0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.18 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.ECYjtZ3zvr true 0.17/0.38 % Computer : n020.cluster.edu 0.17/0.38 % Model : x86_64 x86_64 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.17/0.38 % Memory : 8042.1875MB 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64 0.17/0.38 % CPULimit : 1200 0.17/0.38 % WCLimit : 120 0.17/0.38 % DateTime : Tue Jul 13 13:17:06 EDT 2021 0.17/0.38 % CPUTime : 0.17/0.38 % Running portfolio for 120 s 0.17/0.38 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.17/0.39 % Number of cores: 8 0.17/0.39 % Python version: Python 3.6.8 0.17/0.39 % Running in HO mode 0.54/0.69 % Total configuration time : 828 0.54/0.69 % Estimated wc time : 983 0.54/0.69 % Estimated cpu time (8 cpus) : 122.875 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.58/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.58/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.58/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.59/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 9.48/1.87 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 53s 68.16/9.30 % Solved by lams/40_b.comb.sh. 68.16/9.30 % running E: timeout 28 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.ECYjtZ3zvr/e_inpute2d956 --cpu-limit=26 --auto-schedule -s -p 68.16/9.30 % done 0 iterations in 8.456s 68.16/9.30 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 68.16/9.30 % SZS output start Refutation 68.16/9.30 thf(rat_type, type, rat: $i). 68.16/9.30 thf('#ty_enc12_type', type, '#ty_enc12': ($i > ($i > $o) > $i > $o > $o) > 68.16/9.30 ($i > $o) > $i > $i > $o > $o). 68.16/9.30 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 68.16/9.30 thf(orec3_type, type, orec3: $o > $o > $o > $o). 68.16/9.30 thf(anec_type, type, anec: $i > ($i > $i > $o) > $i > $o). 68.16/9.30 thf(or3_type, type, or3: $o > $o > $o > $o). 68.16/9.30 thf('#ty_enc16_type', type, '#ty_enc16': ($i > $o > $o) > ($i > $o) > $i > $o). 68.16/9.30 thf(rt_less_type, type, rt_less: $i > $i > $o). 68.16/9.30 thf(n_eq_type, type, n_eq: $i > $i > $o). 68.16/9.30 thf(power_type, type, power: $i > $i). 68.16/9.30 thf(l_or_type, type, l_or: $o > $o > $o). 68.16/9.30 thf(rt_is_type, type, rt_is: $i > $i > $o). 68.16/9.30 thf(frac_type, type, frac: $i). 68.16/9.30 thf(and3_type, type, and3: $o > $o > $o > $o). 68.16/9.30 thf(d_and_type, type, d_and: $o > $o > $o). 68.16/9.30 thf(in_type, type, in: $i > $i > $o). 68.16/9.30 thf(lessf_type, type, lessf: $i > $i > $o). 68.16/9.30 thf(e_in_type, type, e_in: $i > ($i > $o) > $i > $i). 68.16/9.30 thf(imp_type, type, imp: $o > $o > $o). 68.16/9.30 thf('#ty_enc13_type', type, '#ty_enc13': (($o > $o > $o) > ($i > $o) > $i > 68.16/9.30 $o > $o) > 68.16/9.30 ($i > $o > $o > $o) > $i > 68.16/9.30 ($i > $o) > $i > $o > $o). 68.16/9.30 thf(rt_lessis_type, type, rt_lessis: $i > $i > $o). 68.16/9.30 thf('#ty_enc14_type', type, '#ty_enc14': ($o > $o > $o > $o) > ($i > $o) > 68.16/9.30 $i > $o > $o > $o). 68.16/9.30 thf('#sk3_type', type, '#sk3': $i). 68.16/9.30 thf(inf_type, type, inf: $i > $i > $o). 68.16/9.30 thf(moref_type, type, moref: $i > $i > $o). 68.16/9.30 thf(ecect_type, type, ecect: $i > ($i > $i > $o) > $i > $i). 68.16/9.30 thf(ec3_type, type, ec3: $o > $o > $o > $o). 68.16/9.30 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 68.16/9.30 thf('#ty_enc8_type', type, '#ty_enc8': ($i > $i > $o) > $i > $i > $o). 68.16/9.30 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 68.16/9.30 thf(e_is_type, type, e_is: $i > $i > $i > $o). 68.16/9.30 thf('#ty_enc9_type', type, '#ty_enc9': (($i > $o) > $o) > ($i > $i > $o) > $i > $o). 68.16/9.30 thf('#ty_enc11_type', type, '#ty_enc11': (($i > $o > $o) > ($i > $o) > $i > $o) > 68.16/9.30 ($i > $i > $o > $o) > $i > 68.16/9.30 ($i > $o) > $i > $o). 68.16/9.30 thf(class_type, type, class: $i > $i). 68.16/9.30 thf('#ty_enc15_type', type, '#ty_enc15': ($o > $o > $o) > ($i > $o) > $i > $o > $o). 68.16/9.30 thf(l_ec_type, type, l_ec: $o > $o > $o). 68.16/9.30 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 68.16/9.30 thf(rt_more_type, type, rt_more: $i > $i > $o). 68.16/9.30 thf(d_not_type, type, d_not: $o > $o). 68.16/9.30 thf('#ty_enc10_type', type, '#ty_enc10': ($i > ($i > $o) > $i > $o) > 68.16/9.30 ($i > $i > $o) > $i > $i > $o). 68.16/9.30 thf(ect_type, type, ect: $i > ($i > $i > $o) > $i). 68.16/9.30 thf('#sk2_type', type, '#sk2': $i). 68.16/9.30 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 68.16/9.30 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 68.16/9.30 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 68.16/9.30 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 68.16/9.30 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 68.16/9.30 thf(satz81d, conjecture, 68.16/9.30 (all_of @ 68.16/9.30 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 68.16/9.30 ( ^[X0:$i]: 68.16/9.30 ( all_of @ 68.16/9.30 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 68.16/9.30 ( ^[X1:$i]: 68.16/9.30 ( ( rt_lessis @ X0 @ X1 ) => ( d_not @ ( rt_more @ X0 @ X1 ) ) ) ) ) ))). 68.16/9.30 thf(zf_stmt_0, negated_conjecture, 68.16/9.30 (~( all_of @ 68.16/9.30 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 68.16/9.30 ( ^[X0:$i]: 68.16/9.30 ( all_of @ 68.16/9.30 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 68.16/9.30 ( ^[X1:$i]: 68.16/9.30 ( ( rt_lessis @ X0 @ X1 ) => ( d_not @ ( rt_more @ X0 @ X1 ) ) ) ) ) ) )), 68.16/9.30 inference('cnf.neg', [status(esa)], [satz81d])). 68.16/9.30 thf(zip_derived_cl499, plain, 68.16/9.30 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @ 68.16/9.30 (^[Y0 : $i]: 68.16/9.30 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @ 68.16/9.30 (^[Y1 : $i]: 68.16/9.30 (((rt_lessis @ Y0 @ Y1) => (d_not @ (rt_more @ Y0 @ Y1))))))))), 68.16/9.30 inference('cnf', [status(esa)], [zf_stmt_0])). 68.16/9.30 thf(zip_derived_cl500, plain, 68.16/9.30 (~ (all_of @ ((('#C') @ in @ rat)) @ 68.16/9.30 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))) @ 68.16/9.30 ((('#B') @ ((('#B') @ d_not)) @ rt_more)))))))), 68.16/9.30 inference('lams2combs', [status(thm)], [zip_derived_cl499])). 68.16/9.30 thf(def_ect, axiom,(( ect @ (X0)@ (X1)) = 68.16/9.30 ((d_Sep @ (power @ X0) @ (anec @ X0 @ X1))))). 68.16/9.30 thf('0', plain, 68.16/9.30 (![X1:( $i > $i > $o ),X0:$i]: 68.16/9.30 ( ( ect @ X0 @ X1 ) = ( d_Sep @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(def_rat, axiom,(( rat ) = ((ect @ frac @ n_eq)))). 68.16/9.30 thf('1', plain, (( rat ) = ( ect @ frac @ n_eq )), define([status(thm)])). 68.16/9.30 thf(zip_derived_cl636, plain, 68.16/9.30 (~ (all_of @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 68.16/9.30 ((('#B') @ (all_of @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))) @ 68.16/9.30 ((('#B') @ ((('#B') @ d_not)) @ rt_more)))))))), 68.16/9.30 inference('rw', [status(thm)], [zip_derived_cl500, '0', '1'])). 68.16/9.30 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 68.16/9.30 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 68.16/9.30 thf('2', plain, 68.16/9.30 (![X0:( $i > $o ),X1:( $i > $o )]: 68.16/9.30 ( ( ~( all_of @ X0 @ X1 ) ) <=> 68.16/9.30 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 68.16/9.30 inference('rw.lit', [status(esa)], [def_all_of])). 68.16/9.30 thf(zip_derived_cl637, plain, 68.16/9.30 (~ (((!!) @ (^[Y0 : $i]: 68.16/9.30 (((is_of @ Y0 @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 68.16/9.30 ((('#B') @ (all_of @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ 68.16/9.30 (anec @ frac @ n_eq))))) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))) @ 68.16/9.30 ((('#B') @ ((('#B') @ d_not)) @ rt_more)))) @ 68.16/9.30 Y0)))))))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl636, '2'])). 68.16/9.30 thf(zip_derived_cl638, plain, 68.16/9.30 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.16/9.30 ((('#C') @ is_of @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ 68.16/9.30 (anec @ frac @ n_eq)))))))) @ 68.16/9.30 ((('#B') @ (all_of @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ 68.16/9.30 (anec @ frac @ n_eq))))) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))) @ 68.16/9.30 ((('#B') @ ((('#B') @ d_not)) @ rt_more))))))))))), 68.16/9.30 inference('comb-normalize', [status(thm)], [zip_derived_cl637])). 68.16/9.30 thf(zip_derived_cl639, plain, 68.16/9.30 (~ (((is_of @ '#sk2' @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 68.16/9.30 (all_of @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 68.16/9.30 ((('#S') @ ((('#B') @ (=>) @ (rt_lessis @ '#sk2'))) @ 68.16/9.30 ((('#B') @ d_not @ (rt_more @ '#sk2'))))))))), 68.16/9.30 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl638])). 68.16/9.30 thf(zip_derived_cl641, plain, 68.16/9.30 (~ (all_of @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 68.16/9.30 ((('#S') @ ((('#B') @ (=>) @ (rt_lessis @ '#sk2'))) @ 68.16/9.30 ((('#B') @ d_not @ (rt_more @ '#sk2'))))))), 68.16/9.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl639])). 68.16/9.30 thf(zip_derived_cl642, plain, 68.16/9.30 (~ (((!!) @ (^[Y0 : $i]: 68.16/9.30 (((is_of @ Y0 @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 68.16/9.30 ((('#S') @ ((('#B') @ (=>) @ (rt_lessis @ '#sk2'))) @ 68.16/9.30 ((('#B') @ d_not @ (rt_more @ '#sk2'))) @ Y0)))))))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl641, '2'])). 68.16/9.30 thf(zip_derived_cl643, plain, 68.16/9.30 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.16/9.30 ((('#C') @ is_of @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ 68.16/9.30 (anec @ frac @ n_eq)))))))) @ 68.16/9.30 ((('#S') @ ((('#B') @ (=>) @ (rt_lessis @ '#sk2'))) @ 68.16/9.30 ((('#B') @ d_not @ (rt_more @ '#sk2')))))))))), 68.16/9.30 inference('comb-normalize', [status(thm)], [zip_derived_cl642])). 68.16/9.30 thf(zip_derived_cl644, plain, 68.16/9.30 (~ (((is_of @ '#sk3' @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 68.16/9.30 (((rt_lessis @ '#sk2' @ '#sk3') => (d_not @ 68.16/9.30 (rt_more @ '#sk2' @ '#sk3'))))))), 68.16/9.30 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl643])). 68.16/9.30 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 68.16/9.30 thf('3', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 68.16/9.30 thf('4', plain, 68.16/9.30 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))). 68.16/9.30 thf('5', plain, 68.16/9.30 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(def_e_in, axiom,(( e_in @ (X1)@ (X2)@ (X0)) = ((X0)))). 68.16/9.30 thf('6', plain, 68.16/9.30 (![X2:( $i > $o ),X1:$i,X0:$i]: ( ( e_in @ X1 @ X2 @ X0 ) = ( X0 ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(def_ecect, axiom,(( ecect @ (X0)@ (X1)@ (X2)) = 68.16/9.30 ((e_in @ (power @ X0) @ (anec @ X0 @ X1) @ X2)))). 68.16/9.30 thf('7', plain, 68.16/9.30 (![X2:$i,X1:( $i > $i > $o ),X0:$i]: 68.16/9.30 ( ( ecect @ X0 @ X1 @ X2 ) = 68.16/9.30 ( e_in @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) @ X2 ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(def_rt_is, axiom,(( rt_is @ (X0)@ (X1)) = ((e_is @ rat @ X0 @ X1)))). 68.16/9.30 thf('8', plain, 68.16/9.30 (![X1:$i,X0:$i]: ( ( rt_is @ X0 @ X1 ) = ( e_is @ rat @ X0 @ X1 ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(def_class, axiom,(( class @ (X0)) = ((ecect @ frac @ n_eq @ X0)))). 68.16/9.30 thf('9', plain, 68.16/9.30 (![X0:$i]: ( ( class @ X0 ) = ( ecect @ frac @ n_eq @ X0 ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(def_rt_more, axiom,(( rt_more @ (X0)@ (X1)) = 68.16/9.30 ((l_some @ frac @ 68.16/9.30 (^[Y0 : $i]: 68.16/9.30 (l_some @ frac @ 68.16/9.30 (^[Y1 : $i]: 68.16/9.30 (and3 @ (inf @ Y0 @ (class @ X0)) @ (inf @ Y1 @ (class @ X1)) @ 68.16/9.30 (moref @ Y0 @ Y1))))))))). 68.16/9.30 thf('10', plain, 68.16/9.30 (![X1:$i,X0:$i]: 68.16/9.30 ( ( rt_more @ X0 @ X1 ) = 68.16/9.30 ( l_some @ 68.16/9.30 frac @ 68.16/9.30 ( ^[V_1:$i]: 68.16/9.30 ( l_some @ 68.16/9.30 frac @ 68.16/9.30 ( ^[V_2:$i]: 68.16/9.30 ( and3 @ 68.16/9.30 ( inf @ V_1 @ ( class @ X0 ) ) @ 68.16/9.30 ( inf @ V_2 @ ( class @ X1 ) ) @ ( moref @ V_1 @ V_2 ) ) ) ) ) ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(def_rt_less, axiom,(( rt_less @ (X0)@ (X1)) = 68.16/9.30 ((l_some @ frac @ 68.16/9.30 (^[Y0 : $i]: 68.16/9.30 (l_some @ frac @ 68.16/9.30 (^[Y1 : $i]: 68.16/9.30 (and3 @ (inf @ Y0 @ (class @ X0)) @ (inf @ Y1 @ (class @ X1)) @ 68.16/9.30 (lessf @ Y0 @ Y1))))))))). 68.16/9.30 thf('11', plain, 68.16/9.30 (![X1:$i,X0:$i]: 68.16/9.30 ( ( rt_less @ X0 @ X1 ) = 68.16/9.30 ( l_some @ 68.16/9.30 frac @ 68.16/9.30 ( ^[V_1:$i]: 68.16/9.30 ( l_some @ 68.16/9.30 frac @ 68.16/9.30 ( ^[V_2:$i]: 68.16/9.30 ( and3 @ 68.16/9.30 ( inf @ V_1 @ ( class @ X0 ) ) @ 68.16/9.30 ( inf @ V_2 @ ( class @ X1 ) ) @ ( lessf @ V_1 @ V_2 ) ) ) ) ) ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(def_rt_lessis, axiom,(( rt_lessis @ (X0)@ (X1)) = 68.16/9.30 ((l_or @ (rt_less @ X0 @ X1) @ (rt_is @ X0 @ X1))))). 68.16/9.30 thf('12', plain, 68.16/9.30 (![X1:$i,X0:$i]: 68.16/9.30 ( ( rt_lessis @ X0 @ X1 ) = 68.16/9.30 ( l_or @ ( rt_less @ X0 @ X1 ) @ ( rt_is @ X0 @ X1 ) ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(zip_derived_cl645, plain, 68.16/9.30 (~ (((is_of @ '#sk3' @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 68.16/9.30 (((imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ '#sk2')))))) @ 68.16/9.30 ((('#C') @ inf @ '#sk3')))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ((('#sk2') = ('#sk3')))) => (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ '#sk2')))))) @ 68.16/9.30 ((('#C') @ inf @ '#sk3')))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 ($false))))))), 68.16/9.30 inference('rw', [status(thm)], 68.16/9.30 [zip_derived_cl644, '3', '3', '4', '5', '6', '6', '0', '7', 68.16/9.30 '7', '1', '8', '9', '9', '10', '11', '12'])). 68.16/9.30 thf(zip_derived_cl647, plain, 68.16/9.30 (~ (((imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ '#sk2')))))) @ 68.16/9.30 ((('#C') @ inf @ '#sk3')))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ((('#sk2') = ('#sk3')))) => (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ '#sk2')))))) @ 68.16/9.30 ((('#C') @ inf @ '#sk3')))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 ($false))))), 68.16/9.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl645])). 68.16/9.30 thf(zip_derived_cl648, plain, 68.16/9.30 ( (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ '#sk2')))))) @ 68.16/9.30 ((('#C') @ inf @ '#sk3')))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ((('#sk2') = ('#sk3'))))), 68.16/9.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl647])). 68.16/9.30 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 68.16/9.30 thf('13', plain, 68.16/9.30 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 68.16/9.30 inference('rw.lit', [status(esa)], [def_imp])). 68.16/9.30 thf(zip_derived_cl650, plain, 68.16/9.30 ( (((imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ '#sk2')))))) @ 68.16/9.30 ((('#C') @ inf @ '#sk3')))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false)) => ((('#sk2') = ('#sk3')))))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl648, '13'])). 68.16/9.30 thf(zip_derived_cl652, plain, 68.16/9.30 ((~ (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ '#sk2')))))) @ 68.16/9.30 ((('#C') @ inf @ '#sk3')))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false)) 68.16/9.30 | ((('#sk2') = ('#sk3'))))), 68.16/9.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl650])). 68.16/9.30 thf(zip_derived_cl655, plain, 68.16/9.30 ((~ (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ '#sk2')))))) @ 68.16/9.30 ((('#C') @ inf @ '#sk3')))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false)) 68.16/9.30 | (('#sk2') = ('#sk3')))), 68.16/9.30 inference('simplify nested equalities', [status(thm)], 68.16/9.30 [zip_derived_cl652])). 68.16/9.30 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 68.16/9.30 thf('14', plain, 68.16/9.30 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 68.16/9.30 inference('rw.lit', [status(esa)], [def_imp])). 68.16/9.30 thf(zip_derived_cl656, plain, 68.16/9.30 ((~ (((l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ '#sk2')))))) @ 68.16/9.30 ((('#C') @ inf @ '#sk3')))))) @ 68.16/9.30 lessf))))) => 68.16/9.30 ($false))) 68.16/9.30 | (('#sk2') = ('#sk3')))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl655, '14'])). 68.16/9.30 thf(zip_derived_cl657, plain, 68.16/9.30 ((~ (((~) @ (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ '#sk2')))))) @ 68.16/9.30 ((('#C') @ inf @ '#sk3')))))) @ 68.16/9.30 lessf))))))) 68.16/9.30 | (('#sk2') = ('#sk3')))), 68.16/9.30 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl656])). 68.16/9.30 thf(zip_derived_cl658, plain, 68.16/9.30 (( (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ '#sk2')))))) @ 68.16/9.30 ((('#C') @ inf @ '#sk3')))))) @ 68.16/9.30 lessf))))) 68.16/9.30 | (('#sk2') = ('#sk3')))), 68.16/9.30 inference('simplify nested equalities', [status(thm)], 68.16/9.30 [zip_derived_cl657])). 68.16/9.30 thf(zip_derived_cl5000, plain, 68.16/9.30 (( (l_some @ frac @ 68.16/9.30 ('#ty_enc9' @ (l_some @ frac) @ 68.16/9.30 ('#ty_enc10' @ 68.16/9.30 ('#ty_enc11' @ '#ty_enc16' @ 68.16/9.30 ('#ty_enc12' @ 68.16/9.30 ('#ty_enc13' @ '#ty_enc15' @ 68.16/9.30 ('#ty_enc14' @ and3 @ ('#ty_enc8' @ inf @ '#sk2'))) @ 68.16/9.30 ('#ty_enc8' @ inf @ '#sk3'))) @ 68.16/9.30 lessf))) 68.16/9.30 | (('#sk2') = ('#sk3')))), 68.16/9.30 inference('remove_ty_args', [status(thm)], [zip_derived_cl658])). 68.16/9.30 thf(satz82, axiom, 68.16/9.30 (all_of @ 68.16/9.30 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 68.16/9.30 ( ^[X0:$i]: 68.16/9.30 ( all_of @ 68.16/9.30 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 68.16/9.30 ( ^[X1:$i]: ( ( rt_more @ X0 @ X1 ) => ( rt_less @ X1 @ X0 ) ) ) ) ))). 68.16/9.30 thf(zip_derived_cl483, plain, 68.16/9.30 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @ 68.16/9.30 (^[Y0 : $i]: 68.16/9.30 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @ 68.16/9.30 (^[Y1 : $i]: (((rt_more @ Y0 @ Y1) => (rt_less @ Y1 @ Y0)))))))), 68.16/9.30 inference('cnf', [status(esa)], [satz82])). 68.16/9.30 thf(zip_derived_cl484, plain, 68.16/9.30 ( (all_of @ ((('#C') @ in @ rat)) @ 68.16/9.30 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#B') @ ((('#B') @ (=>))) @ rt_more)))) @ 68.16/9.30 ((('#C') @ rt_less)))))))), 68.16/9.30 inference('lams2combs', [status(thm)], [zip_derived_cl483])). 68.16/9.30 thf(zip_derived_cl765, plain, 68.16/9.30 ( (all_of @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 68.16/9.30 ((('#B') @ (all_of @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#B') @ ((('#B') @ (=>))) @ rt_more)))) @ 68.16/9.30 ((('#C') @ rt_less)))))))), 68.16/9.30 inference('rw', [status(thm)], [zip_derived_cl484, '0', '1'])). 68.16/9.30 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 68.16/9.30 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 68.16/9.30 thf('15', plain, 68.16/9.30 (![X0:( $i > $o ),X1:( $i > $o )]: 68.16/9.30 ( ( all_of @ X0 @ X1 ) <=> 68.16/9.30 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 68.16/9.30 inference('rw.lit', [status(esa)], [def_all_of])). 68.16/9.30 thf(zip_derived_cl766, plain, 68.16/9.30 ( (((!!) @ (^[Y0 : $i]: 68.16/9.30 (((is_of @ Y0 @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 68.16/9.30 ((('#B') @ (all_of @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ 68.16/9.30 (anec @ frac @ n_eq))))) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#B') @ ((('#B') @ (=>))) @ rt_more)))) @ 68.16/9.30 ((('#C') @ rt_less)))) @ 68.16/9.30 Y0)))))))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl765, '15'])). 68.16/9.30 thf(zip_derived_cl767, plain, 68.16/9.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.16/9.30 ((('#C') @ is_of @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ 68.16/9.30 (anec @ frac @ n_eq)))))))) @ 68.16/9.30 ((('#B') @ (all_of @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#B') @ ((('#B') @ (=>))) @ rt_more)))) @ 68.16/9.30 ((('#C') @ rt_less))))))))))), 68.16/9.30 inference('comb-normalize', [status(thm)], [zip_derived_cl766])). 68.16/9.30 thf(zip_derived_cl768, plain, 68.16/9.30 (![X2 : $i]: 68.16/9.30 (((is_of @ X2 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 68.16/9.30 (all_of @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 68.16/9.30 ((('#S') @ ((('#B') @ (=>) @ (rt_more @ X2))) @ 68.16/9.30 ((('#C') @ rt_less @ X2)))))))), 68.16/9.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl767])). 68.16/9.30 thf(zip_derived_cl769, plain, 68.16/9.30 (![X2 : $i]: 68.16/9.30 (~ (is_of @ X2 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | (all_of @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 68.16/9.30 ((('#S') @ ((('#B') @ (=>) @ (rt_more @ X2))) @ 68.16/9.30 ((('#C') @ rt_less @ X2))))))), 68.16/9.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl768])). 68.16/9.30 thf(zip_derived_cl770, plain, 68.16/9.30 (![X0 : $i]: 68.16/9.30 ( (((!!) @ (^[Y0 : $i]: 68.16/9.30 (((is_of @ Y0 @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 68.16/9.30 ((('#S') @ ((('#B') @ (=>) @ (rt_more @ X0))) @ 68.16/9.30 ((('#C') @ rt_less @ X0)) @ Y0))))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl769, '15'])). 68.16/9.30 thf(zip_derived_cl771, plain, 68.16/9.30 (![X0 : $i]: 68.16/9.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.16/9.30 ((('#C') @ is_of @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ 68.16/9.30 (anec @ frac @ n_eq)))))))) @ 68.16/9.30 ((('#S') @ ((('#B') @ (=>) @ (rt_more @ X0))) @ 68.16/9.30 ((('#C') @ rt_less @ X0)))))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('comb-normalize', [status(thm)], [zip_derived_cl770])). 68.16/9.30 thf(zip_derived_cl772, plain, 68.16/9.30 (![X0 : $i, X2 : $i]: 68.16/9.30 ( (((is_of @ X2 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 68.16/9.30 (((rt_more @ X0 @ X2) => (rt_less @ X2 @ X0))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl771])). 68.16/9.30 thf(zip_derived_cl773, plain, 68.16/9.30 (![X0 : $i, X2 : $i]: 68.16/9.30 ( (((is_of @ X2 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 68.16/9.30 (((l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X2)))))) @ 68.16/9.30 moref))))) => 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X2)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('rw', [status(thm)], 68.16/9.30 [zip_derived_cl772, '6', '6', '7', '7', '9', '9', '10', '11'])). 68.16/9.30 thf(zip_derived_cl774, plain, 68.16/9.30 (![X0 : $i, X2 : $i]: 68.16/9.30 (~ (is_of @ X2 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | (((l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X2)))))) @ 68.16/9.30 moref))))) => 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X2)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl773])). 68.16/9.30 thf(zip_derived_cl775, plain, 68.16/9.30 (![X0 : $i, X2 : $i]: 68.16/9.30 (~ (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X2)))))) @ 68.16/9.30 moref))))) 68.16/9.30 | (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X2)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X2 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl774])). 68.16/9.30 thf(zip_derived_cl5010, plain, 68.16/9.30 (![X0 : $i, X2 : $i]: 68.16/9.30 (~ (l_some @ frac @ 68.16/9.30 ('#ty_enc9' @ (l_some @ frac) @ 68.16/9.30 ('#ty_enc10' @ 68.16/9.30 ('#ty_enc11' @ '#ty_enc16' @ 68.16/9.30 ('#ty_enc12' @ 68.16/9.30 ('#ty_enc13' @ '#ty_enc15' @ 68.16/9.30 ('#ty_enc14' @ and3 @ ('#ty_enc8' @ inf @ X0))) @ 68.16/9.30 ('#ty_enc8' @ inf @ X2))) @ 68.16/9.30 moref))) 68.16/9.30 | (l_some @ frac @ 68.16/9.30 ('#ty_enc9' @ (l_some @ frac) @ 68.16/9.30 ('#ty_enc10' @ 68.16/9.30 ('#ty_enc11' @ '#ty_enc16' @ 68.16/9.30 ('#ty_enc12' @ 68.16/9.30 ('#ty_enc13' @ '#ty_enc15' @ 68.16/9.30 ('#ty_enc14' @ and3 @ ('#ty_enc8' @ inf @ X2))) @ 68.16/9.30 ('#ty_enc8' @ inf @ X0))) @ 68.16/9.30 lessf))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ('#ty_enc8' @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) 68.16/9.30 | ~ (is_of @ X2 @ 68.16/9.30 ('#ty_enc8' @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))), 68.16/9.30 inference('remove_ty_args', [status(thm)], [zip_derived_cl775])). 68.16/9.30 thf(zip_derived_cl640, plain, 68.16/9.30 ( (is_of @ '#sk2' @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))), 68.16/9.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl639])). 68.16/9.30 thf(zip_derived_cl4997, plain, 68.16/9.30 ( (is_of @ '#sk2' @ 68.16/9.30 ('#ty_enc8' @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))), 68.16/9.30 inference('remove_ty_args', [status(thm)], [zip_derived_cl640])). 68.16/9.30 thf(zip_derived_cl646, plain, 68.16/9.30 ( (is_of @ '#sk3' @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))), 68.16/9.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl645])). 68.16/9.30 thf(zip_derived_cl4998, plain, 68.16/9.30 ( (is_of @ '#sk3' @ 68.16/9.30 ('#ty_enc8' @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))), 68.16/9.30 inference('remove_ty_args', [status(thm)], [zip_derived_cl646])). 68.16/9.30 thf(zip_derived_cl649, plain, 68.16/9.30 (~ (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ '#sk2')))))) @ 68.16/9.30 ((('#C') @ inf @ '#sk3')))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 ($false))), 68.16/9.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl647])). 68.16/9.30 thf(zip_derived_cl651, plain, 68.16/9.30 (~ (((l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ '#sk2')))))) @ 68.16/9.30 ((('#C') @ inf @ '#sk3')))))) @ 68.16/9.30 moref))))) => 68.16/9.30 ($false)))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl649, '14'])). 68.16/9.30 thf(zip_derived_cl653, plain, 68.16/9.30 (~ (((~) @ (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ '#sk2')))))) @ 68.16/9.30 ((('#C') @ inf @ '#sk3')))))) @ 68.16/9.30 moref)))))))), 68.16/9.30 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl651])). 68.16/9.30 thf(zip_derived_cl654, plain, 68.16/9.30 ( (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ '#sk2')))))) @ 68.16/9.30 ((('#C') @ inf @ '#sk3')))))) @ 68.16/9.30 moref)))))), 68.16/9.30 inference('simplify nested equalities', [status(thm)], 68.16/9.30 [zip_derived_cl653])). 68.16/9.30 thf(zip_derived_cl4999, plain, 68.16/9.30 ( (l_some @ frac @ 68.16/9.30 ('#ty_enc9' @ (l_some @ frac) @ 68.16/9.30 ('#ty_enc10' @ 68.16/9.30 ('#ty_enc11' @ '#ty_enc16' @ 68.16/9.30 ('#ty_enc12' @ 68.16/9.30 ('#ty_enc13' @ '#ty_enc15' @ 68.16/9.30 ('#ty_enc14' @ and3 @ ('#ty_enc8' @ inf @ '#sk2'))) @ 68.16/9.30 ('#ty_enc8' @ inf @ '#sk3'))) @ 68.16/9.30 moref)))), 68.16/9.30 inference('remove_ty_args', [status(thm)], [zip_derived_cl654])). 68.16/9.30 thf(satz81, axiom, 68.16/9.30 (all_of @ 68.16/9.30 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 68.16/9.30 ( ^[X0:$i]: 68.16/9.30 ( all_of @ 68.16/9.30 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 68.16/9.30 ( ^[X1:$i]: 68.16/9.30 ( orec3 @ 68.16/9.30 ( rt_is @ X0 @ X1 ) @ ( rt_more @ X0 @ X1 ) @ 68.16/9.30 ( rt_less @ X0 @ X1 ) ) ) ) ))). 68.16/9.30 thf(zip_derived_cl491, plain, 68.16/9.30 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @ 68.16/9.30 (^[Y0 : $i]: 68.16/9.30 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @ 68.16/9.30 (^[Y1 : $i]: 68.16/9.30 (orec3 @ (rt_is @ Y0 @ Y1) @ (rt_more @ Y0 @ Y1) @ 68.16/9.30 (rt_less @ Y0 @ Y1))))))), 68.16/9.30 inference('cnf', [status(esa)], [satz81])). 68.16/9.30 thf(zip_derived_cl492, plain, 68.16/9.30 ( (all_of @ ((('#C') @ in @ rat)) @ 68.16/9.30 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#B') @ ((('#B') @ orec3)) @ rt_is)))) @ 68.16/9.30 rt_more)))) @ 68.16/9.30 rt_less)))))), 68.16/9.30 inference('lams2combs', [status(thm)], [zip_derived_cl491])). 68.16/9.30 thf(zip_derived_cl1773, plain, 68.16/9.30 ( (all_of @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 68.16/9.30 ((('#B') @ (all_of @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#B') @ ((('#B') @ orec3)) @ rt_is)))) @ 68.16/9.30 rt_more)))) @ 68.16/9.30 rt_less)))))), 68.16/9.30 inference('rw', [status(thm)], [zip_derived_cl492, '0', '1'])). 68.16/9.30 thf(zip_derived_cl1774, plain, 68.16/9.30 ( (((!!) @ (^[Y0 : $i]: 68.16/9.30 (((is_of @ Y0 @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 68.16/9.30 ((('#B') @ (all_of @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ 68.16/9.30 (anec @ frac @ n_eq))))) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#B') @ ((('#B') @ orec3)) @ 68.16/9.30 rt_is)))) @ 68.16/9.30 rt_more)))) @ 68.16/9.30 rt_less)) @ 68.16/9.30 Y0)))))))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl1773, '15'])). 68.16/9.30 thf(zip_derived_cl1775, plain, 68.16/9.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.16/9.30 ((('#C') @ is_of @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ 68.16/9.30 (anec @ frac @ n_eq)))))))) @ 68.16/9.30 ((('#B') @ (all_of @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#B') @ ((('#B') @ orec3)) @ 68.16/9.30 rt_is)))) @ 68.16/9.30 rt_more)))) @ 68.16/9.30 rt_less))))))))), 68.16/9.30 inference('comb-normalize', [status(thm)], [zip_derived_cl1774])). 68.16/9.30 thf(zip_derived_cl1776, plain, 68.16/9.30 (![X2 : $i]: 68.16/9.30 (((is_of @ X2 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 68.16/9.30 (all_of @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 68.16/9.30 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X2))) @ 68.16/9.30 (rt_more @ X2))) @ 68.16/9.30 (rt_less @ X2))))))), 68.16/9.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1775])). 68.16/9.30 thf(zip_derived_cl1777, plain, 68.16/9.30 (![X2 : $i]: 68.16/9.30 (~ (is_of @ X2 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | (all_of @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 68.16/9.30 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X2))) @ 68.16/9.30 (rt_more @ X2))) @ 68.16/9.30 (rt_less @ X2)))))), 68.16/9.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1776])). 68.16/9.30 thf(zip_derived_cl1778, plain, 68.16/9.30 (![X0 : $i]: 68.16/9.30 ( (((!!) @ (^[Y0 : $i]: 68.16/9.30 (((is_of @ Y0 @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 68.16/9.30 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X0))) @ 68.16/9.30 (rt_more @ X0))) @ 68.16/9.30 (rt_less @ X0) @ Y0))))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl1777, '15'])). 68.16/9.30 thf(zip_derived_cl1779, plain, 68.16/9.30 (![X0 : $i]: 68.16/9.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.16/9.30 ((('#C') @ is_of @ 68.16/9.30 ((('#C') @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ 68.16/9.30 (anec @ frac @ n_eq)))))))) @ 68.16/9.30 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X0))) @ 68.16/9.30 (rt_more @ X0))) @ 68.16/9.30 (rt_less @ X0))))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('comb-normalize', [status(thm)], [zip_derived_cl1778])). 68.16/9.30 thf(zip_derived_cl1780, plain, 68.16/9.30 (![X0 : $i, X2 : $i]: 68.16/9.30 ( (((is_of @ X2 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 68.16/9.30 (orec3 @ (rt_is @ X0 @ X2) @ (rt_more @ X0 @ X2) @ 68.16/9.30 (rt_less @ X0 @ X2)))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1779])). 68.16/9.30 thf(def_l_ec, axiom,(( l_ec @ (X0)@ (X1)) = ((imp @ X0 @ (d_not @ X1))))). 68.16/9.30 thf('16', plain, 68.16/9.30 (![X1:$o,X0:$o]: ( ( l_ec @ X0 @ X1 ) = ( imp @ X0 @ ( d_not @ X1 ) ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(def_d_and, axiom,(( d_and @ (X0)@ (X1)) = ((d_not @ (l_ec @ X0 @ X1))))). 68.16/9.30 thf('17', plain, 68.16/9.30 (![X1:$o,X0:$o]: ( ( d_and @ X0 @ X1 ) = ( d_not @ ( l_ec @ X0 @ X1 ) ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(def_or3, axiom,(( or3 @ (X0)@ (X1)@ (X2)) = 68.16/9.30 ((l_or @ X0 @ (l_or @ X1 @ X2))))). 68.16/9.30 thf('18', plain, 68.16/9.30 (![X2:$o,X1:$o,X0:$o]: 68.16/9.30 ( ( or3 @ X0 @ X1 @ X2 ) = ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(def_and3, axiom,(( and3 @ (X0)@ (X1)@ (X2)) = 68.16/9.30 ((d_and @ X0 @ (d_and @ X1 @ X2))))). 68.16/9.30 thf('19', plain, 68.16/9.30 (![X2:$o,X1:$o,X0:$o]: 68.16/9.30 ( ( and3 @ X0 @ X1 @ X2 ) = ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(def_ec3, axiom,(( ec3 @ (X0)@ (X1)@ (X2)) = 68.16/9.30 ((and3 @ (l_ec @ X0 @ X1) @ (l_ec @ X1 @ X2) @ (l_ec @ X2 @ X0))))). 68.16/9.30 thf('20', plain, 68.16/9.30 (![X2:$o,X1:$o,X0:$o]: 68.16/9.30 ( ( ec3 @ X0 @ X1 @ X2 ) = 68.16/9.30 ( and3 @ ( l_ec @ X0 @ X1 ) @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X0 ) ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(def_orec3, axiom,(( orec3 @ (X0)@ (X1)@ (X2)) = 68.16/9.30 ((d_and @ (or3 @ X0 @ X1 @ X2) @ (ec3 @ X0 @ X1 @ X2))))). 68.16/9.30 thf('21', plain, 68.16/9.30 (![X2:$o,X1:$o,X0:$o]: 68.16/9.30 ( ( orec3 @ X0 @ X1 @ X2 ) = 68.16/9.30 ( d_and @ ( or3 @ X0 @ X1 @ X2 ) @ ( ec3 @ X0 @ X1 @ X2 ) ) )), 68.16/9.30 define([status(thm)])). 68.16/9.30 thf(zip_derived_cl1781, plain, 68.16/9.30 (![X0 : $i, X2 : $i]: 68.16/9.30 ( (((is_of @ X2 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ (imp @ (((X0) = (X2))) @ ($false)) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X2)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 ($false)) @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X2)))))) @ 68.16/9.30 lessf))))))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ (((X0) = (X2))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X2)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X2)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X2)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X2)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X0) = (X2))) @ ($false))) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('rw', [status(thm)], 68.16/9.30 [zip_derived_cl1780, '3', '3', '3', '3', '3', '3', '3', '3', 68.16/9.30 '3', '16', '16', '16', '16', '16', '16', '17', '17', '17', 68.16/9.30 '4', '4', '18', '19', '20', '21', '5', '6', '6', '0', '7', 68.16/9.30 '7', '1', '8', '9', '9', '10', '11'])). 68.16/9.30 thf(zip_derived_cl1782, plain, 68.16/9.30 (![X0 : $i, X2 : $i]: 68.16/9.30 (~ (is_of @ X2 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ (imp @ (((X0) = (X2))) @ ($false)) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ 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@ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X0) = (X1))) @ ($false))) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ($false))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('simplify boolean subterms', [status(thm)], 68.16/9.30 [zip_derived_cl1783])). 68.16/9.30 thf(zip_derived_cl1785, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 (~ (imp @ 68.16/9.30 (imp @ (imp @ (((X0) = (X1))) @ ($false)) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ 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((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X1) = (X0))) @ ($false))) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ($false)))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl1785, '14'])). 68.16/9.30 thf(zip_derived_cl1788, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 (~ (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ (((X1) = (X0))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X1) = (X0))) @ ($false))) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ($false)) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1786])). 68.16/9.30 thf(zip_derived_cl1790, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 (~ (((imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ (((X1) = (X0))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X1) = (X0))) @ ($false))) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) => ($false))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl1788, '14'])). 68.16/9.30 thf(zip_derived_cl1792, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 (~ (((~) @ (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ (((X1) = (X0))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X1) = (X0))) @ ($false))) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('simplify boolean subterms', [status(thm)], 68.16/9.30 [zip_derived_cl1790])). 68.16/9.30 thf(zip_derived_cl1793, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 ( (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ (((X1) = (X0))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X1) = (X0))) @ ($false))) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('simplify nested equalities', [status(thm)], 68.16/9.30 [zip_derived_cl1792])). 68.16/9.30 thf(zip_derived_cl1794, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 ( (((imp @ 68.16/9.30 (imp @ (((X0) = (X1))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X0) = (X1))) @ ($false))) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ($false))) => 68.16/9.30 ($false))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl1793, '13'])). 68.16/9.30 thf(zip_derived_cl1796, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 ( (((~) @ (imp @ 68.16/9.30 (imp @ (((X0) = (X1))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X0) = (X1))) @ ($false))) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ($false))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('simplify boolean subterms', [status(thm)], 68.16/9.30 [zip_derived_cl1794])). 68.16/9.30 thf(zip_derived_cl1797, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 (~ (imp @ 68.16/9.30 (imp @ (((X0) = (X1))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X0) = (X1))) @ ($false))) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ($false))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('simplify nested equalities', [status(thm)], 68.16/9.30 [zip_derived_cl1796])). 68.16/9.30 thf(zip_derived_cl1798, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 (~ (((imp @ (((X1) = (X0))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 ($false))) => 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X1) = (X0))) @ ($false))) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ($false)))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl1797, '14'])). 68.16/9.30 thf(zip_derived_cl1803, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 (~ (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X1) = (X0))) @ ($false))) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) @ 68.16/9.30 ($false)) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1798])). 68.16/9.30 thf(zip_derived_cl1806, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 (~ (((imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X1) = (X0))) @ ($false))) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) => ($false))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl1803, '14'])). 68.16/9.30 thf(zip_derived_cl1809, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 (~ (((~) @ (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X1) = (X0))) @ ($false))) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('simplify boolean subterms', [status(thm)], 68.16/9.30 [zip_derived_cl1806])). 68.16/9.30 thf(zip_derived_cl1810, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 ( (imp @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X1) = (X0))) @ ($false))) @ 68.16/9.30 ($false))) @ 68.16/9.30 ($false)) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('simplify nested equalities', [status(thm)], 68.16/9.30 [zip_derived_cl1809])). 68.16/9.30 thf(zip_derived_cl1811, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 ( (((imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X0) = (X1))) @ ($false))) @ 68.16/9.30 ($false))) => 68.16/9.30 ($false))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl1810, '13'])). 68.16/9.30 thf(zip_derived_cl1816, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 ( (((~) @ (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X0) = (X1))) @ ($false))) @ 68.16/9.30 ($false))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('simplify boolean subterms', [status(thm)], 68.16/9.30 [zip_derived_cl1811])). 68.16/9.30 thf(zip_derived_cl1817, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 (~ (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) @ 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X0) = (X1))) @ ($false))) @ 68.16/9.30 ($false))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('simplify nested equalities', [status(thm)], 68.16/9.30 [zip_derived_cl1816])). 68.16/9.30 thf(zip_derived_cl1818, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 (~ (((imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) => 68.16/9.30 (imp @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 (imp @ (((X1) = (X0))) @ ($false))) @ 68.16/9.30 ($false)))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl1817, '14'])). 68.16/9.30 thf(zip_derived_cl1821, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 ( (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) @ 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1818])). 68.16/9.30 thf(zip_derived_cl1823, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 ( (((l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) => 68.16/9.30 (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false)))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl1821, '13'])). 68.16/9.30 thf(zip_derived_cl1825, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 (~ (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))) 68.16/9.30 | (imp @ 68.16/9.30 (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) @ 68.16/9.30 ($false)) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 68.16/9.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1823])). 68.16/9.30 thf(zip_derived_cl1829, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 ( (((l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) => 68.16/9.30 ($false))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))))), 68.16/9.30 inference('rw_clause', [status(thm)], [zip_derived_cl1825, '13'])). 68.16/9.30 thf(zip_derived_cl1831, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 ( (((~) @ (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))))), 68.16/9.30 inference('simplify boolean subterms', [status(thm)], 68.16/9.30 [zip_derived_cl1829])). 68.16/9.30 thf(zip_derived_cl1832, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 (~ (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 lessf))))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 68.16/9.30 | ~ (l_some @ frac @ 68.16/9.30 ((('#B') @ (l_some @ frac) @ 68.16/9.30 ((('#S') @ ((('#B') @ ('#S') @ 68.16/9.30 ((('#C') @ ((('#B') @ ('#B') @ 68.16/9.30 ((('#B') @ and3 @ 68.16/9.30 ((('#C') @ inf @ X1)))))) @ 68.16/9.30 ((('#C') @ inf @ X0)))))) @ 68.16/9.30 moref))))))), 68.16/9.30 inference('simplify nested equalities', [status(thm)], 68.16/9.30 [zip_derived_cl1831])). 68.16/9.30 thf(zip_derived_cl5038, plain, 68.16/9.30 (![X0 : $i, X1 : $i]: 68.16/9.30 (~ (l_some @ frac @ 68.16/9.30 ('#ty_enc9' @ (l_some @ frac) @ 68.16/9.30 ('#ty_enc10' @ 68.16/9.30 ('#ty_enc11' @ '#ty_enc16' @ 68.16/9.30 ('#ty_enc12' @ 68.16/9.30 ('#ty_enc13' @ '#ty_enc15' @ 68.16/9.30 ('#ty_enc14' @ and3 @ ('#ty_enc8' @ inf @ X1))) @ 68.16/9.30 ('#ty_enc8' @ inf @ X0))) @ 68.16/9.30 lessf))) 68.16/9.30 | ~ (is_of @ X0 @ 68.16/9.30 ('#ty_enc8' @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) 68.16/9.30 | ~ (is_of @ X1 @ 68.16/9.30 ('#ty_enc8' @ in @ 68.16/9.30 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) 68.16/9.30 | ~ (l_some @ frac @ 68.16/9.30 ('#ty_enc9' @ (l_some @ frac) @ 68.16/9.30 ('#ty_enc10' @ 68.16/9.30 ('#ty_enc11' @ '#ty_enc16' @ 68.16/9.30 ('#ty_enc12' @ 68.16/9.30 ('#ty_enc13' @ '#ty_enc15' @ 68.16/9.30 ('#ty_enc14' @ and3 @ ('#ty_enc8' @ inf @ X1))) @ 68.16/9.30 ('#ty_enc8' @ inf @ X0))) @ 68.16/9.30 moref))))), 68.16/9.30 inference('remove_ty_args', [status(thm)], [zip_derived_cl1832])). 68.16/9.30 thf(zip_derived_cl5126, plain, ($false), 68.16/9.30 inference('eprover', [status(thm)], 68.16/9.30 [zip_derived_cl5000, zip_derived_cl5010, zip_derived_cl4997, 68.16/9.30 zip_derived_cl4998, zip_derived_cl4999, zip_derived_cl5038])). 68.16/9.30 68.16/9.30 % SZS output end Refutation 68.16/9.30 68.16/9.30 68.16/9.30 % Terminating... 69.04/9.44 % Runner terminated. 69.04/9.45 % Zipperpin 1.5 exiting 69.04/9.45 EOF