TSTP Solution File: NUM788^4 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM788^4 : 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.la4CYBwn5R true
% Computer : n009.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 12:44:10 EDT 2023
% Result : Theorem 98.93s 13.16s
% Output : Refutation 98.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM788^4 : TPTP v8.1.2. Released v7.1.0.
% 0.14/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.la4CYBwn5R true
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 11:18:36 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.21/0.36 % Running in HO mode
% 0.22/0.66 % Total configuration time : 828
% 0.22/0.66 % Estimated wc time : 1656
% 0.22/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.25/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.25/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.25/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.25/0.78 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.25/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.47/0.80 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.47/0.80 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.51/1.27 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 98.93/13.16 % Solved by lams/40_b.comb.sh.
% 98.93/13.16 % done 341 iterations in 12.330s
% 98.93/13.16 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 98.93/13.16 % SZS output start Refutation
% 98.93/13.16 thf(rt_is_type, type, rt_is: $i > $i > $o).
% 98.93/13.16 thf(lessf_type, type, lessf: $i > $i > $o).
% 98.93/13.16 thf(inf_type, type, inf: $i > $i > $o).
% 98.93/13.16 thf(orec3_type, type, orec3: $o > $o > $o > $o).
% 98.93/13.16 thf(rt_less_type, type, rt_less: $i > $i > $o).
% 98.93/13.16 thf(and3_type, type, and3: $o > $o > $o > $o).
% 98.93/13.16 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 98.93/13.16 thf(in_type, type, in: $i > $i > $o).
% 98.93/13.16 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 98.93/13.16 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 98.93/13.16 thf('#sk2_type', type, '#sk2': $i).
% 98.93/13.16 thf(l_ec_type, type, l_ec: $o > $o > $o).
% 98.93/13.16 thf(ect_type, type, ect: $i > ($i > $i > $o) > $i).
% 98.93/13.16 thf('#sk3_type', type, '#sk3': $i).
% 98.93/13.16 thf(imp_type, type, imp: $o > $o > $o).
% 98.93/13.16 thf(rat_type, type, rat: $i).
% 98.93/13.16 thf(rt_lessis_type, type, rt_lessis: $i > $i > $o).
% 98.93/13.16 thf(ec3_type, type, ec3: $o > $o > $o > $o).
% 98.93/13.16 thf(frac_type, type, frac: $i).
% 98.93/13.16 thf(e_in_type, type, e_in: $i > ($i > $o) > $i > $i).
% 98.93/13.16 thf(n_eq_type, type, n_eq: $i > $i > $o).
% 98.93/13.16 thf(d_and_type, type, d_and: $o > $o > $o).
% 98.93/13.16 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 98.93/13.16 thf(ecect_type, type, ecect: $i > ($i > $i > $o) > $i > $i).
% 98.93/13.16 thf(anec_type, type, anec: $i > ($i > $i > $o) > $i > $o).
% 98.93/13.16 thf(l_or_type, type, l_or: $o > $o > $o).
% 98.93/13.16 thf(class_type, type, class: $i > $i).
% 98.93/13.16 thf(moref_type, type, moref: $i > $i > $o).
% 98.93/13.16 thf(d_not_type, type, d_not: $o > $o).
% 98.93/13.16 thf(power_type, type, power: $i > $i).
% 98.93/13.16 thf(or3_type, type, or3: $o > $o > $o > $o).
% 98.93/13.16 thf(rt_more_type, type, rt_more: $i > $i > $o).
% 98.93/13.16 thf(e_is_type, type, e_is: $i > $i > $i > $o).
% 98.93/13.16 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 98.93/13.16 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 98.93/13.16 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 98.93/13.16 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 98.93/13.16 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 98.93/13.16 thf(satz81g, conjecture,
% 98.93/13.16 (all_of @
% 98.93/13.16 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @
% 98.93/13.16 ( ^[X0:$i]:
% 98.93/13.16 ( all_of @
% 98.93/13.16 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @
% 98.93/13.16 ( ^[X1:$i]:
% 98.93/13.16 ( ( rt_more @ X0 @ X1 ) => ( d_not @ ( rt_lessis @ X0 @ X1 ) ) ) ) ) ))).
% 98.93/13.16 thf(zf_stmt_0, negated_conjecture,
% 98.93/13.16 (~( all_of @
% 98.93/13.16 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @
% 98.93/13.16 ( ^[X0:$i]:
% 98.93/13.16 ( all_of @
% 98.93/13.16 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @
% 98.93/13.16 ( ^[X1:$i]:
% 98.93/13.16 ( ( rt_more @ X0 @ X1 ) => ( d_not @ ( rt_lessis @ X0 @ X1 ) ) ) ) ) ) )),
% 98.93/13.16 inference('cnf.neg', [status(esa)], [satz81g])).
% 98.93/13.16 thf(zip_derived_cl503, plain,
% 98.93/13.16 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @
% 98.93/13.16 (^[Y0 : $i]:
% 98.93/13.16 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @
% 98.93/13.16 (^[Y1 : $i]:
% 98.93/13.16 (((rt_more @ Y0 @ Y1) => (d_not @ (rt_lessis @ Y0 @ Y1))))))))),
% 98.93/13.16 inference('cnf', [status(esa)], [zf_stmt_0])).
% 98.93/13.16 thf(zip_derived_cl504, plain,
% 98.93/13.16 (~ (all_of @ ((('#C') @ in @ rat)) @
% 98.93/13.16 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#B') @ ((('#B') @ (=>))) @ rt_more)))) @
% 98.93/13.16 ((('#B') @ ((('#B') @ d_not)) @ rt_lessis)))))))),
% 98.93/13.16 inference('lams2combs', [status(thm)], [zip_derived_cl503])).
% 98.93/13.16 thf(def_ect, axiom,(( ect @ (X0)@ (X1)) =
% 98.93/13.16 ((d_Sep @ (power @ X0) @ (anec @ X0 @ X1))))).
% 98.93/13.16 thf('0', plain,
% 98.93/13.16 (![X1:( $i > $i > $o ),X0:$i]:
% 98.93/13.16 ( ( ect @ X0 @ X1 ) = ( d_Sep @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) ) )),
% 98.93/13.16 define([status(thm)])).
% 98.93/13.16 thf(def_rat, axiom,(( rat ) = ((ect @ frac @ n_eq)))).
% 98.93/13.16 thf('1', plain, (( rat ) = ( ect @ frac @ n_eq )), define([status(thm)])).
% 98.93/13.16 thf(zip_derived_cl640, plain,
% 98.93/13.16 (~ (all_of @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 98.93/13.16 ((('#B') @ (all_of @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#B') @ ((('#B') @ (=>))) @ rt_more)))) @
% 98.93/13.16 ((('#B') @ ((('#B') @ d_not)) @ rt_lessis)))))))),
% 98.93/13.16 inference('rw', [status(thm)], [zip_derived_cl504, '0', '1'])).
% 98.93/13.16 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 98.93/13.16 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 98.93/13.16 thf('2', plain,
% 98.93/13.16 (![X0:( $i > $o ),X1:( $i > $o )]:
% 98.93/13.16 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 98.93/13.16 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 98.93/13.16 inference('rw.lit', [status(esa)], [def_all_of])).
% 98.93/13.16 thf(zip_derived_cl641, plain,
% 98.93/13.16 (~ (((!!) @ (^[Y0 : $i]:
% 98.93/13.16 (((is_of @ Y0 @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 98.93/13.16 ((('#B') @ (all_of @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @
% 98.93/13.16 (anec @ frac @ n_eq))))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#B') @ ((('#B') @ (=>))) @ rt_more)))) @
% 98.93/13.16 ((('#B') @ ((('#B') @ d_not)) @ rt_lessis)))) @
% 98.93/13.16 Y0)))))))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl640, '2'])).
% 98.93/13.16 thf(zip_derived_cl642, plain,
% 98.93/13.16 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 98.93/13.16 ((('#C') @ is_of @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @
% 98.93/13.16 (anec @ frac @ n_eq)))))))) @
% 98.93/13.16 ((('#B') @ (all_of @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @
% 98.93/13.16 (anec @ frac @ n_eq))))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#B') @ ((('#B') @ (=>))) @ rt_more)))) @
% 98.93/13.16 ((('#B') @ ((('#B') @ d_not)) @ rt_lessis))))))))))),
% 98.93/13.16 inference('comb-normalize', [status(thm)], [zip_derived_cl641])).
% 98.93/13.16 thf(zip_derived_cl643, plain,
% 98.93/13.16 (~ (((is_of @ '#sk2' @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 98.93/13.16 (all_of @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ (=>) @ (rt_more @ '#sk2'))) @
% 98.93/13.16 ((('#B') @ d_not @ (rt_lessis @ '#sk2'))))))))),
% 98.93/13.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl642])).
% 98.93/13.16 thf(zip_derived_cl645, plain,
% 98.93/13.16 (~ (all_of @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ (=>) @ (rt_more @ '#sk2'))) @
% 98.93/13.16 ((('#B') @ d_not @ (rt_lessis @ '#sk2'))))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl643])).
% 98.93/13.16 thf(zip_derived_cl646, plain,
% 98.93/13.16 (~ (((!!) @ (^[Y0 : $i]:
% 98.93/13.16 (((is_of @ Y0 @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 98.93/13.16 ((('#S') @ ((('#B') @ (=>) @ (rt_more @ '#sk2'))) @
% 98.93/13.16 ((('#B') @ d_not @ (rt_lessis @ '#sk2'))) @ Y0)))))))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl645, '2'])).
% 98.93/13.16 thf(zip_derived_cl647, plain,
% 98.93/13.16 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 98.93/13.16 ((('#C') @ is_of @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @
% 98.93/13.16 (anec @ frac @ n_eq)))))))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ (=>) @ (rt_more @ '#sk2'))) @
% 98.93/13.16 ((('#B') @ d_not @ (rt_lessis @ '#sk2')))))))))),
% 98.93/13.16 inference('comb-normalize', [status(thm)], [zip_derived_cl646])).
% 98.93/13.16 thf(zip_derived_cl648, plain,
% 98.93/13.16 (~ (((is_of @ '#sk3' @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 98.93/13.16 (((rt_more @ '#sk2' @ '#sk3') => (d_not @
% 98.93/13.16 (rt_lessis @ '#sk2' @ '#sk3'))))))),
% 98.93/13.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl647])).
% 98.93/13.16 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 98.93/13.16 thf('3', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 98.93/13.16 define([status(thm)])).
% 98.93/13.16 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 98.93/13.16 thf('4', plain,
% 98.93/13.16 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 98.93/13.16 define([status(thm)])).
% 98.93/13.16 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))).
% 98.93/13.16 thf('5', plain,
% 98.93/13.16 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )),
% 98.93/13.16 define([status(thm)])).
% 98.93/13.16 thf(def_e_in, axiom,(( e_in @ (X1)@ (X2)@ (X0)) = ((X0)))).
% 98.93/13.16 thf('6', plain,
% 98.93/13.16 (![X2:( $i > $o ),X1:$i,X0:$i]: ( ( e_in @ X1 @ X2 @ X0 ) = ( X0 ) )),
% 98.93/13.16 define([status(thm)])).
% 98.93/13.16 thf(def_ecect, axiom,(( ecect @ (X0)@ (X1)@ (X2)) =
% 98.93/13.16 ((e_in @ (power @ X0) @ (anec @ X0 @ X1) @ X2)))).
% 98.93/13.16 thf('7', plain,
% 98.93/13.16 (![X2:$i,X1:( $i > $i > $o ),X0:$i]:
% 98.93/13.16 ( ( ecect @ X0 @ X1 @ X2 ) =
% 98.93/13.16 ( e_in @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) @ X2 ) )),
% 98.93/13.16 define([status(thm)])).
% 98.93/13.16 thf(def_rt_is, axiom,(( rt_is @ (X0)@ (X1)) = ((e_is @ rat @ X0 @ X1)))).
% 98.93/13.16 thf('8', plain,
% 98.93/13.16 (![X1:$i,X0:$i]: ( ( rt_is @ X0 @ X1 ) = ( e_is @ rat @ X0 @ X1 ) )),
% 98.93/13.16 define([status(thm)])).
% 98.93/13.16 thf(def_class, axiom,(( class @ (X0)) = ((ecect @ frac @ n_eq @ X0)))).
% 98.93/13.16 thf('9', plain,
% 98.93/13.16 (![X0:$i]: ( ( class @ X0 ) = ( ecect @ frac @ n_eq @ X0 ) )),
% 98.93/13.16 define([status(thm)])).
% 98.93/13.16 thf(def_rt_more, axiom,(( rt_more @ (X0)@ (X1)) =
% 98.93/13.16 ((l_some @ frac @
% 98.93/13.16 (^[Y0 : $i]:
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 (^[Y1 : $i]:
% 98.93/13.16 (and3 @ (inf @ Y0 @ (class @ X0)) @ (inf @ Y1 @ (class @ X1)) @
% 98.93/13.16 (moref @ Y0 @ Y1))))))))).
% 98.93/13.16 thf('10', plain,
% 98.93/13.16 (![X1:$i,X0:$i]:
% 98.93/13.16 ( ( rt_more @ X0 @ X1 ) =
% 98.93/13.16 ( l_some @
% 98.93/13.16 frac @
% 98.93/13.16 ( ^[V_1:$i]:
% 98.93/13.16 ( l_some @
% 98.93/13.16 frac @
% 98.93/13.16 ( ^[V_2:$i]:
% 98.93/13.16 ( and3 @
% 98.93/13.16 ( inf @ V_1 @ ( class @ X0 ) ) @
% 98.93/13.16 ( inf @ V_2 @ ( class @ X1 ) ) @ ( moref @ V_1 @ V_2 ) ) ) ) ) ) )),
% 98.93/13.16 define([status(thm)])).
% 98.93/13.16 thf(def_rt_less, axiom,(( rt_less @ (X0)@ (X1)) =
% 98.93/13.16 ((l_some @ frac @
% 98.93/13.16 (^[Y0 : $i]:
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 (^[Y1 : $i]:
% 98.93/13.16 (and3 @ (inf @ Y0 @ (class @ X0)) @ (inf @ Y1 @ (class @ X1)) @
% 98.93/13.16 (lessf @ Y0 @ Y1))))))))).
% 98.93/13.16 thf('11', plain,
% 98.93/13.16 (![X1:$i,X0:$i]:
% 98.93/13.16 ( ( rt_less @ X0 @ X1 ) =
% 98.93/13.16 ( l_some @
% 98.93/13.16 frac @
% 98.93/13.16 ( ^[V_1:$i]:
% 98.93/13.16 ( l_some @
% 98.93/13.16 frac @
% 98.93/13.16 ( ^[V_2:$i]:
% 98.93/13.16 ( and3 @
% 98.93/13.16 ( inf @ V_1 @ ( class @ X0 ) ) @
% 98.93/13.16 ( inf @ V_2 @ ( class @ X1 ) ) @ ( lessf @ V_1 @ V_2 ) ) ) ) ) ) )),
% 98.93/13.16 define([status(thm)])).
% 98.93/13.16 thf(def_rt_lessis, axiom,(( rt_lessis @ (X0)@ (X1)) =
% 98.93/13.16 ((l_or @ (rt_less @ X0 @ X1) @ (rt_is @ X0 @ X1))))).
% 98.93/13.16 thf('12', plain,
% 98.93/13.16 (![X1:$i,X0:$i]:
% 98.93/13.16 ( ( rt_lessis @ X0 @ X1 ) =
% 98.93/13.16 ( l_or @ ( rt_less @ X0 @ X1 ) @ ( rt_is @ X0 @ X1 ) ) )),
% 98.93/13.16 define([status(thm)])).
% 98.93/13.16 thf(zip_derived_cl649, plain,
% 98.93/13.16 (~ (((is_of @ '#sk3' @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 98.93/13.16 (((l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 moref))))) =>
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false)) @
% 98.93/13.16 ((('#sk2') = ('#sk3')))) @
% 98.93/13.16 ($false))))))),
% 98.93/13.16 inference('rw', [status(thm)],
% 98.93/13.16 [zip_derived_cl648, '3', '3', '4', '5', '6', '6', '0', '7',
% 98.93/13.16 '7', '1', '8', '9', '9', '10', '11', '12'])).
% 98.93/13.16 thf(zip_derived_cl651, plain,
% 98.93/13.16 (~ (((l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 moref))))) =>
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false)) @
% 98.93/13.16 ((('#sk2') = ('#sk3')))) @
% 98.93/13.16 ($false))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl649])).
% 98.93/13.16 thf(zip_derived_cl653, plain,
% 98.93/13.16 (~ (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false)) @
% 98.93/13.16 ((('#sk2') = ('#sk3')))) @
% 98.93/13.16 ($false))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl651])).
% 98.93/13.16 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 98.93/13.16 thf('13', plain,
% 98.93/13.16 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 98.93/13.16 inference('rw.lit', [status(esa)], [def_imp])).
% 98.93/13.16 thf(zip_derived_cl654, plain,
% 98.93/13.16 (~ (((imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false)) @
% 98.93/13.16 ((('#sk2') = ('#sk3')))) => ($false)))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl653, '13'])).
% 98.93/13.16 thf(zip_derived_cl655, plain,
% 98.93/13.16 (~ (((~) @ (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false)) @
% 98.93/13.16 ((('#sk2') = ('#sk3'))))))),
% 98.93/13.16 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl654])).
% 98.93/13.16 thf(zip_derived_cl656, plain,
% 98.93/13.16 ( (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false)) @
% 98.93/13.16 ((('#sk2') = ('#sk3'))))),
% 98.93/13.16 inference('simplify nested equalities', [status(thm)],
% 98.93/13.16 [zip_derived_cl655])).
% 98.93/13.16 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 98.93/13.16 thf('14', plain,
% 98.93/13.16 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 98.93/13.16 inference('rw.lit', [status(esa)], [def_imp])).
% 98.93/13.16 thf(zip_derived_cl657, plain,
% 98.93/13.16 ( (((imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false)) => ((('#sk2') = ('#sk3')))))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl656, '14'])).
% 98.93/13.16 thf(zip_derived_cl658, plain,
% 98.93/13.16 ((~ (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false))
% 98.93/13.16 | ((('#sk2') = ('#sk3'))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl657])).
% 98.93/13.16 thf(zip_derived_cl659, plain,
% 98.93/13.16 ((~ (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false))
% 98.93/13.16 | (('#sk2') = ('#sk3')))),
% 98.93/13.16 inference('simplify nested equalities', [status(thm)],
% 98.93/13.16 [zip_derived_cl658])).
% 98.93/13.16 thf(zip_derived_cl660, plain,
% 98.93/13.16 ((~ (((l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 lessf))))) =>
% 98.93/13.16 ($false)))
% 98.93/13.16 | (('#sk2') = ('#sk3')))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl659, '13'])).
% 98.93/13.16 thf(zip_derived_cl661, plain,
% 98.93/13.16 ((~ (((~) @ (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 lessf)))))))
% 98.93/13.16 | (('#sk2') = ('#sk3')))),
% 98.93/13.16 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl660])).
% 98.93/13.16 thf(zip_derived_cl662, plain,
% 98.93/13.16 (( (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 lessf)))))
% 98.93/13.16 | (('#sk2') = ('#sk3')))),
% 98.93/13.16 inference('simplify nested equalities', [status(thm)],
% 98.93/13.16 [zip_derived_cl661])).
% 98.93/13.16 thf(satz81, axiom,
% 98.93/13.16 (all_of @
% 98.93/13.16 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @
% 98.93/13.16 ( ^[X0:$i]:
% 98.93/13.16 ( all_of @
% 98.93/13.16 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @
% 98.93/13.16 ( ^[X1:$i]:
% 98.93/13.16 ( orec3 @
% 98.93/13.16 ( rt_is @ X0 @ X1 ) @ ( rt_more @ X0 @ X1 ) @
% 98.93/13.16 ( rt_less @ X0 @ X1 ) ) ) ) ))).
% 98.93/13.16 thf(zip_derived_cl489, plain,
% 98.93/13.16 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @
% 98.93/13.16 (^[Y0 : $i]:
% 98.93/13.16 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @
% 98.93/13.16 (^[Y1 : $i]:
% 98.93/13.16 (orec3 @ (rt_is @ Y0 @ Y1) @ (rt_more @ Y0 @ Y1) @
% 98.93/13.16 (rt_less @ Y0 @ Y1))))))),
% 98.93/13.16 inference('cnf', [status(esa)], [satz81])).
% 98.93/13.16 thf(zip_derived_cl490, plain,
% 98.93/13.16 ( (all_of @ ((('#C') @ in @ rat)) @
% 98.93/13.16 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#B') @ ((('#B') @ orec3)) @ rt_is)))) @
% 98.93/13.16 rt_more)))) @
% 98.93/13.16 rt_less)))))),
% 98.93/13.16 inference('lams2combs', [status(thm)], [zip_derived_cl489])).
% 98.93/13.16 thf(zip_derived_cl1786, plain,
% 98.93/13.16 ( (all_of @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 98.93/13.16 ((('#B') @ (all_of @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#B') @ ((('#B') @ orec3)) @ rt_is)))) @
% 98.93/13.16 rt_more)))) @
% 98.93/13.16 rt_less)))))),
% 98.93/13.16 inference('rw', [status(thm)], [zip_derived_cl490, '0', '1'])).
% 98.93/13.16 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 98.93/13.16 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 98.93/13.16 thf('15', plain,
% 98.93/13.16 (![X0:( $i > $o ),X1:( $i > $o )]:
% 98.93/13.16 ( ( all_of @ X0 @ X1 ) <=>
% 98.93/13.16 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 98.93/13.16 inference('rw.lit', [status(esa)], [def_all_of])).
% 98.93/13.16 thf(zip_derived_cl1787, plain,
% 98.93/13.16 ( (((!!) @ (^[Y0 : $i]:
% 98.93/13.16 (((is_of @ Y0 @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 98.93/13.16 ((('#B') @ (all_of @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @
% 98.93/13.16 (anec @ frac @ n_eq))))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#B') @ ((('#B') @ orec3)) @
% 98.93/13.16 rt_is)))) @
% 98.93/13.16 rt_more)))) @
% 98.93/13.16 rt_less)) @
% 98.93/13.16 Y0)))))))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl1786, '15'])).
% 98.93/13.16 thf(zip_derived_cl1788, plain,
% 98.93/13.16 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 98.93/13.16 ((('#C') @ is_of @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @
% 98.93/13.16 (anec @ frac @ n_eq)))))))) @
% 98.93/13.16 ((('#B') @ (all_of @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#B') @ ((('#B') @ orec3)) @
% 98.93/13.16 rt_is)))) @
% 98.93/13.16 rt_more)))) @
% 98.93/13.16 rt_less))))))))),
% 98.93/13.16 inference('comb-normalize', [status(thm)], [zip_derived_cl1787])).
% 98.93/13.16 thf(zip_derived_cl1789, plain,
% 98.93/13.16 (![X2 : $i]:
% 98.93/13.16 (((is_of @ X2 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 98.93/13.16 (all_of @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 98.93/13.16 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X2))) @
% 98.93/13.16 (rt_more @ X2))) @
% 98.93/13.16 (rt_less @ X2))))))),
% 98.93/13.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1788])).
% 98.93/13.16 thf(zip_derived_cl1790, plain,
% 98.93/13.16 (![X2 : $i]:
% 98.93/13.16 (~ (is_of @ X2 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | (all_of @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 98.93/13.16 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X2))) @
% 98.93/13.16 (rt_more @ X2))) @
% 98.93/13.16 (rt_less @ X2)))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1789])).
% 98.93/13.16 thf(zip_derived_cl1791, plain,
% 98.93/13.16 (![X0 : $i]:
% 98.93/13.16 ( (((!!) @ (^[Y0 : $i]:
% 98.93/13.16 (((is_of @ Y0 @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 98.93/13.16 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X0))) @
% 98.93/13.16 (rt_more @ X0))) @
% 98.93/13.16 (rt_less @ X0) @ Y0)))))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl1790, '15'])).
% 98.93/13.16 thf(zip_derived_cl1792, plain,
% 98.93/13.16 (![X0 : $i]:
% 98.93/13.16 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 98.93/13.16 ((('#C') @ is_of @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @
% 98.93/13.16 (anec @ frac @ n_eq)))))))) @
% 98.93/13.16 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X0))) @
% 98.93/13.16 (rt_more @ X0))) @
% 98.93/13.16 (rt_less @ X0)))))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('comb-normalize', [status(thm)], [zip_derived_cl1791])).
% 98.93/13.16 thf(zip_derived_cl1793, plain,
% 98.93/13.16 (![X0 : $i, X2 : $i]:
% 98.93/13.16 ( (((is_of @ X2 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 98.93/13.16 (orec3 @ (rt_is @ X0 @ X2) @ (rt_more @ X0 @ X2) @
% 98.93/13.16 (rt_less @ X0 @ X2))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1792])).
% 98.93/13.16 thf(def_l_ec, axiom,(( l_ec @ (X0)@ (X1)) = ((imp @ X0 @ (d_not @ X1))))).
% 98.93/13.16 thf('16', plain,
% 98.93/13.16 (![X1:$o,X0:$o]: ( ( l_ec @ X0 @ X1 ) = ( imp @ X0 @ ( d_not @ X1 ) ) )),
% 98.93/13.16 define([status(thm)])).
% 98.93/13.16 thf(def_d_and, axiom,(( d_and @ (X0)@ (X1)) = ((d_not @ (l_ec @ X0 @ X1))))).
% 98.93/13.16 thf('17', plain,
% 98.93/13.16 (![X1:$o,X0:$o]: ( ( d_and @ X0 @ X1 ) = ( d_not @ ( l_ec @ X0 @ X1 ) ) )),
% 98.93/13.16 define([status(thm)])).
% 98.93/13.16 thf(def_or3, axiom,(( or3 @ (X0)@ (X1)@ (X2)) =
% 98.93/13.16 ((l_or @ X0 @ (l_or @ X1 @ X2))))).
% 98.93/13.16 thf('18', plain,
% 98.93/13.16 (![X2:$o,X1:$o,X0:$o]:
% 98.93/13.16 ( ( or3 @ X0 @ X1 @ X2 ) = ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) )),
% 98.93/13.16 define([status(thm)])).
% 98.93/13.16 thf(def_and3, axiom,(( and3 @ (X0)@ (X1)@ (X2)) =
% 98.93/13.16 ((d_and @ X0 @ (d_and @ X1 @ X2))))).
% 98.93/13.16 thf('19', plain,
% 98.93/13.16 (![X2:$o,X1:$o,X0:$o]:
% 98.93/13.16 ( ( and3 @ X0 @ X1 @ X2 ) = ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) )),
% 98.93/13.16 define([status(thm)])).
% 98.93/13.16 thf(def_ec3, axiom,(( ec3 @ (X0)@ (X1)@ (X2)) =
% 98.93/13.16 ((and3 @ (l_ec @ X0 @ X1) @ (l_ec @ X1 @ X2) @ (l_ec @ X2 @ X0))))).
% 98.93/13.16 thf('20', plain,
% 98.93/13.16 (![X2:$o,X1:$o,X0:$o]:
% 98.93/13.16 ( ( ec3 @ X0 @ X1 @ X2 ) =
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% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 (imp @ (((X0) = (X1))) @ ($false))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 ($false)) @
% 98.93/13.16 ($false)))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('simplify boolean subterms', [status(thm)],
% 98.93/13.16 [zip_derived_cl1807])).
% 98.93/13.16 thf(zip_derived_cl1810, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 (~ (imp @
% 98.93/13.16 (imp @ (((X0) = (X1))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 (imp @ (((X0) = (X1))) @ ($false))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 ($false)) @
% 98.93/13.16 ($false)))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('simplify nested equalities', [status(thm)],
% 98.93/13.16 [zip_derived_cl1809])).
% 98.93/13.16 thf(zip_derived_cl1811, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 (~ (((imp @ (((X1) = (X0))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 ($false))) =>
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 (imp @ (((X1) = (X0))) @ ($false))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 ($false)) @
% 98.93/13.16 ($false))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl1810, '13'])).
% 98.93/13.16 thf(zip_derived_cl1816, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 (~ (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 (imp @ (((X1) = (X0))) @ ($false))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 ($false)) @
% 98.93/13.16 ($false))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1811])).
% 98.93/13.16 thf(zip_derived_cl1819, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 (~ (((imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 (imp @ (((X1) = (X0))) @ ($false))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 ($false)) => ($false)))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl1816, '13'])).
% 98.93/13.16 thf(zip_derived_cl1822, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 (~ (((~) @ (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 (imp @ (((X1) = (X0))) @ ($false))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 ($false))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('simplify boolean subterms', [status(thm)],
% 98.93/13.16 [zip_derived_cl1819])).
% 98.93/13.16 thf(zip_derived_cl1823, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 ( (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 (imp @ (((X1) = (X0))) @ ($false))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 ($false))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('simplify nested equalities', [status(thm)],
% 98.93/13.16 [zip_derived_cl1822])).
% 98.93/13.16 thf(zip_derived_cl1824, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 ( (((imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 (imp @ (((X0) = (X1))) @ ($false))) @
% 98.93/13.16 ($false))) =>
% 98.93/13.16 ($false)))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl1823, '14'])).
% 98.93/13.16 thf(zip_derived_cl1829, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 ( (((~) @ (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 (imp @ (((X0) = (X1))) @ ($false))) @
% 98.93/13.16 ($false)))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('simplify boolean subterms', [status(thm)],
% 98.93/13.16 [zip_derived_cl1824])).
% 98.93/13.16 thf(zip_derived_cl1830, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 (~ (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 (imp @ (((X0) = (X1))) @ ($false))) @
% 98.93/13.16 ($false)))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('simplify nested equalities', [status(thm)],
% 98.93/13.16 [zip_derived_cl1829])).
% 98.93/13.16 thf(zip_derived_cl1831, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 (~ (((imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false))) =>
% 98.93/13.16 (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 (imp @ (((X1) = (X0))) @ ($false))) @
% 98.93/13.16 ($false))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl1830, '13'])).
% 98.93/13.16 thf(zip_derived_cl1834, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 ( (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false)))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1831])).
% 98.93/13.16 thf(zip_derived_cl1836, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 ( (((l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 moref))))) =>
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl1834, '14'])).
% 98.93/13.16 thf(zip_derived_cl1838, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 (~ (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 moref)))))
% 98.93/13.16 | (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1836])).
% 98.93/13.16 thf(zip_derived_cl1842, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 ( (((l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) =>
% 98.93/13.16 ($false)))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 moref))))))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl1838, '14'])).
% 98.93/13.16 thf(zip_derived_cl1844, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 ( (((~) @ (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf)))))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 moref))))))),
% 98.93/13.16 inference('simplify boolean subterms', [status(thm)],
% 98.93/13.16 [zip_derived_cl1842])).
% 98.93/13.16 thf(zip_derived_cl1845, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 (~ (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf)))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 moref))))))),
% 98.93/13.16 inference('simplify nested equalities', [status(thm)],
% 98.93/13.16 [zip_derived_cl1844])).
% 98.93/13.16 thf(zip_derived_cl9082, plain,
% 98.93/13.16 (((('#sk2') = ('#sk3'))
% 98.93/13.16 | ~ (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 moref)))))
% 98.93/13.16 | ~ (is_of @ '#sk2' @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ '#sk3' @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('sup-', [status(thm)], [zip_derived_cl662, zip_derived_cl1845])).
% 98.93/13.16 thf(zip_derived_cl652, plain,
% 98.93/13.16 ( (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 moref)))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl651])).
% 98.93/13.16 thf(zip_derived_cl644, plain,
% 98.93/13.16 ( (is_of @ '#sk2' @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl643])).
% 98.93/13.16 thf(zip_derived_cl650, plain,
% 98.93/13.16 ( (is_of @ '#sk3' @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl649])).
% 98.93/13.16 thf(zip_derived_cl9110, plain, ((('#sk2') = ('#sk3'))),
% 98.93/13.16 inference('demod', [status(thm)],
% 98.93/13.16 [zip_derived_cl9082, zip_derived_cl652, zip_derived_cl644,
% 98.93/13.16 zip_derived_cl650])).
% 98.93/13.16 thf(zip_derived_cl652, plain,
% 98.93/13.16 ( (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ '#sk2')))))) @
% 98.93/13.16 ((('#C') @ inf @ '#sk3')))))) @
% 98.93/13.16 moref)))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl651])).
% 98.93/13.16 thf(satz81d, axiom,
% 98.93/13.16 (all_of @
% 98.93/13.16 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @
% 98.93/13.16 ( ^[X0:$i]:
% 98.93/13.16 ( all_of @
% 98.93/13.16 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @
% 98.93/13.16 ( ^[X1:$i]:
% 98.93/13.16 ( ( rt_lessis @ X0 @ X1 ) => ( d_not @ ( rt_more @ X0 @ X1 ) ) ) ) ) ))).
% 98.93/13.16 thf(zip_derived_cl499, plain,
% 98.93/13.16 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @
% 98.93/13.16 (^[Y0 : $i]:
% 98.93/13.16 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @
% 98.93/13.16 (^[Y1 : $i]:
% 98.93/13.16 (((rt_lessis @ Y0 @ Y1) => (d_not @ (rt_more @ Y0 @ Y1))))))))),
% 98.93/13.16 inference('cnf', [status(esa)], [satz81d])).
% 98.93/13.16 thf(zip_derived_cl500, plain,
% 98.93/13.16 ( (all_of @ ((('#C') @ in @ rat)) @
% 98.93/13.16 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))) @
% 98.93/13.16 ((('#B') @ ((('#B') @ d_not)) @ rt_more)))))))),
% 98.93/13.16 inference('lams2combs', [status(thm)], [zip_derived_cl499])).
% 98.93/13.16 thf(zip_derived_cl1027, plain,
% 98.93/13.16 ( (all_of @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 98.93/13.16 ((('#B') @ (all_of @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))) @
% 98.93/13.16 ((('#B') @ ((('#B') @ d_not)) @ rt_more)))))))),
% 98.93/13.16 inference('rw', [status(thm)], [zip_derived_cl500, '0', '1'])).
% 98.93/13.16 thf(zip_derived_cl1028, plain,
% 98.93/13.16 ( (((!!) @ (^[Y0 : $i]:
% 98.93/13.16 (((is_of @ Y0 @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 98.93/13.16 ((('#B') @ (all_of @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @
% 98.93/13.16 (anec @ frac @ n_eq))))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))) @
% 98.93/13.16 ((('#B') @ ((('#B') @ d_not)) @ rt_more)))) @
% 98.93/13.16 Y0)))))))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl1027, '15'])).
% 98.93/13.16 thf(zip_derived_cl1029, plain,
% 98.93/13.16 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 98.93/13.16 ((('#C') @ is_of @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @
% 98.93/13.16 (anec @ frac @ n_eq)))))))) @
% 98.93/13.16 ((('#B') @ (all_of @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))) @
% 98.93/13.16 ((('#B') @ ((('#B') @ d_not)) @ rt_more))))))))))),
% 98.93/13.16 inference('comb-normalize', [status(thm)], [zip_derived_cl1028])).
% 98.93/13.16 thf(zip_derived_cl1030, plain,
% 98.93/13.16 (![X2 : $i]:
% 98.93/13.16 (((is_of @ X2 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 98.93/13.16 (all_of @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ (=>) @ (rt_lessis @ X2))) @
% 98.93/13.16 ((('#B') @ d_not @ (rt_more @ X2))))))))),
% 98.93/13.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1029])).
% 98.93/13.16 thf(zip_derived_cl1031, plain,
% 98.93/13.16 (![X2 : $i]:
% 98.93/13.16 (~ (is_of @ X2 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | (all_of @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ (=>) @ (rt_lessis @ X2))) @
% 98.93/13.16 ((('#B') @ d_not @ (rt_more @ X2)))))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1030])).
% 98.93/13.16 thf(zip_derived_cl1032, plain,
% 98.93/13.16 (![X0 : $i]:
% 98.93/13.16 ( (((!!) @ (^[Y0 : $i]:
% 98.93/13.16 (((is_of @ Y0 @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 98.93/13.16 ((('#S') @ ((('#B') @ (=>) @ (rt_lessis @ X0))) @
% 98.93/13.16 ((('#B') @ d_not @ (rt_more @ X0))) @ Y0)))))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl1031, '15'])).
% 98.93/13.16 thf(zip_derived_cl1033, plain,
% 98.93/13.16 (![X0 : $i]:
% 98.93/13.16 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 98.93/13.16 ((('#C') @ is_of @
% 98.93/13.16 ((('#C') @ in @
% 98.93/13.16 (d_Sep @ (power @ frac) @
% 98.93/13.16 (anec @ frac @ n_eq)))))))) @
% 98.93/13.16 ((('#S') @ ((('#B') @ (=>) @ (rt_lessis @ X0))) @
% 98.93/13.16 ((('#B') @ d_not @ (rt_more @ X0)))))))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('comb-normalize', [status(thm)], [zip_derived_cl1032])).
% 98.93/13.16 thf(zip_derived_cl1034, plain,
% 98.93/13.16 (![X0 : $i, X2 : $i]:
% 98.93/13.16 ( (((is_of @ X2 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 98.93/13.16 (((rt_lessis @ X0 @ X2) => (d_not @ (rt_more @ X0 @ X2))))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1033])).
% 98.93/13.16 thf(zip_derived_cl1035, plain,
% 98.93/13.16 (![X0 : $i, X2 : $i]:
% 98.93/13.16 ( (((is_of @ X2 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 98.93/13.16 (((imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X2)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false)) @
% 98.93/13.16 (((X0) = (X2)))) => (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X2)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 ($false))))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('rw', [status(thm)],
% 98.93/13.16 [zip_derived_cl1034, '3', '3', '4', '5', '6', '6', '0', '7',
% 98.93/13.16 '7', '1', '8', '9', '9', '10', '11', '12'])).
% 98.93/13.16 thf(zip_derived_cl1036, plain,
% 98.93/13.16 (![X0 : $i, X2 : $i]:
% 98.93/13.16 (~ (is_of @ X2 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | (((imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X2)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false)) @
% 98.93/13.16 (((X0) = (X2)))) => (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X2)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 ($false))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1035])).
% 98.93/13.16 thf(zip_derived_cl1037, plain,
% 98.93/13.16 (![X0 : $i, X2 : $i]:
% 98.93/13.16 (~ (imp @
% 98.93/13.16 (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X2)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false)) @
% 98.93/13.16 (((X0) = (X2))))
% 98.93/13.16 | (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X2)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 ($false))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X2 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1036])).
% 98.93/13.16 thf(zip_derived_cl1038, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 (~ (((imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false)) => (((X1) = (X0)))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | (imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 moref))))) @
% 98.93/13.16 ($false)))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl1037, '13'])).
% 98.93/13.16 thf(zip_derived_cl1039, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 ( (((l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 moref))))) =>
% 98.93/13.16 ($false)))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (((imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false)) => (((X0) = (X1))))))),
% 98.93/13.16 inference('rw_clause', [status(thm)], [zip_derived_cl1038, '14'])).
% 98.93/13.16 thf(zip_derived_cl1040, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 ( (((~) @ (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 moref)))))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (((imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false)) => (((X0) = (X1))))))),
% 98.93/13.16 inference('simplify boolean subterms', [status(thm)],
% 98.93/13.16 [zip_derived_cl1039])).
% 98.93/13.16 thf(zip_derived_cl1041, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 (~ (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 moref)))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (((imp @
% 98.93/13.16 (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 lessf))))) @
% 98.93/13.16 ($false)) => (((X0) = (X1))))))),
% 98.93/13.16 inference('simplify nested equalities', [status(thm)],
% 98.93/13.16 [zip_derived_cl1040])).
% 98.93/13.16 thf(zip_derived_cl1043, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 (~ (((X0) = (X1)))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 moref))))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1041])).
% 98.93/13.16 thf(zip_derived_cl1045, plain,
% 98.93/13.16 (![X0 : $i, X1 : $i]:
% 98.93/13.16 (((X0) != (X1))
% 98.93/13.16 | ~ (is_of @ X1 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ X0 @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (l_some @ frac @
% 98.93/13.16 ((('#B') @ (l_some @ frac) @
% 98.93/13.16 ((('#S') @ ((('#B') @ ('#S') @
% 98.93/13.16 ((('#C') @ ((('#B') @ ('#B') @
% 98.93/13.16 ((('#B') @ and3 @
% 98.93/13.16 ((('#C') @ inf @ X0)))))) @
% 98.93/13.16 ((('#C') @ inf @ X1)))))) @
% 98.93/13.16 moref))))))),
% 98.93/13.16 inference('simplify nested equalities', [status(thm)],
% 98.93/13.16 [zip_derived_cl1043])).
% 98.93/13.16 thf(zip_derived_cl6963, plain,
% 98.93/13.16 ((~ (is_of @ '#sk2' @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | ~ (is_of @ '#sk3' @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 98.93/13.16 | (('#sk2') != ('#sk3')))),
% 98.93/13.16 inference('sup-', [status(thm)], [zip_derived_cl652, zip_derived_cl1045])).
% 98.93/13.16 thf(zip_derived_cl644, plain,
% 98.93/13.16 ( (is_of @ '#sk2' @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl643])).
% 98.93/13.16 thf(zip_derived_cl650, plain,
% 98.93/13.16 ( (is_of @ '#sk3' @
% 98.93/13.16 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))),
% 98.93/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl649])).
% 98.93/13.16 thf(zip_derived_cl6971, plain, ((('#sk2') != ('#sk3'))),
% 98.93/13.16 inference('demod', [status(thm)],
% 98.93/13.16 [zip_derived_cl6963, zip_derived_cl644, zip_derived_cl650])).
% 98.93/13.16 thf(zip_derived_cl9111, plain, ($false),
% 98.93/13.16 inference('simplify_reflect-', [status(thm)],
% 98.93/13.16 [zip_derived_cl9110, zip_derived_cl6971])).
% 98.93/13.16
% 98.93/13.16 % SZS output end Refutation
% 98.93/13.16
% 98.93/13.16
% 98.93/13.16 % Terminating...
% 99.06/13.21 % Runner terminated.
% 99.06/13.23 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------