TSTP Solution File: NUM765^4 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM765^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.jDlNDVZCOO true
% Computer : n029.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 Aug 31 12:44:01 EDT 2023
% Result : Theorem 93.83s 12.79s
% Output : Refutation 93.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM765^4 : TPTP v8.1.2. Released v7.1.0.
% 0.00/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.jDlNDVZCOO true
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 09:29:09 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.14/0.37 % Running portfolio for 300 s
% 0.14/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.37 % Number of cores: 8
% 0.14/0.37 % Python version: Python 3.6.8
% 0.14/0.37 % Running in HO mode
% 0.22/0.67 % Total configuration time : 828
% 0.22/0.67 % Estimated wc time : 1656
% 0.22/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 93.83/12.79 % Solved by lams/40_b.comb.sh.
% 93.83/12.79 % done 647 iterations in 11.934s
% 93.83/12.79 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 93.83/12.79 % SZS output start Refutation
% 93.83/12.79 thf(moreq_type, type, moreq: $i > $i > $o).
% 93.83/12.79 thf(nat_type, type, nat: $i).
% 93.83/12.79 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 93.83/12.79 thf(in_type, type, in: $i > $i > $o).
% 93.83/12.79 thf('#sk4_type', type, '#sk4': $i).
% 93.83/12.79 thf(n_pf_type, type, n_pf: $i > $i > $i).
% 93.83/12.79 thf(n_fr_type, type, n_fr: $i > $i > $i).
% 93.83/12.79 thf(imp_type, type, imp: $o > $o > $o).
% 93.83/12.79 thf(frac_type, type, frac: $i).
% 93.83/12.79 thf(n_ts_type, type, n_ts: $i > $i > $i).
% 93.83/12.79 thf(n_eq_type, type, n_eq: $i > $i > $o).
% 93.83/12.79 thf(pair1type_type, type, pair1type: $i > $i).
% 93.83/12.79 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 93.83/12.79 thf('#ty_enc6_type', type, '#ty_enc6': ($i > $i > $o) > $i > $i > $o).
% 93.83/12.79 thf(num_type, type, num: $i > $i).
% 93.83/12.79 thf(l_or_type, type, l_or: $o > $o > $o).
% 93.83/12.79 thf('#sk3_type', type, '#sk3': $i).
% 93.83/12.79 thf(moref_type, type, moref: $i > $i > $o).
% 93.83/12.79 thf('#sk2_type', type, '#sk2': $i).
% 93.83/12.79 thf(d_not_type, type, d_not: $o > $o).
% 93.83/12.79 thf(den_type, type, den: $i > $i).
% 93.83/12.79 thf('#sk5_type', type, '#sk5': $i).
% 93.83/12.79 thf(n_pl_type, type, n_pl: $i > $i > $i).
% 93.83/12.79 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 93.83/12.79 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 93.83/12.79 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 93.83/12.79 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 93.83/12.79 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 93.83/12.79 thf(satz66, conjecture,
% 93.83/12.79 (all_of @
% 93.83/12.79 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 93.83/12.79 ( ^[X0:$i]:
% 93.83/12.79 ( all_of @
% 93.83/12.79 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 93.83/12.79 ( ^[X1:$i]:
% 93.83/12.79 ( all_of @
% 93.83/12.79 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 93.83/12.79 ( ^[X2:$i]:
% 93.83/12.79 ( all_of @
% 93.83/12.79 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 93.83/12.79 ( ^[X3:$i]:
% 93.83/12.79 ( ( moreq @ X0 @ X1 ) =>
% 93.83/12.79 ( ( moreq @ X2 @ X3 ) =>
% 93.83/12.79 ( moreq @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 93.83/12.79 thf(zf_stmt_0, negated_conjecture,
% 93.83/12.79 (~( all_of @
% 93.83/12.79 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 93.83/12.79 ( ^[X0:$i]:
% 93.83/12.79 ( all_of @
% 93.83/12.79 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 93.83/12.79 ( ^[X1:$i]:
% 93.83/12.79 ( all_of @
% 93.83/12.79 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 93.83/12.79 ( ^[X2:$i]:
% 93.83/12.79 ( all_of @
% 93.83/12.79 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 93.83/12.79 ( ^[X3:$i]:
% 93.83/12.79 ( ( moreq @ X0 @ X1 ) =>
% 93.83/12.79 ( ( moreq @ X2 @ X3 ) =>
% 93.83/12.79 ( moreq @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) )),
% 93.83/12.79 inference('cnf.neg', [status(esa)], [satz66])).
% 93.83/12.79 thf(zip_derived_cl354, plain,
% 93.83/12.79 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 93.83/12.79 (^[Y0 : $i]:
% 93.83/12.79 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 93.83/12.79 (^[Y1 : $i]:
% 93.83/12.79 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 93.83/12.79 (^[Y2 : $i]:
% 93.83/12.79 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 93.83/12.79 (^[Y3 : $i]:
% 93.83/12.79 (((moreq @ Y0 @ Y1) =>
% 93.83/12.79 (((moreq @ Y2 @ Y3) => (moreq @ (n_pf @ Y0 @ Y2) @
% 93.83/12.79 (n_pf @ Y1 @ Y3))))))))))))))),
% 93.83/12.79 inference('cnf', [status(esa)], [zf_stmt_0])).
% 93.83/12.79 thf(zip_derived_cl355, plain,
% 93.83/12.79 (~ (all_of @ ((('#C') @ in @ frac)) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 moreq)))))))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#C') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ moreq)) @ n_pf)))))))) @
% 93.83/12.79 n_pf)))))))))))))),
% 93.83/12.79 inference('lams2combs', [status(thm)], [zip_derived_cl354])).
% 93.83/12.79 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))).
% 93.83/12.79 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])).
% 93.83/12.79 thf(zip_derived_cl1286, plain,
% 93.83/12.79 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 moreq)))))))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#C') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ moreq)) @ n_pf)))))))) @
% 93.83/12.79 n_pf)))))))))))))),
% 93.83/12.79 inference('rw', [status(thm)], [zip_derived_cl355, '0'])).
% 93.83/12.79 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 93.83/12.79 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 93.83/12.79 thf('1', plain,
% 93.83/12.79 (![X0:( $i > $o ),X1:( $i > $o )]:
% 93.83/12.79 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 93.83/12.79 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 93.83/12.79 inference('rw.lit', [status(esa)], [def_all_of])).
% 93.83/12.79 thf(zip_derived_cl1287, plain,
% 93.83/12.79 (~ (((!!) @ (^[Y0 : $i]:
% 93.83/12.79 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 moreq)))))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 93.83/12.79 '#S') @
% 93.83/12.79 ((('#B') @ (
% 93.83/12.79 (('#B') @ (
% 93.83/12.79 =>))) @
% 93.83/12.79 moreq)))))))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#C') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ moreq)) @
% 93.83/12.79 n_pf)))))))) @
% 93.83/12.79 n_pf)))))))))) @
% 93.83/12.79 Y0)))))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl1286, '1'])).
% 93.83/12.79 thf(zip_derived_cl1288, plain,
% 93.83/12.79 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 93.83/12.79 ((('#C') @ is_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))))))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 93.83/12.79 '#S') @
% 93.83/12.79 ((('#B') @ (
% 93.83/12.79 (('#B') @ (=>))) @
% 93.83/12.79 moreq)))))))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#C') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ moreq)) @
% 93.83/12.79 n_pf)))))))) @
% 93.83/12.79 n_pf))))))))))))))))),
% 93.83/12.79 inference('comb-normalize', [status(thm)], [zip_derived_cl1287])).
% 93.83/12.79 thf(zip_derived_cl1289, plain,
% 93.83/12.79 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @
% 93.83/12.79 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @
% 93.83/12.79 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moreq @ (n_pf @ '#sk2'))))))) @
% 93.83/12.79 n_pf)))))))))))))),
% 93.83/12.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1288])).
% 93.83/12.79 thf(zip_derived_cl1291, plain,
% 93.83/12.79 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @
% 93.83/12.79 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @
% 93.83/12.79 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moreq @ (n_pf @ '#sk2'))))))) @
% 93.83/12.79 n_pf)))))))))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1289])).
% 93.83/12.79 thf(zip_derived_cl1292, plain,
% 93.83/12.79 (~ (((!!) @ (^[Y0 : $i]:
% 93.83/12.79 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @
% 93.83/12.79 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 moreq)))))) @
% 93.83/12.79 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moreq @
% 93.83/12.79 (n_pf @ '#sk2'))))))) @
% 93.83/12.79 n_pf)))))))) @
% 93.83/12.79 Y0)))))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl1291, '1'])).
% 93.83/12.79 thf(zip_derived_cl1293, plain,
% 93.83/12.79 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 93.83/12.79 ((('#C') @ is_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))))))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @
% 93.83/12.79 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 moreq)))))) @
% 93.83/12.79 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moreq @
% 93.83/12.79 (n_pf @ '#sk2'))))))) @
% 93.83/12.79 n_pf))))))))))))))),
% 93.83/12.79 inference('comb-normalize', [status(thm)], [zip_derived_cl1292])).
% 93.83/12.79 thf(zip_derived_cl1294, plain,
% 93.83/12.79 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (moreq @ '#sk2' @ '#sk3'))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moreq @ (n_pf @ '#sk2'))))) @
% 93.83/12.79 (n_pf @ '#sk3'))))))))))))),
% 93.83/12.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1293])).
% 93.83/12.79 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 93.83/12.79 thf('2', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 93.83/12.79 define([status(thm)])).
% 93.83/12.79 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 93.83/12.79 thf('3', plain,
% 93.83/12.79 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 93.83/12.79 define([status(thm)])).
% 93.83/12.79 thf(def_moreq, axiom,(( moreq @ (X0)@ (X1)) =
% 93.83/12.79 ((l_or @ (moref @ X0 @ X1) @ (n_eq @ X0 @ X1))))).
% 93.83/12.79 thf('4', plain,
% 93.83/12.79 (![X1:$i,X0:$i]:
% 93.83/12.79 ( ( moreq @ X0 @ X1 ) =
% 93.83/12.79 ( l_or @ ( moref @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )),
% 93.83/12.79 define([status(thm)])).
% 93.83/12.79 thf(zip_derived_cl1295, plain,
% 93.83/12.79 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 93.83/12.79 (imp @
% 93.83/12.79 (moref @ '#sk2' @ '#sk3') @
% 93.83/12.79 ($false)) @
% 93.83/12.79 (n_eq @ '#sk2' @ '#sk3')))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moreq @ (n_pf @ '#sk2'))))) @
% 93.83/12.79 (n_pf @ '#sk3'))))))))))))),
% 93.83/12.79 inference('rw', [status(thm)], [zip_derived_cl1294, '2', '3', '4'])).
% 93.83/12.79 thf(zip_derived_cl1297, plain,
% 93.83/12.79 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 93.83/12.79 (imp @ (moref @ '#sk2' @ '#sk3') @
% 93.83/12.79 ($false)) @
% 93.83/12.79 (n_eq @ '#sk2' @ '#sk3')))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moreq @ (n_pf @ '#sk2'))))) @
% 93.83/12.79 (n_pf @ '#sk3'))))))))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1295])).
% 93.83/12.79 thf(zip_derived_cl1298, plain,
% 93.83/12.79 (~ (((!!) @ (^[Y0 : $i]:
% 93.83/12.79 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 93.83/12.79 (imp @
% 93.83/12.79 (moref @ '#sk2' @
% 93.83/12.79 '#sk3') @
% 93.83/12.79 ($false)) @
% 93.83/12.79 (n_eq @ '#sk2' @
% 93.83/12.79 '#sk3')))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moreq @ (n_pf @ '#sk2'))))) @
% 93.83/12.79 (n_pf @ '#sk3'))))))) @
% 93.83/12.79 Y0)))))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl1297, '1'])).
% 93.83/12.79 thf(zip_derived_cl1299, plain,
% 93.83/12.79 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 93.83/12.79 ((('#C') @ is_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))))))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 93.83/12.79 (imp @
% 93.83/12.79 (moref @ '#sk2' @ '#sk3') @
% 93.83/12.79 ($false)) @
% 93.83/12.79 (n_eq @ '#sk2' @ '#sk3')))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moreq @ (n_pf @ '#sk2'))))) @
% 93.83/12.79 (n_pf @ '#sk3')))))))))))))),
% 93.83/12.79 inference('comb-normalize', [status(thm)], [zip_derived_cl1298])).
% 93.83/12.79 thf(zip_derived_cl1300, plain,
% 93.83/12.79 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (((=>) @ (imp @
% 93.83/12.79 (imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) @
% 93.83/12.79 (n_eq @ '#sk2' @ '#sk3')))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @
% 93.83/12.79 ((('#B') @ (moreq @ (n_pf @ '#sk2' @ '#sk4')) @ (n_pf @ '#sk3'))))))))))),
% 93.83/12.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1299])).
% 93.83/12.79 thf(def_n_pf, axiom,(( n_pf @ (X0)@ (X1)) =
% 93.83/12.79 ((n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 93.83/12.79 (n_ts @ (num @ X1) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X1)))))).
% 93.83/12.79 thf('5', plain,
% 93.83/12.79 (![X1:$i,X0:$i]:
% 93.83/12.79 ( ( n_pf @ X0 @ X1 ) =
% 93.83/12.79 ( n_fr @
% 93.83/12.79 ( n_pl @
% 93.83/12.79 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 93.83/12.79 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) @
% 93.83/12.79 ( n_ts @ ( den @ X0 ) @ ( den @ X1 ) ) ) )),
% 93.83/12.79 define([status(thm)])).
% 93.83/12.79 thf(zip_derived_cl1301, plain,
% 93.83/12.79 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (((=>) @ (imp @
% 93.83/12.79 (imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) @
% 93.83/12.79 (n_eq @ '#sk2' @ '#sk3')))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @
% 93.83/12.79 ((('#B') @ (moreq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 93.83/12.79 (n_pf @ '#sk3'))))))))))),
% 93.83/12.79 inference('rw', [status(thm)], [zip_derived_cl1300, '5'])).
% 93.83/12.79 thf(zip_derived_cl1303, plain,
% 93.83/12.79 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (((=>) @ (imp @
% 93.83/12.79 (imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) @
% 93.83/12.79 (n_eq @ '#sk2' @ '#sk3')))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @
% 93.83/12.79 ((('#B') @ (moreq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 93.83/12.79 (n_pf @ '#sk3'))))))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1301])).
% 93.83/12.79 thf(zip_derived_cl1304, plain,
% 93.83/12.79 (~ (((!!) @ (^[Y0 : $i]:
% 93.83/12.79 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 ((('#B') @ (((=>) @ (imp @
% 93.83/12.79 (imp @ (moref @ '#sk2' @ '#sk3') @
% 93.83/12.79 ($false)) @
% 93.83/12.79 (n_eq @ '#sk2' @ '#sk3')))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @
% 93.83/12.79 ((('#B') @ (moreq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @
% 93.83/12.79 (n_ts @ (num @ '#sk2') @
% 93.83/12.79 (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @
% 93.83/12.79 (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 93.83/12.79 (n_pf @ '#sk3'))))) @
% 93.83/12.79 Y0)))))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl1303, '1'])).
% 93.83/12.79 thf(zip_derived_cl1305, plain,
% 93.83/12.79 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 93.83/12.79 ((('#C') @ is_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))))))) @
% 93.83/12.79 ((('#B') @ (((=>) @ (imp @
% 93.83/12.79 (imp @ (moref @ '#sk2' @ '#sk3') @
% 93.83/12.79 ($false)) @
% 93.83/12.79 (n_eq @ '#sk2' @ '#sk3')))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @
% 93.83/12.79 ((('#B') @ (moreq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @
% 93.83/12.79 (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @
% 93.83/12.79 (n_pf @ '#sk3')))))))))))),
% 93.83/12.79 inference('comb-normalize', [status(thm)], [zip_derived_cl1304])).
% 93.83/12.79 thf(zip_derived_cl1306, plain,
% 93.83/12.79 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 (((imp @ (imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) @
% 93.83/12.79 (n_eq @ '#sk2' @ '#sk3')) =>
% 93.83/12.79 (((moreq @ '#sk4' @ '#sk5') => (moreq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 93.83/12.79 (n_pf @ '#sk3' @ '#sk5'))))))))),
% 93.83/12.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1305])).
% 93.83/12.79 thf(zip_derived_cl1307, plain,
% 93.83/12.79 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 (((imp @ (imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) @
% 93.83/12.79 (n_eq @ '#sk2' @ '#sk3')) =>
% 93.83/12.79 (((imp @ (imp @ (moref @ '#sk4' @ '#sk5') @ ($false)) @
% 93.83/12.79 (n_eq @ '#sk4' @ '#sk5')) => (imp @
% 93.83/12.79 (imp @
% 93.83/12.79 (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 93.83/12.79 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @
% 93.83/12.79 ($false)) @
% 93.83/12.79 (n_eq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 93.83/12.79 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))))))))))),
% 93.83/12.79 inference('rw', [status(thm)],
% 93.83/12.79 [zip_derived_cl1306, '2', '2', '3', '3', '4', '4', '5'])).
% 93.83/12.79 thf(zip_derived_cl1309, plain,
% 93.83/12.79 (~ (((imp @ (imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) @
% 93.83/12.79 (n_eq @ '#sk2' @ '#sk3')) =>
% 93.83/12.79 (((imp @ (imp @ (moref @ '#sk4' @ '#sk5') @ ($false)) @
% 93.83/12.79 (n_eq @ '#sk4' @ '#sk5')) => (imp @
% 93.83/12.79 (imp @
% 93.83/12.79 (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 93.83/12.79 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @
% 93.83/12.79 ($false)) @
% 93.83/12.79 (n_eq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 93.83/12.79 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))))))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1307])).
% 93.83/12.79 thf(zip_derived_cl1310, plain,
% 93.83/12.79 ( (imp @ (imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) @
% 93.83/12.79 (n_eq @ '#sk2' @ '#sk3'))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1309])).
% 93.83/12.79 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 93.83/12.79 thf('6', plain,
% 93.83/12.79 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 93.83/12.79 inference('rw.lit', [status(esa)], [def_imp])).
% 93.83/12.79 thf(zip_derived_cl1312, plain,
% 93.83/12.79 ( (((imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) => (n_eq @ '#sk2' @
% 93.83/12.79 '#sk3')))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl1310, '6'])).
% 93.83/12.79 thf(zip_derived_cl1315, plain,
% 93.83/12.79 ((~ (imp @ (moref @ '#sk2' @ '#sk3') @ ($false))
% 93.83/12.79 | (n_eq @ '#sk2' @ '#sk3'))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1312])).
% 93.83/12.79 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 93.83/12.79 thf('7', plain,
% 93.83/12.79 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 93.83/12.79 inference('rw.lit', [status(esa)], [def_imp])).
% 93.83/12.79 thf(zip_derived_cl1318, plain,
% 93.83/12.79 ((~ (((moref @ '#sk2' @ '#sk3') => ($false))) | (n_eq @ '#sk2' @ '#sk3'))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl1315, '7'])).
% 93.83/12.79 thf(zip_derived_cl1322, plain,
% 93.83/12.79 ((~ (((~) @ (moref @ '#sk2' @ '#sk3'))) | (n_eq @ '#sk2' @ '#sk3'))),
% 93.83/12.79 inference('simplify boolean subterms', [status(thm)],
% 93.83/12.79 [zip_derived_cl1318])).
% 93.83/12.79 thf(zip_derived_cl1323, plain,
% 93.83/12.79 (( (moref @ '#sk2' @ '#sk3') | (n_eq @ '#sk2' @ '#sk3'))),
% 93.83/12.79 inference('simplify nested equalities', [status(thm)],
% 93.83/12.79 [zip_derived_cl1322])).
% 93.83/12.79 thf(satz65b, axiom,
% 93.83/12.79 (all_of @
% 93.83/12.79 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 93.83/12.79 ( ^[X0:$i]:
% 93.83/12.79 ( all_of @
% 93.83/12.79 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 93.83/12.79 ( ^[X1:$i]:
% 93.83/12.79 ( all_of @
% 93.83/12.79 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 93.83/12.79 ( ^[X2:$i]:
% 93.83/12.79 ( all_of @
% 93.83/12.79 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 93.83/12.79 ( ^[X3:$i]:
% 93.83/12.79 ( ( moref @ X0 @ X1 ) =>
% 93.83/12.79 ( ( moreq @ X2 @ X3 ) =>
% 93.83/12.79 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 93.83/12.79 thf(zip_derived_cl348, plain,
% 93.83/12.79 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 93.83/12.79 (^[Y0 : $i]:
% 93.83/12.79 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 93.83/12.79 (^[Y1 : $i]:
% 93.83/12.79 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 93.83/12.79 (^[Y2 : $i]:
% 93.83/12.79 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 93.83/12.79 (^[Y3 : $i]:
% 93.83/12.79 (((moref @ Y0 @ Y1) =>
% 93.83/12.79 (((moreq @ Y2 @ Y3) => (moref @ (n_pf @ Y0 @ Y2) @
% 93.83/12.79 (n_pf @ Y1 @ Y3))))))))))))))),
% 93.83/12.79 inference('cnf', [status(esa)], [satz65b])).
% 93.83/12.79 thf(zip_derived_cl349, plain,
% 93.83/12.79 ( (all_of @ ((('#C') @ in @ frac)) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 moreq)))))))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#C') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @
% 93.83/12.79 n_pf)))))))))))))),
% 93.83/12.79 inference('lams2combs', [status(thm)], [zip_derived_cl348])).
% 93.83/12.79 thf(zip_derived_cl2609, plain,
% 93.83/12.79 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 moreq)))))))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#C') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @
% 93.83/12.79 n_pf)))))))))))))),
% 93.83/12.79 inference('rw', [status(thm)], [zip_derived_cl349, '0'])).
% 93.83/12.79 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 93.83/12.79 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 93.83/12.79 thf('8', plain,
% 93.83/12.79 (![X0:( $i > $o ),X1:( $i > $o )]:
% 93.83/12.79 ( ( all_of @ X0 @ X1 ) <=>
% 93.83/12.79 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 93.83/12.79 inference('rw.lit', [status(esa)], [def_all_of])).
% 93.83/12.79 thf(zip_derived_cl2610, plain,
% 93.83/12.79 ( (((!!) @ (^[Y0 : $i]:
% 93.83/12.79 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 moref)))))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 93.83/12.79 '#S') @
% 93.83/12.79 ((('#B') @ (
% 93.83/12.79 (('#B') @ (
% 93.83/12.79 =>))) @
% 93.83/12.79 moreq)))))))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#C') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ moref)) @
% 93.83/12.79 n_pf)))))))) @
% 93.83/12.79 n_pf)))))))))) @
% 93.83/12.79 Y0)))))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl2609, '8'])).
% 93.83/12.79 thf(zip_derived_cl2611, plain,
% 93.83/12.79 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 93.83/12.79 ((('#C') @ is_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))))))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 93.83/12.79 '#S') @
% 93.83/12.79 ((('#B') @ (
% 93.83/12.79 (('#B') @ (=>))) @
% 93.83/12.79 moreq)))))))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#C') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ moref)) @
% 93.83/12.79 n_pf)))))))) @
% 93.83/12.79 n_pf))))))))))))))))),
% 93.83/12.79 inference('comb-normalize', [status(thm)], [zip_derived_cl2610])).
% 93.83/12.79 thf(zip_derived_cl2612, plain,
% 93.83/12.79 (![X2 : $i]:
% 93.83/12.79 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ (=>) @ (moref @ X2))))))) @
% 93.83/12.79 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @
% 93.83/12.79 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @ (n_pf @ X2))))))) @
% 93.83/12.79 n_pf)))))))))))))),
% 93.83/12.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2611])).
% 93.83/12.79 thf(zip_derived_cl2613, plain,
% 93.83/12.79 (![X2 : $i]:
% 93.83/12.79 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ (=>) @ (moref @ X2))))))) @
% 93.83/12.79 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 moreq)))))) @
% 93.83/12.79 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @ (n_pf @ X2))))))) @
% 93.83/12.79 n_pf))))))))))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2612])).
% 93.83/12.79 thf(zip_derived_cl2614, plain,
% 93.83/12.79 (![X0 : $i]:
% 93.83/12.79 ( (((!!) @ (^[Y0 : $i]:
% 93.83/12.79 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ (=>) @ (moref @ X0))))))) @
% 93.83/12.79 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (
% 93.83/12.79 =>))) @
% 93.83/12.79 moreq)))))) @
% 93.83/12.79 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @
% 93.83/12.79 (n_pf @ X0))))))) @
% 93.83/12.79 n_pf)))))))) @
% 93.83/12.79 Y0)))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl2613, '8'])).
% 93.83/12.79 thf(zip_derived_cl2615, plain,
% 93.83/12.79 (![X0 : $i]:
% 93.83/12.79 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 93.83/12.79 ((('#C') @ is_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))))))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ (=>) @ (moref @ X0))))))) @
% 93.83/12.79 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 moreq)))))) @
% 93.83/12.79 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @
% 93.83/12.79 (n_pf @ X0))))))) @
% 93.83/12.79 n_pf))))))))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('comb-normalize', [status(thm)], [zip_derived_cl2614])).
% 93.83/12.79 thf(zip_derived_cl2616, plain,
% 93.83/12.79 (![X0 : $i, X2 : $i]:
% 93.83/12.79 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X2))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @ (n_pf @ X0))))) @
% 93.83/12.79 (n_pf @ X2))))))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2615])).
% 93.83/12.79 thf(zip_derived_cl2617, plain,
% 93.83/12.79 (![X0 : $i, X2 : $i]:
% 93.83/12.79 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X2))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @ (n_pf @ X0))))) @
% 93.83/12.79 (n_pf @ X2))))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2616])).
% 93.83/12.79 thf(zip_derived_cl2618, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i]:
% 93.83/12.79 ( (((!!) @ (^[Y0 : $i]:
% 93.83/12.79 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X1))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @ (n_pf @ X0))))) @
% 93.83/12.79 (n_pf @ X1))))))) @
% 93.83/12.79 Y0)))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl2617, '8'])).
% 93.83/12.79 thf(zip_derived_cl2619, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i]:
% 93.83/12.79 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 93.83/12.79 ((('#C') @ is_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))))))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X1))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @ (n_pf @ X0))))) @
% 93.83/12.79 (n_pf @ X1)))))))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('comb-normalize', [status(thm)], [zip_derived_cl2618])).
% 93.83/12.79 thf(zip_derived_cl2620, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X3 : $i]:
% 93.83/12.79 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (((=>) @ (moref @ X0 @ X1))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X3))) @
% 93.83/12.79 ((('#B') @ (moref @ (n_pf @ X0 @ X3)) @ (n_pf @ X1))))))))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2619])).
% 93.83/12.79 thf(zip_derived_cl2621, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X3 : $i]:
% 93.83/12.79 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (((=>) @ (moref @ X0 @ X1))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X3))) @
% 93.83/12.79 ((('#B') @ (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X3)))) @
% 93.83/12.79 (n_pf @ X1))))))))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('rw', [status(thm)], [zip_derived_cl2620, '5'])).
% 93.83/12.79 thf(zip_derived_cl2622, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X3 : $i]:
% 93.83/12.79 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (((=>) @ (moref @ X0 @ X1))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X3))) @
% 93.83/12.79 ((('#B') @ (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X3)))) @
% 93.83/12.79 (n_pf @ X1))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2621])).
% 93.83/12.79 thf(zip_derived_cl2623, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 93.83/12.79 ( (((!!) @ (^[Y0 : $i]:
% 93.83/12.79 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 ((('#B') @ (((=>) @ (moref @ X1 @ X0))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X2))) @
% 93.83/12.79 ((('#B') @ (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @
% 93.83/12.79 (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 93.83/12.79 (n_pf @ X0))))) @
% 93.83/12.79 Y0)))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl2622, '8'])).
% 93.83/12.79 thf(zip_derived_cl2624, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 93.83/12.79 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 93.83/12.79 ((('#C') @ is_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))))))) @
% 93.83/12.79 ((('#B') @ (((=>) @ (moref @ X1 @ X0))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X2))) @
% 93.83/12.79 ((('#B') @ (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @
% 93.83/12.79 (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 93.83/12.79 (n_pf @ X0)))))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('comb-normalize', [status(thm)], [zip_derived_cl2623])).
% 93.83/12.79 thf(zip_derived_cl2625, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 93.83/12.79 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 (((moref @ X1 @ X0) =>
% 93.83/12.79 (((moreq @ X2 @ X4) => (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_pf @ X0 @ X4))))))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2624])).
% 93.83/12.79 thf(zip_derived_cl2626, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 93.83/12.79 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 (((moref @ X1 @ X0) =>
% 93.83/12.79 (((imp @ (imp @ (moref @ X2 @ X4) @ ($false)) @
% 93.83/12.79 (n_eq @ X2 @ X4)) => (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 93.83/12.79 (n_ts @ (num @ X4) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X4))))))))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('rw', [status(thm)], [zip_derived_cl2625, '2', '3', '4', '5'])).
% 93.83/12.79 thf(zip_derived_cl2627, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 93.83/12.79 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (((moref @ X1 @ X0) =>
% 93.83/12.79 (((imp @ (imp @ (moref @ X2 @ X4) @ ($false)) @
% 93.83/12.79 (n_eq @ X2 @ X4)) => (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 93.83/12.79 (n_ts @ (num @ X4) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X4))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2626])).
% 93.83/12.79 thf(zip_derived_cl2628, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 93.83/12.79 (~ (moref @ X1 @ X0)
% 93.83/12.79 | (((imp @ (imp @ (moref @ X2 @ X4) @ ($false)) @
% 93.83/12.79 (n_eq @ X2 @ X4)) => (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 93.83/12.79 (n_ts @ (num @ X4) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X4))))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2627])).
% 93.83/12.79 thf(zip_derived_cl2629, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 93.83/12.79 (~ (imp @ (imp @ (moref @ X2 @ X4) @ ($false)) @ (n_eq @ X2 @ X4))
% 93.83/12.79 | (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 93.83/12.79 (n_ts @ (num @ X4) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X4))))
% 93.83/12.79 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (moref @ X1 @ X0))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2628])).
% 93.83/12.79 thf(zip_derived_cl2630, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 93.83/12.79 (~ (((imp @ (moref @ X2 @ X3) @ ($false)) => (n_eq @ X2 @ X3)))
% 93.83/12.79 | ~ (moref @ X1 @ X0)
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X3)))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl2629, '7'])).
% 93.83/12.79 thf(zip_derived_cl2632, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 93.83/12.79 (~ (n_eq @ X2 @ X3)
% 93.83/12.79 | (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X3))))
% 93.83/12.79 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (moref @ X1 @ X0))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2630])).
% 93.83/12.79 thf(zip_derived_cl16983, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 93.83/12.79 (~ (n_eq @ X2 @ X3)
% 93.83/12.79 | (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X3))))
% 93.83/12.79 | ~ (is_of @ X3 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 93.83/12.79 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 93.83/12.79 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 93.83/12.79 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 93.83/12.79 | ~ (moref @ X1 @ X0))),
% 93.83/12.79 inference('remove_ty_args', [status(thm)], [zip_derived_cl2632])).
% 93.83/12.79 thf(zip_derived_cl1311, plain,
% 93.83/12.79 (~ (((imp @ (imp @ (moref @ '#sk4' @ '#sk5') @ ($false)) @
% 93.83/12.79 (n_eq @ '#sk4' @ '#sk5')) => (imp @
% 93.83/12.79 (imp @
% 93.83/12.79 (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 93.83/12.79 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @
% 93.83/12.79 ($false)) @
% 93.83/12.79 (n_eq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 93.83/12.79 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1309])).
% 93.83/12.79 thf(zip_derived_cl1313, plain,
% 93.83/12.79 ( (imp @ (imp @ (moref @ '#sk4' @ '#sk5') @ ($false)) @
% 93.83/12.79 (n_eq @ '#sk4' @ '#sk5'))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1311])).
% 93.83/12.79 thf(zip_derived_cl1316, plain,
% 93.83/12.79 ( (((imp @ (moref @ '#sk4' @ '#sk5') @ ($false)) => (n_eq @ '#sk4' @
% 93.83/12.79 '#sk5')))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl1313, '6'])).
% 93.83/12.79 thf(zip_derived_cl1319, plain,
% 93.83/12.79 ((~ (imp @ (moref @ '#sk4' @ '#sk5') @ ($false))
% 93.83/12.79 | (n_eq @ '#sk4' @ '#sk5'))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1316])).
% 93.83/12.79 thf(zip_derived_cl1324, plain,
% 93.83/12.79 ((~ (((moref @ '#sk4' @ '#sk5') => ($false))) | (n_eq @ '#sk4' @ '#sk5'))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl1319, '7'])).
% 93.83/12.79 thf(zip_derived_cl1326, plain,
% 93.83/12.79 ((~ (((~) @ (moref @ '#sk4' @ '#sk5'))) | (n_eq @ '#sk4' @ '#sk5'))),
% 93.83/12.79 inference('simplify boolean subterms', [status(thm)],
% 93.83/12.79 [zip_derived_cl1324])).
% 93.83/12.79 thf(zip_derived_cl1327, plain,
% 93.83/12.79 (( (moref @ '#sk4' @ '#sk5') | (n_eq @ '#sk4' @ '#sk5'))),
% 93.83/12.79 inference('simplify nested equalities', [status(thm)],
% 93.83/12.79 [zip_derived_cl1326])).
% 93.83/12.79 thf(zip_derived_cl1302, plain,
% 93.83/12.79 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1301])).
% 93.83/12.79 thf(zip_derived_cl16931, plain,
% 93.83/12.79 ( (is_of @ '#sk4' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 93.83/12.79 inference('remove_ty_args', [status(thm)], [zip_derived_cl1302])).
% 93.83/12.79 thf(zip_derived_cl1308, plain,
% 93.83/12.79 ( (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1307])).
% 93.83/12.79 thf(zip_derived_cl16932, plain,
% 93.83/12.79 ( (is_of @ '#sk5' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 93.83/12.79 inference('remove_ty_args', [status(thm)], [zip_derived_cl1308])).
% 93.83/12.79 thf(zip_derived_cl1290, plain,
% 93.83/12.79 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1289])).
% 93.83/12.79 thf(zip_derived_cl16929, plain,
% 93.83/12.79 ( (is_of @ '#sk2' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 93.83/12.79 inference('remove_ty_args', [status(thm)], [zip_derived_cl1290])).
% 93.83/12.79 thf(zip_derived_cl1296, plain,
% 93.83/12.79 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1295])).
% 93.83/12.79 thf(zip_derived_cl16930, plain,
% 93.83/12.79 ( (is_of @ '#sk3' @ ('#ty_enc6' @ in @ (pair1type @ nat)))),
% 93.83/12.79 inference('remove_ty_args', [status(thm)], [zip_derived_cl1296])).
% 93.83/12.79 thf(satz65a, axiom,
% 93.83/12.79 (all_of @
% 93.83/12.79 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 93.83/12.79 ( ^[X0:$i]:
% 93.83/12.79 ( all_of @
% 93.83/12.79 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 93.83/12.79 ( ^[X1:$i]:
% 93.83/12.79 ( all_of @
% 93.83/12.79 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 93.83/12.79 ( ^[X2:$i]:
% 93.83/12.79 ( all_of @
% 93.83/12.79 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 93.83/12.79 ( ^[X3:$i]:
% 93.83/12.79 ( ( moreq @ X0 @ X1 ) =>
% 93.83/12.79 ( ( moref @ X2 @ X3 ) =>
% 93.83/12.79 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 93.83/12.79 thf(zip_derived_cl346, plain,
% 93.83/12.79 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 93.83/12.79 (^[Y0 : $i]:
% 93.83/12.79 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 93.83/12.79 (^[Y1 : $i]:
% 93.83/12.79 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 93.83/12.79 (^[Y2 : $i]:
% 93.83/12.79 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 93.83/12.79 (^[Y3 : $i]:
% 93.83/12.79 (((moreq @ Y0 @ Y1) =>
% 93.83/12.79 (((moref @ Y2 @ Y3) => (moref @ (n_pf @ Y0 @ Y2) @
% 93.83/12.79 (n_pf @ Y1 @ Y3))))))))))))))),
% 93.83/12.79 inference('cnf', [status(esa)], [satz65a])).
% 93.83/12.79 thf(zip_derived_cl347, plain,
% 93.83/12.79 ( (all_of @ ((('#C') @ in @ frac)) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 moref)))))))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#C') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @
% 93.83/12.79 n_pf)))))))))))))),
% 93.83/12.79 inference('lams2combs', [status(thm)], [zip_derived_cl346])).
% 93.83/12.79 thf(zip_derived_cl2580, plain,
% 93.83/12.79 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 moref)))))))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#C') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @
% 93.83/12.79 n_pf)))))))))))))),
% 93.83/12.79 inference('rw', [status(thm)], [zip_derived_cl347, '0'])).
% 93.83/12.79 thf(zip_derived_cl2581, plain,
% 93.83/12.79 ( (((!!) @ (^[Y0 : $i]:
% 93.83/12.79 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 moreq)))))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 93.83/12.79 '#S') @
% 93.83/12.79 ((('#B') @ (
% 93.83/12.79 (('#B') @ (
% 93.83/12.79 =>))) @
% 93.83/12.79 moref)))))))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#C') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ moref)) @
% 93.83/12.79 n_pf)))))))) @
% 93.83/12.79 n_pf)))))))))) @
% 93.83/12.79 Y0)))))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl2580, '8'])).
% 93.83/12.79 thf(zip_derived_cl2582, plain,
% 93.83/12.79 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 93.83/12.79 ((('#C') @ is_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))))))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 93.83/12.79 '#S') @
% 93.83/12.79 ((('#B') @ (
% 93.83/12.79 (('#B') @ (=>))) @
% 93.83/12.79 moref)))))))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#C') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ moref)) @
% 93.83/12.79 n_pf)))))))) @
% 93.83/12.79 n_pf))))))))))))))))),
% 93.83/12.79 inference('comb-normalize', [status(thm)], [zip_derived_cl2581])).
% 93.83/12.79 thf(zip_derived_cl2583, plain,
% 93.83/12.79 (![X2 : $i]:
% 93.83/12.79 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ (=>) @ (moreq @ X2))))))) @
% 93.83/12.79 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @
% 93.83/12.79 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @ (n_pf @ X2))))))) @
% 93.83/12.79 n_pf)))))))))))))),
% 93.83/12.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2582])).
% 93.83/12.79 thf(zip_derived_cl2584, plain,
% 93.83/12.79 (![X2 : $i]:
% 93.83/12.79 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ (=>) @ (moreq @ X2))))))) @
% 93.83/12.79 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 moref)))))) @
% 93.83/12.79 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @ (n_pf @ X2))))))) @
% 93.83/12.79 n_pf))))))))))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2583])).
% 93.83/12.79 thf(zip_derived_cl2585, plain,
% 93.83/12.79 (![X0 : $i]:
% 93.83/12.79 ( (((!!) @ (^[Y0 : $i]:
% 93.83/12.79 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ (=>) @ (moreq @ X0))))))) @
% 93.83/12.79 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (
% 93.83/12.79 =>))) @
% 93.83/12.79 moref)))))) @
% 93.83/12.79 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @
% 93.83/12.79 (n_pf @ X0))))))) @
% 93.83/12.79 n_pf)))))))) @
% 93.83/12.79 Y0)))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl2584, '8'])).
% 93.83/12.79 thf(zip_derived_cl2586, plain,
% 93.83/12.79 (![X0 : $i]:
% 93.83/12.79 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 93.83/12.79 ((('#C') @ is_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))))))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ (=>) @ (moreq @ X0))))))) @
% 93.83/12.79 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 moref)))))) @
% 93.83/12.79 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @
% 93.83/12.79 (n_pf @ X0))))))) @
% 93.83/12.79 n_pf))))))))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('comb-normalize', [status(thm)], [zip_derived_cl2585])).
% 93.83/12.79 thf(zip_derived_cl2587, plain,
% 93.83/12.79 (![X0 : $i, X2 : $i]:
% 93.83/12.79 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (moreq @ X0 @ X2))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @ (n_pf @ X0))))) @
% 93.83/12.79 (n_pf @ X2))))))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2586])).
% 93.83/12.79 thf(zip_derived_cl2588, plain,
% 93.83/12.79 (![X0 : $i, X2 : $i]:
% 93.83/12.79 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 93.83/12.79 (imp @ (moref @ X0 @ X2) @
% 93.83/12.79 ($false)) @
% 93.83/12.79 (n_eq @ X0 @ X2)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @ (n_pf @ X0))))) @
% 93.83/12.79 (n_pf @ X2))))))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('rw', [status(thm)], [zip_derived_cl2587, '2', '3', '4'])).
% 93.83/12.79 thf(zip_derived_cl2589, plain,
% 93.83/12.79 (![X0 : $i, X2 : $i]:
% 93.83/12.79 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 93.83/12.79 (imp @ (moref @ X0 @ X2) @
% 93.83/12.79 ($false)) @
% 93.83/12.79 (n_eq @ X0 @ X2)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @ (n_pf @ X0))))) @
% 93.83/12.79 (n_pf @ X2))))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2588])).
% 93.83/12.79 thf(zip_derived_cl2590, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i]:
% 93.83/12.79 ( (((!!) @ (^[Y0 : $i]:
% 93.83/12.79 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 93.83/12.79 (imp @
% 93.83/12.79 (moref @ X0 @ X1) @
% 93.83/12.79 ($false)) @
% 93.83/12.79 (n_eq @ X0 @ X1)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @ (n_pf @ X0))))) @
% 93.83/12.79 (n_pf @ X1))))))) @
% 93.83/12.79 Y0)))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl2589, '8'])).
% 93.83/12.79 thf(zip_derived_cl2591, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i]:
% 93.83/12.79 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 93.83/12.79 ((('#C') @ is_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))))))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (imp @
% 93.83/12.79 (imp @
% 93.83/12.79 (moref @ X0 @ X1) @
% 93.83/12.79 ($false)) @
% 93.83/12.79 (n_eq @ X0 @ X1)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ moref @ (n_pf @ X0))))) @
% 93.83/12.79 (n_pf @ X1)))))))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('comb-normalize', [status(thm)], [zip_derived_cl2590])).
% 93.83/12.79 thf(zip_derived_cl2592, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X3 : $i]:
% 93.83/12.79 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (((=>) @ (imp @ (imp @ (moref @ X0 @ X1) @ ($false)) @
% 93.83/12.79 (n_eq @ X0 @ X1)))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @
% 93.83/12.79 ((('#B') @ (moref @ (n_pf @ X0 @ X3)) @ (n_pf @ X1))))))))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2591])).
% 93.83/12.79 thf(zip_derived_cl2593, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X3 : $i]:
% 93.83/12.79 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (((=>) @ (imp @ (imp @ (moref @ X0 @ X1) @ ($false)) @
% 93.83/12.79 (n_eq @ X0 @ X1)))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @
% 93.83/12.79 ((('#B') @ (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X3)))) @
% 93.83/12.79 (n_pf @ X1))))))))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('rw', [status(thm)], [zip_derived_cl2592, '5'])).
% 93.83/12.79 thf(zip_derived_cl2594, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X3 : $i]:
% 93.83/12.79 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (((=>) @ (imp @
% 93.83/12.79 (imp @ (moref @ X0 @ X1) @ ($false)) @
% 93.83/12.79 (n_eq @ X0 @ X1)))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @
% 93.83/12.79 ((('#B') @ (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X3)))) @
% 93.83/12.79 (n_pf @ X1))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2593])).
% 93.83/12.79 thf(zip_derived_cl2595, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 93.83/12.79 ( (((!!) @ (^[Y0 : $i]:
% 93.83/12.79 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 ((('#B') @ (((=>) @ (imp @
% 93.83/12.79 (imp @ (moref @ X1 @ X0) @
% 93.83/12.79 ($false)) @
% 93.83/12.79 (n_eq @ X1 @ X0)))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @
% 93.83/12.79 ((('#B') @ (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @
% 93.83/12.79 (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 93.83/12.79 (n_pf @ X0))))) @
% 93.83/12.79 Y0)))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl2594, '8'])).
% 93.83/12.79 thf(zip_derived_cl2596, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 93.83/12.79 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 93.83/12.79 ((('#C') @ is_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))))))) @
% 93.83/12.79 ((('#B') @ (((=>) @ (imp @
% 93.83/12.79 (imp @ (moref @ X1 @ X0) @ ($false)) @
% 93.83/12.79 (n_eq @ X1 @ X0)))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @
% 93.83/12.79 ((('#B') @ (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @
% 93.83/12.79 (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 93.83/12.79 (n_pf @ X0)))))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('comb-normalize', [status(thm)], [zip_derived_cl2595])).
% 93.83/12.79 thf(zip_derived_cl2597, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 93.83/12.79 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 (((imp @ (imp @ (moref @ X1 @ X0) @ ($false)) @
% 93.83/12.79 (n_eq @ X1 @ X0)) =>
% 93.83/12.79 (((moref @ X2 @ X4) => (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_pf @ X0 @ X4))))))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2596])).
% 93.83/12.79 thf(zip_derived_cl2598, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 93.83/12.79 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 (((imp @ (imp @ (moref @ X1 @ X0) @ ($false)) @
% 93.83/12.79 (n_eq @ X1 @ X0)) =>
% 93.83/12.79 (((moref @ X2 @ X4) => (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 93.83/12.79 (n_ts @ (num @ X4) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X4))))))))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('rw', [status(thm)], [zip_derived_cl2597, '5'])).
% 93.83/12.79 thf(zip_derived_cl2599, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 93.83/12.79 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (((imp @ (imp @ (moref @ X1 @ X0) @ ($false)) @
% 93.83/12.79 (n_eq @ X1 @ X0)) =>
% 93.83/12.79 (((moref @ X2 @ X4) => (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 93.83/12.79 (n_ts @ (num @ X4) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X4))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2598])).
% 93.83/12.79 thf(zip_derived_cl2600, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 93.83/12.79 (~ (imp @ (imp @ (moref @ X1 @ X0) @ ($false)) @ (n_eq @ X1 @ X0))
% 93.83/12.79 | (((moref @ X2 @ X4) => (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 93.83/12.79 (n_ts @ (num @ X4) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X4))))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2599])).
% 93.83/12.79 thf(zip_derived_cl2601, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 93.83/12.79 (~ (((imp @ (moref @ X2 @ X1) @ ($false)) => (n_eq @ X2 @ X1)))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (((moref @ X3 @ X0) => (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X2) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X2))) @
% 93.83/12.79 (n_ts @ (den @ X2) @ (den @ X3))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 93.83/12.79 (n_ts @ (num @ X0) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X0)))))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl2600, '7'])).
% 93.83/12.79 thf(zip_derived_cl2602, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 93.83/12.79 ( (imp @ (moref @ X2 @ X1) @ ($false))
% 93.83/12.79 | (((moref @ X3 @ X0) => (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X2) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X2))) @
% 93.83/12.79 (n_ts @ (den @ X2) @ (den @ X3))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 93.83/12.79 (n_ts @ (num @ X0) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X0))))))
% 93.83/12.79 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2601])).
% 93.83/12.79 thf(zip_derived_cl2604, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 93.83/12.79 ( (((moref @ X2 @ X1) => ($false)))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (((moref @ X3 @ X0) => (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X2) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X2))) @
% 93.83/12.79 (n_ts @ (den @ X2) @ (den @ X3))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 93.83/12.79 (n_ts @ (num @ X0) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X0)))))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl2602, '6'])).
% 93.83/12.79 thf(zip_derived_cl2606, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 93.83/12.79 ( (((~) @ (moref @ X2 @ X1)))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (((moref @ X3 @ X0) => (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X2) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X2))) @
% 93.83/12.79 (n_ts @ (den @ X2) @ (den @ X3))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 93.83/12.79 (n_ts @ (num @ X0) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X0)))))))),
% 93.83/12.79 inference('simplify boolean subterms', [status(thm)],
% 93.83/12.79 [zip_derived_cl2604])).
% 93.83/12.79 thf(zip_derived_cl2607, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 93.83/12.79 (~ (moref @ X2 @ X1)
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (((moref @ X3 @ X0) => (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X2) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X2))) @
% 93.83/12.79 (n_ts @ (den @ X2) @ (den @ X3))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 93.83/12.79 (n_ts @ (num @ X0) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X0)))))))),
% 93.83/12.79 inference('simplify nested equalities', [status(thm)],
% 93.83/12.79 [zip_derived_cl2606])).
% 93.83/12.79 thf(zip_derived_cl2608, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 93.83/12.79 (~ (moref @ X3 @ X0)
% 93.83/12.79 | (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X2) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X2))) @
% 93.83/12.79 (n_ts @ (den @ X2) @ (den @ X3))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 93.83/12.79 (n_ts @ (num @ X0) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X0))))
% 93.83/12.79 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (moref @ X2 @ X1))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2607])).
% 93.83/12.79 thf(zip_derived_cl16982, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 93.83/12.79 (~ (moref @ X3 @ X0)
% 93.83/12.79 | (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X2) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X2))) @
% 93.83/12.79 (n_ts @ (den @ X2) @ (den @ X3))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 93.83/12.79 (n_ts @ (num @ X0) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X0))))
% 93.83/12.79 | ~ (is_of @ X3 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 93.83/12.79 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 93.83/12.79 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 93.83/12.79 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 93.83/12.79 | ~ (moref @ X2 @ X1))),
% 93.83/12.79 inference('remove_ty_args', [status(thm)], [zip_derived_cl2608])).
% 93.83/12.79 thf(zip_derived_cl1314, plain,
% 93.83/12.79 (~ (imp @
% 93.83/12.79 (imp @
% 93.83/12.79 (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 93.83/12.79 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @
% 93.83/12.79 ($false)) @
% 93.83/12.79 (n_eq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 93.83/12.79 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1311])).
% 93.83/12.79 thf(zip_derived_cl1317, plain,
% 93.83/12.79 (~ (((imp @
% 93.83/12.79 (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 93.83/12.79 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @
% 93.83/12.79 ($false)) => (n_eq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 93.83/12.79 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl1314, '7'])).
% 93.83/12.79 thf(zip_derived_cl1321, plain,
% 93.83/12.79 (~ (n_eq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 93.83/12.79 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1317])).
% 93.83/12.79 thf(zip_derived_cl1320, plain,
% 93.83/12.79 ( (imp @
% 93.83/12.79 (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 93.83/12.79 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @
% 93.83/12.79 ($false))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1317])).
% 93.83/12.79 thf(zip_derived_cl1325, plain,
% 93.83/12.79 ( (((moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 93.83/12.79 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) =>
% 93.83/12.79 ($false)))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl1320, '6'])).
% 93.83/12.79 thf(zip_derived_cl1328, plain,
% 93.83/12.79 ( (((~) @ (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 93.83/12.79 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))))),
% 93.83/12.79 inference('simplify boolean subterms', [status(thm)],
% 93.83/12.79 [zip_derived_cl1325])).
% 93.83/12.79 thf(zip_derived_cl1329, plain,
% 93.83/12.79 (~ (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @
% 93.83/12.79 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @
% 93.83/12.79 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @
% 93.83/12.79 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))),
% 93.83/12.79 inference('simplify nested equalities', [status(thm)],
% 93.83/12.79 [zip_derived_cl1328])).
% 93.83/12.79 thf(satz56, axiom,
% 93.83/12.79 (all_of @
% 93.83/12.79 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 93.83/12.79 ( ^[X0:$i]:
% 93.83/12.79 ( all_of @
% 93.83/12.79 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 93.83/12.79 ( ^[X1:$i]:
% 93.83/12.79 ( all_of @
% 93.83/12.79 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 93.83/12.79 ( ^[X2:$i]:
% 93.83/12.79 ( all_of @
% 93.83/12.79 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 93.83/12.79 ( ^[X3:$i]:
% 93.83/12.79 ( ( n_eq @ X0 @ X1 ) =>
% 93.83/12.79 ( ( n_eq @ X2 @ X3 ) =>
% 93.83/12.79 ( n_eq @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 93.83/12.79 thf(zip_derived_cl300, plain,
% 93.83/12.79 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 93.83/12.79 (^[Y0 : $i]:
% 93.83/12.79 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 93.83/12.79 (^[Y1 : $i]:
% 93.83/12.79 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 93.83/12.79 (^[Y2 : $i]:
% 93.83/12.79 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 93.83/12.79 (^[Y3 : $i]:
% 93.83/12.79 (((n_eq @ Y0 @ Y1) =>
% 93.83/12.79 (((n_eq @ Y2 @ Y3) => (n_eq @ (n_pf @ Y0 @ Y2) @
% 93.83/12.79 (n_pf @ Y1 @ Y3))))))))))))))),
% 93.83/12.79 inference('cnf', [status(esa)], [satz56])).
% 93.83/12.79 thf(zip_derived_cl301, plain,
% 93.83/12.79 ( (all_of @ ((('#C') @ in @ frac)) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 n_eq)))))))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#C') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ n_eq)) @ n_pf)))))))) @
% 93.83/12.79 n_pf)))))))))))))),
% 93.83/12.79 inference('lams2combs', [status(thm)], [zip_derived_cl300])).
% 93.83/12.79 thf(zip_derived_cl2636, plain,
% 93.83/12.79 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 n_eq)))))))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#C') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ n_eq)) @ n_pf)))))))) @
% 93.83/12.79 n_pf)))))))))))))),
% 93.83/12.79 inference('rw', [status(thm)], [zip_derived_cl301, '0'])).
% 93.83/12.79 thf(zip_derived_cl2637, plain,
% 93.83/12.79 ( (((!!) @ (^[Y0 : $i]:
% 93.83/12.79 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 n_eq)))))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 93.83/12.79 '#S') @
% 93.83/12.79 ((('#B') @ (
% 93.83/12.79 (('#B') @ (
% 93.83/12.79 =>))) @
% 93.83/12.79 n_eq)))))))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#C') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ n_eq)) @
% 93.83/12.79 n_pf)))))))) @
% 93.83/12.79 n_pf)))))))))) @
% 93.83/12.79 Y0)))))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl2636, '8'])).
% 93.83/12.79 thf(zip_derived_cl2638, plain,
% 93.83/12.79 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 93.83/12.79 ((('#C') @ is_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))))))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 93.83/12.79 '#S') @
% 93.83/12.79 ((('#B') @ (
% 93.83/12.79 (('#B') @ (=>))) @
% 93.83/12.79 n_eq)))))))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#C') @
% 93.83/12.79 ((('#B') @ ((('#B') @ ('#B'))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ n_eq)) @
% 93.83/12.79 n_pf)))))))) @
% 93.83/12.79 n_pf))))))))))))))))),
% 93.83/12.79 inference('comb-normalize', [status(thm)], [zip_derived_cl2637])).
% 93.83/12.79 thf(zip_derived_cl2639, plain,
% 93.83/12.79 (![X2 : $i]:
% 93.83/12.79 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ (=>) @ (n_eq @ X2))))))) @
% 93.83/12.79 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 93.83/12.79 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ n_eq @ (n_pf @ X2))))))) @
% 93.83/12.79 n_pf)))))))))))))),
% 93.83/12.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2638])).
% 93.83/12.79 thf(zip_derived_cl2640, plain,
% 93.83/12.79 (![X2 : $i]:
% 93.83/12.79 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ (=>) @ (n_eq @ X2))))))) @
% 93.83/12.79 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 93.83/12.79 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ n_eq @ (n_pf @ X2))))))) @
% 93.83/12.79 n_pf))))))))))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2639])).
% 93.83/12.79 thf(zip_derived_cl2641, plain,
% 93.83/12.79 (![X0 : $i]:
% 93.83/12.79 ( (((!!) @ (^[Y0 : $i]:
% 93.83/12.79 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ (=>) @ (n_eq @ X0))))))) @
% 93.83/12.79 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (
% 93.83/12.79 =>))) @
% 93.83/12.79 n_eq)))))) @
% 93.83/12.79 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ n_eq @
% 93.83/12.79 (n_pf @ X0))))))) @
% 93.83/12.79 n_pf)))))))) @
% 93.83/12.79 Y0)))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl2640, '8'])).
% 93.83/12.79 thf(zip_derived_cl2642, plain,
% 93.83/12.79 (![X0 : $i]:
% 93.83/12.79 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 93.83/12.79 ((('#C') @ is_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))))))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @
% 93.83/12.79 (pair1type @ nat)))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ (=>) @ (n_eq @ X0))))))) @
% 93.83/12.79 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @
% 93.83/12.79 n_eq)))))) @
% 93.83/12.79 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ n_eq @
% 93.83/12.79 (n_pf @ X0))))))) @
% 93.83/12.79 n_pf))))))))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('comb-normalize', [status(thm)], [zip_derived_cl2641])).
% 93.83/12.79 thf(zip_derived_cl2643, plain,
% 93.83/12.79 (![X0 : $i, X2 : $i]:
% 93.83/12.79 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ n_eq @ (n_pf @ X0))))) @
% 93.83/12.79 (n_pf @ X2))))))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2642])).
% 93.83/12.79 thf(zip_derived_cl2644, plain,
% 93.83/12.79 (![X0 : $i, X2 : $i]:
% 93.83/12.79 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ n_eq @ (n_pf @ X0))))) @
% 93.83/12.79 (n_pf @ X2))))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2643])).
% 93.83/12.79 thf(zip_derived_cl2645, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i]:
% 93.83/12.79 ( (((!!) @ (^[Y0 : $i]:
% 93.83/12.79 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 ((('#B') @ (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ n_eq @ (n_pf @ X0))))) @
% 93.83/12.79 (n_pf @ X1))))))) @
% 93.83/12.79 Y0)))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl2644, '8'])).
% 93.83/12.79 thf(zip_derived_cl2646, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i]:
% 93.83/12.79 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 93.83/12.79 ((('#C') @ is_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))))))) @
% 93.83/12.79 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 93.83/12.79 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ ('#S') @
% 93.83/12.79 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 93.83/12.79 ((('#C') @ ((('#B') @ ('#B') @
% 93.83/12.79 ((('#B') @ n_eq @ (n_pf @ X0))))) @
% 93.83/12.79 (n_pf @ X1)))))))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('comb-normalize', [status(thm)], [zip_derived_cl2645])).
% 93.83/12.79 thf(zip_derived_cl2647, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X3 : $i]:
% 93.83/12.79 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X3))) @
% 93.83/12.79 ((('#B') @ (n_eq @ (n_pf @ X0 @ X3)) @ (n_pf @ X1))))))))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2646])).
% 93.83/12.79 thf(zip_derived_cl2648, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X3 : $i]:
% 93.83/12.79 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X3))) @
% 93.83/12.79 ((('#B') @ (n_eq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X3)))) @
% 93.83/12.79 (n_pf @ X1))))))))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('rw', [status(thm)], [zip_derived_cl2647, '5'])).
% 93.83/12.79 thf(zip_derived_cl2649, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X3 : $i]:
% 93.83/12.79 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 93.83/12.79 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X3))) @
% 93.83/12.79 ((('#B') @ (n_eq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X3)))) @
% 93.83/12.79 (n_pf @ X1))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2648])).
% 93.83/12.79 thf(zip_derived_cl2650, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 93.83/12.79 ( (((!!) @ (^[Y0 : $i]:
% 93.83/12.79 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 ((('#B') @ (((=>) @ (n_eq @ X1 @ X0))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @
% 93.83/12.79 ((('#B') @ (n_eq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @
% 93.83/12.79 (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 93.83/12.79 (n_pf @ X0))))) @
% 93.83/12.79 Y0)))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('rw_clause', [status(thm)], [zip_derived_cl2649, '8'])).
% 93.83/12.79 thf(zip_derived_cl2651, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 93.83/12.79 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 93.83/12.79 ((('#C') @ is_of @
% 93.83/12.79 ((('#C') @ in @ (pair1type @ nat))))))) @
% 93.83/12.79 ((('#B') @ (((=>) @ (n_eq @ X1 @ X0))) @
% 93.83/12.79 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @
% 93.83/12.79 ((('#B') @ (n_eq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @
% 93.83/12.79 (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 93.83/12.79 (n_pf @ X0)))))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('comb-normalize', [status(thm)], [zip_derived_cl2650])).
% 93.83/12.79 thf(zip_derived_cl2652, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 93.83/12.79 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 (((n_eq @ X1 @ X0) =>
% 93.83/12.79 (((n_eq @ X2 @ X4) => (n_eq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_pf @ X0 @ X4))))))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2651])).
% 93.83/12.79 thf(zip_derived_cl2653, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 93.83/12.79 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 93.83/12.79 (((n_eq @ X1 @ X0) =>
% 93.83/12.79 (((n_eq @ X2 @ X4) => (n_eq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 93.83/12.79 (n_ts @ (num @ X4) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X4))))))))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('rw', [status(thm)], [zip_derived_cl2652, '5'])).
% 93.83/12.79 thf(zip_derived_cl2654, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 93.83/12.79 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | (((n_eq @ X1 @ X0) =>
% 93.83/12.79 (((n_eq @ X2 @ X4) => (n_eq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 93.83/12.79 (n_ts @ (num @ X4) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X4))))))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2653])).
% 93.83/12.79 thf(zip_derived_cl2655, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 93.83/12.79 (~ (n_eq @ X1 @ X0)
% 93.83/12.79 | (((n_eq @ X2 @ X4) => (n_eq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 93.83/12.79 (n_ts @ (num @ X4) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X4))))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2654])).
% 93.83/12.79 thf(zip_derived_cl2656, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 93.83/12.79 (~ (n_eq @ X2 @ X4)
% 93.83/12.79 | (n_eq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 93.83/12.79 (n_ts @ (num @ X4) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X4))))
% 93.83/12.79 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (n_eq @ X1 @ X0))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2655])).
% 93.83/12.79 thf(zip_derived_cl16984, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 93.83/12.79 (~ (n_eq @ X2 @ X4)
% 93.83/12.79 | (n_eq @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 93.83/12.79 (n_ts @ (num @ X2) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X2))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 93.83/12.79 (n_ts @ (num @ X4) @ (den @ X0))) @
% 93.83/12.79 (n_ts @ (den @ X0) @ (den @ X4))))
% 93.83/12.79 | ~ (is_of @ X4 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 93.83/12.79 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 93.83/12.79 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 93.83/12.79 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 93.83/12.79 | ~ (n_eq @ X1 @ X0))),
% 93.83/12.79 inference('remove_ty_args', [status(thm)], [zip_derived_cl2656])).
% 93.83/12.79 thf(zip_derived_cl2603, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 93.83/12.79 (~ (n_eq @ X2 @ X1)
% 93.83/12.79 | (((moref @ X3 @ X0) => (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X2) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X2))) @
% 93.83/12.79 (n_ts @ (den @ X2) @ (den @ X3))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 93.83/12.79 (n_ts @ (num @ X0) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X0))))))
% 93.83/12.79 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2601])).
% 93.83/12.79 thf(zip_derived_cl2605, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 93.83/12.79 (~ (moref @ X3 @ X0)
% 93.83/12.79 | (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X2) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X2))) @
% 93.83/12.79 (n_ts @ (den @ X2) @ (den @ X3))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 93.83/12.79 (n_ts @ (num @ X0) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X0))))
% 93.83/12.79 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 93.83/12.79 | ~ (n_eq @ X2 @ X1))),
% 93.83/12.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2603])).
% 93.83/12.79 thf(zip_derived_cl16981, plain,
% 93.83/12.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 93.83/12.79 (~ (moref @ X3 @ X0)
% 93.83/12.79 | (moref @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X2) @ (den @ X3)) @
% 93.83/12.79 (n_ts @ (num @ X3) @ (den @ X2))) @
% 93.83/12.79 (n_ts @ (den @ X2) @ (den @ X3))) @
% 93.83/12.79 (n_fr @
% 93.83/12.79 (n_pl @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 93.83/12.79 (n_ts @ (num @ X0) @ (den @ X1))) @
% 93.83/12.79 (n_ts @ (den @ X1) @ (den @ X0))))
% 93.83/12.79 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 93.83/12.79 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 93.83/12.79 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 93.83/12.79 | ~ (is_of @ X3 @ ('#ty_enc6' @ in @ (pair1type @ nat)))
% 93.83/12.79 | ~ (n_eq @ X2 @ X1))),
% 93.83/12.79 inference('remove_ty_args', [status(thm)], [zip_derived_cl2605])).
% 93.83/12.79 thf(zip_derived_cl17022, plain, ($false),
% 93.83/12.79 inference('eprover', [status(thm)],
% 93.83/12.79 [zip_derived_cl1323, zip_derived_cl16983, zip_derived_cl1327,
% 93.83/12.79 zip_derived_cl16931, zip_derived_cl16932,
% 93.83/12.79 zip_derived_cl16929, zip_derived_cl16930,
% 93.83/12.79 zip_derived_cl16982, zip_derived_cl1321, zip_derived_cl1329,
% 93.83/12.79 zip_derived_cl16984, zip_derived_cl16981])).
% 93.83/12.79
% 93.83/12.79 % SZS output end Refutation
% 93.83/12.79
% 93.83/12.79
% 93.83/12.81 % Terminating...
% 94.81/12.93 % Runner terminated.
% 94.81/12.93 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------