%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM750^4 : TPTP v9.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.DMuY3nSvof true
% Computer : n005.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 04:48:13 PM UTC 2025
% Result : Theorem 97.95s 13.03s
% Output : Refutation 97.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM750^4 : TPTP v9.2.0. Released v7.1.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.DMuY3nSvof true
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Oct 1 16:33:23 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.36 % Running in HO mode
% 0.64/0.70 % Total configuration time : 828
% 0.64/0.70 % Estimated wc time : 1656
% 0.64/0.70 % Estimated cpu time (8 cpus) : 207.0
% 0.64/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.64/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.64/0.80 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.66/0.80 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.66/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.66/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.66/0.82 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.66/0.83 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 97.95/13.03 % Solved by lams/40_b.comb.sh.
% 97.95/13.03 % done 210 iterations in 12.147s
% 97.95/13.03 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 97.95/13.03 % SZS output start Refutation
% 97.95/13.03 thf(nat_type, type, nat: $i).
% 97.95/13.03 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 97.95/13.03 thf(in_type, type, in: $i > $i > $o).
% 97.95/13.03 thf(n_pf_type, type, n_pf: $i > $i > $i).
% 97.95/13.03 thf(n_fr_type, type, n_fr: $i > $i > $i).
% 97.95/13.03 thf(n_is_type, type, n_is: $i > $i > $o).
% 97.95/13.03 thf('#sk2_type', type, '#sk2': $i).
% 97.95/13.03 thf(frac_type, type, frac: $i).
% 97.95/13.03 thf('#sk3_type', type, '#sk3': $i).
% 97.95/13.03 thf('#sk4_type', type, '#sk4': $i).
% 97.95/13.03 thf(n_ts_type, type, n_ts: $i > $i > $i).
% 97.95/13.03 thf(n_eq_type, type, n_eq: $i > $i > $o).
% 97.95/13.03 thf(pair1type_type, type, pair1type: $i > $i).
% 97.95/13.03 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 97.95/13.03 thf(num_type, type, num: $i > $i).
% 97.95/13.03 thf(den_type, type, den: $i > $i).
% 97.95/13.03 thf('#ty_enc5_type', type, '#ty_enc5': ($i > $i > $o) > $i > $i > $o).
% 97.95/13.03 thf(n_pl_type, type, n_pl: $i > $i > $i).
% 97.95/13.03 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 97.95/13.03 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 97.95/13.03 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 97.95/13.03 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 97.95/13.03 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 97.95/13.03 thf(satz62b, conjecture,
% 97.95/13.03 (all_of @
% 97.95/13.03 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 97.95/13.03 ( ^[X0:$i]:
% 97.95/13.03 ( all_of @
% 97.95/13.03 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 97.95/13.03 ( ^[X1:$i]:
% 97.95/13.03 ( all_of @
% 97.95/13.03 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 97.95/13.03 ( ^[X2:$i]:
% 97.95/13.03 ( ( n_eq @ X0 @ X1 ) =>
% 97.95/13.03 ( n_eq @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X2 ) ) ) ) ) ) ) ))).
% 97.95/13.03 thf(zf_stmt_0, negated_conjecture,
% 97.95/13.03 (~( all_of @
% 97.95/13.03 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 97.95/13.03 ( ^[X0:$i]:
% 97.95/13.03 ( all_of @
% 97.95/13.03 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 97.95/13.03 ( ^[X1:$i]:
% 97.95/13.03 ( all_of @
% 97.95/13.03 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 97.95/13.03 ( ^[X2:$i]:
% 97.95/13.03 ( ( n_eq @ X0 @ X1 ) =>
% 97.95/13.03 ( n_eq @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X2 ) ) ) ) ) ) ) ) )),
% 97.95/13.03 inference('cnf.neg', [status(esa)], [satz62b])).
% 97.95/13.03 thf(zip_derived_cl321, plain,
% 97.95/13.03 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 97.95/13.03 (^[Y0 : $i]:
% 97.95/13.03 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 97.95/13.03 (^[Y1 : $i]:
% 97.95/13.03 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 97.95/13.03 (^[Y2 : $i]:
% 97.95/13.03 (((n_eq @ Y0 @ Y1) => (n_eq @ (n_pf @ Y0 @ Y2) @
% 97.95/13.03 (n_pf @ Y1 @ Y2))))))))))),
% 97.95/13.03 inference('cnf', [status(esa)], [zf_stmt_0])).
% 97.95/13.03 thf(zip_derived_cl322, plain,
% 97.95/13.03 (~ (all_of @ ((('#C') @ in @ frac)) @
% 97.95/13.03 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 97.95/13.03 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 97.95/13.03 ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.03 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.95/13.03 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.95/13.03 ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.03 ((('#B') @ ('#S') @
% 97.95/13.03 ((('#B') @ ((('#B') @ n_eq)) @ n_pf)))))) @
% 97.95/13.03 n_pf)))))))))),
% 97.95/13.03 inference('lams2combs', [status(thm)], [zip_derived_cl321])).
% 97.95/13.03 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))).
% 97.95/13.03 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])).
% 97.95/13.03 thf(zip_derived_cl558, plain,
% 97.95/13.03 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.95/13.03 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.03 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.95/13.03 ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.03 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.95/13.03 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.95/13.03 ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.03 ((('#B') @ ('#S') @
% 97.95/13.03 ((('#B') @ ((('#B') @ n_eq)) @ n_pf)))))) @
% 97.95/13.03 n_pf)))))))))),
% 97.95/13.03 inference('rw', [status(thm)], [zip_derived_cl322, '0'])).
% 97.95/13.03 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 97.95/13.03 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 97.95/13.03 thf('1', plain,
% 97.95/13.03 (![X0:( $i > $o ),X1:( $i > $o )]:
% 97.95/13.03 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 97.95/13.03 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 97.95/13.03 inference('rw.lit', [status(esa)], [def_all_of])).
% 97.95/13.03 thf(zip_derived_cl559, plain,
% 97.95/13.03 (~ (((!!) @ (^[Y0 : $i]:
% 97.95/13.03 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.95/13.03 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.03 ((('#B') @ ((('#B') @ (all_of @
% 97.95/13.03 ((('#C') @ in @
% 97.95/13.03 (pair1type @ nat)))))) @
% 97.95/13.03 ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.03 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.95/13.03 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.95/13.03 ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.03 ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ n_eq)) @ n_pf)))))) @
% 97.95/13.04 n_pf)))))) @
% 97.95/13.04 Y0)))))))),
% 97.95/13.04 inference('rw_clause', [status(thm)], [zip_derived_cl558, '1'])).
% 97.95/13.04 thf(zip_derived_cl560, plain,
% 97.95/13.04 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.95/13.04 ((('#C') @ is_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.95/13.04 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (all_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.95/13.04 ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ n_eq)) @ n_pf)))))) @
% 97.95/13.04 n_pf))))))))))))),
% 97.95/13.04 inference('comb-normalize', [status(thm)], [zip_derived_cl559])).
% 97.95/13.04 thf(zip_derived_cl561, plain,
% 97.95/13.04 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat))) @
% 97.95/13.04 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 97.95/13.04 ((('#B') @ ((('#S') @ ((('#B') @ n_eq @ (n_pf @ '#sk2'))))) @
% 97.95/13.04 n_pf)))))))))),
% 97.95/13.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl560])).
% 97.95/13.04 thf(zip_derived_cl563, plain,
% 97.95/13.04 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.95/13.04 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 97.95/13.04 ((('#B') @ ((('#S') @ ((('#B') @ n_eq @ (n_pf @ '#sk2'))))) @
% 97.95/13.04 n_pf)))))))),
% 97.95/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl561])).
% 97.95/13.04 thf(zip_derived_cl564, plain,
% 97.95/13.04 (~ (((!!) @ (^[Y0 : $i]:
% 97.95/13.04 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.95/13.04 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 97.95/13.04 ((('#B') @ ((('#S') @ ((('#B') @ n_eq @
% 97.95/13.04 (n_pf @ '#sk2'))))) @
% 97.95/13.04 n_pf)))) @
% 97.95/13.04 Y0)))))))),
% 97.95/13.04 inference('rw_clause', [status(thm)], [zip_derived_cl563, '1'])).
% 97.95/13.04 thf(zip_derived_cl565, plain,
% 97.95/13.04 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.95/13.04 ((('#C') @ is_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.95/13.04 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 97.95/13.04 ((('#B') @ ((('#S') @ ((('#B') @ n_eq @ (n_pf @ '#sk2'))))) @
% 97.95/13.04 n_pf))))))))))),
% 97.95/13.04 inference('comb-normalize', [status(thm)], [zip_derived_cl564])).
% 97.95/13.04 thf(zip_derived_cl566, plain,
% 97.95/13.04 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat))) @
% 97.95/13.04 ((('#B') @ (((=>) @ (n_eq @ '#sk2' @ '#sk3'))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ n_eq @ (n_pf @ '#sk2'))) @ (n_pf @ '#sk3'))))))))),
% 97.95/13.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl565])).
% 97.95/13.04 thf(def_n_eq, axiom,(( n_eq @ (X0)@ (X1)) =
% 97.95/13.04 ((n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 97.95/13.04 (n_ts @ (num @ X1) @ (den @ X0)))))).
% 97.95/13.04 thf('2', plain,
% 97.95/13.04 (![X1:$i,X0:$i]:
% 97.95/13.04 ( ( n_eq @ X0 @ X1 ) =
% 97.95/13.04 ( n_is @
% 97.95/13.04 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 97.95/13.04 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )),
% 97.95/13.04 define([status(thm)])).
% 97.95/13.04 thf(zip_derived_cl567, plain,
% 97.95/13.04 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat))) @
% 97.95/13.04 ((('#B') @ (((=>) @ (n_is @
% 97.95/13.04 (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.95/13.04 (n_ts @ (num @ '#sk3') @ (den @ '#sk2'))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ n_eq @ (n_pf @ '#sk2'))) @ (n_pf @ '#sk3'))))))))),
% 97.95/13.04 inference('rw', [status(thm)], [zip_derived_cl566, '2'])).
% 97.95/13.04 thf(zip_derived_cl569, plain,
% 97.95/13.04 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.95/13.04 ((('#B') @ (((=>) @ (n_is @
% 97.95/13.04 (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.95/13.04 (n_ts @ (num @ '#sk3') @ (den @ '#sk2'))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ n_eq @ (n_pf @ '#sk2'))) @ (n_pf @ '#sk3'))))))),
% 97.95/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl567])).
% 97.95/13.04 thf(zip_derived_cl570, plain,
% 97.95/13.04 (~ (((!!) @ (^[Y0 : $i]:
% 97.95/13.04 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.95/13.04 ((('#B') @ (((=>) @ (n_is @
% 97.95/13.04 (n_ts @ (num @ '#sk2') @
% 97.95/13.04 (den @ '#sk3')) @
% 97.95/13.04 (n_ts @ (num @ '#sk3') @
% 97.95/13.04 (den @ '#sk2'))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ n_eq @ (n_pf @ '#sk2'))) @
% 97.95/13.04 (n_pf @ '#sk3'))) @
% 97.95/13.04 Y0)))))))),
% 97.95/13.04 inference('rw_clause', [status(thm)], [zip_derived_cl569, '1'])).
% 97.95/13.04 thf(zip_derived_cl571, plain,
% 97.95/13.04 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.95/13.04 ((('#C') @ is_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.95/13.04 ((('#B') @ (((=>) @ (n_is @
% 97.95/13.04 (n_ts @ (num @ '#sk2') @
% 97.95/13.04 (den @ '#sk3')) @
% 97.95/13.04 (n_ts @ (num @ '#sk3') @
% 97.95/13.04 (den @ '#sk2'))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ n_eq @ (n_pf @ '#sk2'))) @
% 97.95/13.04 (n_pf @ '#sk3')))))))))),
% 97.95/13.04 inference('comb-normalize', [status(thm)], [zip_derived_cl570])).
% 97.95/13.04 thf(zip_derived_cl572, plain,
% 97.95/13.04 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.95/13.04 (((n_is @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.95/13.04 (n_ts @ (num @ '#sk3') @ (den @ '#sk2'))) => (n_eq @
% 97.95/13.04 (n_pf @ '#sk2' @ '#sk4') @ (n_pf @ '#sk3' @ '#sk4'))))))),
% 97.95/13.04 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl571])).
% 97.95/13.04 thf(def_n_pf, axiom,(( n_pf @ (X0)@ (X1)) =
% 97.95/13.04 ((n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 97.95/13.04 (n_ts @ (num @ X1) @ (den @ X0))) @
% 97.95/13.04 (n_ts @ (den @ X0) @ (den @ X1)))))).
% 97.95/13.04 thf('3', plain,
% 97.95/13.04 (![X1:$i,X0:$i]:
% 97.95/13.04 ( ( n_pf @ X0 @ X1 ) =
% 97.95/13.04 ( n_fr @
% 97.95/13.04 ( n_pl @
% 97.95/13.04 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 97.95/13.04 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) @
% 97.95/13.04 ( n_ts @ ( den @ X0 ) @ ( den @ X1 ) ) ) )),
% 97.95/13.04 define([status(thm)])).
% 97.95/13.04 thf(zip_derived_cl573, plain,
% 97.95/13.04 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.95/13.04 (((n_is @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.95/13.04 (n_ts @ (num @ '#sk3') @ (den @ '#sk2'))) => (n_is @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.95/13.04 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.95/13.04 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 97.95/13.04 (den @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk4')) @
% 97.95/13.04 (n_ts @ (num @ '#sk4') @ (den @ '#sk3'))) @
% 97.95/13.04 (n_ts @ (den @ '#sk3') @ (den @ '#sk4'))))) @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk4')) @
% 97.95/13.04 (n_ts @ (num @ '#sk4') @ (den @ '#sk3'))) @
% 97.95/13.04 (n_ts @ (den @ '#sk3') @ (den @ '#sk4')))) @
% 97.95/13.04 (den @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.95/13.04 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.95/13.04 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))))))))))),
% 97.95/13.04 inference('rw', [status(thm)], [zip_derived_cl572, '2', '3', '3'])).
% 97.95/13.04 thf(zip_derived_cl574, plain,
% 97.95/13.04 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.95/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl573])).
% 97.95/13.04 thf(zip_derived_cl5878, plain,
% 97.95/13.04 ( (is_of @ '#sk4' @ ('#ty_enc5' @ in @ (pair1type @ nat)))),
% 97.95/13.04 inference('remove_ty_args', [status(thm)], [zip_derived_cl574])).
% 97.95/13.04 thf(zip_derived_cl562, plain,
% 97.95/13.04 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.95/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl561])).
% 97.95/13.04 thf(zip_derived_cl5876, plain,
% 97.95/13.04 ( (is_of @ '#sk2' @ ('#ty_enc5' @ in @ (pair1type @ nat)))),
% 97.95/13.04 inference('remove_ty_args', [status(thm)], [zip_derived_cl562])).
% 97.95/13.04 thf(zip_derived_cl568, plain,
% 97.95/13.04 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))),
% 97.95/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl567])).
% 97.95/13.04 thf(zip_derived_cl5877, plain,
% 97.95/13.04 ( (is_of @ '#sk3' @ ('#ty_enc5' @ in @ (pair1type @ nat)))),
% 97.95/13.04 inference('remove_ty_args', [status(thm)], [zip_derived_cl568])).
% 97.95/13.04 thf(zip_derived_cl575, plain,
% 97.95/13.04 (~ (((n_is @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.95/13.04 (n_ts @ (num @ '#sk3') @ (den @ '#sk2'))) => (n_is @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.95/13.04 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.95/13.04 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 97.95/13.04 (den @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk4')) @
% 97.95/13.04 (n_ts @ (num @ '#sk4') @ (den @ '#sk3'))) @
% 97.95/13.04 (n_ts @ (den @ '#sk3') @ (den @ '#sk4'))))) @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk4')) @
% 97.95/13.04 (n_ts @ (num @ '#sk4') @ (den @ '#sk3'))) @
% 97.95/13.04 (n_ts @ (den @ '#sk3') @ (den @ '#sk4')))) @
% 97.95/13.04 (den @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.95/13.04 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.95/13.04 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))))))))),
% 97.95/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl573])).
% 97.95/13.04 thf(zip_derived_cl576, plain,
% 97.95/13.04 ( (n_is @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 97.95/13.04 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))),
% 97.95/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl575])).
% 97.95/13.04 thf(satz37, axiom,
% 97.95/13.04 (all_of @
% 97.95/13.04 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ ( ^[X0:$i]: ( n_eq @ X0 @ X0 ) ))).
% 97.95/13.04 thf(zip_derived_cl239, plain,
% 97.95/13.04 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 97.95/13.04 (^[Y0 : $i]: (n_eq @ Y0 @ Y0)))),
% 97.95/13.04 inference('cnf', [status(esa)], [satz37])).
% 97.95/13.04 thf(zip_derived_cl240, plain,
% 97.95/13.04 ( (all_of @ ((('#C') @ in @ frac)) @ ((('#S') @ n_eq @ ('#I'))))),
% 97.95/13.04 inference('lams2combs', [status(thm)], [zip_derived_cl239])).
% 97.95/13.04 thf(zip_derived_cl337, plain,
% 97.95/13.04 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.95/13.04 ((('#S') @ n_eq @ ('#I'))))),
% 97.95/13.04 inference('rw', [status(thm)], [zip_derived_cl240, '0'])).
% 97.95/13.04 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 97.95/13.04 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 97.95/13.04 thf('4', plain,
% 97.95/13.04 (![X0:( $i > $o ),X1:( $i > $o )]:
% 97.95/13.04 ( ( all_of @ X0 @ X1 ) <=>
% 97.95/13.04 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 97.95/13.04 inference('rw.lit', [status(esa)], [def_all_of])).
% 97.95/13.04 thf(zip_derived_cl338, plain,
% 97.95/13.04 ( (((!!) @ (^[Y0 : $i]:
% 97.95/13.04 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.95/13.04 ((('#S') @ n_eq @ ('#I') @ Y0)))))))),
% 97.95/13.04 inference('rw_clause', [status(thm)], [zip_derived_cl337, '4'])).
% 97.95/13.04 thf(zip_derived_cl339, plain,
% 97.95/13.04 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.95/13.04 ((('#C') @ is_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.95/13.04 ((('#S') @ n_eq @ ('#I')))))))),
% 97.95/13.04 inference('comb-normalize', [status(thm)], [zip_derived_cl338])).
% 97.95/13.04 thf(zip_derived_cl340, plain,
% 97.95/13.04 (![X2 : $i]:
% 97.95/13.04 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (n_eq @ X2 @
% 97.95/13.04 X2)))),
% 97.95/13.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl339])).
% 97.95/13.04 thf(zip_derived_cl341, plain,
% 97.95/13.04 (![X2 : $i]:
% 97.95/13.04 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (n_is @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X2)))))),
% 97.95/13.04 inference('rw', [status(thm)], [zip_derived_cl340, '2'])).
% 97.95/13.04 thf(zip_derived_cl342, plain,
% 97.95/13.04 (![X2 : $i]:
% 97.95/13.04 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | (n_is @ (n_ts @ (num @ X2) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X2))))),
% 97.95/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl341])).
% 97.95/13.04 thf(zip_derived_cl5856, plain,
% 97.95/13.04 (![X2 : $i]:
% 97.95/13.04 (~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 97.95/13.04 | (n_is @ (n_ts @ (num @ X2) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X2))))),
% 97.95/13.04 inference('remove_ty_args', [status(thm)], [zip_derived_cl342])).
% 97.95/13.04 thf(zip_derived_cl577, plain,
% 97.95/13.04 (~ (n_is @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.95/13.04 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.95/13.04 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 97.95/13.04 (den @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk4')) @
% 97.95/13.04 (n_ts @ (num @ '#sk4') @ (den @ '#sk3'))) @
% 97.95/13.04 (n_ts @ (den @ '#sk3') @ (den @ '#sk4'))))) @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk4')) @
% 97.95/13.04 (n_ts @ (num @ '#sk4') @ (den @ '#sk3'))) @
% 97.95/13.04 (n_ts @ (den @ '#sk3') @ (den @ '#sk4')))) @
% 97.95/13.04 (den @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 97.95/13.04 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 97.95/13.04 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))))))),
% 97.95/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl575])).
% 97.95/13.04 thf(satz56, axiom,
% 97.95/13.04 (all_of @
% 97.95/13.04 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 97.95/13.04 ( ^[X0:$i]:
% 97.95/13.04 ( all_of @
% 97.95/13.04 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 97.95/13.04 ( ^[X1:$i]:
% 97.95/13.04 ( all_of @
% 97.95/13.04 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 97.95/13.04 ( ^[X2:$i]:
% 97.95/13.04 ( all_of @
% 97.95/13.04 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 97.95/13.04 ( ^[X3:$i]:
% 97.95/13.04 ( ( n_eq @ X0 @ X1 ) =>
% 97.95/13.04 ( ( n_eq @ X2 @ X3 ) =>
% 97.95/13.04 ( n_eq @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 97.95/13.04 thf(zip_derived_cl305, plain,
% 97.95/13.04 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 97.95/13.04 (^[Y0 : $i]:
% 97.95/13.04 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 97.95/13.04 (^[Y1 : $i]:
% 97.95/13.04 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 97.95/13.04 (^[Y2 : $i]:
% 97.95/13.04 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 97.95/13.04 (^[Y3 : $i]:
% 97.95/13.04 (((n_eq @ Y0 @ Y1) =>
% 97.95/13.04 (((n_eq @ Y2 @ Y3) => (n_eq @ (n_pf @ Y0 @ Y2) @
% 97.95/13.04 (n_pf @ Y1 @ Y3))))))))))))))),
% 97.95/13.04 inference('cnf', [status(esa)], [satz56])).
% 97.95/13.04 thf(zip_derived_cl306, plain,
% 97.95/13.04 ( (all_of @ ((('#C') @ in @ frac)) @
% 97.95/13.04 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ (=>))) @
% 97.95/13.04 n_eq)))))))) @
% 97.95/13.04 ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ ('#C') @
% 97.95/13.04 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ n_eq)) @ n_pf)))))))) @
% 97.95/13.04 n_pf)))))))))))))),
% 97.95/13.04 inference('lams2combs', [status(thm)], [zip_derived_cl305])).
% 97.95/13.04 thf(zip_derived_cl2394, plain,
% 97.95/13.04 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.95/13.04 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.95/13.04 ((('#C') @ in @
% 97.95/13.04 (pair1type @ nat)))))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ (=>))) @
% 97.95/13.04 n_eq)))))))) @
% 97.95/13.04 ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ ('#C') @
% 97.95/13.04 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ n_eq)) @ n_pf)))))))) @
% 97.95/13.04 n_pf)))))))))))))),
% 97.95/13.04 inference('rw', [status(thm)], [zip_derived_cl306, '0'])).
% 97.95/13.04 thf(zip_derived_cl2395, plain,
% 97.95/13.04 ( (((!!) @ (^[Y0 : $i]:
% 97.95/13.04 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.95/13.04 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (all_of @
% 97.95/13.04 ((('#C') @ in @
% 97.95/13.04 (pair1type @ nat)))))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.95/13.04 ((('#C') @ in @
% 97.95/13.04 (pair1type @ nat)))))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (=>))) @
% 97.95/13.04 n_eq)))))))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 97.95/13.04 '#S') @
% 97.95/13.04 ((('#B') @ (
% 97.95/13.04 (('#B') @ (
% 97.95/13.04 =>))) @
% 97.95/13.04 n_eq)))))))) @
% 97.95/13.04 ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ ('#C') @
% 97.95/13.04 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ n_eq)) @
% 97.95/13.04 n_pf)))))))) @
% 97.95/13.04 n_pf)))))))))) @
% 97.95/13.04 Y0)))))))),
% 97.95/13.04 inference('rw_clause', [status(thm)], [zip_derived_cl2394, '4'])).
% 97.95/13.04 thf(zip_derived_cl2396, plain,
% 97.95/13.04 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.95/13.04 ((('#C') @ is_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.95/13.04 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (all_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 97.95/13.04 ((('#C') @ in @
% 97.95/13.04 (pair1type @ nat)))))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 97.95/13.04 '#S') @
% 97.95/13.04 ((('#B') @ (
% 97.95/13.04 (('#B') @ (=>))) @
% 97.95/13.04 n_eq)))))))) @
% 97.95/13.04 ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ ('#C') @
% 97.95/13.04 ((('#B') @ ((('#B') @ ('#B'))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ n_eq)) @
% 97.95/13.04 n_pf)))))))) @
% 97.95/13.04 n_pf))))))))))))))))),
% 97.95/13.04 inference('comb-normalize', [status(thm)], [zip_derived_cl2395])).
% 97.95/13.04 thf(zip_derived_cl2397, plain,
% 97.95/13.04 (![X2 : $i]:
% 97.95/13.04 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat))) @
% 97.95/13.04 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (all_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ (=>) @ (n_eq @ X2))))))) @
% 97.95/13.04 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.95/13.04 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ n_eq @ (n_pf @ X2))))))) @
% 97.95/13.04 n_pf)))))))))))))),
% 97.95/13.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2396])).
% 97.95/13.04 thf(zip_derived_cl2398, plain,
% 97.95/13.04 (![X2 : $i]:
% 97.95/13.04 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.95/13.04 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (all_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat)))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ (=>) @ (n_eq @ X2))))))) @
% 97.95/13.04 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 97.95/13.04 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ n_eq @ (n_pf @ X2))))))) @
% 97.95/13.04 n_pf))))))))))))),
% 97.95/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2397])).
% 97.95/13.04 thf(zip_derived_cl2399, plain,
% 97.95/13.04 (![X0 : $i]:
% 97.95/13.04 ( (((!!) @ (^[Y0 : $i]:
% 97.95/13.04 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.95/13.04 ((('#B') @ (all_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (all_of @
% 97.95/13.04 ((('#C') @ in @
% 97.95/13.04 (pair1type @ nat)))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ (=>) @ (n_eq @ X0))))))) @
% 97.95/13.04 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ (
% 97.95/13.04 =>))) @
% 97.95/13.04 n_eq)))))) @
% 97.95/13.04 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ n_eq @
% 97.95/13.04 (n_pf @ X0))))))) @
% 97.95/13.04 n_pf)))))))) @
% 97.95/13.04 Y0)))))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.95/13.04 inference('rw_clause', [status(thm)], [zip_derived_cl2398, '4'])).
% 97.95/13.04 thf(zip_derived_cl2400, plain,
% 97.95/13.04 (![X0 : $i]:
% 97.95/13.04 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.95/13.04 ((('#C') @ is_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.95/13.04 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (all_of @
% 97.95/13.04 ((('#C') @ in @
% 97.95/13.04 (pair1type @ nat)))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ (=>) @ (n_eq @ X0))))))) @
% 97.95/13.04 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ (=>))) @
% 97.95/13.04 n_eq)))))) @
% 97.95/13.04 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ n_eq @
% 97.95/13.04 (n_pf @ X0))))))) @
% 97.95/13.04 n_pf))))))))))))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.95/13.04 inference('comb-normalize', [status(thm)], [zip_derived_cl2399])).
% 97.95/13.04 thf(zip_derived_cl2401, plain,
% 97.95/13.04 (![X0 : $i, X2 : $i]:
% 97.95/13.04 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat))) @
% 97.95/13.04 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 97.95/13.04 ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ n_eq @ (n_pf @ X0))))) @
% 97.95/13.04 (n_pf @ X2))))))))))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.95/13.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2400])).
% 97.95/13.04 thf(zip_derived_cl2402, plain,
% 97.95/13.04 (![X0 : $i, X2 : $i]:
% 97.95/13.04 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat))) @
% 97.95/13.04 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (((=>) @ (n_is @
% 97.95/13.04 (n_ts @ (num @ X0) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X0))))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 97.95/13.04 ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ n_eq @ (n_pf @ X0))))) @
% 97.95/13.04 (n_pf @ X2))))))))))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.95/13.04 inference('rw', [status(thm)], [zip_derived_cl2401, '2'])).
% 97.95/13.04 thf(zip_derived_cl2403, plain,
% 97.95/13.04 (![X0 : $i, X2 : $i]:
% 97.95/13.04 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.95/13.04 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (((=>) @ (n_is @
% 97.95/13.04 (n_ts @ (num @ X0) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X0))))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 97.95/13.04 ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ n_eq @ (n_pf @ X0))))) @
% 97.95/13.04 (n_pf @ X2))))))))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.95/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2402])).
% 97.95/13.04 thf(zip_derived_cl2404, plain,
% 97.95/13.04 (![X0 : $i, X1 : $i]:
% 97.95/13.04 ( (((!!) @ (^[Y0 : $i]:
% 97.95/13.04 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.95/13.04 ((('#B') @ (all_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (((=>) @ (n_is @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @ X0) @
% 97.95/13.04 (den @ X1)) @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @ X1) @
% 97.95/13.04 (den @ X0))))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 97.95/13.04 ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ n_eq @ (n_pf @ X0))))) @
% 97.95/13.04 (n_pf @ X1))))))) @
% 97.95/13.04 Y0)))))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.95/13.04 inference('rw_clause', [status(thm)], [zip_derived_cl2403, '4'])).
% 97.95/13.04 thf(zip_derived_cl2405, plain,
% 97.95/13.04 (![X0 : $i, X1 : $i]:
% 97.95/13.04 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.95/13.04 ((('#C') @ is_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.95/13.04 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 97.95/13.04 ((('#B') @ ((('#B') @ (((=>) @ (n_is @
% 97.95/13.04 (n_ts @ (num @ X0) @
% 97.95/13.04 (den @ X1)) @
% 97.95/13.04 (n_ts @ (num @ X1) @
% 97.95/13.04 (den @ X0))))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ ('#S') @
% 97.95/13.04 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 97.95/13.04 ((('#C') @ ((('#B') @ ('#B') @
% 97.95/13.04 ((('#B') @ n_eq @ (n_pf @ X0))))) @
% 97.95/13.04 (n_pf @ X1)))))))))))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.95/13.04 inference('comb-normalize', [status(thm)], [zip_derived_cl2404])).
% 97.95/13.04 thf(zip_derived_cl2406, plain,
% 97.95/13.04 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.95/13.04 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat))) @
% 97.95/13.04 ((('#B') @ (((=>) @ (n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 97.95/13.04 (n_ts @ (num @ X1) @ (den @ X0))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X3))) @
% 97.95/13.04 ((('#B') @ (n_eq @ (n_pf @ X0 @ X3)) @ (n_pf @ X1))))))))))
% 97.95/13.04 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.95/13.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2405])).
% 97.95/13.04 thf(zip_derived_cl2407, plain,
% 97.95/13.04 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.95/13.04 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat))) @
% 97.95/13.04 ((('#B') @ (((=>) @ (n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 97.95/13.04 (n_ts @ (num @ X1) @ (den @ X0))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X3))) @
% 97.95/13.04 ((('#B') @ (n_eq @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 97.95/13.04 (n_ts @ (num @ X3) @ (den @ X0))) @
% 97.95/13.04 (n_ts @ (den @ X0) @ (den @ X3)))) @
% 97.95/13.04 (n_pf @ X1))))))))))
% 97.95/13.04 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.95/13.04 inference('rw', [status(thm)], [zip_derived_cl2406, '3'])).
% 97.95/13.04 thf(zip_derived_cl2408, plain,
% 97.95/13.04 (![X0 : $i, X1 : $i, X3 : $i]:
% 97.95/13.04 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 97.95/13.04 ((('#B') @ (((=>) @ (n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 97.95/13.04 (n_ts @ (num @ X1) @ (den @ X0))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X3))) @
% 97.95/13.04 ((('#B') @ (n_eq @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 97.95/13.04 (n_ts @ (num @ X3) @ (den @ X0))) @
% 97.95/13.04 (n_ts @ (den @ X0) @ (den @ X3)))) @
% 97.95/13.04 (n_pf @ X1))))))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.95/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2407])).
% 97.95/13.04 thf(zip_derived_cl2409, plain,
% 97.95/13.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 97.95/13.04 ( (((!!) @ (^[Y0 : $i]:
% 97.95/13.04 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.95/13.04 ((('#B') @ (((=>) @ (n_is @
% 97.95/13.04 (n_ts @ (num @ X1) @ (den @ X0)) @
% 97.95/13.04 (n_ts @ (num @ X0) @ (den @ X1))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @
% 97.95/13.04 ((('#B') @ (n_eq @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @
% 97.95/13.04 (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.95/13.04 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.95/13.04 (n_pf @ X0))))) @
% 97.95/13.04 Y0)))))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.95/13.04 inference('rw_clause', [status(thm)], [zip_derived_cl2408, '4'])).
% 97.95/13.04 thf(zip_derived_cl2410, plain,
% 97.95/13.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 97.95/13.04 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 97.95/13.04 ((('#C') @ is_of @
% 97.95/13.04 ((('#C') @ in @ (pair1type @ nat))))))) @
% 97.95/13.04 ((('#B') @ (((=>) @ (n_is @
% 97.95/13.04 (n_ts @ (num @ X1) @ (den @ X0)) @
% 97.95/13.04 (n_ts @ (num @ X0) @ (den @ X1))))) @
% 97.95/13.04 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @
% 97.95/13.04 ((('#B') @ (n_eq @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @
% 97.95/13.04 (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.95/13.04 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.95/13.04 (n_pf @ X0)))))))))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.95/13.04 inference('comb-normalize', [status(thm)], [zip_derived_cl2409])).
% 97.95/13.04 thf(zip_derived_cl2411, plain,
% 97.95/13.04 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.95/13.04 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.95/13.04 (((n_is @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 97.95/13.04 (n_ts @ (num @ X0) @ (den @ X1))) =>
% 97.95/13.04 (((n_eq @ X2 @ X4) => (n_eq @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.95/13.04 (n_ts @ (den @ X1) @ (den @ X2))) @
% 97.95/13.04 (n_pf @ X0 @ X4))))))))
% 97.95/13.04 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.95/13.04 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2410])).
% 97.95/13.04 thf(zip_derived_cl2412, plain,
% 97.95/13.04 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.95/13.04 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 97.95/13.04 (((n_is @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 97.95/13.04 (n_ts @ (num @ X0) @ (den @ X1))) =>
% 97.95/13.04 (((n_is @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 97.95/13.04 (n_ts @ (num @ X4) @ (den @ X2))) => (n_is @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.95/13.04 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.95/13.04 (den @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.95/13.04 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.95/13.04 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.95/13.04 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.95/13.04 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 97.95/13.04 (den @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.95/13.04 (n_ts @ (den @ X1) @ (den @ X2))))))))))))
% 97.95/13.04 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.95/13.04 inference('rw', [status(thm)], [zip_derived_cl2411, '2', '2', '3'])).
% 97.95/13.04 thf(zip_derived_cl2413, plain,
% 97.95/13.04 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.95/13.04 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | (((n_is @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 97.95/13.04 (n_ts @ (num @ X0) @ (den @ X1))) =>
% 97.95/13.04 (((n_is @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 97.95/13.04 (n_ts @ (num @ X4) @ (den @ X2))) => (n_is @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.95/13.04 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.95/13.04 (den @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.95/13.04 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.95/13.04 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.95/13.04 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.95/13.04 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 97.95/13.04 (den @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.95/13.04 (n_ts @ (den @ X1) @ (den @ X2))))))))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.95/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2412])).
% 97.95/13.04 thf(zip_derived_cl2414, plain,
% 97.95/13.04 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.95/13.04 (~ (n_is @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 97.95/13.04 (n_ts @ (num @ X0) @ (den @ X1)))
% 97.95/13.04 | (((n_is @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 97.95/13.04 (n_ts @ (num @ X4) @ (den @ X2))) => (n_is @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.95/13.04 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.95/13.04 (den @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.95/13.04 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.95/13.04 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.95/13.04 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.95/13.04 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 97.95/13.04 (den @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.95/13.04 (n_ts @ (den @ X1) @ (den @ X2))))))))
% 97.95/13.04 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 97.95/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2413])).
% 97.95/13.04 thf(zip_derived_cl2415, plain,
% 97.95/13.04 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.95/13.04 (~ (n_is @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 97.95/13.04 (n_ts @ (num @ X4) @ (den @ X2)))
% 97.95/13.04 | (n_is @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.95/13.04 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.95/13.04 (den @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.95/13.04 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.95/13.04 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.95/13.04 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.95/13.04 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 97.95/13.04 (den @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.95/13.04 (n_ts @ (den @ X1) @ (den @ X2))))))
% 97.95/13.04 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 97.95/13.04 | ~ (n_is @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 97.95/13.04 (n_ts @ (num @ X0) @ (den @ X1))))),
% 97.95/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2414])).
% 97.95/13.04 thf(zip_derived_cl5950, plain,
% 97.95/13.04 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 97.95/13.04 (~ (n_is @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 97.95/13.04 (n_ts @ (num @ X4) @ (den @ X2)))
% 97.95/13.04 | (n_is @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.95/13.04 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 97.95/13.04 (den @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.95/13.04 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.95/13.04 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 97.95/13.04 (n_ts @
% 97.95/13.04 (num @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 97.95/13.04 (n_ts @ (num @ X4) @ (den @ X0))) @
% 97.95/13.04 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 97.95/13.04 (den @
% 97.95/13.04 (n_fr @
% 97.95/13.04 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 97.95/13.04 (n_ts @ (num @ X2) @ (den @ X1))) @
% 97.95/13.04 (n_ts @ (den @ X1) @ (den @ X2))))))
% 97.95/13.04 | ~ (is_of @ X4 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 97.95/13.04 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 97.95/13.04 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 97.95/13.04 | ~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 97.95/13.04 | ~ (n_is @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 97.95/13.04 (n_ts @ (num @ X0) @ (den @ X1))))),
% 97.95/13.04 inference('remove_ty_args', [status(thm)], [zip_derived_cl2415])).
% 97.95/13.04 thf(zip_derived_cl5970, plain, ($false),
% 97.95/13.04 inference('eprover', [status(thm)],
% 97.95/13.04 [zip_derived_cl5878, zip_derived_cl5876, zip_derived_cl5877,
% 97.95/13.04 zip_derived_cl576, zip_derived_cl5856, zip_derived_cl577,
% 97.95/13.04 zip_derived_cl5950])).
% 97.95/13.04
% 97.95/13.04 % SZS output end Refutation
% 97.95/13.04
% 97.95/13.04
% 97.95/13.04 % Terminating...
% 98.37/13.16 % Runner terminated.
% 98.37/13.17 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------