TSTP Solution File: NUM752^4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM752^4 : 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.9An27CkCm1 true
% Computer : n014.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 12:43:55 EDT 2023
% Result : Theorem 100.18s 13.50s
% Output : Refutation 100.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM752^4 : TPTP v8.1.2. Released v7.1.0.
% 0.13/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.9An27CkCm1 true
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 09:05:03 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.21/0.66 % Total configuration time : 828
% 0.21/0.66 % Estimated wc time : 1656
% 0.21/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.31/0.78 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.31/0.78 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.31/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.31/0.78 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.31/0.78 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 100.18/13.50 % Solved by lams/40_b.comb.sh.
% 100.18/13.50 % done 633 iterations in 12.679s
% 100.18/13.50 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 100.18/13.50 % SZS output start Refutation
% 100.18/13.50 thf(nat_type, type, nat: $i).
% 100.18/13.50 thf('#sk2_type', type, '#sk2': $i).
% 100.18/13.50 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 100.18/13.50 thf(in_type, type, in: $i > $i > $o).
% 100.18/13.50 thf(n_pf_type, type, n_pf: $i > $i > $i).
% 100.18/13.50 thf(n_fr_type, type, n_fr: $i > $i > $i).
% 100.18/13.50 thf('#sk4_type', type, '#sk4': $i).
% 100.18/13.50 thf(n_is_type, type, n_is: $i > $i > $o).
% 100.18/13.50 thf(frac_type, type, frac: $i).
% 100.18/13.50 thf(n_ts_type, type, n_ts: $i > $i > $i).
% 100.18/13.50 thf(n_eq_type, type, n_eq: $i > $i > $o).
% 100.18/13.50 thf(pair1type_type, type, pair1type: $i > $i).
% 100.18/13.50 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 100.18/13.50 thf('#ty_enc5_type', type, '#ty_enc5': ($i > $i > $o) > $i > $i > $o).
% 100.18/13.50 thf(num_type, type, num: $i > $i).
% 100.18/13.50 thf(den_type, type, den: $i > $i).
% 100.18/13.50 thf('#sk3_type', type, '#sk3': $i).
% 100.18/13.50 thf(n_pl_type, type, n_pl: $i > $i > $i).
% 100.18/13.50 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 100.18/13.50 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 100.18/13.50 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 100.18/13.50 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 100.18/13.50 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 100.18/13.50 thf(satz62e, conjecture,
% 100.18/13.50 (all_of @
% 100.18/13.50 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 100.18/13.50 ( ^[X0:$i]:
% 100.18/13.50 ( all_of @
% 100.18/13.50 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 100.18/13.50 ( ^[X1:$i]:
% 100.18/13.50 ( all_of @
% 100.18/13.50 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 100.18/13.50 ( ^[X2:$i]:
% 100.18/13.50 ( ( n_eq @ X0 @ X1 ) =>
% 100.18/13.50 ( n_eq @ ( n_pf @ X2 @ X0 ) @ ( n_pf @ X2 @ X1 ) ) ) ) ) ) ) ))).
% 100.18/13.50 thf(zf_stmt_0, negated_conjecture,
% 100.18/13.50 (~( all_of @
% 100.18/13.50 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 100.18/13.50 ( ^[X0:$i]:
% 100.18/13.50 ( all_of @
% 100.18/13.50 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 100.18/13.50 ( ^[X1:$i]:
% 100.18/13.50 ( all_of @
% 100.18/13.50 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 100.18/13.50 ( ^[X2:$i]:
% 100.18/13.50 ( ( n_eq @ X0 @ X1 ) =>
% 100.18/13.50 ( n_eq @ ( n_pf @ X2 @ X0 ) @ ( n_pf @ X2 @ X1 ) ) ) ) ) ) ) ) )),
% 100.18/13.50 inference('cnf.neg', [status(esa)], [satz62e])).
% 100.18/13.50 thf(zip_derived_cl323, plain,
% 100.18/13.50 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 100.18/13.50 (^[Y0 : $i]:
% 100.18/13.50 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 100.18/13.50 (^[Y1 : $i]:
% 100.18/13.50 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 100.18/13.50 (^[Y2 : $i]:
% 100.18/13.50 (((n_eq @ Y0 @ Y1) => (n_eq @ (n_pf @ Y2 @ Y0) @
% 100.18/13.50 (n_pf @ Y2 @ Y1))))))))))),
% 100.18/13.50 inference('cnf', [status(esa)], [zf_stmt_0])).
% 100.18/13.50 thf(zip_derived_cl324, plain,
% 100.18/13.50 (~ (all_of @ ((('#C') @ in @ frac)) @
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ ('#B'))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 100.18/13.50 ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ n_eq)) @ ((('#C') @ n_pf)))))))) @
% 100.18/13.50 ((('#C') @ n_pf)))))))))))),
% 100.18/13.50 inference('lams2combs', [status(thm)], [zip_derived_cl323])).
% 100.18/13.50 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))).
% 100.18/13.50 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])).
% 100.18/13.50 thf(zip_derived_cl661, plain,
% 100.18/13.50 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ ('#B'))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 100.18/13.50 ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ n_eq)) @ ((('#C') @ n_pf)))))))) @
% 100.18/13.50 ((('#C') @ n_pf)))))))))))),
% 100.18/13.50 inference('rw', [status(thm)], [zip_derived_cl324, '0'])).
% 100.18/13.50 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 100.18/13.50 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 100.18/13.50 thf('1', plain,
% 100.18/13.50 (![X0:( $i > $o ),X1:( $i > $o )]:
% 100.18/13.50 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 100.18/13.50 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 100.18/13.50 inference('rw.lit', [status(esa)], [def_all_of])).
% 100.18/13.50 thf(zip_derived_cl662, plain,
% 100.18/13.50 (~ (((!!) @ (^[Y0 : $i]:
% 100.18/13.50 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (all_of @
% 100.18/13.50 ((('#C') @ in @
% 100.18/13.50 (pair1type @ nat)))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ ('#B'))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 100.18/13.50 ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ n_eq)) @
% 100.18/13.50 ((('#C') @ n_pf)))))))) @
% 100.18/13.50 ((('#C') @ n_pf)))))))) @
% 100.18/13.50 Y0)))))))),
% 100.18/13.50 inference('rw_clause', [status(thm)], [zip_derived_cl661, '1'])).
% 100.18/13.50 thf(zip_derived_cl663, plain,
% 100.18/13.50 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 100.18/13.50 ((('#C') @ is_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat))))))) @
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (all_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat)))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ ('#B'))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 100.18/13.50 ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ n_eq)) @
% 100.18/13.50 ((('#C') @ n_pf)))))))) @
% 100.18/13.50 ((('#C') @ n_pf))))))))))))))),
% 100.18/13.50 inference('comb-normalize', [status(thm)], [zip_derived_cl662])).
% 100.18/13.50 thf(zip_derived_cl664, plain,
% 100.18/13.50 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat))) @
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 100.18/13.50 ((('#B') @ ((('#S') @ ((('#B') @ n_eq @
% 100.18/13.50 ((('#C') @ n_pf @ '#sk2')))))) @
% 100.18/13.50 ((('#C') @ n_pf)))))))))))),
% 100.18/13.50 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl663])).
% 100.18/13.50 thf(zip_derived_cl665, plain,
% 100.18/13.50 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))),
% 100.18/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl664])).
% 100.18/13.50 thf(zip_derived_cl18863, plain,
% 100.18/13.50 ( (is_of @ '#sk2' @ ('#ty_enc5' @ in @ (pair1type @ nat)))),
% 100.18/13.50 inference('remove_ty_args', [status(thm)], [zip_derived_cl665])).
% 100.18/13.50 thf(zip_derived_cl666, plain,
% 100.18/13.50 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 100.18/13.50 ((('#B') @ ((('#S') @ ((('#B') @ n_eq @
% 100.18/13.50 ((('#C') @ n_pf @ '#sk2')))))) @
% 100.18/13.50 ((('#C') @ n_pf)))))))))),
% 100.18/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl664])).
% 100.18/13.50 thf(zip_derived_cl667, plain,
% 100.18/13.50 (~ (((!!) @ (^[Y0 : $i]:
% 100.18/13.50 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 100.18/13.50 ((('#B') @ ((('#S') @ ((('#B') @ n_eq @
% 100.18/13.50 ((('#C') @ n_pf @ '#sk2')))))) @
% 100.18/13.50 ((('#C') @ n_pf)))))) @
% 100.18/13.50 Y0)))))))),
% 100.18/13.50 inference('rw_clause', [status(thm)], [zip_derived_cl666, '1'])).
% 100.18/13.50 thf(zip_derived_cl668, plain,
% 100.18/13.50 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 100.18/13.50 ((('#C') @ is_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat))))))) @
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @
% 100.18/13.50 ((('#B') @ ((('#S') @ ((('#B') @ n_eq @
% 100.18/13.50 ((('#C') @ n_pf @ '#sk2')))))) @
% 100.18/13.50 ((('#C') @ n_pf))))))))))))),
% 100.18/13.50 inference('comb-normalize', [status(thm)], [zip_derived_cl667])).
% 100.18/13.50 thf(zip_derived_cl669, plain,
% 100.18/13.50 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat))) @
% 100.18/13.50 ((('#B') @ (((=>) @ (n_eq @ '#sk2' @ '#sk3'))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ n_eq @ ((('#C') @ n_pf @ '#sk2')))) @
% 100.18/13.50 ((('#C') @ n_pf @ '#sk3')))))))))),
% 100.18/13.50 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl668])).
% 100.18/13.50 thf(def_n_eq, axiom,(( n_eq @ (X0)@ (X1)) =
% 100.18/13.50 ((n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 100.18/13.50 (n_ts @ (num @ X1) @ (den @ X0)))))).
% 100.18/13.50 thf('2', plain,
% 100.18/13.50 (![X1:$i,X0:$i]:
% 100.18/13.50 ( ( n_eq @ X0 @ X1 ) =
% 100.18/13.50 ( n_is @
% 100.18/13.50 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 100.18/13.50 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )),
% 100.18/13.50 define([status(thm)])).
% 100.18/13.50 thf(zip_derived_cl670, plain,
% 100.18/13.50 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat))) @
% 100.18/13.50 ((('#B') @ (((=>) @ (n_is @
% 100.18/13.50 (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 100.18/13.50 (n_ts @ (num @ '#sk3') @ (den @ '#sk2'))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ n_eq @ ((('#C') @ n_pf @ '#sk2')))) @
% 100.18/13.50 ((('#C') @ n_pf @ '#sk3')))))))))),
% 100.18/13.50 inference('rw', [status(thm)], [zip_derived_cl669, '2'])).
% 100.18/13.50 thf(zip_derived_cl671, plain,
% 100.18/13.50 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))),
% 100.18/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl670])).
% 100.18/13.50 thf(zip_derived_cl18864, plain,
% 100.18/13.50 ( (is_of @ '#sk3' @ ('#ty_enc5' @ in @ (pair1type @ nat)))),
% 100.18/13.50 inference('remove_ty_args', [status(thm)], [zip_derived_cl671])).
% 100.18/13.50 thf(zip_derived_cl672, plain,
% 100.18/13.50 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 100.18/13.50 ((('#B') @ (((=>) @ (n_is @
% 100.18/13.50 (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 100.18/13.50 (n_ts @ (num @ '#sk3') @ (den @ '#sk2'))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ n_eq @ ((('#C') @ n_pf @ '#sk2')))) @
% 100.18/13.50 ((('#C') @ n_pf @ '#sk3')))))))),
% 100.18/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl670])).
% 100.18/13.50 thf(zip_derived_cl673, plain,
% 100.18/13.50 (~ (((!!) @ (^[Y0 : $i]:
% 100.18/13.50 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 100.18/13.50 ((('#B') @ (((=>) @ (n_is @
% 100.18/13.50 (n_ts @ (num @ '#sk2') @
% 100.18/13.50 (den @ '#sk3')) @
% 100.18/13.50 (n_ts @ (num @ '#sk3') @
% 100.18/13.50 (den @ '#sk2'))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ n_eq @
% 100.18/13.50 ((('#C') @ n_pf @ '#sk2')))) @
% 100.18/13.50 ((('#C') @ n_pf @ '#sk3')))) @
% 100.18/13.50 Y0)))))))),
% 100.18/13.50 inference('rw_clause', [status(thm)], [zip_derived_cl672, '1'])).
% 100.18/13.50 thf(zip_derived_cl674, plain,
% 100.18/13.50 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 100.18/13.50 ((('#C') @ is_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat))))))) @
% 100.18/13.50 ((('#B') @ (((=>) @ (n_is @
% 100.18/13.50 (n_ts @ (num @ '#sk2') @
% 100.18/13.50 (den @ '#sk3')) @
% 100.18/13.50 (n_ts @ (num @ '#sk3') @
% 100.18/13.50 (den @ '#sk2'))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ n_eq @ ((('#C') @ n_pf @ '#sk2')))) @
% 100.18/13.50 ((('#C') @ n_pf @ '#sk3'))))))))))),
% 100.18/13.50 inference('comb-normalize', [status(thm)], [zip_derived_cl673])).
% 100.18/13.50 thf(zip_derived_cl675, plain,
% 100.18/13.50 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 100.18/13.50 (((n_is @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 100.18/13.50 (n_ts @ (num @ '#sk3') @ (den @ '#sk2'))) => (n_eq @
% 100.18/13.50 (n_pf @ '#sk4' @ '#sk2') @ (n_pf @ '#sk4' @ '#sk3'))))))),
% 100.18/13.50 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl674])).
% 100.18/13.50 thf(def_n_pf, axiom,(( n_pf @ (X0)@ (X1)) =
% 100.18/13.50 ((n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 100.18/13.50 (n_ts @ (num @ X1) @ (den @ X0))) @
% 100.18/13.50 (n_ts @ (den @ X0) @ (den @ X1)))))).
% 100.18/13.50 thf('3', plain,
% 100.18/13.50 (![X1:$i,X0:$i]:
% 100.18/13.50 ( ( n_pf @ X0 @ X1 ) =
% 100.18/13.50 ( n_fr @
% 100.18/13.50 ( n_pl @
% 100.18/13.50 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 100.18/13.50 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) @
% 100.18/13.50 ( n_ts @ ( den @ X0 ) @ ( den @ X1 ) ) ) )),
% 100.18/13.50 define([status(thm)])).
% 100.18/13.50 thf(zip_derived_cl676, plain,
% 100.18/13.50 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 100.18/13.50 (((n_is @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 100.18/13.50 (n_ts @ (num @ '#sk3') @ (den @ '#sk2'))) => (n_is @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ '#sk4') @ (den @ '#sk2')) @
% 100.18/13.50 (n_ts @ (num @ '#sk2') @ (den @ '#sk4'))) @
% 100.18/13.50 (n_ts @ (den @ '#sk4') @ (den @ '#sk2')))) @
% 100.18/13.50 (den @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ '#sk4') @ (den @ '#sk3')) @
% 100.18/13.50 (n_ts @ (num @ '#sk3') @ (den @ '#sk4'))) @
% 100.18/13.50 (n_ts @ (den @ '#sk4') @ (den @ '#sk3'))))) @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ '#sk4') @ (den @ '#sk3')) @
% 100.18/13.50 (n_ts @ (num @ '#sk3') @ (den @ '#sk4'))) @
% 100.18/13.50 (n_ts @ (den @ '#sk4') @ (den @ '#sk3')))) @
% 100.18/13.50 (den @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ '#sk4') @ (den @ '#sk2')) @
% 100.18/13.50 (n_ts @ (num @ '#sk2') @ (den @ '#sk4'))) @
% 100.18/13.50 (n_ts @ (den @ '#sk4') @ (den @ '#sk2'))))))))))),
% 100.18/13.50 inference('rw', [status(thm)], [zip_derived_cl675, '2', '3', '3'])).
% 100.18/13.50 thf(zip_derived_cl678, plain,
% 100.18/13.50 (~ (((n_is @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 100.18/13.50 (n_ts @ (num @ '#sk3') @ (den @ '#sk2'))) => (n_is @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ '#sk4') @ (den @ '#sk2')) @
% 100.18/13.50 (n_ts @ (num @ '#sk2') @ (den @ '#sk4'))) @
% 100.18/13.50 (n_ts @ (den @ '#sk4') @ (den @ '#sk2')))) @
% 100.18/13.50 (den @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ '#sk4') @ (den @ '#sk3')) @
% 100.18/13.50 (n_ts @ (num @ '#sk3') @ (den @ '#sk4'))) @
% 100.18/13.50 (n_ts @ (den @ '#sk4') @ (den @ '#sk3'))))) @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ '#sk4') @ (den @ '#sk3')) @
% 100.18/13.50 (n_ts @ (num @ '#sk3') @ (den @ '#sk4'))) @
% 100.18/13.50 (n_ts @ (den @ '#sk4') @ (den @ '#sk3')))) @
% 100.18/13.50 (den @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ '#sk4') @ (den @ '#sk2')) @
% 100.18/13.50 (n_ts @ (num @ '#sk2') @ (den @ '#sk4'))) @
% 100.18/13.50 (n_ts @ (den @ '#sk4') @ (den @ '#sk2'))))))))),
% 100.18/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl676])).
% 100.18/13.50 thf(zip_derived_cl679, plain,
% 100.18/13.50 ( (n_is @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @
% 100.18/13.50 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))),
% 100.18/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl678])).
% 100.18/13.50 thf(zip_derived_cl677, plain,
% 100.18/13.50 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))),
% 100.18/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl676])).
% 100.18/13.50 thf(zip_derived_cl18865, plain,
% 100.18/13.50 ( (is_of @ '#sk4' @ ('#ty_enc5' @ in @ (pair1type @ nat)))),
% 100.18/13.50 inference('remove_ty_args', [status(thm)], [zip_derived_cl677])).
% 100.18/13.50 thf(zip_derived_cl680, plain,
% 100.18/13.50 (~ (n_is @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ '#sk4') @ (den @ '#sk2')) @
% 100.18/13.50 (n_ts @ (num @ '#sk2') @ (den @ '#sk4'))) @
% 100.18/13.50 (n_ts @ (den @ '#sk4') @ (den @ '#sk2')))) @
% 100.18/13.50 (den @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ '#sk4') @ (den @ '#sk3')) @
% 100.18/13.50 (n_ts @ (num @ '#sk3') @ (den @ '#sk4'))) @
% 100.18/13.50 (n_ts @ (den @ '#sk4') @ (den @ '#sk3'))))) @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ '#sk4') @ (den @ '#sk3')) @
% 100.18/13.50 (n_ts @ (num @ '#sk3') @ (den @ '#sk4'))) @
% 100.18/13.50 (n_ts @ (den @ '#sk4') @ (den @ '#sk3')))) @
% 100.18/13.50 (den @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ '#sk4') @ (den @ '#sk2')) @
% 100.18/13.50 (n_ts @ (num @ '#sk2') @ (den @ '#sk4'))) @
% 100.18/13.50 (n_ts @ (den @ '#sk4') @ (den @ '#sk2'))))))),
% 100.18/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl678])).
% 100.18/13.50 thf(satz56, axiom,
% 100.18/13.50 (all_of @
% 100.18/13.50 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 100.18/13.50 ( ^[X0:$i]:
% 100.18/13.50 ( all_of @
% 100.18/13.50 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @
% 100.18/13.50 ( ^[X1:$i]:
% 100.18/13.50 ( all_of @
% 100.18/13.50 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @
% 100.18/13.50 ( ^[X2:$i]:
% 100.18/13.50 ( all_of @
% 100.18/13.50 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @
% 100.18/13.50 ( ^[X3:$i]:
% 100.18/13.50 ( ( n_eq @ X0 @ X1 ) =>
% 100.18/13.50 ( ( n_eq @ X2 @ X3 ) =>
% 100.18/13.50 ( n_eq @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))).
% 100.18/13.50 thf(zip_derived_cl301, plain,
% 100.18/13.50 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 100.18/13.50 (^[Y0 : $i]:
% 100.18/13.50 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @
% 100.18/13.50 (^[Y1 : $i]:
% 100.18/13.50 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @
% 100.18/13.50 (^[Y2 : $i]:
% 100.18/13.50 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @
% 100.18/13.50 (^[Y3 : $i]:
% 100.18/13.50 (((n_eq @ Y0 @ Y1) =>
% 100.18/13.50 (((n_eq @ Y2 @ Y3) => (n_eq @ (n_pf @ Y0 @ Y2) @
% 100.18/13.50 (n_pf @ Y1 @ Y3))))))))))))))),
% 100.18/13.50 inference('cnf', [status(esa)], [satz56])).
% 100.18/13.50 thf(zip_derived_cl302, plain,
% 100.18/13.50 ( (all_of @ ((('#C') @ in @ frac)) @
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ ('#B'))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ ('#B'))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @
% 100.18/13.50 n_eq)))))))) @
% 100.18/13.50 ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ ('#C') @
% 100.18/13.50 ((('#B') @ ((('#B') @ ('#B'))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ n_eq)) @ n_pf)))))))) @
% 100.18/13.50 n_pf)))))))))))))),
% 100.18/13.50 inference('lams2combs', [status(thm)], [zip_derived_cl301])).
% 100.18/13.50 thf(zip_derived_cl1967, plain,
% 100.18/13.50 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 100.18/13.50 ((('#C') @ in @
% 100.18/13.50 (pair1type @ nat)))))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ ('#B'))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ ('#B'))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @
% 100.18/13.50 n_eq)))))))) @
% 100.18/13.50 ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ ('#C') @
% 100.18/13.50 ((('#B') @ ((('#B') @ ('#B'))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ n_eq)) @ n_pf)))))))) @
% 100.18/13.50 n_pf)))))))))))))),
% 100.18/13.50 inference('rw', [status(thm)], [zip_derived_cl302, '0'])).
% 100.18/13.50 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 100.18/13.50 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 100.18/13.50 thf('4', plain,
% 100.18/13.50 (![X0:( $i > $o ),X1:( $i > $o )]:
% 100.18/13.50 ( ( all_of @ X0 @ X1 ) <=>
% 100.18/13.50 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 100.18/13.50 inference('rw.lit', [status(esa)], [def_all_of])).
% 100.18/13.50 thf(zip_derived_cl1968, plain,
% 100.18/13.50 ( (((!!) @ (^[Y0 : $i]:
% 100.18/13.50 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (all_of @
% 100.18/13.50 ((('#C') @ in @
% 100.18/13.50 (pair1type @ nat)))))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 100.18/13.50 ((('#C') @ in @
% 100.18/13.50 (pair1type @ nat)))))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ ('#B'))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ ('#B'))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @
% 100.18/13.50 n_eq)))))))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 100.18/13.50 '#S') @
% 100.18/13.50 ((('#B') @ (
% 100.18/13.50 (('#B') @ (
% 100.18/13.50 =>))) @
% 100.18/13.50 n_eq)))))))) @
% 100.18/13.50 ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ ('#C') @
% 100.18/13.50 ((('#B') @ ((('#B') @ ('#B'))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ n_eq)) @
% 100.18/13.50 n_pf)))))))) @
% 100.18/13.50 n_pf)))))))))) @
% 100.18/13.50 Y0)))))))),
% 100.18/13.50 inference('rw_clause', [status(thm)], [zip_derived_cl1967, '4'])).
% 100.18/13.50 thf(zip_derived_cl1969, plain,
% 100.18/13.50 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 100.18/13.50 ((('#C') @ is_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat))))))) @
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (all_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat)))))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @
% 100.18/13.50 ((('#C') @ in @
% 100.18/13.50 (pair1type @ nat)))))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ ('#B'))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ ('#B'))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 100.18/13.50 '#S') @
% 100.18/13.50 ((('#B') @ (
% 100.18/13.50 (('#B') @ (=>))) @
% 100.18/13.50 n_eq)))))))) @
% 100.18/13.50 ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ ('#C') @
% 100.18/13.50 ((('#B') @ ((('#B') @ ('#B'))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ n_eq)) @
% 100.18/13.50 n_pf)))))))) @
% 100.18/13.50 n_pf))))))))))))))))),
% 100.18/13.50 inference('comb-normalize', [status(thm)], [zip_derived_cl1968])).
% 100.18/13.50 thf(zip_derived_cl1970, plain,
% 100.18/13.50 (![X2 : $i]:
% 100.18/13.50 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat))) @
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (all_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat)))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ (=>) @ (n_eq @ X2))))))) @
% 100.18/13.50 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 100.18/13.50 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ n_eq @ (n_pf @ X2))))))) @
% 100.18/13.50 n_pf)))))))))))))),
% 100.18/13.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1969])).
% 100.18/13.50 thf(zip_derived_cl1971, plain,
% 100.18/13.50 (![X2 : $i]:
% 100.18/13.50 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (all_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat)))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ (=>) @ (n_eq @ X2))))))) @
% 100.18/13.50 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @
% 100.18/13.50 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ n_eq @ (n_pf @ X2))))))) @
% 100.18/13.50 n_pf))))))))))))),
% 100.18/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1970])).
% 100.18/13.50 thf(zip_derived_cl1972, plain,
% 100.18/13.50 (![X0 : $i]:
% 100.18/13.50 ( (((!!) @ (^[Y0 : $i]:
% 100.18/13.50 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 100.18/13.50 ((('#B') @ (all_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (all_of @
% 100.18/13.50 ((('#C') @ in @
% 100.18/13.50 (pair1type @ nat)))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ (=>) @ (n_eq @ X0))))))) @
% 100.18/13.50 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ (
% 100.18/13.50 =>))) @
% 100.18/13.50 n_eq)))))) @
% 100.18/13.50 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ n_eq @
% 100.18/13.50 (n_pf @ X0))))))) @
% 100.18/13.50 n_pf)))))))) @
% 100.18/13.50 Y0)))))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 100.18/13.50 inference('rw_clause', [status(thm)], [zip_derived_cl1971, '4'])).
% 100.18/13.50 thf(zip_derived_cl1973, plain,
% 100.18/13.50 (![X0 : $i]:
% 100.18/13.50 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 100.18/13.50 ((('#C') @ is_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat))))))) @
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (all_of @
% 100.18/13.50 ((('#C') @ in @
% 100.18/13.50 (pair1type @ nat)))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ (=>) @ (n_eq @ X0))))))) @
% 100.18/13.50 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @
% 100.18/13.50 n_eq)))))) @
% 100.18/13.50 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ n_eq @
% 100.18/13.50 (n_pf @ X0))))))) @
% 100.18/13.50 n_pf))))))))))))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 100.18/13.50 inference('comb-normalize', [status(thm)], [zip_derived_cl1972])).
% 100.18/13.50 thf(zip_derived_cl1974, plain,
% 100.18/13.50 (![X0 : $i, X2 : $i]:
% 100.18/13.50 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat))) @
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 100.18/13.50 ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ n_eq @ (n_pf @ X0))))) @
% 100.18/13.50 (n_pf @ X2))))))))))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 100.18/13.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1973])).
% 100.18/13.50 thf(zip_derived_cl1975, plain,
% 100.18/13.50 (![X0 : $i, X2 : $i]:
% 100.18/13.50 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat))) @
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (((=>) @ (n_is @
% 100.18/13.50 (n_ts @ (num @ X0) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X0))))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 100.18/13.50 ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ n_eq @ (n_pf @ X0))))) @
% 100.18/13.50 (n_pf @ X2))))))))))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 100.18/13.50 inference('rw', [status(thm)], [zip_derived_cl1974, '2'])).
% 100.18/13.50 thf(zip_derived_cl1976, plain,
% 100.18/13.50 (![X0 : $i, X2 : $i]:
% 100.18/13.50 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (((=>) @ (n_is @
% 100.18/13.50 (n_ts @ (num @ X0) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X0))))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 100.18/13.50 ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ n_eq @ (n_pf @ X0))))) @
% 100.18/13.50 (n_pf @ X2))))))))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 100.18/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1975])).
% 100.18/13.50 thf(zip_derived_cl1977, plain,
% 100.18/13.50 (![X0 : $i, X1 : $i]:
% 100.18/13.50 ( (((!!) @ (^[Y0 : $i]:
% 100.18/13.50 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 100.18/13.50 ((('#B') @ (all_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (((=>) @ (n_is @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @ X0) @
% 100.18/13.50 (den @ X1)) @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @ X1) @
% 100.18/13.50 (den @ X0))))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 100.18/13.50 ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ n_eq @ (n_pf @ X0))))) @
% 100.18/13.50 (n_pf @ X1))))))) @
% 100.18/13.50 Y0)))))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 100.18/13.50 inference('rw_clause', [status(thm)], [zip_derived_cl1976, '4'])).
% 100.18/13.50 thf(zip_derived_cl1978, plain,
% 100.18/13.50 (![X0 : $i, X1 : $i]:
% 100.18/13.50 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 100.18/13.50 ((('#C') @ is_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat))))))) @
% 100.18/13.50 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @
% 100.18/13.50 ((('#B') @ ((('#B') @ (((=>) @ (n_is @
% 100.18/13.50 (n_ts @ (num @ X0) @
% 100.18/13.50 (den @ X1)) @
% 100.18/13.50 (n_ts @ (num @ X1) @
% 100.18/13.50 (den @ X0))))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ ('#S') @
% 100.18/13.50 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @
% 100.18/13.50 ((('#C') @ ((('#B') @ ('#B') @
% 100.18/13.50 ((('#B') @ n_eq @ (n_pf @ X0))))) @
% 100.18/13.50 (n_pf @ X1)))))))))))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 100.18/13.50 inference('comb-normalize', [status(thm)], [zip_derived_cl1977])).
% 100.18/13.50 thf(zip_derived_cl1979, plain,
% 100.18/13.50 (![X0 : $i, X1 : $i, X3 : $i]:
% 100.18/13.50 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat))) @
% 100.18/13.50 ((('#B') @ (((=>) @ (n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 100.18/13.50 (n_ts @ (num @ X1) @ (den @ X0))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X3))) @
% 100.18/13.50 ((('#B') @ (n_eq @ (n_pf @ X0 @ X3)) @ (n_pf @ X1))))))))))
% 100.18/13.50 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 100.18/13.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1978])).
% 100.18/13.50 thf(zip_derived_cl1980, plain,
% 100.18/13.50 (![X0 : $i, X1 : $i, X3 : $i]:
% 100.18/13.50 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat))) @
% 100.18/13.50 ((('#B') @ (((=>) @ (n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 100.18/13.50 (n_ts @ (num @ X1) @ (den @ X0))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X3))) @
% 100.18/13.50 ((('#B') @ (n_eq @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 100.18/13.50 (n_ts @ (num @ X3) @ (den @ X0))) @
% 100.18/13.50 (n_ts @ (den @ X0) @ (den @ X3)))) @
% 100.18/13.50 (n_pf @ X1))))))))))
% 100.18/13.50 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 100.18/13.50 inference('rw', [status(thm)], [zip_derived_cl1979, '3'])).
% 100.18/13.50 thf(zip_derived_cl1981, plain,
% 100.18/13.50 (![X0 : $i, X1 : $i, X3 : $i]:
% 100.18/13.50 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 100.18/13.50 ((('#B') @ (((=>) @ (n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 100.18/13.50 (n_ts @ (num @ X1) @ (den @ X0))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X3))) @
% 100.18/13.50 ((('#B') @ (n_eq @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @
% 100.18/13.50 (n_ts @ (num @ X3) @ (den @ X0))) @
% 100.18/13.50 (n_ts @ (den @ X0) @ (den @ X3)))) @
% 100.18/13.50 (n_pf @ X1))))))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 100.18/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1980])).
% 100.18/13.50 thf(zip_derived_cl1982, plain,
% 100.18/13.50 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.18/13.50 ( (((!!) @ (^[Y0 : $i]:
% 100.18/13.50 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 100.18/13.50 ((('#B') @ (((=>) @ (n_is @
% 100.18/13.50 (n_ts @ (num @ X1) @ (den @ X0)) @
% 100.18/13.50 (n_ts @ (num @ X0) @ (den @ X1))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @
% 100.18/13.50 ((('#B') @ (n_eq @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @
% 100.18/13.50 (n_ts @ (num @ X1) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X1))) @
% 100.18/13.50 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 100.18/13.50 (n_pf @ X0))))) @
% 100.18/13.50 Y0)))))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 100.18/13.50 inference('rw_clause', [status(thm)], [zip_derived_cl1981, '4'])).
% 100.18/13.50 thf(zip_derived_cl1983, plain,
% 100.18/13.50 (![X0 : $i, X1 : $i, X2 : $i]:
% 100.18/13.50 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 100.18/13.50 ((('#C') @ is_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat))))))) @
% 100.18/13.50 ((('#B') @ (((=>) @ (n_is @
% 100.18/13.50 (n_ts @ (num @ X1) @ (den @ X0)) @
% 100.18/13.50 (n_ts @ (num @ X0) @ (den @ X1))))) @
% 100.18/13.50 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @
% 100.18/13.50 ((('#B') @ (n_eq @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @
% 100.18/13.50 (n_ts @ (num @ X1) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X1))) @
% 100.18/13.50 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 100.18/13.50 (n_pf @ X0)))))))))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 100.18/13.50 inference('comb-normalize', [status(thm)], [zip_derived_cl1982])).
% 100.18/13.50 thf(zip_derived_cl1984, plain,
% 100.18/13.50 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 100.18/13.50 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 100.18/13.50 (((n_is @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 100.18/13.50 (n_ts @ (num @ X0) @ (den @ X1))) =>
% 100.18/13.50 (((n_eq @ X2 @ X4) => (n_eq @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X1))) @
% 100.18/13.50 (n_ts @ (den @ X1) @ (den @ X2))) @
% 100.18/13.50 (n_pf @ X0 @ X4))))))))
% 100.18/13.50 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 100.18/13.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1983])).
% 100.18/13.50 thf(zip_derived_cl1985, plain,
% 100.18/13.50 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 100.18/13.50 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 100.18/13.50 (((n_is @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 100.18/13.50 (n_ts @ (num @ X0) @ (den @ X1))) =>
% 100.18/13.50 (((n_is @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 100.18/13.50 (n_ts @ (num @ X4) @ (den @ X2))) => (n_is @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X1))) @
% 100.18/13.50 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 100.18/13.50 (den @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 100.18/13.50 (n_ts @ (num @ X4) @ (den @ X0))) @
% 100.18/13.50 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 100.18/13.50 (n_ts @ (num @ X4) @ (den @ X0))) @
% 100.18/13.50 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 100.18/13.50 (den @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X1))) @
% 100.18/13.50 (n_ts @ (den @ X1) @ (den @ X2))))))))))))
% 100.18/13.50 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 100.18/13.50 inference('rw', [status(thm)], [zip_derived_cl1984, '2', '2', '3'])).
% 100.18/13.50 thf(zip_derived_cl1986, plain,
% 100.18/13.50 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 100.18/13.50 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | (((n_is @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 100.18/13.50 (n_ts @ (num @ X0) @ (den @ X1))) =>
% 100.18/13.50 (((n_is @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 100.18/13.50 (n_ts @ (num @ X4) @ (den @ X2))) => (n_is @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X1))) @
% 100.18/13.50 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 100.18/13.50 (den @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 100.18/13.50 (n_ts @ (num @ X4) @ (den @ X0))) @
% 100.18/13.50 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 100.18/13.50 (n_ts @ (num @ X4) @ (den @ X0))) @
% 100.18/13.50 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 100.18/13.50 (den @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X1))) @
% 100.18/13.50 (n_ts @ (den @ X1) @ (den @ X2))))))))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 100.18/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1985])).
% 100.18/13.50 thf(zip_derived_cl1987, plain,
% 100.18/13.50 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 100.18/13.50 (~ (n_is @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 100.18/13.50 (n_ts @ (num @ X0) @ (den @ X1)))
% 100.18/13.50 | (((n_is @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 100.18/13.50 (n_ts @ (num @ X4) @ (den @ X2))) => (n_is @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X1))) @
% 100.18/13.50 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 100.18/13.50 (den @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 100.18/13.50 (n_ts @ (num @ X4) @ (den @ X0))) @
% 100.18/13.50 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 100.18/13.50 (n_ts @ (num @ X4) @ (den @ X0))) @
% 100.18/13.50 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 100.18/13.50 (den @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X1))) @
% 100.18/13.50 (n_ts @ (den @ X1) @ (den @ X2))))))))
% 100.18/13.50 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))),
% 100.18/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1986])).
% 100.18/13.50 thf(zip_derived_cl1988, plain,
% 100.18/13.50 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 100.18/13.50 (~ (n_is @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 100.18/13.50 (n_ts @ (num @ X4) @ (den @ X2)))
% 100.18/13.50 | (n_is @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X1))) @
% 100.18/13.50 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 100.18/13.50 (den @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 100.18/13.50 (n_ts @ (num @ X4) @ (den @ X0))) @
% 100.18/13.50 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 100.18/13.50 (n_ts @ (num @ X4) @ (den @ X0))) @
% 100.18/13.50 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 100.18/13.50 (den @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X1))) @
% 100.18/13.50 (n_ts @ (den @ X1) @ (den @ X2))))))
% 100.18/13.50 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | ~ (n_is @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 100.18/13.50 (n_ts @ (num @ X0) @ (den @ X1))))),
% 100.18/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1987])).
% 100.18/13.50 thf(zip_derived_cl18951, plain,
% 100.18/13.50 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 100.18/13.50 (~ (n_is @ (n_ts @ (num @ X2) @ (den @ X4)) @
% 100.18/13.50 (n_ts @ (num @ X4) @ (den @ X2)))
% 100.18/13.50 | (n_is @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X1))) @
% 100.18/13.50 (n_ts @ (den @ X1) @ (den @ X2)))) @
% 100.18/13.50 (den @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 100.18/13.50 (n_ts @ (num @ X4) @ (den @ X0))) @
% 100.18/13.50 (n_ts @ (den @ X0) @ (den @ X4))))) @
% 100.18/13.50 (n_ts @
% 100.18/13.50 (num @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @
% 100.18/13.50 (n_ts @ (num @ X4) @ (den @ X0))) @
% 100.18/13.50 (n_ts @ (den @ X0) @ (den @ X4)))) @
% 100.18/13.50 (den @
% 100.18/13.50 (n_fr @
% 100.18/13.50 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X1))) @
% 100.18/13.50 (n_ts @ (den @ X1) @ (den @ X2))))))
% 100.18/13.50 | ~ (is_of @ X4 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 100.18/13.50 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 100.18/13.50 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 100.18/13.50 | ~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 100.18/13.50 | ~ (n_is @ (n_ts @ (num @ X1) @ (den @ X0)) @
% 100.18/13.50 (n_ts @ (num @ X0) @ (den @ X1))))),
% 100.18/13.50 inference('remove_ty_args', [status(thm)], [zip_derived_cl1988])).
% 100.18/13.50 thf(satz37, axiom,
% 100.18/13.50 (all_of @
% 100.18/13.50 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ ( ^[X0:$i]: ( n_eq @ X0 @ X0 ) ))).
% 100.18/13.50 thf(zip_derived_cl237, plain,
% 100.18/13.50 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 100.18/13.50 (^[Y0 : $i]: (n_eq @ Y0 @ Y0)))),
% 100.18/13.50 inference('cnf', [status(esa)], [satz37])).
% 100.18/13.50 thf(zip_derived_cl238, plain,
% 100.18/13.50 ( (all_of @ ((('#C') @ in @ frac)) @ ((('#S') @ n_eq @ ('#I'))))),
% 100.18/13.50 inference('lams2combs', [status(thm)], [zip_derived_cl237])).
% 100.18/13.50 thf(zip_derived_cl334, plain,
% 100.18/13.50 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @
% 100.18/13.50 ((('#S') @ n_eq @ ('#I'))))),
% 100.18/13.50 inference('rw', [status(thm)], [zip_derived_cl238, '0'])).
% 100.18/13.50 thf(zip_derived_cl335, plain,
% 100.18/13.50 ( (((!!) @ (^[Y0 : $i]:
% 100.18/13.50 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) =>
% 100.18/13.50 ((('#S') @ n_eq @ ('#I') @ Y0)))))))),
% 100.18/13.50 inference('rw_clause', [status(thm)], [zip_derived_cl334, '4'])).
% 100.18/13.50 thf(zip_derived_cl336, plain,
% 100.18/13.50 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 100.18/13.50 ((('#C') @ is_of @
% 100.18/13.50 ((('#C') @ in @ (pair1type @ nat))))))) @
% 100.18/13.50 ((('#S') @ n_eq @ ('#I')))))))),
% 100.18/13.50 inference('comb-normalize', [status(thm)], [zip_derived_cl335])).
% 100.18/13.50 thf(zip_derived_cl337, plain,
% 100.18/13.50 (![X2 : $i]:
% 100.18/13.50 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (n_eq @ X2 @
% 100.18/13.50 X2)))),
% 100.18/13.50 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl336])).
% 100.18/13.50 thf(zip_derived_cl338, plain,
% 100.18/13.50 (![X2 : $i]:
% 100.18/13.50 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (n_is @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X2)))))),
% 100.18/13.50 inference('rw', [status(thm)], [zip_derived_cl337, '2'])).
% 100.18/13.50 thf(zip_derived_cl339, plain,
% 100.18/13.50 (![X2 : $i]:
% 100.18/13.50 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat))))
% 100.18/13.50 | (n_is @ (n_ts @ (num @ X2) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X2))))),
% 100.18/13.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl338])).
% 100.18/13.50 thf(zip_derived_cl18832, plain,
% 100.18/13.50 (![X2 : $i]:
% 100.18/13.50 (~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat)))
% 100.18/13.50 | (n_is @ (n_ts @ (num @ X2) @ (den @ X2)) @
% 100.18/13.50 (n_ts @ (num @ X2) @ (den @ X2))))),
% 100.18/13.50 inference('remove_ty_args', [status(thm)], [zip_derived_cl339])).
% 100.18/13.50 thf(zip_derived_cl18974, plain, ($false),
% 100.18/13.50 inference('eprover', [status(thm)],
% 100.18/13.50 [zip_derived_cl18863, zip_derived_cl18864, zip_derived_cl679,
% 100.18/13.50 zip_derived_cl18865, zip_derived_cl680, zip_derived_cl18951,
% 100.18/13.50 zip_derived_cl18832])).
% 100.18/13.50
% 100.18/13.50 % SZS output end Refutation
% 100.18/13.50
% 100.18/13.50
% 100.18/13.50 % Terminating...
% 100.26/13.64 % Runner terminated.
% 100.26/13.66 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------