TSTP Solution File: NUM783^4 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM783^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.u0EY1TXG5n true
% Computer : n017.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 12:44:07 EDT 2023
% Result : Theorem 96.98s 13.08s
% Output : Refutation 96.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM783^4 : TPTP v8.1.2. Released v7.1.0.
% 0.10/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.u0EY1TXG5n true
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 14:15:55 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.35 % Python version: Python 3.6.8
% 0.12/0.35 % Running in HO mode
% 0.20/0.67 % Total configuration time : 828
% 0.20/0.67 % Estimated wc time : 1656
% 0.20/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.13/0.73 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.13/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.27/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.27/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.27/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.27/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 96.98/13.08 % Solved by lams/40_b.comb.sh.
% 96.98/13.08 % done 286 iterations in 12.265s
% 96.98/13.08 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 96.98/13.08 % SZS output start Refutation
% 96.98/13.08 thf('#ty_enc9_type', type, '#ty_enc9': (($i > $o) > $o) > ($i > $i > $o) > $i > $o).
% 96.98/13.08 thf('#ty_enc15_type', type, '#ty_enc15': ($o > $o > $o) > ($i > $o) > $i > $o > $o).
% 96.98/13.08 thf(rt_is_type, type, rt_is: $i > $i > $o).
% 96.98/13.08 thf('#ty_enc13_type', type, '#ty_enc13': (($o > $o > $o) > ($i > $o) > $i >
% 96.98/13.08 $o > $o) >
% 96.98/13.08 ($i > $o > $o > $o) > $i >
% 96.98/13.08 ($i > $o) > $i > $o > $o).
% 96.98/13.08 thf(lessf_type, type, lessf: $i > $i > $o).
% 96.98/13.08 thf(inf_type, type, inf: $i > $i > $o).
% 96.98/13.08 thf(orec3_type, type, orec3: $o > $o > $o > $o).
% 96.98/13.08 thf(rt_less_type, type, rt_less: $i > $i > $o).
% 96.98/13.08 thf(and3_type, type, and3: $o > $o > $o > $o).
% 96.98/13.08 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 96.98/13.08 thf('#sk2_type', type, '#sk2': $i).
% 96.98/13.08 thf(in_type, type, in: $i > $i > $o).
% 96.98/13.08 thf('#ty_enc8_type', type, '#ty_enc8': ($i > $i > $o) > $i > $i > $o).
% 96.98/13.08 thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
% 96.98/13.08 thf('#ty_enc16_type', type, '#ty_enc16': ($i > $o > $o) > ($i > $o) > $i > $o).
% 96.98/13.08 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 96.98/13.08 thf('#sk3_type', type, '#sk3': $i).
% 96.98/13.08 thf(l_ec_type, type, l_ec: $o > $o > $o).
% 96.98/13.08 thf(ect_type, type, ect: $i > ($i > $i > $o) > $i).
% 96.98/13.08 thf(imp_type, type, imp: $o > $o > $o).
% 96.98/13.08 thf(rat_type, type, rat: $i).
% 96.98/13.08 thf(ec3_type, type, ec3: $o > $o > $o > $o).
% 96.98/13.08 thf(frac_type, type, frac: $i).
% 96.98/13.08 thf(e_in_type, type, e_in: $i > ($i > $o) > $i > $i).
% 96.98/13.08 thf(n_eq_type, type, n_eq: $i > $i > $o).
% 96.98/13.08 thf(d_and_type, type, d_and: $o > $o > $o).
% 96.98/13.08 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 96.98/13.08 thf(ecect_type, type, ecect: $i > ($i > $i > $o) > $i > $i).
% 96.98/13.08 thf(anec_type, type, anec: $i > ($i > $i > $o) > $i > $o).
% 96.98/13.08 thf('#ty_enc12_type', type, '#ty_enc12': ($i > ($i > $o) > $i > $o > $o) >
% 96.98/13.08 ($i > $o) > $i > $i > $o > $o).
% 96.98/13.08 thf('#ty_enc10_type', type, '#ty_enc10': ($i > ($i > $o) > $i > $o) >
% 96.98/13.08 ($i > $i > $o) > $i > $i > $o).
% 96.98/13.08 thf(l_or_type, type, l_or: $o > $o > $o).
% 96.98/13.08 thf(class_type, type, class: $i > $i).
% 96.98/13.08 thf(moref_type, type, moref: $i > $i > $o).
% 96.98/13.08 thf(d_not_type, type, d_not: $o > $o).
% 96.98/13.08 thf('#ty_enc14_type', type, '#ty_enc14': ($o > $o > $o > $o) > ($i > $o) >
% 96.98/13.08 $i > $o > $o > $o).
% 96.98/13.08 thf(power_type, type, power: $i > $i).
% 96.98/13.08 thf('#ty_enc11_type', type, '#ty_enc11': (($i > $o > $o) > ($i > $o) > $i > $o) >
% 96.98/13.08 ($i > $i > $o > $o) > $i >
% 96.98/13.08 ($i > $o) > $i > $o).
% 96.98/13.08 thf(or3_type, type, or3: $o > $o > $o > $o).
% 96.98/13.08 thf(rt_more_type, type, rt_more: $i > $i > $o).
% 96.98/13.08 thf(e_is_type, type, e_is: $i > $i > $i > $o).
% 96.98/13.08 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 96.98/13.08 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 96.98/13.08 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 96.98/13.08 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 96.98/13.08 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 96.98/13.08 thf(satz81a, conjecture,
% 96.98/13.08 (all_of @
% 96.98/13.08 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @
% 96.98/13.08 ( ^[X0:$i]:
% 96.98/13.08 ( all_of @
% 96.98/13.08 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @
% 96.98/13.08 ( ^[X1:$i]:
% 96.98/13.08 ( or3 @
% 96.98/13.08 ( rt_is @ X0 @ X1 ) @ ( rt_more @ X0 @ X1 ) @
% 96.98/13.08 ( rt_less @ X0 @ X1 ) ) ) ) ))).
% 96.98/13.08 thf(zf_stmt_0, negated_conjecture,
% 96.98/13.08 (~( all_of @
% 96.98/13.08 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @
% 96.98/13.08 ( ^[X0:$i]:
% 96.98/13.08 ( all_of @
% 96.98/13.08 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @
% 96.98/13.08 ( ^[X1:$i]:
% 96.98/13.08 ( or3 @
% 96.98/13.08 ( rt_is @ X0 @ X1 ) @ ( rt_more @ X0 @ X1 ) @
% 96.98/13.08 ( rt_less @ X0 @ X1 ) ) ) ) ) )),
% 96.98/13.08 inference('cnf.neg', [status(esa)], [satz81a])).
% 96.98/13.08 thf(zip_derived_cl491, plain,
% 96.98/13.08 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @
% 96.98/13.08 (^[Y0 : $i]:
% 96.98/13.08 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @
% 96.98/13.08 (^[Y1 : $i]:
% 96.98/13.08 (or3 @ (rt_is @ Y0 @ Y1) @ (rt_more @ Y0 @ Y1) @
% 96.98/13.08 (rt_less @ Y0 @ Y1))))))),
% 96.98/13.08 inference('cnf', [status(esa)], [zf_stmt_0])).
% 96.98/13.08 thf(zip_derived_cl492, plain,
% 96.98/13.08 (~ (all_of @ ((('#C') @ in @ rat)) @
% 96.98/13.08 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#B') @ ((('#B') @ or3)) @ rt_is)))) @
% 96.98/13.08 rt_more)))) @
% 96.98/13.08 rt_less)))))),
% 96.98/13.08 inference('lams2combs', [status(thm)], [zip_derived_cl491])).
% 96.98/13.08 thf(def_ect, axiom,(( ect @ (X0)@ (X1)) =
% 96.98/13.08 ((d_Sep @ (power @ X0) @ (anec @ X0 @ X1))))).
% 96.98/13.08 thf('0', plain,
% 96.98/13.08 (![X1:( $i > $i > $o ),X0:$i]:
% 96.98/13.08 ( ( ect @ X0 @ X1 ) = ( d_Sep @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) ) )),
% 96.98/13.08 define([status(thm)])).
% 96.98/13.08 thf(def_rat, axiom,(( rat ) = ((ect @ frac @ n_eq)))).
% 96.98/13.08 thf('1', plain, (( rat ) = ( ect @ frac @ n_eq )), define([status(thm)])).
% 96.98/13.08 thf(zip_derived_cl628, plain,
% 96.98/13.08 (~ (all_of @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 96.98/13.08 ((('#B') @ (all_of @
% 96.98/13.08 ((('#C') @ in @
% 96.98/13.08 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#B') @ ((('#B') @ or3)) @ rt_is)))) @
% 96.98/13.08 rt_more)))) @
% 96.98/13.08 rt_less)))))),
% 96.98/13.08 inference('rw', [status(thm)], [zip_derived_cl492, '0', '1'])).
% 96.98/13.08 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 96.98/13.08 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 96.98/13.08 thf('2', plain,
% 96.98/13.08 (![X0:( $i > $o ),X1:( $i > $o )]:
% 96.98/13.08 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 96.98/13.08 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 96.98/13.08 inference('rw.lit', [status(esa)], [def_all_of])).
% 96.98/13.08 thf(zip_derived_cl629, plain,
% 96.98/13.08 (~ (((!!) @ (^[Y0 : $i]:
% 96.98/13.08 (((is_of @ Y0 @
% 96.98/13.08 ((('#C') @ in @
% 96.98/13.08 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.98/13.08 ((('#B') @ (all_of @
% 96.98/13.08 ((('#C') @ in @
% 96.98/13.08 (d_Sep @ (power @ frac) @
% 96.98/13.08 (anec @ frac @ n_eq))))) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#B') @ ((('#B') @ or3)) @
% 96.98/13.08 rt_is)))) @
% 96.98/13.08 rt_more)))) @
% 96.98/13.08 rt_less)) @
% 96.98/13.08 Y0)))))))),
% 96.98/13.08 inference('rw_clause', [status(thm)], [zip_derived_cl628, '2'])).
% 96.98/13.08 thf(zip_derived_cl630, plain,
% 96.98/13.08 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 96.98/13.08 ((('#C') @ is_of @
% 96.98/13.08 ((('#C') @ in @
% 96.98/13.08 (d_Sep @ (power @ frac) @
% 96.98/13.08 (anec @ frac @ n_eq)))))))) @
% 96.98/13.08 ((('#B') @ (all_of @
% 96.98/13.08 ((('#C') @ in @
% 96.98/13.08 (d_Sep @ (power @ frac) @
% 96.98/13.08 (anec @ frac @ n_eq))))) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#B') @ ((('#B') @ or3)) @
% 96.98/13.08 rt_is)))) @
% 96.98/13.08 rt_more)))) @
% 96.98/13.08 rt_less))))))))),
% 96.98/13.08 inference('comb-normalize', [status(thm)], [zip_derived_cl629])).
% 96.98/13.08 thf(zip_derived_cl631, plain,
% 96.98/13.08 (~ (((is_of @ '#sk2' @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.98/13.08 (all_of @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 96.98/13.08 ((('#S') @ ((('#S') @ ((('#B') @ or3 @ (rt_is @ '#sk2'))) @
% 96.98/13.08 (rt_more @ '#sk2'))) @
% 96.98/13.08 (rt_less @ '#sk2'))))))),
% 96.98/13.08 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl630])).
% 96.98/13.08 thf(zip_derived_cl633, plain,
% 96.98/13.08 (~ (all_of @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 96.98/13.08 ((('#S') @ ((('#S') @ ((('#B') @ or3 @ (rt_is @ '#sk2'))) @
% 96.98/13.08 (rt_more @ '#sk2'))) @
% 96.98/13.08 (rt_less @ '#sk2'))))),
% 96.98/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl631])).
% 96.98/13.08 thf(zip_derived_cl634, plain,
% 96.98/13.08 (~ (((!!) @ (^[Y0 : $i]:
% 96.98/13.08 (((is_of @ Y0 @
% 96.98/13.08 ((('#C') @ in @
% 96.98/13.08 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.98/13.08 ((('#S') @ ((('#S') @ ((('#B') @ or3 @ (rt_is @ '#sk2'))) @
% 96.98/13.08 (rt_more @ '#sk2'))) @
% 96.98/13.08 (rt_less @ '#sk2') @ Y0)))))))),
% 96.98/13.08 inference('rw_clause', [status(thm)], [zip_derived_cl633, '2'])).
% 96.98/13.08 thf(zip_derived_cl635, plain,
% 96.98/13.08 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 96.98/13.08 ((('#C') @ is_of @
% 96.98/13.08 ((('#C') @ in @
% 96.98/13.08 (d_Sep @ (power @ frac) @
% 96.98/13.08 (anec @ frac @ n_eq)))))))) @
% 96.98/13.08 ((('#S') @ ((('#S') @ ((('#B') @ or3 @ (rt_is @ '#sk2'))) @
% 96.98/13.08 (rt_more @ '#sk2'))) @
% 96.98/13.08 (rt_less @ '#sk2')))))))),
% 96.98/13.08 inference('comb-normalize', [status(thm)], [zip_derived_cl634])).
% 96.98/13.08 thf(zip_derived_cl636, plain,
% 96.98/13.08 (~ (((is_of @ '#sk3' @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.98/13.08 (or3 @ (rt_is @ '#sk2' @ '#sk3') @ (rt_more @ '#sk2' @ '#sk3') @
% 96.98/13.08 (rt_less @ '#sk2' @ '#sk3'))))),
% 96.98/13.08 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl635])).
% 96.98/13.08 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
% 96.98/13.08 thf('3', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
% 96.98/13.08 define([status(thm)])).
% 96.98/13.08 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
% 96.98/13.08 thf('4', plain,
% 96.98/13.08 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
% 96.98/13.08 define([status(thm)])).
% 96.98/13.08 thf(def_or3, axiom,(( or3 @ (X0)@ (X1)@ (X2)) =
% 96.98/13.08 ((l_or @ X0 @ (l_or @ X1 @ X2))))).
% 96.98/13.08 thf('5', plain,
% 96.98/13.08 (![X2:$o,X1:$o,X0:$o]:
% 96.98/13.08 ( ( or3 @ X0 @ X1 @ X2 ) = ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) )),
% 96.98/13.08 define([status(thm)])).
% 96.98/13.08 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))).
% 96.98/13.08 thf('6', plain,
% 96.98/13.08 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )),
% 96.98/13.08 define([status(thm)])).
% 96.98/13.08 thf(def_e_in, axiom,(( e_in @ (X1)@ (X2)@ (X0)) = ((X0)))).
% 96.98/13.08 thf('7', plain,
% 96.98/13.08 (![X2:( $i > $o ),X1:$i,X0:$i]: ( ( e_in @ X1 @ X2 @ X0 ) = ( X0 ) )),
% 96.98/13.08 define([status(thm)])).
% 96.98/13.08 thf(def_ecect, axiom,(( ecect @ (X0)@ (X1)@ (X2)) =
% 96.98/13.08 ((e_in @ (power @ X0) @ (anec @ X0 @ X1) @ X2)))).
% 96.98/13.08 thf('8', plain,
% 96.98/13.08 (![X2:$i,X1:( $i > $i > $o ),X0:$i]:
% 96.98/13.08 ( ( ecect @ X0 @ X1 @ X2 ) =
% 96.98/13.08 ( e_in @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) @ X2 ) )),
% 96.98/13.08 define([status(thm)])).
% 96.98/13.08 thf(def_rt_is, axiom,(( rt_is @ (X0)@ (X1)) = ((e_is @ rat @ X0 @ X1)))).
% 96.98/13.08 thf('9', plain,
% 96.98/13.08 (![X1:$i,X0:$i]: ( ( rt_is @ X0 @ X1 ) = ( e_is @ rat @ X0 @ X1 ) )),
% 96.98/13.08 define([status(thm)])).
% 96.98/13.08 thf(def_class, axiom,(( class @ (X0)) = ((ecect @ frac @ n_eq @ X0)))).
% 96.98/13.08 thf('10', plain,
% 96.98/13.08 (![X0:$i]: ( ( class @ X0 ) = ( ecect @ frac @ n_eq @ X0 ) )),
% 96.98/13.08 define([status(thm)])).
% 96.98/13.08 thf(def_rt_more, axiom,(( rt_more @ (X0)@ (X1)) =
% 96.98/13.08 ((l_some @ frac @
% 96.98/13.08 (^[Y0 : $i]:
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 (^[Y1 : $i]:
% 96.98/13.08 (and3 @ (inf @ Y0 @ (class @ X0)) @ (inf @ Y1 @ (class @ X1)) @
% 96.98/13.08 (moref @ Y0 @ Y1))))))))).
% 96.98/13.08 thf('11', plain,
% 96.98/13.08 (![X1:$i,X0:$i]:
% 96.98/13.08 ( ( rt_more @ X0 @ X1 ) =
% 96.98/13.08 ( l_some @
% 96.98/13.08 frac @
% 96.98/13.08 ( ^[V_1:$i]:
% 96.98/13.08 ( l_some @
% 96.98/13.08 frac @
% 96.98/13.08 ( ^[V_2:$i]:
% 96.98/13.08 ( and3 @
% 96.98/13.08 ( inf @ V_1 @ ( class @ X0 ) ) @
% 96.98/13.08 ( inf @ V_2 @ ( class @ X1 ) ) @ ( moref @ V_1 @ V_2 ) ) ) ) ) ) )),
% 96.98/13.08 define([status(thm)])).
% 96.98/13.08 thf(def_rt_less, axiom,(( rt_less @ (X0)@ (X1)) =
% 96.98/13.08 ((l_some @ frac @
% 96.98/13.08 (^[Y0 : $i]:
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 (^[Y1 : $i]:
% 96.98/13.08 (and3 @ (inf @ Y0 @ (class @ X0)) @ (inf @ Y1 @ (class @ X1)) @
% 96.98/13.08 (lessf @ Y0 @ Y1))))))))).
% 96.98/13.08 thf('12', plain,
% 96.98/13.08 (![X1:$i,X0:$i]:
% 96.98/13.08 ( ( rt_less @ X0 @ X1 ) =
% 96.98/13.08 ( l_some @
% 96.98/13.08 frac @
% 96.98/13.08 ( ^[V_1:$i]:
% 96.98/13.08 ( l_some @
% 96.98/13.08 frac @
% 96.98/13.08 ( ^[V_2:$i]:
% 96.98/13.08 ( and3 @
% 96.98/13.08 ( inf @ V_1 @ ( class @ X0 ) ) @
% 96.98/13.08 ( inf @ V_2 @ ( class @ X1 ) ) @ ( lessf @ V_1 @ V_2 ) ) ) ) ) ) )),
% 96.98/13.08 define([status(thm)])).
% 96.98/13.08 thf(zip_derived_cl637, plain,
% 96.98/13.08 (~ (((is_of @ '#sk3' @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.98/13.08 (imp @ (imp @ ((('#sk2') = ('#sk3'))) @ ($false)) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ '#sk2')))))) @
% 96.98/13.08 ((('#C') @ inf @ '#sk3')))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ '#sk2')))))) @
% 96.98/13.08 ((('#C') @ inf @ '#sk3')))))) @
% 96.98/13.08 lessf)))))))))),
% 96.98/13.08 inference('rw', [status(thm)],
% 96.98/13.08 [zip_derived_cl636, '3', '3', '4', '4', '5', '6', '7', '7',
% 96.98/13.08 '0', '8', '8', '1', '9', '10', '10', '11', '12'])).
% 96.98/13.08 thf(zip_derived_cl639, plain,
% 96.98/13.08 (~ (imp @ (imp @ ((('#sk2') = ('#sk3'))) @ ($false)) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ '#sk2')))))) @
% 96.98/13.08 ((('#C') @ inf @ '#sk3')))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ '#sk2')))))) @
% 96.98/13.08 ((('#C') @ inf @ '#sk3')))))) @
% 96.98/13.08 lessf)))))))),
% 96.98/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl637])).
% 96.98/13.08 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
% 96.98/13.08 thf('13', plain,
% 96.98/13.08 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
% 96.98/13.08 inference('rw.lit', [status(esa)], [def_imp])).
% 96.98/13.08 thf(zip_derived_cl640, plain,
% 96.98/13.08 (~ (((imp @ ((('#sk2') = ('#sk3'))) @ ($false)) => (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ '#sk2')))))) @
% 96.98/13.08 ((('#C') @ inf @ '#sk3')))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ '#sk2')))))) @
% 96.98/13.08 ((('#C') @ inf @ '#sk3')))))) @
% 96.98/13.08 lessf))))))))),
% 96.98/13.08 inference('rw_clause', [status(thm)], [zip_derived_cl639, '13'])).
% 96.98/13.08 thf(zip_derived_cl641, plain, ( (imp @ ((('#sk2') = ('#sk3'))) @ ($false))),
% 96.98/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl640])).
% 96.98/13.08 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
% 96.98/13.08 thf('14', plain,
% 96.98/13.08 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
% 96.98/13.08 inference('rw.lit', [status(esa)], [def_imp])).
% 96.98/13.08 thf(zip_derived_cl643, plain, ( ((((('#sk2') = ('#sk3'))) => ($false)))),
% 96.98/13.08 inference('rw_clause', [status(thm)], [zip_derived_cl641, '14'])).
% 96.98/13.08 thf(zip_derived_cl645, plain, ( (((~) @ ((('#sk2') = ('#sk3')))))),
% 96.98/13.08 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl643])).
% 96.98/13.08 thf(zip_derived_cl646, plain, ((('#sk2') != ('#sk3'))),
% 96.98/13.08 inference('simplify nested equalities', [status(thm)],
% 96.98/13.08 [zip_derived_cl645])).
% 96.98/13.08 thf(zip_derived_cl632, plain,
% 96.98/13.08 ( (is_of @ '#sk2' @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))),
% 96.98/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl631])).
% 96.98/13.08 thf(zip_derived_cl8223, plain,
% 96.98/13.08 ( (is_of @ '#sk2' @
% 96.98/13.08 ('#ty_enc8' @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))),
% 96.98/13.08 inference('remove_ty_args', [status(thm)], [zip_derived_cl632])).
% 96.98/13.08 thf(zip_derived_cl638, plain,
% 96.98/13.08 ( (is_of @ '#sk3' @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))),
% 96.98/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl637])).
% 96.98/13.08 thf(zip_derived_cl8224, plain,
% 96.98/13.08 ( (is_of @ '#sk3' @
% 96.98/13.08 ('#ty_enc8' @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))),
% 96.98/13.08 inference('remove_ty_args', [status(thm)], [zip_derived_cl638])).
% 96.98/13.08 thf(zip_derived_cl642, plain,
% 96.98/13.08 (~ (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ '#sk2')))))) @
% 96.98/13.08 ((('#C') @ inf @ '#sk3')))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ '#sk2')))))) @
% 96.98/13.08 ((('#C') @ inf @ '#sk3')))))) @
% 96.98/13.08 lessf))))))),
% 96.98/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl640])).
% 96.98/13.08 thf(zip_derived_cl644, plain,
% 96.98/13.08 (~ (((imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ '#sk2')))))) @
% 96.98/13.08 ((('#C') @ inf @ '#sk3')))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) => (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ '#sk2')))))) @
% 96.98/13.08 ((('#C') @ inf @ '#sk3')))))) @
% 96.98/13.08 lessf)))))))),
% 96.98/13.08 inference('rw_clause', [status(thm)], [zip_derived_cl642, '13'])).
% 96.98/13.08 thf(zip_derived_cl648, plain,
% 96.98/13.08 (~ (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ '#sk2')))))) @
% 96.98/13.08 ((('#C') @ inf @ '#sk3')))))) @
% 96.98/13.08 lessf)))))),
% 96.98/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl644])).
% 96.98/13.08 thf(zip_derived_cl8225, plain,
% 96.98/13.08 (~ (l_some @ frac @
% 96.98/13.08 ('#ty_enc9' @ (l_some @ frac) @
% 96.98/13.08 ('#ty_enc10' @
% 96.98/13.08 ('#ty_enc11' @ '#ty_enc16' @
% 96.98/13.08 ('#ty_enc12' @
% 96.98/13.08 ('#ty_enc13' @ '#ty_enc15' @
% 96.98/13.08 ('#ty_enc14' @ and3 @ ('#ty_enc8' @ inf @ '#sk2'))) @
% 96.98/13.08 ('#ty_enc8' @ inf @ '#sk3'))) @
% 96.98/13.08 lessf)))),
% 96.98/13.08 inference('remove_ty_args', [status(thm)], [zip_derived_cl648])).
% 96.98/13.08 thf(zip_derived_cl647, plain,
% 96.98/13.08 ( (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ '#sk2')))))) @
% 96.98/13.08 ((('#C') @ inf @ '#sk3')))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false))),
% 96.98/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl644])).
% 96.98/13.08 thf(zip_derived_cl649, plain,
% 96.98/13.08 ( (((l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ '#sk2')))))) @
% 96.98/13.08 ((('#C') @ inf @ '#sk3')))))) @
% 96.98/13.08 moref))))) =>
% 96.98/13.08 ($false)))),
% 96.98/13.08 inference('rw_clause', [status(thm)], [zip_derived_cl647, '14'])).
% 96.98/13.08 thf(zip_derived_cl650, plain,
% 96.98/13.08 ( (((~) @ (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ '#sk2')))))) @
% 96.98/13.08 ((('#C') @ inf @ '#sk3')))))) @
% 96.98/13.08 moref)))))))),
% 96.98/13.08 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl649])).
% 96.98/13.08 thf(zip_derived_cl651, plain,
% 96.98/13.08 (~ (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ '#sk2')))))) @
% 96.98/13.08 ((('#C') @ inf @ '#sk3')))))) @
% 96.98/13.08 moref)))))),
% 96.98/13.08 inference('simplify nested equalities', [status(thm)],
% 96.98/13.08 [zip_derived_cl650])).
% 96.98/13.08 thf(zip_derived_cl8226, plain,
% 96.98/13.08 (~ (l_some @ frac @
% 96.98/13.08 ('#ty_enc9' @ (l_some @ frac) @
% 96.98/13.08 ('#ty_enc10' @
% 96.98/13.08 ('#ty_enc11' @ '#ty_enc16' @
% 96.98/13.08 ('#ty_enc12' @
% 96.98/13.08 ('#ty_enc13' @ '#ty_enc15' @
% 96.98/13.08 ('#ty_enc14' @ and3 @ ('#ty_enc8' @ inf @ '#sk2'))) @
% 96.98/13.08 ('#ty_enc8' @ inf @ '#sk3'))) @
% 96.98/13.08 moref)))),
% 96.98/13.08 inference('remove_ty_args', [status(thm)], [zip_derived_cl651])).
% 96.98/13.08 thf(satz81, axiom,
% 96.98/13.08 (all_of @
% 96.98/13.08 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @
% 96.98/13.08 ( ^[X0:$i]:
% 96.98/13.08 ( all_of @
% 96.98/13.08 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @
% 96.98/13.08 ( ^[X1:$i]:
% 96.98/13.08 ( orec3 @
% 96.98/13.08 ( rt_is @ X0 @ X1 ) @ ( rt_more @ X0 @ X1 ) @
% 96.98/13.08 ( rt_less @ X0 @ X1 ) ) ) ) ))).
% 96.98/13.08 thf(zip_derived_cl489, plain,
% 96.98/13.08 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @
% 96.98/13.08 (^[Y0 : $i]:
% 96.98/13.08 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @
% 96.98/13.08 (^[Y1 : $i]:
% 96.98/13.08 (orec3 @ (rt_is @ Y0 @ Y1) @ (rt_more @ Y0 @ Y1) @
% 96.98/13.08 (rt_less @ Y0 @ Y1))))))),
% 96.98/13.08 inference('cnf', [status(esa)], [satz81])).
% 96.98/13.08 thf(zip_derived_cl490, plain,
% 96.98/13.08 ( (all_of @ ((('#C') @ in @ rat)) @
% 96.98/13.08 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#B') @ ((('#B') @ orec3)) @ rt_is)))) @
% 96.98/13.08 rt_more)))) @
% 96.98/13.08 rt_less)))))),
% 96.98/13.08 inference('lams2combs', [status(thm)], [zip_derived_cl489])).
% 96.98/13.08 thf(zip_derived_cl1681, plain,
% 96.98/13.08 ( (all_of @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 96.98/13.08 ((('#B') @ (all_of @
% 96.98/13.08 ((('#C') @ in @
% 96.98/13.08 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#B') @ ((('#B') @ orec3)) @ rt_is)))) @
% 96.98/13.08 rt_more)))) @
% 96.98/13.08 rt_less)))))),
% 96.98/13.08 inference('rw', [status(thm)], [zip_derived_cl490, '0', '1'])).
% 96.98/13.08 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 96.98/13.08 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 96.98/13.08 thf('15', plain,
% 96.98/13.08 (![X0:( $i > $o ),X1:( $i > $o )]:
% 96.98/13.08 ( ( all_of @ X0 @ X1 ) <=>
% 96.98/13.08 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 96.98/13.08 inference('rw.lit', [status(esa)], [def_all_of])).
% 96.98/13.08 thf(zip_derived_cl1682, plain,
% 96.98/13.08 ( (((!!) @ (^[Y0 : $i]:
% 96.98/13.08 (((is_of @ Y0 @
% 96.98/13.08 ((('#C') @ in @
% 96.98/13.08 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.98/13.08 ((('#B') @ (all_of @
% 96.98/13.08 ((('#C') @ in @
% 96.98/13.08 (d_Sep @ (power @ frac) @
% 96.98/13.08 (anec @ frac @ n_eq))))) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#B') @ ((('#B') @ orec3)) @
% 96.98/13.08 rt_is)))) @
% 96.98/13.08 rt_more)))) @
% 96.98/13.08 rt_less)) @
% 96.98/13.08 Y0)))))))),
% 96.98/13.08 inference('rw_clause', [status(thm)], [zip_derived_cl1681, '15'])).
% 96.98/13.08 thf(zip_derived_cl1683, plain,
% 96.98/13.08 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 96.98/13.08 ((('#C') @ is_of @
% 96.98/13.08 ((('#C') @ in @
% 96.98/13.08 (d_Sep @ (power @ frac) @
% 96.98/13.08 (anec @ frac @ n_eq)))))))) @
% 96.98/13.08 ((('#B') @ (all_of @
% 96.98/13.08 ((('#C') @ in @
% 96.98/13.08 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#B') @ ((('#B') @ orec3)) @
% 96.98/13.08 rt_is)))) @
% 96.98/13.08 rt_more)))) @
% 96.98/13.08 rt_less))))))))),
% 96.98/13.08 inference('comb-normalize', [status(thm)], [zip_derived_cl1682])).
% 96.98/13.08 thf(zip_derived_cl1684, plain,
% 96.98/13.08 (![X2 : $i]:
% 96.98/13.08 (((is_of @ X2 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.98/13.08 (all_of @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 96.98/13.08 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X2))) @
% 96.98/13.08 (rt_more @ X2))) @
% 96.98/13.08 (rt_less @ X2))))))),
% 96.98/13.08 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1683])).
% 96.98/13.08 thf(zip_derived_cl1685, plain,
% 96.98/13.08 (![X2 : $i]:
% 96.98/13.08 (~ (is_of @ X2 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | (all_of @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @
% 96.98/13.08 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X2))) @
% 96.98/13.08 (rt_more @ X2))) @
% 96.98/13.08 (rt_less @ X2)))))),
% 96.98/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1684])).
% 96.98/13.08 thf(zip_derived_cl1686, plain,
% 96.98/13.08 (![X0 : $i]:
% 96.98/13.08 ( (((!!) @ (^[Y0 : $i]:
% 96.98/13.08 (((is_of @ Y0 @
% 96.98/13.08 ((('#C') @ in @
% 96.98/13.08 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.98/13.08 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X0))) @
% 96.98/13.08 (rt_more @ X0))) @
% 96.98/13.08 (rt_less @ X0) @ Y0)))))))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.98/13.08 inference('rw_clause', [status(thm)], [zip_derived_cl1685, '15'])).
% 96.98/13.08 thf(zip_derived_cl1687, plain,
% 96.98/13.08 (![X0 : $i]:
% 96.98/13.08 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 96.98/13.08 ((('#C') @ is_of @
% 96.98/13.08 ((('#C') @ in @
% 96.98/13.08 (d_Sep @ (power @ frac) @
% 96.98/13.08 (anec @ frac @ n_eq)))))))) @
% 96.98/13.08 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X0))) @
% 96.98/13.08 (rt_more @ X0))) @
% 96.98/13.08 (rt_less @ X0)))))))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.98/13.08 inference('comb-normalize', [status(thm)], [zip_derived_cl1686])).
% 96.98/13.08 thf(zip_derived_cl1688, plain,
% 96.98/13.08 (![X0 : $i, X2 : $i]:
% 96.98/13.08 ( (((is_of @ X2 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.98/13.08 (orec3 @ (rt_is @ X0 @ X2) @ (rt_more @ X0 @ X2) @
% 96.98/13.08 (rt_less @ X0 @ X2))))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.98/13.08 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1687])).
% 96.98/13.08 thf(def_l_ec, axiom,(( l_ec @ (X0)@ (X1)) = ((imp @ X0 @ (d_not @ X1))))).
% 96.98/13.08 thf('16', plain,
% 96.98/13.08 (![X1:$o,X0:$o]: ( ( l_ec @ X0 @ X1 ) = ( imp @ X0 @ ( d_not @ X1 ) ) )),
% 96.98/13.08 define([status(thm)])).
% 96.98/13.08 thf(def_d_and, axiom,(( d_and @ (X0)@ (X1)) = ((d_not @ (l_ec @ X0 @ X1))))).
% 96.98/13.08 thf('17', plain,
% 96.98/13.08 (![X1:$o,X0:$o]: ( ( d_and @ X0 @ X1 ) = ( d_not @ ( l_ec @ X0 @ X1 ) ) )),
% 96.98/13.08 define([status(thm)])).
% 96.98/13.08 thf(def_and3, axiom,(( and3 @ (X0)@ (X1)@ (X2)) =
% 96.98/13.08 ((d_and @ X0 @ (d_and @ X1 @ X2))))).
% 96.98/13.08 thf('18', plain,
% 96.98/13.08 (![X2:$o,X1:$o,X0:$o]:
% 96.98/13.08 ( ( and3 @ X0 @ X1 @ X2 ) = ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) )),
% 96.98/13.08 define([status(thm)])).
% 96.98/13.08 thf(def_ec3, axiom,(( ec3 @ (X0)@ (X1)@ (X2)) =
% 96.98/13.08 ((and3 @ (l_ec @ X0 @ X1) @ (l_ec @ X1 @ X2) @ (l_ec @ X2 @ X0))))).
% 96.98/13.08 thf('19', plain,
% 96.98/13.08 (![X2:$o,X1:$o,X0:$o]:
% 96.98/13.08 ( ( ec3 @ X0 @ X1 @ X2 ) =
% 96.98/13.08 ( and3 @ ( l_ec @ X0 @ X1 ) @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X0 ) ) )),
% 96.98/13.08 define([status(thm)])).
% 96.98/13.08 thf(def_orec3, axiom,(( orec3 @ (X0)@ (X1)@ (X2)) =
% 96.98/13.08 ((d_and @ (or3 @ X0 @ X1 @ X2) @ (ec3 @ X0 @ X1 @ X2))))).
% 96.98/13.08 thf('20', plain,
% 96.98/13.08 (![X2:$o,X1:$o,X0:$o]:
% 96.98/13.08 ( ( orec3 @ X0 @ X1 @ X2 ) =
% 96.98/13.08 ( d_and @ ( or3 @ X0 @ X1 @ X2 ) @ ( ec3 @ X0 @ X1 @ X2 ) ) )),
% 96.98/13.08 define([status(thm)])).
% 96.98/13.08 thf(zip_derived_cl1689, plain,
% 96.98/13.08 (![X0 : $i, X2 : $i]:
% 96.98/13.08 ( (((is_of @ X2 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) =>
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @ (imp @ (((X0) = (X2))) @ ($false)) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X2)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X2)))))) @
% 96.98/13.08 lessf))))))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @ (((X0) = (X2))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X2)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X2)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X2)))))) @
% 96.98/13.08 lessf))))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X2)))))) @
% 96.98/13.08 lessf))))) @
% 96.98/13.08 (imp @ (((X0) = (X2))) @ ($false))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 ($false))))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.98/13.08 inference('rw', [status(thm)],
% 96.98/13.08 [zip_derived_cl1688, '3', '3', '3', '3', '3', '3', '3', '3',
% 96.98/13.08 '3', '16', '16', '16', '16', '16', '16', '17', '17', '17',
% 96.98/13.08 '4', '4', '5', '18', '19', '20', '6', '7', '7', '0', '8',
% 96.98/13.08 '8', '1', '9', '10', '10', '11', '12'])).
% 96.98/13.08 thf(zip_derived_cl1690, plain,
% 96.98/13.08 (![X0 : $i, X2 : $i]:
% 96.98/13.08 (~ (is_of @ X2 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @ (imp @ (((X0) = (X2))) @ ($false)) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X2)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X2)))))) @
% 96.98/13.08 lessf))))))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @ (((X0) = (X2))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X2)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X2)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X2)))))) @
% 96.98/13.08 lessf))))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X2)))))) @
% 96.98/13.08 lessf))))) @
% 96.98/13.08 (imp @ (((X0) = (X2))) @ ($false))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 ($false))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.98/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1689])).
% 96.98/13.08 thf(zip_derived_cl1691, plain,
% 96.98/13.08 (![X0 : $i, X1 : $i]:
% 96.98/13.08 ( (((imp @
% 96.98/13.08 (imp @ (imp @ (((X0) = (X1))) @ ($false)) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 lessf))))))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @ (((X0) = (X1))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 lessf))))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 lessf))))) @
% 96.98/13.08 (imp @ (((X0) = (X1))) @ ($false))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 ($false))) =>
% 96.98/13.08 ($false)))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ~ (is_of @ X1 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.98/13.08 inference('rw_clause', [status(thm)], [zip_derived_cl1690, '14'])).
% 96.98/13.08 thf(zip_derived_cl1692, plain,
% 96.98/13.08 (![X0 : $i, X1 : $i]:
% 96.98/13.08 ( (((~) @ (imp @
% 96.98/13.08 (imp @ (imp @ (((X0) = (X1))) @ ($false)) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 lessf))))))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @ (((X0) = (X1))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 lessf))))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 lessf))))) @
% 96.98/13.08 (imp @ (((X0) = (X1))) @ ($false))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 ($false)))))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ~ (is_of @ X1 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.98/13.08 inference('simplify boolean subterms', [status(thm)],
% 96.98/13.08 [zip_derived_cl1691])).
% 96.98/13.08 thf(zip_derived_cl1693, plain,
% 96.98/13.08 (![X0 : $i, X1 : $i]:
% 96.98/13.08 (~ (imp @
% 96.98/13.08 (imp @ (imp @ (((X0) = (X1))) @ ($false)) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 lessf))))))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @ (((X0) = (X1))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 lessf))))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 lessf))))) @
% 96.98/13.08 (imp @ (((X0) = (X1))) @ ($false))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 ($false)))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ~ (is_of @ X1 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.98/13.08 inference('simplify nested equalities', [status(thm)],
% 96.98/13.08 [zip_derived_cl1692])).
% 96.98/13.08 thf(zip_derived_cl1694, plain,
% 96.98/13.08 (![X0 : $i, X1 : $i]:
% 96.98/13.08 (~ (((imp @ (imp @ (((X1) = (X0))) @ ($false)) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 lessf))))))) =>
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @ (((X1) = (X0))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 lessf))))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 lessf))))) @
% 96.98/13.08 (imp @ (((X1) = (X0))) @ ($false))) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 ($false))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 ($false))))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ~ (is_of @ X1 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.98/13.08 inference('rw_clause', [status(thm)], [zip_derived_cl1693, '13'])).
% 96.98/13.08 thf(zip_derived_cl1695, plain,
% 96.98/13.08 (![X0 : $i, X1 : $i]:
% 96.98/13.08 ( (imp @ (imp @ (((X1) = (X0))) @ ($false)) @
% 96.98/13.08 (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 lessf)))))))
% 96.98/13.08 | ~ (is_of @ X1 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.98/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1694])).
% 96.98/13.08 thf(zip_derived_cl1697, plain,
% 96.98/13.08 (![X0 : $i, X1 : $i]:
% 96.98/13.08 ( (((imp @ (((X1) = (X0))) @ ($false)) => (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 lessf))))))))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ~ (is_of @ X1 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.98/13.08 inference('rw_clause', [status(thm)], [zip_derived_cl1695, '14'])).
% 96.98/13.08 thf(zip_derived_cl1699, plain,
% 96.98/13.08 (![X0 : $i, X1 : $i]:
% 96.98/13.08 (~ (imp @ (((X1) = (X0))) @ ($false))
% 96.98/13.08 | (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 lessf))))))
% 96.98/13.08 | ~ (is_of @ X1 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.98/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1697])).
% 96.98/13.08 thf(zip_derived_cl1703, plain,
% 96.98/13.08 (![X0 : $i, X1 : $i]:
% 96.98/13.08 (~ (((((X1) = (X0))) => ($false)))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ~ (is_of @ X1 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 lessf)))))))),
% 96.98/13.08 inference('rw_clause', [status(thm)], [zip_derived_cl1699, '13'])).
% 96.98/13.08 thf(zip_derived_cl1707, plain,
% 96.98/13.08 (![X0 : $i, X1 : $i]:
% 96.98/13.08 (~ (((~) @ (((X1) = (X0)))))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ~ (is_of @ X1 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 lessf)))))))),
% 96.98/13.08 inference('simplify boolean subterms', [status(thm)],
% 96.98/13.08 [zip_derived_cl1703])).
% 96.98/13.08 thf(zip_derived_cl1708, plain,
% 96.98/13.08 (![X0 : $i, X1 : $i]:
% 96.98/13.08 (((X1) = (X0))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ~ (is_of @ X1 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | (imp @
% 96.98/13.08 (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 lessf)))))))),
% 96.98/13.08 inference('simplify nested equalities', [status(thm)],
% 96.98/13.08 [zip_derived_cl1707])).
% 96.98/13.08 thf(zip_derived_cl1709, plain,
% 96.98/13.08 (![X0 : $i, X1 : $i]:
% 96.98/13.08 ( (((imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false)) => (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 lessf)))))))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ~ (is_of @ X1 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ((X0) = (X1)))),
% 96.98/13.08 inference('rw_clause', [status(thm)], [zip_derived_cl1708, '14'])).
% 96.98/13.08 thf(zip_derived_cl1712, plain,
% 96.98/13.08 (![X0 : $i, X1 : $i]:
% 96.98/13.08 (~ (imp @
% 96.98/13.08 (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 moref))))) @
% 96.98/13.08 ($false))
% 96.98/13.08 | (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 lessf)))))
% 96.98/13.08 | ((X0) = (X1))
% 96.98/13.08 | ~ (is_of @ X1 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))),
% 96.98/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1709])).
% 96.98/13.08 thf(zip_derived_cl1715, plain,
% 96.98/13.08 (![X0 : $i, X1 : $i]:
% 96.98/13.08 (~ (((l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 moref))))) =>
% 96.98/13.08 ($false)))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ~ (is_of @ X1 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ((X0) = (X1))
% 96.98/13.08 | (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 lessf))))))),
% 96.98/13.08 inference('rw_clause', [status(thm)], [zip_derived_cl1712, '13'])).
% 96.98/13.08 thf(zip_derived_cl1720, plain,
% 96.98/13.08 (![X0 : $i, X1 : $i]:
% 96.98/13.08 (~ (((~) @ (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 moref)))))))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ~ (is_of @ X1 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ((X0) = (X1))
% 96.98/13.08 | (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 lessf))))))),
% 96.98/13.08 inference('simplify boolean subterms', [status(thm)],
% 96.98/13.08 [zip_derived_cl1715])).
% 96.98/13.08 thf(zip_derived_cl1721, plain,
% 96.98/13.08 (![X0 : $i, X1 : $i]:
% 96.98/13.08 ( (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @ ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 moref)))))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ~ (is_of @ X1 @
% 96.98/13.08 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))
% 96.98/13.08 | ((X0) = (X1))
% 96.98/13.08 | (l_some @ frac @
% 96.98/13.08 ((('#B') @ (l_some @ frac) @
% 96.98/13.08 ((('#S') @ ((('#B') @ ('#S') @
% 96.98/13.08 ((('#C') @ ((('#B') @ ('#B') @
% 96.98/13.08 ((('#B') @ and3 @
% 96.98/13.08 ((('#C') @ inf @ X0)))))) @
% 96.98/13.08 ((('#C') @ inf @ X1)))))) @
% 96.98/13.08 lessf))))))),
% 96.98/13.08 inference('simplify nested equalities', [status(thm)],
% 96.98/13.08 [zip_derived_cl1720])).
% 96.98/13.08 thf(zip_derived_cl8256, plain,
% 96.98/13.08 (![X0 : $i, X1 : $i]:
% 96.98/13.08 ( (l_some @ frac @
% 96.98/13.08 ('#ty_enc9' @ (l_some @ frac) @
% 96.98/13.08 ('#ty_enc10' @
% 96.98/13.08 ('#ty_enc11' @ '#ty_enc16' @
% 96.98/13.08 ('#ty_enc12' @
% 96.98/13.08 ('#ty_enc13' @ '#ty_enc15' @
% 96.98/13.08 ('#ty_enc14' @ and3 @ ('#ty_enc8' @ inf @ X0))) @
% 96.98/13.08 ('#ty_enc8' @ inf @ X1))) @
% 96.98/13.08 moref)))
% 96.98/13.08 | ~ (is_of @ X0 @
% 96.98/13.08 ('#ty_enc8' @ in @
% 96.98/13.08 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))
% 96.98/13.08 | ~ (is_of @ X1 @
% 96.98/13.08 ('#ty_enc8' @ in @
% 96.98/13.08 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))
% 96.98/13.08 | ((X0) = (X1))
% 96.98/13.08 | (l_some @ frac @
% 96.98/13.08 ('#ty_enc9' @ (l_some @ frac) @
% 96.98/13.08 ('#ty_enc10' @
% 96.98/13.08 ('#ty_enc11' @ '#ty_enc16' @
% 96.98/13.08 ('#ty_enc12' @
% 96.98/13.08 ('#ty_enc13' @ '#ty_enc15' @
% 96.98/13.08 ('#ty_enc14' @ and3 @ ('#ty_enc8' @ inf @ X0))) @
% 96.98/13.08 ('#ty_enc8' @ inf @ X1))) @
% 96.98/13.08 lessf))))),
% 96.98/13.08 inference('remove_ty_args', [status(thm)], [zip_derived_cl1721])).
% 96.98/13.08 thf(zip_derived_cl8355, plain, ($false),
% 96.98/13.08 inference('eprover', [status(thm)],
% 96.98/13.08 [zip_derived_cl646, zip_derived_cl8223, zip_derived_cl8224,
% 96.98/13.08 zip_derived_cl8225, zip_derived_cl8226, zip_derived_cl8256])).
% 96.98/13.08
% 96.98/13.08 % SZS output end Refutation
% 96.98/13.08
% 96.98/13.08
% 96.98/13.08 % Terminating...
% 97.48/13.25 % Runner terminated.
% 97.48/13.27 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------