%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM762^4 : 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.RJJbp1whet true
% Computer : n015.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 04:48:17 PM UTC 2025
% Result : Theorem 83.23s 13.46s
% Output : Refutation 83.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM762^4 : TPTP v9.2.0. Released v7.1.0.
% 0.07/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.RJJbp1whet true
% 0.13/0.36 % Computer : n015.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Wed Oct 1 16:43:38 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Running portfolio for 300 s
% 0.13/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in HO mode
% 0.55/0.69 % Total configuration time : 828
% 0.55/0.69 % Estimated wc time : 1656
% 0.55/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.58/0.77 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.58/0.77 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.58/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.58/0.87 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 83.23/13.46 % Solved by lams/40_b.comb.sh.
% 83.23/13.46 % done 565 iterations in 12.595s
% 83.23/13.46 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 83.23/13.46 % SZS output start Refutation
% 83.23/13.46 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
% 83.23/13.46 thf(moreq_type, type, moreq: $i > $i > $o).
% 83.23/13.46 thf(nat_type, type, nat: $i).
% 83.23/13.46 thf('#sk3_type', type, '#sk3': $i).
% 83.23/13.46 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 83.23/13.46 thf(in_type, type, in: $i > $i > $o).
% 83.23/13.46 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 83.23/13.46 thf(n_pf_type, type, n_pf: $i > $i > $i).
% 83.23/13.46 thf(n_fr_type, type, n_fr: $i > $i > $i).
% 83.23/13.46 thf('#sk5_type', type, '#sk5': $i).
% 83.23/13.46 thf(imp_type, type, imp: $o > $o > $o).
% 83.23/13.46 thf(frac_type, type, frac: $i).
% 83.23/13.46 thf(n_ts_type, type, n_ts: $i > $i > $i).
% 83.23/13.46 thf(n_eq_type, type, n_eq: $i > $i > $o).
% 83.23/13.46 thf(pair1type_type, type, pair1type: $i > $i).
% 83.23/13.46 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 83.23/13.46 thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
% 83.23/13.46 thf(num_type, type, num: $i > $i).
% 83.23/13.46 thf(n_some_type, type, n_some: ($i > $o) > $o).
% 83.23/13.46 thf(l_or_type, type, l_or: $o > $o > $o).
% 83.23/13.46 thf('#sk4_type', type, '#sk4': $i).
% 83.23/13.46 thf(moref_type, type, moref: $i > $i > $o).
% 83.23/13.46 thf(d_not_type, type, d_not: $o > $o).
% 83.23/13.46 thf('#ty_enc6_type', type, '#ty_enc6': ($i > $i > $o) > $i > $i > $o).
% 83.23/13.46 thf(den_type, type, den: $i > $i).
% 83.23/13.46 thf('#sk2_type', type, '#sk2': $i).
% 83.23/13.46 thf(n_pl_type, type, n_pl: $i > $i > $i).
% 83.23/13.46 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 83.23/13.46 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 83.23/13.46 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 83.23/13.46 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 83.23/13.46 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 83.23/13.46 thf(satz65b, conjecture,
% 83.23/13.46 (all_of @
% 83.23/13.46 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 83.23/13.46 ( ^[X0:$i]:
% 83.23/13.46 ( all_of @
% 83.23/13.46 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 83.23/13.46 ( ^[X1:$i]:
% 83.23/13.46 ( all_of @
% 83.23/13.46 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 83.23/13.46 ( ^[X2:$i]:
% 83.23/13.46 ( all_of @
% 83.23/13.46 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 83.23/13.46 ( ^[X3:$i]:
% 83.23/13.46 ( ( moref @ X0 @ X1 ) =>
% 83.23/13.46 ( ( moreq @ X2 @ X3 ) =>
% 83.23/13.46 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 83.23/13.46 thf(zf_stmt_0, negated_conjecture,
% 83.23/13.46 (~( all_of @
% 83.23/13.46 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 83.23/13.46 ( ^[X0:$i]:
% 83.23/13.46 ( all_of @
% 83.23/13.46 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 83.23/13.46 ( ^[X1:$i]:
% 83.23/13.46 ( all_of @
% 83.23/13.46 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 83.23/13.46 ( ^[X2:$i]:
% 83.23/13.46 ( all_of @
% 83.23/13.46 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 83.23/13.46 ( ^[X3:$i]:
% 83.23/13.46 ( ( moref @ X0 @ X1 ) =>
% 83.23/13.46 ( ( moreq @ X2 @ X3 ) =>
% 83.23/13.46 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) )),
% 83.23/13.46 inference('cnf.neg', [status(esa)], [satz65b])).
% 83.23/13.46 thf(zip_derived_cl358, plain,
% 83.23/13.46 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 83.23/13.46 (^[Y0 : $i]:
% 83.23/13.46 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 83.23/13.46 (^[Y1 : $i]:
% 83.23/13.46 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 83.23/13.46 (^[Y2 : $i]:
% 83.23/13.46 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 83.23/13.46 (^[Y3 : $i]:
% 83.23/13.46 (((moref @ Y0 @ Y1) =>
% 83.23/13.46 (((moreq @ Y2 @ Y3) => (moref @ (n_pf @ Y0 @ Y2) @
% 83.23/13.46 (n_pf @ Y1 @ Y3))))))))))))))),
% 83.23/13.46 inference('cnf', [status(esa)], [zf_stmt_0])).
% 83.23/13.46 thf(zip_derived_cl359, plain,
% 83.23/13.46 (~ (all_of @ ((('#C') @ in @ frac)) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @
% 83.23/13.46 moreq)))))))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#C') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @
% 83.23/13.46 n_pf)))))))))))))),
% 83.23/13.46 inference('lams2combs', [status(thm)], [zip_derived_cl358])).
% 83.23/13.46 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))).
% 83.23/13.46 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])).
% 83.23/13.46 thf(zip_derived_cl1343, plain,
% 83.23/13.46 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @
% 83.23/13.46 (pair1type @ nat)))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @
% 83.23/13.46 moreq)))))))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#C') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @
% 83.23/13.46 n_pf)))))))))))))),
% 83.23/13.46 inference('rw', [status(thm)], [zip_derived_cl359, '0'])).
% 83.23/13.46 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 83.23/13.46 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 83.23/13.46 thf('1', plain,
% 83.23/13.46 (![X0:( $i > $o ),X1:( $i > $o )]:
% 83.23/13.46 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 83.23/13.46 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 83.23/13.46 inference('rw.lit', [status(esa)], [def_all_of])).
% 83.23/13.46 thf(zip_derived_cl1344, plain,
% 83.23/13.46 (~ (((!!) @ (^[Y0 : $i]:
% 83.23/13.46 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @
% 83.23/13.46 (pair1type @ nat)))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @
% 83.23/13.46 (pair1type @ nat)))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @
% 83.23/13.46 moref)))))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 83.23/13.46 '#S') @
% 83.23/13.46 ((('#B') @ (
% 83.23/13.46 (('#B') @ (
% 83.23/13.46 =>))) @
% 83.23/13.46 moreq)))))))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#C') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ moref)) @
% 83.23/13.46 n_pf)))))))) @
% 83.23/13.46 n_pf)))))))))) @
% 83.23/13.46 Y0)))))))),
% 83.23/13.46 inference('rw_clause', [status(thm)], [zip_derived_cl1343, '1'])).
% 83.23/13.46 thf(zip_derived_cl1345, plain,
% 83.23/13.46 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 83.23/13.46 ((('#C') @ is_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))))))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat)))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @
% 83.23/13.46 (pair1type @ nat)))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 83.23/13.46 '#S') @
% 83.23/13.46 ((('#B') @ (
% 83.23/13.46 (('#B') @ (=>))) @
% 83.23/13.46 moreq)))))))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#C') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ moref)) @
% 83.23/13.46 n_pf)))))))) @
% 83.23/13.46 n_pf))))))))))))))))),
% 83.23/13.46 inference('comb-normalize', [status(thm)], [zip_derived_cl1344])).
% 83.23/13.46 thf(zip_derived_cl1346, plain,
% 83.23/13.46 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat)))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ (=>) @ (moref @ '#sk2'))))))) @
% 83.23/13.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @
% 83.23/13.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @ (n_pf @ '#sk2'))))))) @
% 83.23/13.46 n_pf)))))))))))))),
% 83.23/13.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1345])).
% 83.23/13.46 thf(zip_derived_cl1348, plain,
% 83.23/13.46 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ (=>) @ (moref @ '#sk2'))))))) @
% 83.23/13.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @
% 83.23/13.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @ (n_pf @ '#sk2'))))))) @
% 83.23/13.46 n_pf)))))))))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1346])).
% 83.23/13.46 thf(zip_derived_cl1349, plain,
% 83.23/13.46 (~ (((!!) @ (^[Y0 : $i]:
% 83.23/13.46 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @
% 83.23/13.46 (pair1type @ nat)))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ (=>) @ (moref @ '#sk2'))))))) @
% 83.23/13.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @
% 83.23/13.46 moreq)))))) @
% 83.23/13.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @
% 83.23/13.46 (n_pf @ '#sk2'))))))) @
% 83.23/13.46 n_pf)))))))) @
% 83.23/13.46 Y0)))))))),
% 83.23/13.46 inference('rw_clause', [status(thm)], [zip_derived_cl1348, '1'])).
% 83.23/13.46 thf(zip_derived_cl1350, plain,
% 83.23/13.46 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 83.23/13.46 ((('#C') @ is_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))))))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat)))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ (=>) @ (moref @ '#sk2'))))))) @
% 83.23/13.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @
% 83.23/13.46 moreq)))))) @
% 83.23/13.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @
% 83.23/13.46 (n_pf @ '#sk2'))))))) @
% 83.23/13.46 n_pf))))))))))))))),
% 83.23/13.46 inference('comb-normalize', [status(thm)], [zip_derived_cl1349])).
% 83.23/13.46 thf(zip_derived_cl1351, plain,
% 83.23/13.46 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (((=>) @ (moref @ '#sk2' @ '#sk3'))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @
% 83.23/13.46 (n_pf @ '#sk3'))))))))))))),
% 83.23/13.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1350])).
% 83.23/13.46 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
% 83.23/13.46 thf('2', plain,
% 83.23/13.46 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
% 83.23/13.46 define([status(thm)])).
% 83.23/13.46 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) =
% 83.23/13.46 ((n_some @ (diffprop @ X0 @ X1))))).
% 83.23/13.46 thf('3', plain,
% 83.23/13.46 (![X1:$i,X0:$i]:
% 83.23/13.46 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
% 83.23/13.46 define([status(thm)])).
% 83.23/13.46 thf(def_moref, axiom,(( moref @ (X0)@ (X1)) =
% 83.23/13.46 ((d_29_ii @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 83.23/13.46 (n_ts @ (num @ X1) @ (den @ X0)))))).
% 83.23/13.46 thf('4', plain,
% 83.23/13.46 (![X1:$i,X0:$i]:
% 83.23/13.46 ( ( moref @ X0 @ X1 ) =
% 83.23/13.46 ( d_29_ii @
% 83.23/13.46 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 83.23/13.46 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )),
% 83.23/13.46 define([status(thm)])).
% 83.23/13.46 thf(zip_derived_cl1352, plain,
% 83.23/13.46 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @ (num @ '#sk2') @
% 83.23/13.46 (den @ '#sk3')) @
% 83.23/13.46 (n_ts @ (num @ '#sk3') @
% 83.23/13.46 (den @ '#sk2')))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @
% 83.23/13.46 (n_pf @ '#sk3'))))))))))))),
% 83.23/13.46 inference('rw', [status(thm)], [zip_derived_cl1351, '2', '3', '4'])).
% 83.23/13.46 thf(zip_derived_cl1354, plain,
% 83.23/13.46 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @ (num @ '#sk2') @
% 83.23/13.46 (den @ '#sk3')) @
% 83.23/13.46 (n_ts @ (num @ '#sk3') @
% 83.23/13.46 (den @ '#sk2')))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @
% 83.23/13.46 (n_pf @ '#sk3'))))))))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1352])).
% 83.23/13.46 thf(zip_derived_cl1355, plain,
% 83.23/13.46 (~ (((!!) @ (^[Y0 : $i]:
% 83.23/13.46 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @ '#sk2') @
% 83.23/13.46 (den @ '#sk3')) @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @ '#sk3') @
% 83.23/13.46 (den @ '#sk2')))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @
% 83.23/13.46 (n_pf @ '#sk3'))))))) @
% 83.23/13.46 Y0)))))))),
% 83.23/13.46 inference('rw_clause', [status(thm)], [zip_derived_cl1354, '1'])).
% 83.23/13.46 thf(zip_derived_cl1356, plain,
% 83.23/13.46 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 83.23/13.46 ((('#C') @ is_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))))))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @ '#sk2') @
% 83.23/13.46 (den @ '#sk3')) @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @ '#sk3') @
% 83.23/13.46 (den @ '#sk2')))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @
% 83.23/13.46 (n_pf @ '#sk3')))))))))))))),
% 83.23/13.46 inference('comb-normalize', [status(thm)], [zip_derived_cl1355])).
% 83.23/13.46 thf(zip_derived_cl1357, plain,
% 83.23/13.46 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 83.23/13.46 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @
% 83.23/13.46 ((('#B') @ (moref @ (n_pf @ '#sk2' @ '#sk4')) @ (n_pf @ '#sk3'))))))))))),
% 83.23/13.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1356])).
% 83.23/13.46 thf(def_n_pf, axiom,(( n_pf @ (X0)@ (X1)) =
% 83.23/13.46 ((n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 83.23/13.46 (n_ts @ (num @ X1) @ (den @ X0))) @
% 83.23/13.46 (n_ts @ (den @ X0) @ (den @ X1)))))).
% 83.23/13.46 thf('5', plain,
% 83.23/13.46 (![X1:$i,X0:$i]:
% 83.23/13.46 ( ( n_pf @ X0 @ X1 ) =
% 83.23/13.46 ( n_fr @
% 83.23/13.46 ( n_pl @
% 83.23/13.46 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 83.23/13.46 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) @
% 83.23/13.46 ( n_ts @ ( den @ X0 ) @ ( den @ X1 ) ) ) )),
% 83.23/13.46 define([status(thm)])).
% 83.23/13.46 thf(zip_derived_cl1358, plain,
% 83.23/13.46 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 83.23/13.46 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @
% 83.23/13.46 ((('#B') @ (moref @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 83.23/13.46 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 83.23/13.46 (n_pf @ '#sk3'))))))))))),
% 83.23/13.46 inference('rw', [status(thm)], [zip_derived_cl1357, '5'])).
% 83.23/13.46 thf(zip_derived_cl1360, plain,
% 83.23/13.46 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 83.23/13.46 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @
% 83.23/13.46 ((('#B') @ (moref @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 83.23/13.46 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 83.23/13.46 (n_pf @ '#sk3'))))))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1358])).
% 83.23/13.46 thf(zip_derived_cl1361, plain,
% 83.23/13.46 (~ (((!!) @ (^[Y0 : $i]:
% 83.23/13.46 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.46 ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @ (num @ '#sk2') @
% 83.23/13.46 (den @ '#sk3')) @
% 83.23/13.46 (n_ts @ (num @ '#sk3') @
% 83.23/13.46 (den @ '#sk2')))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @
% 83.23/13.46 ((('#B') @ (moref @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @
% 83.23/13.46 (n_ts @ (num @ '#sk2') @
% 83.23/13.46 (den @ '#sk4')) @
% 83.23/13.46 (n_ts @ (num @ '#sk4') @
% 83.23/13.46 (den @ '#sk2'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 83.23/13.46 (n_pf @ '#sk3'))))) @
% 83.23/13.46 Y0)))))))),
% 83.23/13.46 inference('rw_clause', [status(thm)], [zip_derived_cl1360, '1'])).
% 83.23/13.46 thf(zip_derived_cl1362, plain,
% 83.23/13.46 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 83.23/13.46 ((('#C') @ is_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))))))) @
% 83.23/13.46 ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @ (num @ '#sk2') @
% 83.23/13.46 (den @ '#sk3')) @
% 83.23/13.46 (n_ts @ (num @ '#sk3') @
% 83.23/13.46 (den @ '#sk2')))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @
% 83.23/13.46 ((('#B') @ (moref @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @
% 83.23/13.46 (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 83.23/13.46 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 83.23/13.46 (n_pf @ '#sk3')))))))))))),
% 83.23/13.46 inference('comb-normalize', [status(thm)], [zip_derived_cl1361])).
% 83.23/13.46 thf(zip_derived_cl1363, plain,
% 83.23/13.46 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.46 (((l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 83.23/13.46 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) =>
% 83.23/13.46 (((moreq @ '#sk4' @ '#sk5') => (moref @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 83.23/13.46 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 83.23/13.46 (n_pf @ '#sk3' @ '#sk5'))))))))),
% 83.23/13.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1362])).
% 83.23/13.46 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 83.23/13.46 thf('6', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 83.23/13.46 define([status(thm)])).
% 83.23/13.46 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 83.23/13.46 thf('7', plain,
% 83.23/13.46 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 83.23/13.46 define([status(thm)])).
% 83.23/13.46 thf(def_moreq, axiom,(( moreq @ (X0)@ (X1)) =
% 83.23/13.46 ((l_or @ (moref @ X0 @ X1) @ (n_eq @ X0 @ X1))))).
% 83.23/13.46 thf('8', plain,
% 83.23/13.46 (![X1:$i,X0:$i]:
% 83.23/13.46 ( ( moreq @ X0 @ X1 ) =
% 83.23/13.46 ( l_or @ ( moref @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )),
% 83.23/13.46 define([status(thm)])).
% 83.23/13.46 thf(zip_derived_cl1364, plain,
% 83.23/13.46 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.46 (((l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 83.23/13.46 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) =>
% 83.23/13.46 (((imp @
% 83.23/13.46 (imp @
% 83.23/13.46 (l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) @
% 83.23/13.46 ($false)) @
% 83.23/13.46 (n_eq @ '#sk4' @ '#sk5')) => (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 83.23/13.46 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))) @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 83.23/13.46 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))))))))))))),
% 83.23/13.46 inference('rw', [status(thm)],
% 83.23/13.46 [zip_derived_cl1363, '6', '7', '2', '2', '3', '3', '4', '4',
% 83.23/13.46 '8', '5'])).
% 83.23/13.46 thf(zip_derived_cl1366, plain,
% 83.23/13.46 (~ (((l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 83.23/13.46 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) =>
% 83.23/13.46 (((imp @
% 83.23/13.46 (imp @
% 83.23/13.46 (l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) @
% 83.23/13.46 ($false)) @
% 83.23/13.46 (n_eq @ '#sk4' @ '#sk5')) => (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 83.23/13.46 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))) @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 83.23/13.46 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))))))))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1364])).
% 83.23/13.46 thf(zip_derived_cl1368, plain,
% 83.23/13.46 (~ (((imp @
% 83.23/13.46 (imp @
% 83.23/13.46 (l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) @
% 83.23/13.46 ($false)) @
% 83.23/13.46 (n_eq @ '#sk4' @ '#sk5')) => (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 83.23/13.46 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))) @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 83.23/13.46 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))))))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1366])).
% 83.23/13.46 thf(zip_derived_cl1369, plain,
% 83.23/13.46 ( (imp @
% 83.23/13.46 (imp @
% 83.23/13.46 (l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) @
% 83.23/13.46 ($false)) @
% 83.23/13.46 (n_eq @ '#sk4' @ '#sk5'))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1368])).
% 83.23/13.46 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 83.23/13.46 thf('9', plain,
% 83.23/13.46 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 83.23/13.46 inference('rw.lit', [status(esa)], [def_imp])).
% 83.23/13.46 thf(zip_derived_cl1371, plain,
% 83.23/13.46 ( (((imp @
% 83.23/13.46 (l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) @
% 83.23/13.46 ($false)) => (n_eq @ '#sk4' @ '#sk5')))),
% 83.23/13.46 inference('rw_clause', [status(thm)], [zip_derived_cl1369, '9'])).
% 83.23/13.46 thf(zip_derived_cl1372, plain,
% 83.23/13.46 ((~ (imp @
% 83.23/13.46 (l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) @
% 83.23/13.46 ($false))
% 83.23/13.46 | (n_eq @ '#sk4' @ '#sk5'))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1371])).
% 83.23/13.46 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 83.23/13.46 thf('10', plain,
% 83.23/13.46 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 83.23/13.46 inference('rw.lit', [status(esa)], [def_imp])).
% 83.23/13.46 thf(zip_derived_cl1373, plain,
% 83.23/13.46 ((~ (((l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) =>
% 83.23/13.46 ($false)))
% 83.23/13.46 | (n_eq @ '#sk4' @ '#sk5'))),
% 83.23/13.46 inference('rw_clause', [status(thm)], [zip_derived_cl1372, '10'])).
% 83.23/13.46 thf(zip_derived_cl1374, plain,
% 83.23/13.46 ((~ (((~) @ (l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk4'))))))
% 83.23/13.46 | (n_eq @ '#sk4' @ '#sk5'))),
% 83.23/13.46 inference('simplify boolean subterms', [status(thm)],
% 83.23/13.46 [zip_derived_cl1373])).
% 83.23/13.46 thf(zip_derived_cl1375, plain,
% 83.23/13.46 (( (l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk4'))))
% 83.23/13.46 | (n_eq @ '#sk4' @ '#sk5'))),
% 83.23/13.46 inference('simplify nested equalities', [status(thm)],
% 83.23/13.46 [zip_derived_cl1374])).
% 83.23/13.46 thf(zip_derived_cl1347, plain,
% 83.23/13.46 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1346])).
% 83.23/13.46 thf(zip_derived_cl13756, plain,
% 83.23/13.46 ( (is_of @ '#sk2' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 83.23/13.46 inference('remove_ty_args', [status(thm)], [zip_derived_cl1347])).
% 83.23/13.46 thf(zip_derived_cl1353, plain,
% 83.23/13.46 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1352])).
% 83.23/13.46 thf(zip_derived_cl13757, plain,
% 83.23/13.46 ( (is_of @ '#sk3' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 83.23/13.46 inference('remove_ty_args', [status(thm)], [zip_derived_cl1353])).
% 83.23/13.46 thf(zip_derived_cl1359, plain,
% 83.23/13.46 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1358])).
% 83.23/13.46 thf(zip_derived_cl13758, plain,
% 83.23/13.46 ( (is_of @ '#sk4' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 83.23/13.46 inference('remove_ty_args', [status(thm)], [zip_derived_cl1359])).
% 83.23/13.46 thf(zip_derived_cl1365, plain,
% 83.23/13.46 ( (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1364])).
% 83.23/13.46 thf(zip_derived_cl13759, plain,
% 83.23/13.46 ( (is_of @ '#sk5' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 83.23/13.46 inference('remove_ty_args', [status(thm)], [zip_derived_cl1365])).
% 83.23/13.46 thf(zip_derived_cl1367, plain,
% 83.23/13.46 ( (l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 83.23/13.46 (n_ts @ (num @ '#sk3') @ (den @ '#sk2'))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1366])).
% 83.23/13.46 thf(satz64, axiom,
% 83.23/13.46 (all_of @
% 83.23/13.46 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 83.23/13.46 ( ^[X0:$i]:
% 83.23/13.46 ( all_of @
% 83.23/13.46 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 83.23/13.46 ( ^[X1:$i]:
% 83.23/13.46 ( all_of @
% 83.23/13.46 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 83.23/13.46 ( ^[X2:$i]:
% 83.23/13.46 ( all_of @
% 83.23/13.46 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 83.23/13.46 ( ^[X3:$i]:
% 83.23/13.46 ( ( moref @ X0 @ X1 ) =>
% 83.23/13.46 ( ( moref @ X2 @ X3 ) =>
% 83.23/13.46 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 83.23/13.46 thf(zip_derived_cl352, plain,
% 83.23/13.46 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 83.23/13.46 (^[Y0 : $i]:
% 83.23/13.46 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 83.23/13.46 (^[Y1 : $i]:
% 83.23/13.46 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 83.23/13.46 (^[Y2 : $i]:
% 83.23/13.46 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 83.23/13.46 (^[Y3 : $i]:
% 83.23/13.46 (((moref @ Y0 @ Y1) =>
% 83.23/13.46 (((moref @ Y2 @ Y3) => (moref @ (n_pf @ Y0 @ Y2) @
% 83.23/13.46 (n_pf @ Y1 @ Y3))))))))))))))),
% 83.23/13.46 inference('cnf', [status(esa)], [satz64])).
% 83.23/13.46 thf(zip_derived_cl353, plain,
% 83.23/13.46 ( (all_of @ ((('#C') @ in @ frac)) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @
% 83.23/13.46 moref)))))))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#C') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @
% 83.23/13.46 n_pf)))))))))))))),
% 83.23/13.46 inference('lams2combs', [status(thm)], [zip_derived_cl352])).
% 83.23/13.46 thf(zip_derived_cl2599, plain,
% 83.23/13.46 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @
% 83.23/13.46 (pair1type @ nat)))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @
% 83.23/13.46 moref)))))))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#C') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @
% 83.23/13.46 n_pf)))))))))))))),
% 83.23/13.46 inference('rw', [status(thm)], [zip_derived_cl353, '0'])).
% 83.23/13.46 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 83.23/13.46 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 83.23/13.46 thf('11', plain,
% 83.23/13.46 (![X0:( $i > $o ),X1:( $i > $o )]:
% 83.23/13.46 ( ( all_of @ X0 @ X1 ) <=>
% 83.23/13.46 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 83.23/13.46 inference('rw.lit', [status(esa)], [def_all_of])).
% 83.23/13.46 thf(zip_derived_cl2600, plain,
% 83.23/13.46 ( (((!!) @ (^[Y0 : $i]:
% 83.23/13.46 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @
% 83.23/13.46 (pair1type @ nat)))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @
% 83.23/13.46 (pair1type @ nat)))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @
% 83.23/13.46 moref)))))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 83.23/13.46 '#S') @
% 83.23/13.46 ((('#B') @ (
% 83.23/13.46 (('#B') @ (
% 83.23/13.46 =>))) @
% 83.23/13.46 moref)))))))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#C') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ moref)) @
% 83.23/13.46 n_pf)))))))) @
% 83.23/13.46 n_pf)))))))))) @
% 83.23/13.46 Y0)))))))),
% 83.23/13.46 inference('rw_clause', [status(thm)], [zip_derived_cl2599, '11'])).
% 83.23/13.46 thf(zip_derived_cl2601, plain,
% 83.23/13.46 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 83.23/13.46 ((('#C') @ is_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))))))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat)))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @
% 83.23/13.46 (pair1type @ nat)))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 83.23/13.46 '#S') @
% 83.23/13.46 ((('#B') @ (
% 83.23/13.46 (('#B') @ (=>))) @
% 83.23/13.46 moref)))))))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#C') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ moref)) @
% 83.23/13.46 n_pf)))))))) @
% 83.23/13.46 n_pf))))))))))))))))),
% 83.23/13.46 inference('comb-normalize', [status(thm)], [zip_derived_cl2600])).
% 83.23/13.46 thf(zip_derived_cl2602, plain,
% 83.23/13.46 (![X2 : $i]:
% 83.23/13.46 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat)))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ (=>) @ (moref @ X2))))))) @
% 83.23/13.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @
% 83.23/13.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @ (n_pf @ X2))))))) @
% 83.23/13.46 n_pf)))))))))))))),
% 83.23/13.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2601])).
% 83.23/13.46 thf(zip_derived_cl2603, plain,
% 83.23/13.46 (![X2 : $i]:
% 83.23/13.46 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat)))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ (=>) @ (moref @ X2))))))) @
% 83.23/13.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @
% 83.23/13.46 moref)))))) @
% 83.23/13.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @ (n_pf @ X2))))))) @
% 83.23/13.46 n_pf))))))))))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2602])).
% 83.23/13.46 thf(zip_derived_cl2604, plain,
% 83.23/13.46 (![X0 : $i]:
% 83.23/13.46 ( (((!!) @ (^[Y0 : $i]:
% 83.23/13.46 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.46 ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @
% 83.23/13.46 (pair1type @ nat)))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ (=>) @ (moref @ X0))))))) @
% 83.23/13.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (
% 83.23/13.46 =>))) @
% 83.23/13.46 moref)))))) @
% 83.23/13.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @
% 83.23/13.46 (n_pf @ X0))))))) @
% 83.23/13.46 n_pf)))))))) @
% 83.23/13.46 Y0)))))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.46 inference('rw_clause', [status(thm)], [zip_derived_cl2603, '11'])).
% 83.23/13.46 thf(zip_derived_cl2605, plain,
% 83.23/13.46 (![X0 : $i]:
% 83.23/13.46 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 83.23/13.46 ((('#C') @ is_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))))))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @
% 83.23/13.46 (pair1type @ nat)))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ (=>) @ (moref @ X0))))))) @
% 83.23/13.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @
% 83.23/13.46 moref)))))) @
% 83.23/13.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @
% 83.23/13.46 (n_pf @ X0))))))) @
% 83.23/13.46 n_pf))))))))))))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.46 inference('comb-normalize', [status(thm)], [zip_derived_cl2604])).
% 83.23/13.46 thf(zip_derived_cl2606, plain,
% 83.23/13.46 (![X0 : $i, X2 : $i]:
% 83.23/13.46 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X2))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @ (n_pf @ X0))))) @
% 83.23/13.46 (n_pf @ X2))))))))))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2605])).
% 83.23/13.46 thf(zip_derived_cl2607, plain,
% 83.23/13.46 (![X0 : $i, X2 : $i]:
% 83.23/13.46 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @ (num @ X0) @ (den @ X2)) @
% 83.23/13.46 (n_ts @ (num @ X2) @ (den @ X0)))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @ (n_pf @ X0))))) @
% 83.23/13.46 (n_pf @ X2))))))))))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.46 inference('rw', [status(thm)], [zip_derived_cl2606, '2', '3', '4'])).
% 83.23/13.46 thf(zip_derived_cl2608, plain,
% 83.23/13.46 (![X0 : $i, X2 : $i]:
% 83.23/13.46 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @ (num @ X0) @
% 83.23/13.46 (den @ X2)) @
% 83.23/13.46 (n_ts @ (num @ X2) @
% 83.23/13.46 (den @ X0)))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @ (n_pf @ X0))))) @
% 83.23/13.46 (n_pf @ X2))))))))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2607])).
% 83.23/13.46 thf(zip_derived_cl2609, plain,
% 83.23/13.46 (![X0 : $i, X1 : $i]:
% 83.23/13.46 ( (((!!) @ (^[Y0 : $i]:
% 83.23/13.46 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.46 ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @ X0) @
% 83.23/13.46 (den @ X1)) @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @ X1) @
% 83.23/13.46 (den @ X0)))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @ (n_pf @ X0))))) @
% 83.23/13.46 (n_pf @ X1))))))) @
% 83.23/13.46 Y0)))))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.46 inference('rw_clause', [status(thm)], [zip_derived_cl2608, '11'])).
% 83.23/13.46 thf(zip_derived_cl2610, plain,
% 83.23/13.46 (![X0 : $i, X1 : $i]:
% 83.23/13.46 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 83.23/13.46 ((('#C') @ is_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))))))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @ (num @ X0) @
% 83.23/13.46 (den @ X1)) @
% 83.23/13.46 (n_ts @ (num @ X1) @
% 83.23/13.46 (den @ X0)))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ moref @ (n_pf @ X0))))) @
% 83.23/13.46 (n_pf @ X1)))))))))))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.46 inference('comb-normalize', [status(thm)], [zip_derived_cl2609])).
% 83.23/13.46 thf(zip_derived_cl2611, plain,
% 83.23/13.46 (![X0 : $i, X1 : $i, X3 : $i]:
% 83.23/13.46 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @ (num @ X0) @ (den @ X1)) @
% 83.23/13.46 (n_ts @ (num @ X1) @ (den @ X0)))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @
% 83.23/13.46 ((('#B') @ (moref @ (n_pf @ X0 @ X3)) @ (n_pf @ X1))))))))))
% 83.23/13.46 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2610])).
% 83.23/13.46 thf(zip_derived_cl2612, plain,
% 83.23/13.46 (![X0 : $i, X1 : $i, X3 : $i]:
% 83.23/13.46 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @ (num @ X0) @ (den @ X1)) @
% 83.23/13.46 (n_ts @ (num @ X1) @ (den @ X0)))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @
% 83.23/13.46 ((('#B') @ (moref @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 83.23/13.46 (n_ts @ (num @ X3) @ (den @ X0))) @
% 83.23/13.46 (n_ts @ (den @ X0) @ (den @ X3)))) @
% 83.23/13.46 (n_pf @ X1))))))))))
% 83.23/13.46 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.46 inference('rw', [status(thm)], [zip_derived_cl2611, '5'])).
% 83.23/13.46 thf(zip_derived_cl2613, plain,
% 83.23/13.46 (![X0 : $i, X1 : $i, X3 : $i]:
% 83.23/13.46 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @ (num @ X0) @ (den @ X1)) @
% 83.23/13.46 (n_ts @ (num @ X1) @ (den @ X0)))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @
% 83.23/13.46 ((('#B') @ (moref @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 83.23/13.46 (n_ts @ (num @ X3) @ (den @ X0))) @
% 83.23/13.46 (n_ts @ (den @ X0) @ (den @ X3)))) @
% 83.23/13.46 (n_pf @ X1))))))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2612])).
% 83.23/13.46 thf(zip_derived_cl2614, plain,
% 83.23/13.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.23/13.46 ( (((!!) @ (^[Y0 : $i]:
% 83.23/13.46 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.46 ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @ (num @ X1) @ (den @ X0)) @
% 83.23/13.46 (n_ts @ (num @ X0) @ (den @ X1)))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @
% 83.23/13.46 ((('#B') @ (moref @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @
% 83.23/13.46 (n_ts @ (num @ X1) @ (den @ X2)) @
% 83.23/13.46 (n_ts @ (num @ X2) @ (den @ X1))) @
% 83.23/13.46 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 83.23/13.46 (n_pf @ X0))))) @
% 83.23/13.46 Y0)))))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.46 inference('rw_clause', [status(thm)], [zip_derived_cl2613, '11'])).
% 83.23/13.46 thf(zip_derived_cl2615, plain,
% 83.23/13.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.23/13.46 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 83.23/13.46 ((('#C') @ is_of @
% 83.23/13.46 ((('#C') @ in @ (pair1type @ nat))))))) @
% 83.23/13.46 ((('#B') @ (((=>) @ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @ (num @ X1) @ (den @ X0)) @
% 83.23/13.46 (n_ts @ (num @ X0) @ (den @ X1)))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @
% 83.23/13.46 ((('#B') @ (moref @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @
% 83.23/13.46 (n_ts @ (num @ X1) @ (den @ X2)) @
% 83.23/13.46 (n_ts @ (num @ X2) @ (den @ X1))) @
% 83.23/13.46 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 83.23/13.46 (n_pf @ X0)))))))))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.46 inference('comb-normalize', [status(thm)], [zip_derived_cl2614])).
% 83.23/13.46 thf(zip_derived_cl2616, plain,
% 83.23/13.46 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 83.23/13.46 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.46 (((l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 83.23/13.46 (n_ts @ (num @ X0) @ (den @ X1)))) =>
% 83.23/13.46 (((moref @ X2 @ X4) => (moref @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 83.23/13.46 (n_ts @ (num @ X2) @ (den @ X1))) @
% 83.23/13.46 (n_ts @ (den @ X1) @ (den @ X2))) @
% 83.23/13.46 (n_pf @ X0 @ X4))))))))
% 83.23/13.46 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2615])).
% 83.23/13.46 thf(zip_derived_cl2617, plain,
% 83.23/13.46 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 83.23/13.46 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.46 (((l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 83.23/13.46 (n_ts @ (num @ X0) @ (den @ X1)))) =>
% 83.23/13.46 (((l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 83.23/13.46 (n_ts @ (num @ X4) @ (den @ X2)))) =>
% 83.23/13.46 (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 83.23/13.46 (n_ts @ (num @ X2) @ (den @ X1))) @
% 83.23/13.46 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 83.23/13.46 (n_ts @ (num @ X4) @ (den @ X0))) @
% 83.23/13.46 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 83.23/13.46 (n_ts @ (num @ X4) @ (den @ X0))) @
% 83.23/13.46 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 83.23/13.46 (n_ts @ (num @ X2) @ (den @ X1))) @
% 83.23/13.46 (n_ts @ (den @ X1) @ (den @ X2)))))))))))))
% 83.23/13.46 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.46 inference('rw', [status(thm)],
% 83.23/13.46 [zip_derived_cl2616, '2', '2', '3', '3', '4', '4', '5'])).
% 83.23/13.46 thf(zip_derived_cl2618, plain,
% 83.23/13.46 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 83.23/13.46 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | (((l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 83.23/13.46 (n_ts @ (num @ X0) @ (den @ X1)))) =>
% 83.23/13.46 (((l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 83.23/13.46 (n_ts @ (num @ X4) @ (den @ X2)))) =>
% 83.23/13.46 (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 83.23/13.46 (n_ts @ (num @ X2) @ (den @ X1))) @
% 83.23/13.46 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 83.23/13.46 (n_ts @ (num @ X4) @ (den @ X0))) @
% 83.23/13.46 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 83.23/13.46 (n_ts @ (num @ X4) @ (den @ X0))) @
% 83.23/13.46 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 83.23/13.46 (n_ts @ (num @ X2) @ (den @ X1))) @
% 83.23/13.46 (n_ts @ (den @ X1) @ (den @ X2)))))))))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2617])).
% 83.23/13.46 thf(zip_derived_cl2619, plain,
% 83.23/13.46 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 83.23/13.46 (~ (l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 83.23/13.46 (n_ts @ (num @ X0) @ (den @ X1))))
% 83.23/13.46 | (((l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 83.23/13.46 (n_ts @ (num @ X4) @ (den @ X2)))) =>
% 83.23/13.46 (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 83.23/13.46 (n_ts @ (num @ X2) @ (den @ X1))) @
% 83.23/13.46 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 83.23/13.46 (n_ts @ (num @ X4) @ (den @ X0))) @
% 83.23/13.46 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 83.23/13.46 (n_ts @ (num @ X4) @ (den @ X0))) @
% 83.23/13.46 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 83.23/13.46 (n_ts @ (num @ X2) @ (den @ X1))) @
% 83.23/13.46 (n_ts @ (den @ X1) @ (den @ X2)))))))))
% 83.23/13.46 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2618])).
% 83.23/13.46 thf(zip_derived_cl2620, plain,
% 83.23/13.46 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 83.23/13.46 (~ (l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 83.23/13.46 (n_ts @ (num @ X4) @ (den @ X2))))
% 83.23/13.46 | (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 83.23/13.46 (n_ts @ (num @ X2) @ (den @ X1))) @
% 83.23/13.46 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 83.23/13.46 (n_ts @ (num @ X4) @ (den @ X0))) @
% 83.23/13.46 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 83.23/13.46 (n_ts @ (num @ X4) @ (den @ X0))) @
% 83.23/13.46 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 83.23/13.46 (n_ts @ (num @ X2) @ (den @ X1))) @
% 83.23/13.46 (n_ts @ (den @ X1) @ (den @ X2)))))))
% 83.23/13.46 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.46 | ~ (l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 83.23/13.46 (n_ts @ (num @ X0) @ (den @ X1)))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2619])).
% 83.23/13.46 thf(zip_derived_cl13808, plain,
% 83.23/13.46 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 83.23/13.46 (~ (l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 83.23/13.46 (n_ts @ (num @ X4) @ (den @ X2))))
% 83.23/13.46 | (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 83.23/13.46 (n_ts @ (num @ X2) @ (den @ X1))) @
% 83.23/13.46 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 83.23/13.46 (n_ts @ (num @ X4) @ (den @ X0))) @
% 83.23/13.46 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 83.23/13.46 (n_ts @ (num @ X4) @ (den @ X0))) @
% 83.23/13.46 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 83.23/13.46 (n_ts @ (num @ X2) @ (den @ X1))) @
% 83.23/13.46 (n_ts @ (den @ X1) @ (den @ X2)))))))
% 83.23/13.46 | ~ (is_of @ X4 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 83.23/13.46 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 83.23/13.46 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 83.23/13.46 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 83.23/13.46 | ~ (l_some @ nat @
% 83.23/13.46 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 83.23/13.46 (n_ts @ (num @ X0) @ (den @ X1)))))),
% 83.23/13.46 inference('remove_ty_args', [status(thm)], [zip_derived_cl2620])).
% 83.23/13.46 thf(zip_derived_cl1370, plain,
% 83.23/13.46 (~ (l_some @ nat @
% 83.23/13.46 (diffprop @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 83.23/13.46 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))) @
% 83.23/13.46 (n_ts @
% 83.23/13.46 (num @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 83.23/13.46 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @
% 83.23/13.46 (den @
% 83.23/13.46 (n_fr @
% 83.23/13.46 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 83.23/13.46 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 83.23/13.46 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))))))),
% 83.23/13.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1368])).
% 83.23/13.46 thf(satz62h, axiom,
% 83.23/13.46 (all_of @
% 83.23/13.46 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 83.23/13.46 ( ^[X0:$i]:
% 83.23/13.46 ( all_of @
% 83.23/13.46 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 83.23/13.46 ( ^[X1:$i]:
% 83.23/13.46 ( all_of @
% 83.23/13.46 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 83.23/13.46 ( ^[X2:$i]:
% 83.23/13.46 ( all_of @
% 83.23/13.46 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 83.23/13.46 ( ^[X3:$i]:
% 83.23/13.46 ( ( n_eq @ X0 @ X1 ) =>
% 83.23/13.46 ( ( moref @ X2 @ X3 ) =>
% 83.23/13.46 ( moref @ ( n_pf @ X2 @ X0 ) @ ( n_pf @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ))).
% 83.23/13.46 thf(zip_derived_cl334, plain,
% 83.23/13.46 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 83.23/13.46 (^[Y0 : $i]:
% 83.23/13.46 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 83.23/13.46 (^[Y1 : $i]:
% 83.23/13.46 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 83.23/13.46 (^[Y2 : $i]:
% 83.23/13.46 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 83.23/13.46 (^[Y3 : $i]:
% 83.23/13.46 (((n_eq @ Y0 @ Y1) =>
% 83.23/13.46 (((moref @ Y2 @ Y3) => (moref @ (n_pf @ Y2 @ Y0) @
% 83.23/13.46 (n_pf @ Y3 @ Y1))))))))))))))),
% 83.23/13.46 inference('cnf', [status(esa)], [satz62h])).
% 83.23/13.46 thf(zip_derived_cl335, plain,
% 83.23/13.46 ( (all_of @ ((('#C') @ in @ frac)) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @
% 83.23/13.46 moref)))))))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#C') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ moref)) @
% 83.23/13.46 ((('#C') @ n_pf)))))))))) @
% 83.23/13.46 ((('#C') @ n_pf)))))))))))))))),
% 83.23/13.46 inference('lams2combs', [status(thm)], [zip_derived_cl334])).
% 83.23/13.46 thf(zip_derived_cl3270, plain,
% 83.23/13.46 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @
% 83.23/13.46 (pair1type @ nat)))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @
% 83.23/13.46 moref)))))))) @
% 83.23/13.46 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.46 ((('#B') @ ('#C') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ moref)) @
% 83.23/13.46 ((('#C') @ n_pf)))))))))) @
% 83.23/13.46 ((('#C') @ n_pf)))))))))))))))),
% 83.23/13.46 inference('rw', [status(thm)], [zip_derived_cl335, '0'])).
% 83.23/13.46 thf(zip_derived_cl3271, plain,
% 83.23/13.46 ( (((!!) @ (^[Y0 : $i]:
% 83.23/13.46 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.46 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @
% 83.23/13.46 (pair1type @ nat)))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.46 ((('#C') @ in @
% 83.23/13.46 (pair1type @ nat)))))))) @
% 83.23/13.46 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ (=>))) @
% 83.23/13.46 n_eq)))))))) @
% 83.23/13.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 83.23/13.46 '#S') @
% 83.23/13.46 ((('#B') @ (
% 83.23/13.46 (('#B') @ (
% 83.23/13.47 =>))) @
% 83.23/13.47 moref)))))))) @
% 83.23/13.47 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ ('#C') @
% 83.23/13.47 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.47 ((('#B') @ ((('#B') @ moref)) @
% 83.23/13.47 ((('#C') @ n_pf)))))))))) @
% 83.23/13.47 ((('#C') @ n_pf)))))))))))) @
% 83.23/13.47 Y0)))))))),
% 83.23/13.47 inference('rw_clause', [status(thm)], [zip_derived_cl3270, '11'])).
% 83.23/13.47 thf(zip_derived_cl3272, plain,
% 83.23/13.47 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 83.23/13.47 ((('#C') @ is_of @
% 83.23/13.47 ((('#C') @ in @ (pair1type @ nat))))))) @
% 83.23/13.47 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.47 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.47 ((('#C') @ in @ (pair1type @ nat)))))) @
% 83.23/13.47 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.47 ((('#C') @ in @
% 83.23/13.47 (pair1type @ nat)))))))) @
% 83.23/13.47 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.47 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.47 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.47 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 83.23/13.47 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 83.23/13.47 '#S') @
% 83.23/13.47 ((('#B') @ (
% 83.23/13.47 (('#B') @ (=>))) @
% 83.23/13.47 moref)))))))) @
% 83.23/13.47 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ ('#C') @
% 83.23/13.47 ((('#B') @ ((('#B') @ ('#B'))) @
% 83.23/13.47 ((('#B') @ ((('#B') @ moref)) @
% 83.23/13.47 ((('#C') @ n_pf)))))))))) @
% 83.23/13.47 ((('#C') @ n_pf))))))))))))))))))),
% 83.23/13.47 inference('comb-normalize', [status(thm)], [zip_derived_cl3271])).
% 83.23/13.47 thf(zip_derived_cl3273, plain,
% 83.23/13.47 (![X2 : $i]:
% 83.23/13.47 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 83.23/13.47 ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.47 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.47 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.47 ((('#C') @ in @ (pair1type @ nat)))))) @
% 83.23/13.47 ((('#S') @ ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ (=>) @ (n_eq @ X2))))))) @
% 83.23/13.47 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.47 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @
% 83.23/13.47 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ moref @
% 83.23/13.47 ((('#C') @ n_pf @ X2)))))))) @
% 83.23/13.47 ((('#C') @ n_pf)))))))))))))))),
% 83.23/13.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3272])).
% 83.23/13.47 thf(zip_derived_cl3274, plain,
% 83.23/13.47 (![X2 : $i]:
% 83.23/13.47 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.47 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.47 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.47 ((('#C') @ in @ (pair1type @ nat)))))) @
% 83.23/13.47 ((('#S') @ ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ (=>) @ (n_eq @ X2))))))) @
% 83.23/13.47 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.47 ((('#B') @ ((('#B') @ (=>))) @
% 83.23/13.47 moref)))))) @
% 83.23/13.47 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ moref @
% 83.23/13.47 ((('#C') @ n_pf @ X2)))))))) @
% 83.23/13.47 ((('#C') @ n_pf))))))))))))))),
% 83.23/13.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3273])).
% 83.23/13.47 thf(zip_derived_cl3275, plain,
% 83.23/13.47 (![X0 : $i]:
% 83.23/13.47 ( (((!!) @ (^[Y0 : $i]:
% 83.23/13.47 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.47 ((('#B') @ (all_of @
% 83.23/13.47 ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.47 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.47 ((('#C') @ in @
% 83.23/13.47 (pair1type @ nat)))))) @
% 83.23/13.47 ((('#S') @ ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ (=>) @ (n_eq @ X0))))))) @
% 83.23/13.47 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.47 ((('#B') @ ((('#B') @ (
% 83.23/13.47 =>))) @
% 83.23/13.47 moref)))))) @
% 83.23/13.47 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ moref @
% 83.23/13.47 ((('#C') @ n_pf @ X0)))))))) @
% 83.23/13.47 ((('#C') @ n_pf)))))))))) @
% 83.23/13.47 Y0)))))))
% 83.23/13.47 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.47 inference('rw_clause', [status(thm)], [zip_derived_cl3274, '11'])).
% 83.23/13.47 thf(zip_derived_cl3276, plain,
% 83.23/13.47 (![X0 : $i]:
% 83.23/13.47 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 83.23/13.47 ((('#C') @ is_of @
% 83.23/13.47 ((('#C') @ in @ (pair1type @ nat))))))) @
% 83.23/13.47 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.47 ((('#B') @ ((('#B') @ (all_of @
% 83.23/13.47 ((('#C') @ in @
% 83.23/13.47 (pair1type @ nat)))))) @
% 83.23/13.47 ((('#S') @ ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ (=>) @ (n_eq @ X0))))))) @
% 83.23/13.47 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.47 ((('#B') @ ((('#B') @ (=>))) @
% 83.23/13.47 moref)))))) @
% 83.23/13.47 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ moref @
% 83.23/13.47 ((('#C') @ n_pf @ X0)))))))) @
% 83.23/13.47 ((('#C') @ n_pf))))))))))))))))
% 83.23/13.47 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.47 inference('comb-normalize', [status(thm)], [zip_derived_cl3275])).
% 83.23/13.47 thf(zip_derived_cl3277, plain,
% 83.23/13.47 (![X0 : $i, X2 : $i]:
% 83.23/13.47 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 83.23/13.47 ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.47 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.47 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))))) @
% 83.23/13.47 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.47 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 83.23/13.47 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ moref @ ((('#C') @ n_pf @ X0)))))) @
% 83.23/13.47 ((('#C') @ n_pf @ X2)))))))))))))
% 83.23/13.47 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3276])).
% 83.23/13.47 thf(zip_derived_cl3278, plain,
% 83.23/13.47 (![X0 : $i, X2 : $i]:
% 83.23/13.47 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.47 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.47 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))))) @
% 83.23/13.47 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.47 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 83.23/13.47 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ moref @ ((('#C') @ n_pf @ X0)))))) @
% 83.23/13.47 ((('#C') @ n_pf @ X2)))))))))))
% 83.23/13.47 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3277])).
% 83.23/13.47 thf(zip_derived_cl3279, plain,
% 83.23/13.47 (![X0 : $i, X1 : $i]:
% 83.23/13.47 ( (((!!) @ (^[Y0 : $i]:
% 83.23/13.47 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.47 ((('#B') @ (all_of @
% 83.23/13.47 ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.47 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))))) @
% 83.23/13.47 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.47 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 83.23/13.47 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ moref @
% 83.23/13.47 ((('#C') @ n_pf @ X0)))))) @
% 83.23/13.47 ((('#C') @ n_pf @ X1)))))))) @
% 83.23/13.47 Y0)))))))
% 83.23/13.47 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.47 inference('rw_clause', [status(thm)], [zip_derived_cl3278, '11'])).
% 83.23/13.47 thf(zip_derived_cl3280, plain,
% 83.23/13.47 (![X0 : $i, X1 : $i]:
% 83.23/13.47 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 83.23/13.47 ((('#C') @ is_of @
% 83.23/13.47 ((('#C') @ in @ (pair1type @ nat))))))) @
% 83.23/13.47 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 83.23/13.47 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))))) @
% 83.23/13.47 ((('#S') @ ((('#B') @ ('#S') @
% 83.23/13.47 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 83.23/13.47 ((('#C') @ ((('#B') @ ('#B') @
% 83.23/13.47 ((('#B') @ moref @
% 83.23/13.47 ((('#C') @ n_pf @ X0)))))) @
% 83.23/13.47 ((('#C') @ n_pf @ X1))))))))))))))
% 83.23/13.47 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.47 inference('comb-normalize', [status(thm)], [zip_derived_cl3279])).
% 83.23/13.47 thf(zip_derived_cl3281, plain,
% 83.23/13.47 (![X0 : $i, X1 : $i, X3 : $i]:
% 83.23/13.47 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 83.23/13.47 ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.47 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @
% 83.23/13.47 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @
% 83.23/13.47 ((('#B') @ (moref @ (n_pf @ X3 @ X0)) @ ((('#C') @ n_pf @ X1)))))))))))
% 83.23/13.47 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3280])).
% 83.23/13.47 thf(zip_derived_cl3282, plain,
% 83.23/13.47 (![X0 : $i, X1 : $i, X3 : $i]:
% 83.23/13.47 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 83.23/13.47 ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.47 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @
% 83.23/13.47 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @
% 83.23/13.47 ((('#B') @ (moref @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X3) @ (den @ X0)) @
% 83.23/13.47 (n_ts @ (num @ X0) @ (den @ X3))) @
% 83.23/13.47 (n_ts @ (den @ X3) @ (den @ X0)))) @
% 83.23/13.47 ((('#C') @ n_pf @ X1)))))))))))
% 83.23/13.47 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.47 inference('rw', [status(thm)], [zip_derived_cl3281, '5'])).
% 83.23/13.47 thf(zip_derived_cl3283, plain,
% 83.23/13.47 (![X0 : $i, X1 : $i, X3 : $i]:
% 83.23/13.47 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 83.23/13.47 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @
% 83.23/13.47 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @
% 83.23/13.47 ((('#B') @ (moref @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X3) @ (den @ X0)) @
% 83.23/13.47 (n_ts @ (num @ X0) @ (den @ X3))) @
% 83.23/13.47 (n_ts @ (den @ X3) @ (den @ X0)))) @
% 83.23/13.47 ((('#C') @ n_pf @ X1)))))))))
% 83.23/13.47 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3282])).
% 83.23/13.47 thf(zip_derived_cl3284, plain,
% 83.23/13.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.23/13.47 ( (((!!) @ (^[Y0 : $i]:
% 83.23/13.47 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.47 ((('#B') @ (((=>) @ (n_eq @ X1 @ X0))) @
% 83.23/13.47 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @
% 83.23/13.47 ((('#B') @ (moref @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @
% 83.23/13.47 (n_ts @ (num @ X2) @ (den @ X1)) @
% 83.23/13.47 (n_ts @ (num @ X1) @ (den @ X2))) @
% 83.23/13.47 (n_ts @ (den @ X2) @ (den @ X1)))) @
% 83.23/13.47 ((('#C') @ n_pf @ X0)))))) @
% 83.23/13.47 Y0)))))))
% 83.23/13.47 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.47 inference('rw_clause', [status(thm)], [zip_derived_cl3283, '11'])).
% 83.23/13.47 thf(zip_derived_cl3285, plain,
% 83.23/13.47 (![X0 : $i, X1 : $i, X2 : $i]:
% 83.23/13.47 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 83.23/13.47 ((('#C') @ is_of @
% 83.23/13.47 ((('#C') @ in @ (pair1type @ nat))))))) @
% 83.23/13.47 ((('#B') @ (((=>) @ (n_eq @ X1 @ X0))) @
% 83.23/13.47 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @
% 83.23/13.47 ((('#B') @ (moref @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @
% 83.23/13.47 (n_ts @ (num @ X2) @ (den @ X1)) @
% 83.23/13.47 (n_ts @ (num @ X1) @ (den @ X2))) @
% 83.23/13.47 (n_ts @ (den @ X2) @ (den @ X1)))) @
% 83.23/13.47 ((('#C') @ n_pf @ X0))))))))))))
% 83.23/13.47 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.47 inference('comb-normalize', [status(thm)], [zip_derived_cl3284])).
% 83.23/13.47 thf(zip_derived_cl3286, plain,
% 83.23/13.47 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 83.23/13.47 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.47 (((n_eq @ X1 @ X0) =>
% 83.23/13.47 (((moref @ X2 @ X4) => (moref @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @
% 83.23/13.47 (n_ts @ (num @ X1) @ (den @ X2))) @
% 83.23/13.47 (n_ts @ (den @ X2) @ (den @ X1))) @
% 83.23/13.47 (n_pf @ X4 @ X0))))))))
% 83.23/13.47 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3285])).
% 83.23/13.47 thf(zip_derived_cl3287, plain,
% 83.23/13.47 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 83.23/13.47 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 83.23/13.47 (((n_eq @ X1 @ X0) =>
% 83.23/13.47 (((l_some @ nat @
% 83.23/13.47 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 83.23/13.47 (n_ts @ (num @ X4) @ (den @ X2)))) =>
% 83.23/13.47 (l_some @ nat @
% 83.23/13.47 (diffprop @
% 83.23/13.47 (n_ts @
% 83.23/13.47 (num @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @
% 83.23/13.47 (n_ts @ (num @ X1) @ (den @ X2))) @
% 83.23/13.47 (n_ts @ (den @ X2) @ (den @ X1)))) @
% 83.23/13.47 (den @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @
% 83.23/13.47 (n_ts @ (num @ X0) @ (den @ X4))) @
% 83.23/13.47 (n_ts @ (den @ X4) @ (den @ X0))))) @
% 83.23/13.47 (n_ts @
% 83.23/13.47 (num @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @
% 83.23/13.47 (n_ts @ (num @ X0) @ (den @ X4))) @
% 83.23/13.47 (n_ts @ (den @ X4) @ (den @ X0)))) @
% 83.23/13.47 (den @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @
% 83.23/13.47 (n_ts @ (num @ X1) @ (den @ X2))) @
% 83.23/13.47 (n_ts @ (den @ X2) @ (den @ X1)))))))))))))
% 83.23/13.47 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.47 inference('rw', [status(thm)],
% 83.23/13.47 [zip_derived_cl3286, '2', '2', '3', '3', '4', '4', '5'])).
% 83.23/13.47 thf(zip_derived_cl3288, plain,
% 83.23/13.47 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 83.23/13.47 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | (((n_eq @ X1 @ X0) =>
% 83.23/13.47 (((l_some @ nat @
% 83.23/13.47 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 83.23/13.47 (n_ts @ (num @ X4) @ (den @ X2)))) =>
% 83.23/13.47 (l_some @ nat @
% 83.23/13.47 (diffprop @
% 83.23/13.47 (n_ts @
% 83.23/13.47 (num @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @
% 83.23/13.47 (n_ts @ (num @ X1) @ (den @ X2))) @
% 83.23/13.47 (n_ts @ (den @ X2) @ (den @ X1)))) @
% 83.23/13.47 (den @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @
% 83.23/13.47 (n_ts @ (num @ X0) @ (den @ X4))) @
% 83.23/13.47 (n_ts @ (den @ X4) @ (den @ X0))))) @
% 83.23/13.47 (n_ts @
% 83.23/13.47 (num @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @
% 83.23/13.47 (n_ts @ (num @ X0) @ (den @ X4))) @
% 83.23/13.47 (n_ts @ (den @ X4) @ (den @ X0)))) @
% 83.23/13.47 (den @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @
% 83.23/13.47 (n_ts @ (num @ X1) @ (den @ X2))) @
% 83.23/13.47 (n_ts @ (den @ X2) @ (den @ X1)))))))))))
% 83.23/13.47 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3287])).
% 83.23/13.47 thf(zip_derived_cl3289, plain,
% 83.23/13.47 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 83.23/13.47 (~ (n_eq @ X1 @ X0)
% 83.23/13.47 | (((l_some @ nat @
% 83.23/13.47 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 83.23/13.47 (n_ts @ (num @ X4) @ (den @ X2)))) =>
% 83.23/13.47 (l_some @ nat @
% 83.23/13.47 (diffprop @
% 83.23/13.47 (n_ts @
% 83.23/13.47 (num @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @
% 83.23/13.47 (n_ts @ (num @ X1) @ (den @ X2))) @
% 83.23/13.47 (n_ts @ (den @ X2) @ (den @ X1)))) @
% 83.23/13.47 (den @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @
% 83.23/13.47 (n_ts @ (num @ X0) @ (den @ X4))) @
% 83.23/13.47 (n_ts @ (den @ X4) @ (den @ X0))))) @
% 83.23/13.47 (n_ts @
% 83.23/13.47 (num @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @
% 83.23/13.47 (n_ts @ (num @ X0) @ (den @ X4))) @
% 83.23/13.47 (n_ts @ (den @ X4) @ (den @ X0)))) @
% 83.23/13.47 (den @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @
% 83.23/13.47 (n_ts @ (num @ X1) @ (den @ X2))) @
% 83.23/13.47 (n_ts @ (den @ X2) @ (den @ X1)))))))))
% 83.23/13.47 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 83.23/13.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3288])).
% 83.23/13.47 thf(zip_derived_cl3290, plain,
% 83.23/13.47 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 83.23/13.47 (~ (l_some @ nat @
% 83.23/13.47 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 83.23/13.47 (n_ts @ (num @ X4) @ (den @ X2))))
% 83.23/13.47 | (l_some @ nat @
% 83.23/13.47 (diffprop @
% 83.23/13.47 (n_ts @
% 83.23/13.47 (num @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @
% 83.23/13.47 (n_ts @ (num @ X1) @ (den @ X2))) @
% 83.23/13.47 (n_ts @ (den @ X2) @ (den @ X1)))) @
% 83.23/13.47 (den @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @
% 83.23/13.47 (n_ts @ (num @ X0) @ (den @ X4))) @
% 83.23/13.47 (n_ts @ (den @ X4) @ (den @ X0))))) @
% 83.23/13.47 (n_ts @
% 83.23/13.47 (num @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @
% 83.23/13.47 (n_ts @ (num @ X0) @ (den @ X4))) @
% 83.23/13.47 (n_ts @ (den @ X4) @ (den @ X0)))) @
% 83.23/13.47 (den @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @
% 83.23/13.47 (n_ts @ (num @ X1) @ (den @ X2))) @
% 83.23/13.47 (n_ts @ (den @ X2) @ (den @ X1)))))))
% 83.23/13.47 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 83.23/13.47 | ~ (n_eq @ X1 @ X0))),
% 83.23/13.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3289])).
% 83.23/13.47 thf(zip_derived_cl13823, plain,
% 83.23/13.47 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 83.23/13.47 (~ (l_some @ nat @
% 83.23/13.47 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 83.23/13.47 (n_ts @ (num @ X4) @ (den @ X2))))
% 83.23/13.47 | (l_some @ nat @
% 83.23/13.47 (diffprop @
% 83.23/13.47 (n_ts @
% 83.23/13.47 (num @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @
% 83.23/13.47 (n_ts @ (num @ X1) @ (den @ X2))) @
% 83.23/13.47 (n_ts @ (den @ X2) @ (den @ X1)))) @
% 83.23/13.47 (den @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @
% 83.23/13.47 (n_ts @ (num @ X0) @ (den @ X4))) @
% 83.23/13.47 (n_ts @ (den @ X4) @ (den @ X0))))) @
% 83.23/13.47 (n_ts @
% 83.23/13.47 (num @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @
% 83.23/13.47 (n_ts @ (num @ X0) @ (den @ X4))) @
% 83.23/13.47 (n_ts @ (den @ X4) @ (den @ X0)))) @
% 83.23/13.47 (den @
% 83.23/13.47 (n_fr @
% 83.23/13.47 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @
% 83.23/13.47 (n_ts @ (num @ X1) @ (den @ X2))) @
% 83.23/13.47 (n_ts @ (den @ X2) @ (den @ X1)))))))
% 83.23/13.47 | ~ (is_of @ X4 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 83.23/13.47 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 83.23/13.47 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 83.23/13.47 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 83.23/13.47 | ~ (n_eq @ X1 @ X0))),
% 83.23/13.47 inference('remove_ty_args', [status(thm)], [zip_derived_cl3290])).
% 83.23/13.47 thf(zip_derived_cl13846, plain, ($false),
% 83.23/13.47 inference('eprover', [status(thm)],
% 83.23/13.47 [zip_derived_cl1375, zip_derived_cl13756, zip_derived_cl13757,
% 83.23/13.47 zip_derived_cl13758, zip_derived_cl13759, zip_derived_cl1367,
% 83.23/13.47 zip_derived_cl13808, zip_derived_cl1370, zip_derived_cl13823])).
% 83.23/13.47
% 83.23/13.47 % SZS output end Refutation
% 83.23/13.47
% 83.23/13.47
% 83.23/13.47 % Terminating...
% 83.74/13.64 % Runner terminated.
% 83.74/13.65 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------