12.83 (imp @
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @ (num @ '#sk2') @
% 97.28/12.83 (den @ '#sk3')) @
% 97.28/12.83 (n_ts @ (num @ '#sk3') @
% 97.28/12.83 (den @ '#sk2')))) @
% 97.28/12.83 ($false)) @
% 97.28/12.83 (n_eq @ '#sk2' @ '#sk3')))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ '#sk4'))) @
% 97.28/12.83 ((('#B') @ (moref @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @
% 97.28/12.83 (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.28/12.83 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 97.28/12.83 (n_pf @ '#sk3')))))))))))),
% 97.28/12.83 inference('comb-normalize', [status(thm)], [zip_derived_cl1359])).
% 97.28/12.83 thf(zip_derived_cl1361, plain,
% 97.28/12.83 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 (((imp @
% 97.28/12.83 (imp @
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.28/12.83 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @
% 97.28/12.83 ($false)) @
% 97.28/12.83 (n_eq @ '#sk2' @ '#sk3')) =>
% 97.28/12.83 (((moref @ '#sk4' @ '#sk5') => (moref @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.28/12.83 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 97.28/12.83 (n_pf @ '#sk3' @ '#sk5'))))))))),
% 97.28/12.83 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1360])).
% 97.28/12.83 thf(zip_derived_cl1362, plain,
% 97.28/12.83 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 (((imp @
% 97.28/12.83 (imp @
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.28/12.83 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @
% 97.28/12.83 ($false)) @
% 97.28/12.83 (n_eq @ '#sk2' @ '#sk3')) =>
% 97.28/12.83 (((l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @
% 97.28/12.83 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) =>
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.28/12.83 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 97.28/12.83 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 97.28/12.83 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.28/12.83 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))))))))))))),
% 97.28/12.83 inference('rw', [status(thm)],
% 97.28/12.83 [zip_derived_cl1361, '2', '2', '3', '3', '4', '4', '9'])).
% 97.28/12.83 thf(zip_derived_cl1364, plain,
% 97.28/12.83 (~ (((imp @
% 97.28/12.83 (imp @
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.28/12.83 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @
% 97.28/12.83 ($false)) @
% 97.28/12.83 (n_eq @ '#sk2' @ '#sk3')) =>
% 97.28/12.83 (((l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @
% 97.28/12.83 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) =>
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.28/12.83 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 97.28/12.83 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 97.28/12.83 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.28/12.83 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))))))))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1362])).
% 97.28/12.83 thf(zip_derived_cl1365, plain,
% 97.28/12.83 ( (imp @
% 97.28/12.83 (imp @
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.28/12.83 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @
% 97.28/12.83 ($false)) @
% 97.28/12.83 (n_eq @ '#sk2' @ '#sk3'))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1364])).
% 97.28/12.83 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 97.28/12.83 thf('10', plain,
% 97.28/12.83 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 97.28/12.83 inference('rw.lit', [status(esa)], [def_imp])).
% 97.28/12.83 thf(zip_derived_cl1367, plain,
% 97.28/12.83 ( (((imp @
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.28/12.83 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @
% 97.28/12.83 ($false)) => (n_eq @ '#sk2' @ '#sk3')))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl1365, '10'])).
% 97.28/12.83 thf(zip_derived_cl1370, plain,
% 97.28/12.83 ((~ (imp @
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.28/12.83 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @
% 97.28/12.83 ($false))
% 97.28/12.83 | (n_eq @ '#sk2' @ '#sk3'))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1367])).
% 97.28/12.83 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 97.28/12.83 thf('11', plain,
% 97.28/12.83 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 97.28/12.83 inference('rw.lit', [status(esa)], [def_imp])).
% 97.28/12.83 thf(zip_derived_cl1371, plain,
% 97.28/12.83 ((~ (((l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.28/12.83 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) =>
% 97.28/12.83 ($false)))
% 97.28/12.83 | (n_eq @ '#sk2' @ '#sk3'))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl1370, '11'])).
% 97.28/12.83 thf(zip_derived_cl1372, plain,
% 97.28/12.83 ((~ (((~) @ (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.28/12.83 (n_ts @ (num @ '#sk3') @ (den @ '#sk2'))))))
% 97.28/12.83 | (n_eq @ '#sk2' @ '#sk3'))),
% 97.28/12.83 inference('simplify boolean subterms', [status(thm)],
% 97.28/12.83 [zip_derived_cl1371])).
% 97.28/12.83 thf(zip_derived_cl1373, plain,
% 97.28/12.83 (( (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.28/12.83 (n_ts @ (num @ '#sk3') @ (den @ '#sk2'))))
% 97.28/12.83 | (n_eq @ '#sk2' @ '#sk3'))),
% 97.28/12.83 inference('simplify nested equalities', [status(thm)],
% 97.28/12.83 [zip_derived_cl1372])).
% 97.28/12.83 thf(zip_derived_cl13866, plain,
% 97.28/12.83 ((~ (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | (lessf @ '#sk3' @ '#sk2')
% 97.28/12.83 | (n_eq @ '#sk2' @ '#sk3'))),
% 97.28/12.83 inference('sup+', [status(thm)], [zip_derived_cl568, zip_derived_cl1373])).
% 97.28/12.83 thf(zip_derived_cl1351, plain,
% 97.28/12.83 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1350])).
% 97.28/12.83 thf(zip_derived_cl1345, plain,
% 97.28/12.83 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1344])).
% 97.28/12.83 thf(zip_derived_cl13894, plain,
% 97.28/12.83 (( (lessf @ '#sk3' @ '#sk2') | (n_eq @ '#sk2' @ '#sk3'))),
% 97.28/12.83 inference('demod', [status(thm)],
% 97.28/12.83 [zip_derived_cl13866, zip_derived_cl1351, zip_derived_cl1345])).
% 97.28/12.83 thf(zip_derived_cl1357, plain,
% 97.28/12.83 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1356])).
% 97.28/12.83 thf(zip_derived_cl17273, plain,
% 97.28/12.83 ( (is_of @ '#sk4' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 97.28/12.83 inference('remove_ty_args', [status(thm)], [zip_derived_cl1357])).
% 97.28/12.83 thf(zip_derived_cl1363, plain,
% 97.28/12.83 ( (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1362])).
% 97.28/12.83 thf(zip_derived_cl17274, plain,
% 97.28/12.83 ( (is_of @ '#sk5' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 97.28/12.83 inference('remove_ty_args', [status(thm)], [zip_derived_cl1363])).
% 97.28/12.83 thf(zip_derived_cl1345, plain,
% 97.28/12.83 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1344])).
% 97.28/12.83 thf(zip_derived_cl17271, plain,
% 97.28/12.83 ( (is_of @ '#sk2' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 97.28/12.83 inference('remove_ty_args', [status(thm)], [zip_derived_cl1345])).
% 97.28/12.83 thf(zip_derived_cl1351, plain,
% 97.28/12.83 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1350])).
% 97.28/12.83 thf(zip_derived_cl17272, plain,
% 97.28/12.83 ( (is_of @ '#sk3' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 97.28/12.83 inference('remove_ty_args', [status(thm)], [zip_derived_cl1351])).
% 97.28/12.83 thf(zip_derived_cl1366, plain,
% 97.28/12.83 (~ (((l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @
% 97.28/12.83 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) =>
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.28/12.83 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 97.28/12.83 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 97.28/12.83 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.28/12.83 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))))))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1364])).
% 97.28/12.83 thf(zip_derived_cl1368, plain,
% 97.28/12.83 ( (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @
% 97.28/12.83 (n_ts @ (num @ '#sk5') @ (den @ '#sk4'))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1366])).
% 97.28/12.83 thf(satz43, axiom,
% 97.28/12.83 (all_of @
% 97.28/12.83 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 97.28/12.83 ( ^[X0:$i]:
% 97.28/12.83 ( all_of @
% 97.28/12.83 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 97.28/12.83 ( ^[X1:$i]: ( ( lessf @ X0 @ X1 ) => ( moref @ X1 @ X0 ) ) ) ) ))).
% 97.28/12.83 thf(zip_derived_cl262, plain,
% 97.28/12.83 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 97.28/12.83 (^[Y0 : $i]:
% 97.28/12.83 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 97.28/12.83 (^[Y1 : $i]: (((lessf @ Y0 @ Y1) => (moref @ Y1 @ Y0)))))))),
% 97.28/12.83 inference('cnf', [status(esa)], [satz43])).
% 97.28/12.83 thf(zip_derived_cl263, plain,
% 97.28/12.83 ( (all_of @ ((('#C') @ in @ frac)) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @
% 97.28/12.83 ((('#C') @ moref)))))))),
% 97.28/12.83 inference('lams2combs', [status(thm)], [zip_derived_cl262])).
% 97.28/12.83 thf(zip_derived_cl569, plain,
% 97.28/12.83 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @
% 97.28/12.83 ((('#C') @ moref)))))))),
% 97.28/12.83 inference('rw', [status(thm)], [zip_derived_cl263, '0'])).
% 97.28/12.83 thf(zip_derived_cl570, plain,
% 97.28/12.83 ( (((!!) @ (^[Y0 : $i]:
% 97.28/12.83 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @
% 97.28/12.83 ((('#C') @ moref)))) @
% 97.28/12.83 Y0)))))))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl569, '1'])).
% 97.28/12.83 thf(zip_derived_cl571, plain,
% 97.28/12.83 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.28/12.83 ((('#C') @ is_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @
% 97.28/12.83 ((('#C') @ moref))))))))))),
% 97.28/12.83 inference('comb-normalize', [status(thm)], [zip_derived_cl570])).
% 97.28/12.83 thf(zip_derived_cl572, plain,
% 97.28/12.83 (![X2 : $i]:
% 97.28/12.83 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @
% 97.28/12.83 ((('#C') @ moref @ X2)))))))),
% 97.28/12.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl571])).
% 97.28/12.83 thf(zip_derived_cl573, plain,
% 97.28/12.83 (![X2 : $i]:
% 97.28/12.83 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @
% 97.28/12.83 ((('#C') @ moref @ X2))))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl572])).
% 97.28/12.83 thf(zip_derived_cl574, plain,
% 97.28/12.83 (![X0 : $i]:
% 97.28/12.83 ( (((!!) @ (^[Y0 : $i]:
% 97.28/12.83 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X0))) @
% 97.28/12.83 ((('#C') @ moref @ X0)) @ Y0)))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl573, '1'])).
% 97.28/12.83 thf(zip_derived_cl575, plain,
% 97.28/12.83 (![X0 : $i]:
% 97.28/12.83 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.28/12.83 ((('#C') @ is_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X0))) @
% 97.28/12.83 ((('#C') @ moref @ X0))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('comb-normalize', [status(thm)], [zip_derived_cl574])).
% 97.28/12.83 thf(zip_derived_cl576, plain,
% 97.28/12.83 (![X0 : $i, X2 : $i]:
% 97.28/12.83 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 (((lessf @ X0 @ X2) => (moref @ X2 @ X0)))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl575])).
% 97.28/12.83 thf(zip_derived_cl577, plain,
% 97.28/12.83 (![X0 : $i, X2 : $i]:
% 97.28/12.83 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 (((lessf @ X0 @ X2) => (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X2) @ (den @ X0)) @
% 97.28/12.83 (n_ts @ (num @ X0) @ (den @ X2))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('rw', [status(thm)], [zip_derived_cl576, '2', '3', '4'])).
% 97.28/12.83 thf(zip_derived_cl578, plain,
% 97.28/12.83 (![X0 : $i, X2 : $i]:
% 97.28/12.83 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | (((lessf @ X0 @ X2) => (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X2) @ (den @ X0)) @
% 97.28/12.83 (n_ts @ (num @ X0) @ (den @ X2))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl577])).
% 97.28/12.83 thf(zip_derived_cl579, plain,
% 97.28/12.83 (![X0 : $i, X2 : $i]:
% 97.28/12.83 (~ (lessf @ X0 @ X2)
% 97.28/12.83 | (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X2) @ (den @ X0)) @
% 97.28/12.83 (n_ts @ (num @ X0) @ (den @ X2))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
% 97.28/12.83 thf(zip_derived_cl17235, plain,
% 97.28/12.83 (![X0 : $i, X2 : $i]:
% 97.28/12.83 (~ (lessf @ X0 @ X2)
% 97.28/12.83 | (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X2) @ (den @ X0)) @
% 97.28/12.83 (n_ts @ (num @ X0) @ (den @ X2))))
% 97.28/12.83 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.28/12.83 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat))))),
% 97.28/12.83 inference('remove_ty_args', [status(thm)], [zip_derived_cl579])).
% 97.28/12.83 thf(zip_derived_cl1369, plain,
% 97.28/12.83 (~ (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.28/12.83 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 97.28/12.83 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 97.28/12.83 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.28/12.83 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.28/12.83 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1366])).
% 97.28/12.83 thf(satz64, axiom,
% 97.28/12.83 (all_of @
% 97.28/12.83 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 97.28/12.83 ( ^[X0:$i]:
% 97.28/12.83 ( all_of @
% 97.28/12.83 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 97.28/12.83 ( ^[X1:$i]:
% 97.28/12.83 ( all_of @
% 97.28/12.83 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 97.28/12.83 ( ^[X2:$i]:
% 97.28/12.83 ( all_of @
% 97.28/12.83 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 97.28/12.83 ( ^[X3:$i]:
% 97.28/12.83 ( ( moref @ X0 @ X1 ) =>
% 97.28/12.83 ( ( moref @ X2 @ X3 ) =>
% 97.28/12.83 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 97.28/12.83 thf(zip_derived_cl352, plain,
% 97.28/12.83 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 97.28/12.83 (^[Y0 : $i]:
% 97.28/12.83 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 97.28/12.83 (^[Y1 : $i]:
% 97.28/12.83 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 97.28/12.83 (^[Y2 : $i]:
% 97.28/12.83 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 97.28/12.83 (^[Y3 : $i]:
% 97.28/12.83 (((moref @ Y0 @ Y1) =>
% 97.28/12.83 (((moref @ Y2 @ Y3) => (moref @ (n_pf @ Y0 @ Y2) @
% 97.28/12.83 (n_pf @ Y1 @ Y3))))))))))))))),
% 97.28/12.83 inference('cnf', [status(esa)], [satz64])).
% 97.28/12.83 thf(zip_derived_cl353, plain,
% 97.28/12.83 ( (all_of @ ((('#C') @ in @ frac)) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @
% 97.28/12.83 moref)))))))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#C') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @
% 97.28/12.83 n_pf)))))))))))))),
% 97.28/12.83 inference('lams2combs', [status(thm)], [zip_derived_cl352])).
% 97.28/12.83 thf(zip_derived_cl2597, plain,
% 97.28/12.83 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @
% 97.28/12.83 moref)))))))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#C') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @
% 97.28/12.83 n_pf)))))))))))))),
% 97.28/12.83 inference('rw', [status(thm)], [zip_derived_cl353, '0'])).
% 97.28/12.83 thf(zip_derived_cl2598, plain,
% 97.28/12.83 ( (((!!) @ (^[Y0 : $i]:
% 97.28/12.83 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @
% 97.28/12.83 moref)))))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 97.28/12.83 '#S') @
% 97.28/12.83 ((('#B') @ (
% 97.28/12.83 (('#B') @ (
% 97.28/12.83 =>))) @
% 97.28/12.83 moref)))))))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#C') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ moref)) @
% 97.28/12.83 n_pf)))))))) @
% 97.28/12.83 n_pf)))))))))) @
% 97.28/12.83 Y0)))))))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl2597, '1'])).
% 97.28/12.83 thf(zip_derived_cl2599, plain,
% 97.28/12.83 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.28/12.83 ((('#C') @ is_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 97.28/12.83 '#S') @
% 97.28/12.83 ((('#B') @ (
% 97.28/12.83 (('#B') @ (=>))) @
% 97.28/12.83 moref)))))))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#C') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ moref)) @
% 97.28/12.83 n_pf)))))))) @
% 97.28/12.83 n_pf))))))))))))))))),
% 97.28/12.83 inference('comb-normalize', [status(thm)], [zip_derived_cl2598])).
% 97.28/12.83 thf(zip_derived_cl2600, plain,
% 97.28/12.83 (![X2 : $i]:
% 97.28/12.83 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ (=>) @ (moref @ X2))))))) @
% 97.28/12.83 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @
% 97.28/12.83 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ X2))))))) @
% 97.28/12.83 n_pf)))))))))))))),
% 97.28/12.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2599])).
% 97.28/12.83 thf(zip_derived_cl2601, plain,
% 97.28/12.83 (![X2 : $i]:
% 97.28/12.83 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ (=>) @ (moref @ X2))))))) @
% 97.28/12.83 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @
% 97.28/12.83 moref)))))) @
% 97.28/12.83 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ X2))))))) @
% 97.28/12.83 n_pf))))))))))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2600])).
% 97.28/12.83 thf(zip_derived_cl2602, plain,
% 97.28/12.83 (![X0 : $i]:
% 97.28/12.83 ( (((!!) @ (^[Y0 : $i]:
% 97.28/12.83 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ (=>) @ (moref @ X0))))))) @
% 97.28/12.83 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (
% 97.28/12.83 =>))) @
% 97.28/12.83 moref)))))) @
% 97.28/12.83 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @
% 97.28/12.83 (n_pf @ X0))))))) @
% 97.28/12.83 n_pf)))))))) @
% 97.28/12.83 Y0)))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl2601, '1'])).
% 97.28/12.83 thf(zip_derived_cl2603, plain,
% 97.28/12.83 (![X0 : $i]:
% 97.28/12.83 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.28/12.83 ((('#C') @ is_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ (=>) @ (moref @ X0))))))) @
% 97.28/12.83 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @
% 97.28/12.83 moref)))))) @
% 97.28/12.83 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @
% 97.28/12.83 (n_pf @ X0))))))) @
% 97.28/12.83 n_pf))))))))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('comb-normalize', [status(thm)], [zip_derived_cl2602])).
% 97.28/12.83 thf(zip_derived_cl2604, plain,
% 97.28/12.83 (![X0 : $i, X2 : $i]:
% 97.28/12.83 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X2))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ X0))))) @
% 97.28/12.83 (n_pf @ X2))))))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2603])).
% 97.28/12.83 thf(zip_derived_cl2605, plain,
% 97.28/12.83 (![X0 : $i, X2 : $i]:
% 97.28/12.83 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @ (num @ X0) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X0)))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ X0))))) @
% 97.28/12.83 (n_pf @ X2))))))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('rw', [status(thm)], [zip_derived_cl2604, '2', '3', '4'])).
% 97.28/12.83 thf(zip_derived_cl2606, plain,
% 97.28/12.83 (![X0 : $i, X2 : $i]:
% 97.28/12.83 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @ (num @ X0) @
% 97.28/12.83 (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @
% 97.28/12.83 (den @ X0)))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ X0))))) @
% 97.28/12.83 (n_pf @ X2))))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2605])).
% 97.28/12.83 thf(zip_derived_cl2607, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i]:
% 97.28/12.83 ( (((!!) @ (^[Y0 : $i]:
% 97.28/12.83 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @ X0) @
% 97.28/12.83 (den @ X1)) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @ X1) @
% 97.28/12.83 (den @ X0)))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ X0))))) @
% 97.28/12.83 (n_pf @ X1))))))) @
% 97.28/12.83 Y0)))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl2606, '1'])).
% 97.28/12.83 thf(zip_derived_cl2608, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i]:
% 97.28/12.83 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.28/12.83 ((('#C') @ is_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @ (num @ X0) @
% 97.28/12.83 (den @ X1)) @
% 97.28/12.83 (n_ts @ (num @ X1) @
% 97.28/12.83 (den @ X0)))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ X0))))) @
% 97.28/12.83 (n_pf @ X1)))))))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('comb-normalize', [status(thm)], [zip_derived_cl2607])).
% 97.28/12.83 thf(zip_derived_cl2609, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.28/12.83 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (((=>) @ (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @ (num @ X0) @ (den @ X1)) @
% 97.28/12.83 (n_ts @ (num @ X1) @ (den @ X0)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @
% 97.28/12.83 ((('#B') @ (moref @ (n_pf @ X0 @ X3)) @ (n_pf @ X1))))))))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2608])).
% 97.28/12.83 thf(zip_derived_cl2610, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.28/12.83 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (((=>) @ (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @ (num @ X0) @ (den @ X1)) @
% 97.28/12.83 (n_ts @ (num @ X1) @ (den @ X0)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @
% 97.28/12.83 ((('#B') @ (moref @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 97.28/12.83 (n_ts @ (num @ X3) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X3)))) @
% 97.28/12.83 (n_pf @ X1))))))))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('rw', [status(thm)], [zip_derived_cl2609, '9'])).
% 97.28/12.83 thf(zip_derived_cl2611, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.28/12.83 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (((=>) @ (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @ (num @ X0) @ (den @ X1)) @
% 97.28/12.83 (n_ts @ (num @ X1) @ (den @ X0)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @
% 97.28/12.83 ((('#B') @ (moref @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 97.28/12.83 (n_ts @ (num @ X3) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X3)))) @
% 97.28/12.83 (n_pf @ X1))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2610])).
% 97.28/12.83 thf(zip_derived_cl2612, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 97.28/12.83 ( (((!!) @ (^[Y0 : $i]:
% 97.28/12.83 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 ((('#B') @ (((=>) @ (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @ (num @ X1) @ (den @ X0)) @
% 97.28/12.83 (n_ts @ (num @ X0) @ (den @ X1)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @
% 97.28/12.83 ((('#B') @ (moref @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @
% 97.28/12.83 (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.28/12.83 (n_pf @ X0))))) @
% 97.28/12.83 Y0)))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl2611, '1'])).
% 97.28/12.83 thf(zip_derived_cl2613, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 97.28/12.83 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.28/12.83 ((('#C') @ is_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.28/12.83 ((('#B') @ (((=>) @ (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @ (num @ X1) @ (den @ X0)) @
% 97.28/12.83 (n_ts @ (num @ X0) @ (den @ X1)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @
% 97.28/12.83 ((('#B') @ (moref @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @
% 97.28/12.83 (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.28/12.83 (n_pf @ X0)))))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('comb-normalize', [status(thm)], [zip_derived_cl2612])).
% 97.28/12.83 thf(zip_derived_cl2614, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.28/12.83 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 (((l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 97.28/12.83 (n_ts @ (num @ X0) @ (den @ X1)))) =>
% 97.28/12.83 (((moref @ X2 @ X4) => (moref @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2))) @
% 97.28/12.83 (n_pf @ X0 @ X4))))))))
% 97.28/12.83 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2613])).
% 97.28/12.83 thf(zip_derived_cl2615, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.28/12.83 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 (((l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 97.28/12.83 (n_ts @ (num @ X0) @ (den @ X1)))) =>
% 97.28/12.83 (((l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X2)))) =>
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))))))))))))
% 97.28/12.83 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('rw', [status(thm)],
% 97.28/12.83 [zip_derived_cl2614, '2', '2', '3', '3', '4', '4', '9'])).
% 97.28/12.83 thf(zip_derived_cl2616, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.28/12.83 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | (((l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 97.28/12.83 (n_ts @ (num @ X0) @ (den @ X1)))) =>
% 97.28/12.83 (((l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X2)))) =>
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2615])).
% 97.28/12.83 thf(zip_derived_cl2617, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.28/12.83 (~ (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 97.28/12.83 (n_ts @ (num @ X0) @ (den @ X1))))
% 97.28/12.83 | (((l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X2)))) =>
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))))))))
% 97.28/12.83 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2616])).
% 97.28/12.83 thf(zip_derived_cl2618, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.28/12.83 (~ (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X2))))
% 97.28/12.83 | (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))))))
% 97.28/12.83 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 97.28/12.83 (n_ts @ (num @ X0) @ (den @ X1)))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2617])).
% 97.28/12.83 thf(zip_derived_cl17323, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.28/12.83 (~ (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X2))))
% 97.28/12.83 | (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))))))
% 97.28/12.83 | ~ (is_of @ X4 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.28/12.83 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.28/12.83 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.28/12.83 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.28/12.83 | ~ (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 97.28/12.83 (n_ts @ (num @ X0) @ (den @ X1)))))),
% 97.28/12.83 inference('remove_ty_args', [status(thm)], [zip_derived_cl2618])).
% 97.28/12.83 thf(satz62g, axiom,
% 97.28/12.83 (all_of @
% 97.28/12.83 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 97.28/12.83 ( ^[X0:$i]:
% 97.28/12.83 ( all_of @
% 97.28/12.83 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 97.28/12.83 ( ^[X1:$i]:
% 97.28/12.83 ( all_of @
% 97.28/12.83 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 97.28/12.83 ( ^[X2:$i]:
% 97.28/12.83 ( all_of @
% 97.28/12.83 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 97.28/12.83 ( ^[X3:$i]:
% 97.28/12.83 ( ( n_eq @ X0 @ X1 ) =>
% 97.28/12.83 ( ( moref @ X2 @ X3 ) =>
% 97.28/12.83 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 97.28/12.83 thf(zip_derived_cl332, plain,
% 97.28/12.83 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 97.28/12.83 (^[Y0 : $i]:
% 97.28/12.83 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 97.28/12.83 (^[Y1 : $i]:
% 97.28/12.83 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 97.28/12.83 (^[Y2 : $i]:
% 97.28/12.83 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 97.28/12.83 (^[Y3 : $i]:
% 97.28/12.83 (((n_eq @ Y0 @ Y1) =>
% 97.28/12.83 (((moref @ Y2 @ Y3) => (moref @ (n_pf @ Y0 @ Y2) @
% 97.28/12.83 (n_pf @ Y1 @ Y3))))))))))))))),
% 97.28/12.83 inference('cnf', [status(esa)], [satz62g])).
% 97.28/12.83 thf(zip_derived_cl333, plain,
% 97.28/12.83 ( (all_of @ ((('#C') @ in @ frac)) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @
% 97.28/12.83 moref)))))))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#C') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @
% 97.28/12.83 n_pf)))))))))))))),
% 97.28/12.83 inference('lams2combs', [status(thm)], [zip_derived_cl332])).
% 97.28/12.83 thf(zip_derived_cl2619, plain,
% 97.28/12.83 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @
% 97.28/12.83 moref)))))))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#C') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @
% 97.28/12.83 n_pf)))))))))))))),
% 97.28/12.83 inference('rw', [status(thm)], [zip_derived_cl333, '0'])).
% 97.28/12.83 thf(zip_derived_cl2620, plain,
% 97.28/12.83 ( (((!!) @ (^[Y0 : $i]:
% 97.28/12.83 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @
% 97.28/12.83 n_eq)))))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 97.28/12.83 '#S') @
% 97.28/12.83 ((('#B') @ (
% 97.28/12.83 (('#B') @ (
% 97.28/12.83 =>))) @
% 97.28/12.83 moref)))))))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#C') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ moref)) @
% 97.28/12.83 n_pf)))))))) @
% 97.28/12.83 n_pf)))))))))) @
% 97.28/12.83 Y0)))))))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl2619, '1'])).
% 97.28/12.83 thf(zip_derived_cl2621, plain,
% 97.28/12.83 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.28/12.83 ((('#C') @ is_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 97.28/12.83 '#S') @
% 97.28/12.83 ((('#B') @ (
% 97.28/12.83 (('#B') @ (=>))) @
% 97.28/12.83 moref)))))))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#C') @
% 97.28/12.83 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ moref)) @
% 97.28/12.83 n_pf)))))))) @
% 97.28/12.83 n_pf))))))))))))))))),
% 97.28/12.83 inference('comb-normalize', [status(thm)], [zip_derived_cl2620])).
% 97.28/12.83 thf(zip_derived_cl2622, plain,
% 97.28/12.83 (![X2 : $i]:
% 97.28/12.83 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ (=>) @ (n_eq @ X2))))))) @
% 97.28/12.83 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @
% 97.28/12.83 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ X2))))))) @
% 97.28/12.83 n_pf)))))))))))))),
% 97.28/12.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2621])).
% 97.28/12.83 thf(zip_derived_cl2623, plain,
% 97.28/12.83 (![X2 : $i]:
% 97.28/12.83 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ (=>) @ (n_eq @ X2))))))) @
% 97.28/12.83 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @
% 97.28/12.83 moref)))))) @
% 97.28/12.83 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ X2))))))) @
% 97.28/12.83 n_pf))))))))))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2622])).
% 97.28/12.83 thf(zip_derived_cl2624, plain,
% 97.28/12.83 (![X0 : $i]:
% 97.28/12.83 ( (((!!) @ (^[Y0 : $i]:
% 97.28/12.83 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ (=>) @ (n_eq @ X0))))))) @
% 97.28/12.83 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (
% 97.28/12.83 =>))) @
% 97.28/12.83 moref)))))) @
% 97.28/12.83 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @
% 97.28/12.83 (n_pf @ X0))))))) @
% 97.28/12.83 n_pf)))))))) @
% 97.28/12.83 Y0)))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl2623, '1'])).
% 97.28/12.83 thf(zip_derived_cl2625, plain,
% 97.28/12.83 (![X0 : $i]:
% 97.28/12.83 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.28/12.83 ((('#C') @ is_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @
% 97.28/12.83 (pair1type @ nat)))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ (=>) @ (n_eq @ X0))))))) @
% 97.28/12.83 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @
% 97.28/12.83 moref)))))) @
% 97.28/12.83 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @
% 97.28/12.83 (n_pf @ X0))))))) @
% 97.28/12.83 n_pf))))))))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('comb-normalize', [status(thm)], [zip_derived_cl2624])).
% 97.28/12.83 thf(zip_derived_cl2626, plain,
% 97.28/12.83 (![X0 : $i, X2 : $i]:
% 97.28/12.83 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ X0))))) @
% 97.28/12.83 (n_pf @ X2))))))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2625])).
% 97.28/12.83 thf(zip_derived_cl2627, plain,
% 97.28/12.83 (![X0 : $i, X2 : $i]:
% 97.28/12.83 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ X0))))) @
% 97.28/12.83 (n_pf @ X2))))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2626])).
% 97.28/12.83 thf(zip_derived_cl2628, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i]:
% 97.28/12.83 ( (((!!) @ (^[Y0 : $i]:
% 97.28/12.83 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 ((('#B') @ (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ X0))))) @
% 97.28/12.83 (n_pf @ X1))))))) @
% 97.28/12.83 Y0)))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl2627, '1'])).
% 97.28/12.83 thf(zip_derived_cl2629, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i]:
% 97.28/12.83 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.28/12.83 ((('#C') @ is_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.28/12.83 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.28/12.83 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ ('#S') @
% 97.28/12.83 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 97.28/12.83 ((('#C') @ ((('#B') @ ('#B') @
% 97.28/12.83 ((('#B') @ moref @ (n_pf @ X0))))) @
% 97.28/12.83 (n_pf @ X1)))))))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('comb-normalize', [status(thm)], [zip_derived_cl2628])).
% 97.28/12.83 thf(zip_derived_cl2630, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.28/12.83 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @
% 97.28/12.83 ((('#B') @ (moref @ (n_pf @ X0 @ X3)) @ (n_pf @ X1))))))))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2629])).
% 97.28/12.83 thf(zip_derived_cl2631, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.28/12.83 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @
% 97.28/12.83 ((('#B') @ (moref @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 97.28/12.83 (n_ts @ (num @ X3) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X3)))) @
% 97.28/12.83 (n_pf @ X1))))))))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('rw', [status(thm)], [zip_derived_cl2630, '9'])).
% 97.28/12.83 thf(zip_derived_cl2632, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.28/12.83 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.28/12.83 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @
% 97.28/12.83 ((('#B') @ (moref @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 97.28/12.83 (n_ts @ (num @ X3) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X3)))) @
% 97.28/12.83 (n_pf @ X1))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2631])).
% 97.28/12.83 thf(zip_derived_cl2633, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 97.28/12.83 ( (((!!) @ (^[Y0 : $i]:
% 97.28/12.83 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 ((('#B') @ (((=>) @ (n_eq @ X1 @ X0))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @
% 97.28/12.83 ((('#B') @ (moref @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @
% 97.28/12.83 (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.28/12.83 (n_pf @ X0))))) @
% 97.28/12.83 Y0)))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('rw_clause', [status(thm)], [zip_derived_cl2632, '1'])).
% 97.28/12.83 thf(zip_derived_cl2634, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X2 : $i]:
% 97.28/12.83 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.28/12.83 ((('#C') @ is_of @
% 97.28/12.83 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.28/12.83 ((('#B') @ (((=>) @ (n_eq @ X1 @ X0))) @
% 97.28/12.83 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @
% 97.28/12.83 ((('#B') @ (moref @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @
% 97.28/12.83 (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.28/12.83 (n_pf @ X0)))))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('comb-normalize', [status(thm)], [zip_derived_cl2633])).
% 97.28/12.83 thf(zip_derived_cl2635, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.28/12.83 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 (((n_eq @ X1 @ X0) =>
% 97.28/12.83 (((moref @ X2 @ X4) => (moref @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2))) @
% 97.28/12.83 (n_pf @ X0 @ X4))))))))
% 97.28/12.83 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2634])).
% 97.28/12.83 thf(zip_derived_cl2636, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.28/12.83 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.28/12.83 (((n_eq @ X1 @ X0) =>
% 97.28/12.83 (((l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X2)))) =>
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))))))))))))
% 97.28/12.83 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('rw', [status(thm)],
% 97.28/12.83 [zip_derived_cl2635, '2', '2', '3', '3', '4', '4', '9'])).
% 97.28/12.83 thf(zip_derived_cl2637, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.28/12.83 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | (((n_eq @ X1 @ X0) =>
% 97.28/12.83 (((l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X2)))) =>
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))))))))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2636])).
% 97.28/12.83 thf(zip_derived_cl2638, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.28/12.83 (~ (n_eq @ X1 @ X0)
% 97.28/12.83 | (((l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X2)))) =>
% 97.28/12.83 (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))))))))
% 97.28/12.83 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2637])).
% 97.28/12.83 thf(zip_derived_cl2639, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.28/12.83 (~ (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X2))))
% 97.28/12.83 | (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))))))
% 97.28/12.83 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.28/12.83 | ~ (n_eq @ X1 @ X0))),
% 97.28/12.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2638])).
% 97.28/12.83 thf(zip_derived_cl17324, plain,
% 97.28/12.83 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.28/12.83 (~ (l_some @ nat @
% 97.28/12.83 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X2))))
% 97.28/12.83 | (l_some @ nat @
% 97.28/12.83 (diffprop @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 97.28/12.83 (n_ts @
% 97.28/12.83 (num @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.28/12.83 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.28/12.83 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 97.28/12.83 (den @
% 97.28/12.83 (n_fr @
% 97.28/12.83 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.28/12.83 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.28/12.83 (n_ts @ (den @ X1) @ (den @ X2)))))))
% 97.28/12.83 | ~ (is_of @ X4 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.28/12.83 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.28/12.83 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.28/12.83 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 97.28/12.83 | ~ (n_eq @ X1 @ X0))),
% 97.28/12.83 inference('remove_ty_args', [status(thm)], [zip_derived_cl2639])).
% 97.28/12.83 thf(zip_derived_cl17360, plain, ($false),
% 97.28/12.83 inference('eprover', [status(thm)],
% 97.28/12.83 [zip_derived_cl13894, zip_derived_cl17273,
% 97.28/12.83 zip_derived_cl17274, zip_derived_cl17271,
% 97.28/12.83 zip_derived_cl17272, zip_derived_cl1368, zip_derived_cl17235,
% 97.28/12.83 zip_derived_cl1369, zip_derived_cl17323, zip_derived_cl17324])).
% 97.28/12.83
% 97.28/12.83 % SZS output end Refutation
% 97.28/12.83
% 97.28/12.83
% 97.28/12.83 % Terminating...
% 97.29/12.87 % Runner terminated.
% 97.29/12.88 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------