0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.19 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.tA0F4TqHpB true 0.18/0.40 % Computer : n014.cluster.edu 0.18/0.40 % Model : x86_64 x86_64 0.18/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.18/0.40 % Memory : 8042.1875MB 0.18/0.40 % OS : Linux 3.10.0-693.el7.x86_64 0.18/0.40 % CPULimit : 960 0.18/0.40 % WCLimit : 120 0.18/0.40 % DateTime : Tue Aug 9 07:14:46 EDT 2022 0.18/0.41 % CPUTime : 0.18/0.41 % Running portfolio for 960 s 0.18/0.41 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.18/0.41 % Number of cores: 8 0.18/0.41 % Python version: Python 3.6.8 0.18/0.41 % Running in HO mode 0.60/0.78 % Total configuration time : 828 0.60/0.78 % Estimated wc time : 1656 0.60/0.78 % Estimated cpu time (8 cpus) : 207.0 0.61/0.90 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.61/0.90 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.61/1.05 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.61/1.11 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.61/1.17 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 2.11/1.31 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 2.11/1.32 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 2.39/1.34 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 12.67/3.51 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 158.55/27.17 % Solved by lams/40_b.comb.sh. 158.55/27.17 % done 370 iterations in 25.666s 158.55/27.17 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 158.55/27.17 % SZS output start Refutation 158.55/27.17 thf(rt_is_type, type, rt_is: $i > $i > $o). 158.55/27.17 thf(orec3_type, type, orec3: $o > $o > $o > $o). 158.55/27.17 thf(inf_type, type, inf: $i > $i > $o). 158.55/27.17 thf(rt_lessis_type, type, rt_lessis: $i > $i > $o). 158.55/27.17 thf(moref_type, type, moref: $i > $i > $o). 158.55/27.17 thf(ec3_type, type, ec3: $o > $o > $o > $o). 158.55/27.17 thf(l_ec_type, type, l_ec: $o > $o > $o). 158.55/27.17 thf(d_not_type, type, d_not: $o > $o). 158.55/27.17 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 158.55/27.17 thf(in_type, type, in: $i > $i > $o). 158.55/27.17 thf(power_type, type, power: $i > $i). 158.55/27.17 thf(and3_type, type, and3: $o > $o > $o > $o). 158.55/27.17 thf(rt_more_type, type, rt_more: $i > $i > $o). 158.55/27.17 thf(e_is_type, type, e_is: $i > $i > $i > $o). 158.55/27.17 thf('#sk2_type', type, '#sk2': $i). 158.55/27.17 thf(e_in_type, type, e_in: $i > ($i > $o) > $i > $i). 158.55/27.17 thf(l_or_type, type, l_or: $o > $o > $o). 158.55/27.17 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 158.55/27.17 thf(rat_type, type, rat: $i). 158.55/27.17 thf(lessf_type, type, lessf: $i > $i > $o). 158.55/27.17 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 158.55/27.17 thf(frac_type, type, frac: $i). 158.55/27.17 thf(d_and_type, type, d_and: $o > $o > $o). 158.55/27.17 thf(imp_type, type, imp: $o > $o > $o). 158.55/27.17 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 158.55/27.17 thf(rt_less_type, type, rt_less: $i > $i > $o). 158.55/27.17 thf(n_eq_type, type, n_eq: $i > $i > $o). 158.55/27.17 thf(class_type, type, class: $i > $i). 158.55/27.17 thf(anec_type, type, anec: $i > ($i > $i > $o) > $i > $o). 158.55/27.17 thf(or3_type, type, or3: $o > $o > $o > $o). 158.55/27.17 thf(ecect_type, type, ecect: $i > ($i > $i > $o) > $i > $i). 158.55/27.17 thf('#sk1_type', type, '#sk1': $i). 158.55/27.17 thf(ect_type, type, ect: $i > ($i > $i > $o) > $i). 158.55/27.17 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 158.55/27.17 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 158.55/27.17 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 158.55/27.17 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 158.55/27.17 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 158.55/27.17 thf(satz81d, conjecture, 158.55/27.17 (all_of @ 158.55/27.17 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 158.55/27.17 ( ^[X0:$i]: 158.55/27.17 ( all_of @ 158.55/27.17 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 158.55/27.17 ( ^[X1:$i]: 158.55/27.17 ( ( rt_lessis @ X0 @ X1 ) => ( d_not @ ( rt_more @ X0 @ X1 ) ) ) ) ) ))). 158.55/27.17 thf(zf_stmt_0, negated_conjecture, 158.55/27.17 (~( all_of @ 158.55/27.17 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 158.55/27.17 ( ^[X0:$i]: 158.55/27.17 ( all_of @ 158.55/27.17 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 158.55/27.17 ( ^[X1:$i]: 158.55/27.17 ( ( rt_lessis @ X0 @ X1 ) => ( d_not @ ( rt_more @ X0 @ X1 ) ) ) ) ) ) )), 158.55/27.17 inference('cnf.neg', [status(esa)], [satz81d])). 158.55/27.17 thf(zip_derived_cl499, plain, 158.55/27.17 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @ 158.55/27.17 (^[Y0 : $i]: 158.55/27.17 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @ 158.55/27.17 (^[Y1 : $i]: 158.55/27.17 (((rt_lessis @ Y0 @ Y1) => (d_not @ (rt_more @ Y0 @ Y1))))))))), 158.55/27.17 inference('cnf', [status(esa)], [zf_stmt_0])). 158.55/27.17 thf(zip_derived_cl500, plain, 158.55/27.17 (~ (all_of @ ((('#C') @ in @ rat)) @ 158.55/27.17 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @ 158.55/27.17 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.17 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))) @ 158.55/27.17 ((('#B') @ ((('#B') @ d_not)) @ rt_more)))))))), 158.55/27.17 inference('lams2combs', [status(thm)], [zip_derived_cl499])). 158.55/27.17 thf(def_ect, axiom,(( ect @ (X0)@ (X1)) = 158.55/27.17 ((d_Sep @ (power @ X0) @ (anec @ X0 @ X1))))). 158.55/27.17 thf('0', plain, 158.55/27.17 (![X1:( $i > $i > $o ),X0:$i]: 158.55/27.17 ( ( ect @ X0 @ X1 ) = ( d_Sep @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) ) )), 158.55/27.17 define([status(thm)])). 158.55/27.17 thf(def_rat, axiom,(( rat ) = ((ect @ frac @ n_eq)))). 158.55/27.17 thf('1', plain, (( rat ) = ( ect @ frac @ n_eq )), define([status(thm)])). 158.55/27.17 thf(zip_derived_cl635, plain, 158.55/27.17 (~ (all_of @ 158.55/27.17 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 158.55/27.17 ((('#B') @ (all_of @ 158.55/27.17 ((('#C') @ in @ 158.55/27.17 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @ 158.55/27.17 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.17 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))) @ 158.55/27.17 ((('#B') @ ((('#B') @ d_not)) @ rt_more)))))))), 158.55/27.17 inference('rw', [status(thm)], [zip_derived_cl500, '0', '1'])). 158.55/27.17 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 158.55/27.17 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 158.55/27.17 thf('2', plain, 158.55/27.17 (![X0:( $i > $o ),X1:( $i > $o )]: 158.55/27.17 ( ( ~( all_of @ X0 @ X1 ) ) <=> 158.55/27.17 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 158.55/27.17 inference('rw.lit', [status(esa)], [def_all_of])). 158.55/27.17 thf(zip_derived_cl636, plain, 158.55/27.17 (~ (((!!) @ (^[Y0 : $i]: 158.55/27.17 (((is_of @ Y0 @ 158.55/27.17 ((('#C') @ in @ 158.55/27.17 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 158.55/27.17 ((('#B') @ (all_of @ 158.55/27.17 ((('#C') @ in @ 158.55/27.17 (d_Sep @ (power @ frac) @ 158.55/27.17 (anec @ frac @ n_eq))))) @ 158.55/27.17 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.17 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))) @ 158.55/27.17 ((('#B') @ ((('#B') @ d_not)) @ rt_more)))) @ 158.55/27.17 Y0)))))))), 158.55/27.17 inference('rw_clause', [status(thm)], [zip_derived_cl635, '2'])). 158.55/27.17 thf(zip_derived_cl637, plain, 158.55/27.17 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 158.55/27.17 ((('#C') @ is_of @ 158.55/27.17 ((('#C') @ in @ 158.55/27.17 (d_Sep @ (power @ frac) @ 158.55/27.17 (anec @ frac @ n_eq)))))))) @ 158.55/27.17 ((('#B') @ (all_of @ 158.55/27.17 ((('#C') @ in @ 158.55/27.17 (d_Sep @ (power @ frac) @ 158.55/27.17 (anec @ frac @ n_eq))))) @ 158.55/27.17 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.17 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))) @ 158.55/27.17 ((('#B') @ ((('#B') @ d_not)) @ rt_more))))))))))), 158.55/27.17 inference('comb-normalize', [status(thm)], [zip_derived_cl636])). 158.55/27.17 thf(zip_derived_cl638, plain, 158.55/27.17 (~ (((is_of @ '#sk1' @ 158.55/27.17 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 158.55/27.17 (all_of @ 158.55/27.17 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 158.55/27.17 ((('#S') @ ((('#B') @ (=>) @ (rt_lessis @ '#sk1'))) @ 158.55/27.17 ((('#B') @ d_not @ (rt_more @ '#sk1'))))))))), 158.55/27.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl637])). 158.55/27.17 thf(zip_derived_cl640, plain, 158.55/27.17 (~ (all_of @ 158.55/27.17 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 158.55/27.17 ((('#S') @ ((('#B') @ (=>) @ (rt_lessis @ '#sk1'))) @ 158.55/27.17 ((('#B') @ d_not @ (rt_more @ '#sk1'))))))), 158.55/27.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl638])). 158.55/27.17 thf(zip_derived_cl641, plain, 158.55/27.17 (~ (((!!) @ (^[Y0 : $i]: 158.55/27.17 (((is_of @ Y0 @ 158.55/27.17 ((('#C') @ in @ 158.55/27.17 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 158.55/27.17 ((('#S') @ ((('#B') @ (=>) @ (rt_lessis @ '#sk1'))) @ 158.55/27.17 ((('#B') @ d_not @ (rt_more @ '#sk1'))) @ Y0)))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl640, '2'])). 158.55/27.18 thf(zip_derived_cl642, plain, 158.55/27.18 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 158.55/27.18 ((('#C') @ is_of @ 158.55/27.18 ((('#C') @ in @ 158.55/27.18 (d_Sep @ (power @ frac) @ 158.55/27.18 (anec @ frac @ n_eq)))))))) @ 158.55/27.18 ((('#S') @ ((('#B') @ (=>) @ (rt_lessis @ '#sk1'))) @ 158.55/27.18 ((('#B') @ d_not @ (rt_more @ '#sk1')))))))))), 158.55/27.18 inference('comb-normalize', [status(thm)], [zip_derived_cl641])). 158.55/27.18 thf(zip_derived_cl643, plain, 158.55/27.18 (~ (((is_of @ '#sk2' @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 158.55/27.18 (((rt_lessis @ '#sk1' @ '#sk2') => (d_not @ 158.55/27.18 (rt_more @ '#sk1' @ '#sk2'))))))), 158.55/27.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl642])). 158.55/27.18 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 158.55/27.18 thf('3', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 158.55/27.18 define([status(thm)])). 158.55/27.18 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 158.55/27.18 thf('4', plain, 158.55/27.18 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 158.55/27.18 define([status(thm)])). 158.55/27.18 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))). 158.55/27.18 thf('5', plain, 158.55/27.18 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )), 158.55/27.18 define([status(thm)])). 158.55/27.18 thf(def_e_in, axiom,(( e_in @ (X1)@ (X2)@ (X0)) = ((X0)))). 158.55/27.18 thf('6', plain, 158.55/27.18 (![X2:( $i > $o ),X1:$i,X0:$i]: ( ( e_in @ X1 @ X2 @ X0 ) = ( X0 ) )), 158.55/27.18 define([status(thm)])). 158.55/27.18 thf(def_ecect, axiom,(( ecect @ (X0)@ (X1)@ (X2)) = 158.55/27.18 ((e_in @ (power @ X0) @ (anec @ X0 @ X1) @ X2)))). 158.55/27.18 thf('7', plain, 158.55/27.18 (![X2:$i,X1:( $i > $i > $o ),X0:$i]: 158.55/27.18 ( ( ecect @ X0 @ X1 @ X2 ) = 158.55/27.18 ( e_in @ ( power @ X0 ) @ ( anec @ X0 @ X1 ) @ X2 ) )), 158.55/27.18 define([status(thm)])). 158.55/27.18 thf(def_rt_is, axiom,(( rt_is @ (X0)@ (X1)) = ((e_is @ rat @ X0 @ X1)))). 158.55/27.18 thf('8', plain, 158.55/27.18 (![X1:$i,X0:$i]: ( ( rt_is @ X0 @ X1 ) = ( e_is @ rat @ X0 @ X1 ) )), 158.55/27.18 define([status(thm)])). 158.55/27.18 thf(def_class, axiom,(( class @ (X0)) = ((ecect @ frac @ n_eq @ X0)))). 158.55/27.18 thf('9', plain, 158.55/27.18 (![X0:$i]: ( ( class @ X0 ) = ( ecect @ frac @ n_eq @ X0 ) )), 158.55/27.18 define([status(thm)])). 158.55/27.18 thf(def_rt_more, axiom,(( rt_more @ (X0)@ (X1)) = 158.55/27.18 ((l_some @ frac @ 158.55/27.18 (^[Y0 : $i]: 158.55/27.18 (l_some @ frac @ 158.55/27.18 (^[Y1 : $i]: 158.55/27.18 (and3 @ (inf @ Y0 @ (class @ X0)) @ (inf @ Y1 @ (class @ X1)) @ 158.55/27.18 (moref @ Y0 @ Y1))))))))). 158.55/27.18 thf('10', plain, 158.55/27.18 (![X1:$i,X0:$i]: 158.55/27.18 ( ( rt_more @ X0 @ X1 ) = 158.55/27.18 ( l_some @ 158.55/27.18 frac @ 158.55/27.18 ( ^[V_1:$i]: 158.55/27.18 ( l_some @ 158.55/27.18 frac @ 158.55/27.18 ( ^[V_2:$i]: 158.55/27.18 ( and3 @ 158.55/27.18 ( inf @ V_1 @ ( class @ X0 ) ) @ 158.55/27.18 ( inf @ V_2 @ ( class @ X1 ) ) @ ( moref @ V_1 @ V_2 ) ) ) ) ) ) )), 158.55/27.18 define([status(thm)])). 158.55/27.18 thf(def_rt_less, axiom,(( rt_less @ (X0)@ (X1)) = 158.55/27.18 ((l_some @ frac @ 158.55/27.18 (^[Y0 : $i]: 158.55/27.18 (l_some @ frac @ 158.55/27.18 (^[Y1 : $i]: 158.55/27.18 (and3 @ (inf @ Y0 @ (class @ X0)) @ (inf @ Y1 @ (class @ X1)) @ 158.55/27.18 (lessf @ Y0 @ Y1))))))))). 158.55/27.18 thf('11', plain, 158.55/27.18 (![X1:$i,X0:$i]: 158.55/27.18 ( ( rt_less @ X0 @ X1 ) = 158.55/27.18 ( l_some @ 158.55/27.18 frac @ 158.55/27.18 ( ^[V_1:$i]: 158.55/27.18 ( l_some @ 158.55/27.18 frac @ 158.55/27.18 ( ^[V_2:$i]: 158.55/27.18 ( and3 @ 158.55/27.18 ( inf @ V_1 @ ( class @ X0 ) ) @ 158.55/27.18 ( inf @ V_2 @ ( class @ X1 ) ) @ ( lessf @ V_1 @ V_2 ) ) ) ) ) ) )), 158.55/27.18 define([status(thm)])). 158.55/27.18 thf(def_rt_lessis, axiom,(( rt_lessis @ (X0)@ (X1)) = 158.55/27.18 ((l_or @ (rt_less @ X0 @ X1) @ (rt_is @ X0 @ X1))))). 158.55/27.18 thf('12', plain, 158.55/27.18 (![X1:$i,X0:$i]: 158.55/27.18 ( ( rt_lessis @ X0 @ X1 ) = 158.55/27.18 ( l_or @ ( rt_less @ X0 @ X1 ) @ ( rt_is @ X0 @ X1 ) ) )), 158.55/27.18 define([status(thm)])). 158.55/27.18 thf(zip_derived_cl644, plain, 158.55/27.18 (~ (((is_of @ '#sk2' @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 158.55/27.18 (((imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ((('#sk1') = ('#sk2')))) => (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))))))), 158.55/27.18 inference('rw', [status(thm)], 158.55/27.18 [zip_derived_cl643, '3', '3', '4', '5', '6', '6', '0', '7', 158.55/27.18 '7', '1', '8', '9', '9', '10', '11', '12'])). 158.55/27.18 thf(zip_derived_cl646, plain, 158.55/27.18 (~ (((imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ((('#sk1') = ('#sk2')))) => (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl644])). 158.55/27.18 thf(zip_derived_cl647, plain, 158.55/27.18 ( (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ((('#sk1') = ('#sk2'))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl646])). 158.55/27.18 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 158.55/27.18 thf('13', plain, 158.55/27.18 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 158.55/27.18 inference('rw.lit', [status(esa)], [def_imp])). 158.55/27.18 thf(zip_derived_cl649, plain, 158.55/27.18 ( (((imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false)) => ((('#sk1') = ('#sk2')))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl647, '13'])). 158.55/27.18 thf(zip_derived_cl651, plain, 158.55/27.18 ((~ (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false)) 158.55/27.18 | ((('#sk1') = ('#sk2'))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl649])). 158.55/27.18 thf(zip_derived_cl654, plain, 158.55/27.18 ((~ (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false)) 158.55/27.18 | (('#sk1') = ('#sk2')))), 158.55/27.18 inference('simplify nested equalities', [status(thm)], 158.55/27.18 [zip_derived_cl651])). 158.55/27.18 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 158.55/27.18 thf('14', plain, 158.55/27.18 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 158.55/27.18 inference('rw.lit', [status(esa)], [def_imp])). 158.55/27.18 thf(zip_derived_cl655, plain, 158.55/27.18 ((~ (((l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 lessf))))) => 158.55/27.18 ($false))) 158.55/27.18 | (('#sk1') = ('#sk2')))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl654, '14'])). 158.55/27.18 thf(zip_derived_cl656, plain, 158.55/27.18 ((~ (((~) @ (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 lessf))))))) 158.55/27.18 | (('#sk1') = ('#sk2')))), 158.55/27.18 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl655])). 158.55/27.18 thf(zip_derived_cl657, plain, 158.55/27.18 (( (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 lessf))))) 158.55/27.18 | (('#sk1') = ('#sk2')))), 158.55/27.18 inference('simplify nested equalities', [status(thm)], 158.55/27.18 [zip_derived_cl656])). 158.55/27.18 thf(satz81b, axiom, 158.55/27.18 (all_of @ 158.55/27.18 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 158.55/27.18 ( ^[X0:$i]: 158.55/27.18 ( all_of @ 158.55/27.18 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 158.55/27.18 ( ^[X1:$i]: 158.55/27.18 ( ec3 @ 158.55/27.18 ( rt_is @ X0 @ X1 ) @ ( rt_more @ X0 @ X1 ) @ 158.55/27.18 ( rt_less @ X0 @ X1 ) ) ) ) ))). 158.55/27.18 thf(zip_derived_cl489, plain, 158.55/27.18 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @ 158.55/27.18 (^[Y0 : $i]: 158.55/27.18 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @ 158.55/27.18 (^[Y1 : $i]: 158.55/27.18 (ec3 @ (rt_is @ Y0 @ Y1) @ (rt_more @ Y0 @ Y1) @ 158.55/27.18 (rt_less @ Y0 @ Y1))))))), 158.55/27.18 inference('cnf', [status(esa)], [satz81b])). 158.55/27.18 thf(zip_derived_cl490, plain, 158.55/27.18 ( (all_of @ ((('#C') @ in @ rat)) @ 158.55/27.18 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#B') @ ((('#B') @ ec3)) @ rt_is)))) @ 158.55/27.18 rt_more)))) @ 158.55/27.18 rt_less)))))), 158.55/27.18 inference('lams2combs', [status(thm)], [zip_derived_cl489])). 158.55/27.18 thf(zip_derived_cl1806, plain, 158.55/27.18 ( (all_of @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 158.55/27.18 ((('#B') @ (all_of @ 158.55/27.18 ((('#C') @ in @ 158.55/27.18 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#B') @ ((('#B') @ ec3)) @ rt_is)))) @ 158.55/27.18 rt_more)))) @ 158.55/27.18 rt_less)))))), 158.55/27.18 inference('rw', [status(thm)], [zip_derived_cl490, '0', '1'])). 158.55/27.18 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 158.55/27.18 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 158.55/27.18 thf('15', plain, 158.55/27.18 (![X0:( $i > $o ),X1:( $i > $o )]: 158.55/27.18 ( ( all_of @ X0 @ X1 ) <=> 158.55/27.18 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 158.55/27.18 inference('rw.lit', [status(esa)], [def_all_of])). 158.55/27.18 thf(zip_derived_cl1807, plain, 158.55/27.18 ( (((!!) @ (^[Y0 : $i]: 158.55/27.18 (((is_of @ Y0 @ 158.55/27.18 ((('#C') @ in @ 158.55/27.18 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 158.55/27.18 ((('#B') @ (all_of @ 158.55/27.18 ((('#C') @ in @ 158.55/27.18 (d_Sep @ (power @ frac) @ 158.55/27.18 (anec @ frac @ n_eq))))) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#B') @ ((('#B') @ ec3)) @ 158.55/27.18 rt_is)))) @ 158.55/27.18 rt_more)))) @ 158.55/27.18 rt_less)) @ 158.55/27.18 Y0)))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1806, '15'])). 158.55/27.18 thf(zip_derived_cl1808, plain, 158.55/27.18 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 158.55/27.18 ((('#C') @ is_of @ 158.55/27.18 ((('#C') @ in @ 158.55/27.18 (d_Sep @ (power @ frac) @ 158.55/27.18 (anec @ frac @ n_eq)))))))) @ 158.55/27.18 ((('#B') @ (all_of @ 158.55/27.18 ((('#C') @ in @ 158.55/27.18 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#B') @ ((('#B') @ ec3)) @ 158.55/27.18 rt_is)))) @ 158.55/27.18 rt_more)))) @ 158.55/27.18 rt_less))))))))), 158.55/27.18 inference('comb-normalize', [status(thm)], [zip_derived_cl1807])). 158.55/27.18 thf(zip_derived_cl1809, plain, 158.55/27.18 (![X2 : $i]: 158.55/27.18 (((is_of @ X2 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 158.55/27.18 (all_of @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 158.55/27.18 ((('#S') @ ((('#S') @ ((('#B') @ ec3 @ (rt_is @ X2))) @ 158.55/27.18 (rt_more @ X2))) @ 158.55/27.18 (rt_less @ X2))))))), 158.55/27.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1808])). 158.55/27.18 thf(zip_derived_cl1810, plain, 158.55/27.18 (![X2 : $i]: 158.55/27.18 (~ (is_of @ X2 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | (all_of @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 158.55/27.18 ((('#S') @ ((('#S') @ ((('#B') @ ec3 @ (rt_is @ X2))) @ 158.55/27.18 (rt_more @ X2))) @ 158.55/27.18 (rt_less @ X2)))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1809])). 158.55/27.18 thf(zip_derived_cl1811, plain, 158.55/27.18 (![X0 : $i]: 158.55/27.18 ( (((!!) @ (^[Y0 : $i]: 158.55/27.18 (((is_of @ Y0 @ 158.55/27.18 ((('#C') @ in @ 158.55/27.18 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 158.55/27.18 ((('#S') @ ((('#S') @ ((('#B') @ ec3 @ (rt_is @ X0))) @ 158.55/27.18 (rt_more @ X0))) @ 158.55/27.18 (rt_less @ X0) @ Y0))))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1810, '15'])). 158.55/27.18 thf(zip_derived_cl1812, plain, 158.55/27.18 (![X0 : $i]: 158.55/27.18 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 158.55/27.18 ((('#C') @ is_of @ 158.55/27.18 ((('#C') @ in @ 158.55/27.18 (d_Sep @ (power @ frac) @ 158.55/27.18 (anec @ frac @ n_eq)))))))) @ 158.55/27.18 ((('#S') @ ((('#S') @ ((('#B') @ ec3 @ (rt_is @ X0))) @ 158.55/27.18 (rt_more @ X0))) @ 158.55/27.18 (rt_less @ X0))))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('comb-normalize', [status(thm)], [zip_derived_cl1811])). 158.55/27.18 thf(zip_derived_cl1813, plain, 158.55/27.18 (![X0 : $i, X2 : $i]: 158.55/27.18 ( (((is_of @ X2 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 158.55/27.18 (ec3 @ (rt_is @ X0 @ X2) @ (rt_more @ X0 @ X2) @ 158.55/27.18 (rt_less @ X0 @ X2)))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1812])). 158.55/27.18 thf(def_l_ec, axiom,(( l_ec @ (X0)@ (X1)) = ((imp @ X0 @ (d_not @ X1))))). 158.55/27.18 thf('16', plain, 158.55/27.18 (![X1:$o,X0:$o]: ( ( l_ec @ X0 @ X1 ) = ( imp @ X0 @ ( d_not @ X1 ) ) )), 158.55/27.18 define([status(thm)])). 158.55/27.18 thf(def_d_and, axiom,(( d_and @ (X0)@ (X1)) = ((d_not @ (l_ec @ X0 @ X1))))). 158.55/27.18 thf('17', plain, 158.55/27.18 (![X1:$o,X0:$o]: ( ( d_and @ X0 @ X1 ) = ( d_not @ ( l_ec @ X0 @ X1 ) ) )), 158.55/27.18 define([status(thm)])). 158.55/27.18 thf(def_and3, axiom,(( and3 @ (X0)@ (X1)@ (X2)) = 158.55/27.18 ((d_and @ X0 @ (d_and @ X1 @ X2))))). 158.55/27.18 thf('18', plain, 158.55/27.18 (![X2:$o,X1:$o,X0:$o]: 158.55/27.18 ( ( and3 @ X0 @ X1 @ X2 ) = ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) )), 158.55/27.18 define([status(thm)])). 158.55/27.18 thf(def_ec3, axiom,(( ec3 @ (X0)@ (X1)@ (X2)) = 158.55/27.18 ((and3 @ (l_ec @ X0 @ X1) @ (l_ec @ X1 @ X2) @ (l_ec @ X2 @ X0))))). 158.55/27.18 thf('19', plain, 158.55/27.18 (![X2:$o,X1:$o,X0:$o]: 158.55/27.18 ( ( ec3 @ X0 @ X1 @ X2 ) = 158.55/27.18 ( and3 @ ( l_ec @ X0 @ X1 ) @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X0 ) ) )), 158.55/27.18 define([status(thm)])). 158.55/27.18 thf(zip_derived_cl1814, plain, 158.55/27.18 (![X0 : $i, X2 : $i]: 158.55/27.18 ( (((is_of @ X2 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ (((X0) = (X2))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X0) = (X2))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('rw', [status(thm)], 158.55/27.18 [zip_derived_cl1813, '3', '3', '3', '3', '3', '3', '3', '16', 158.55/27.18 '16', '16', '16', '16', '17', '17', '18', '19', '5', '6', 158.55/27.18 '6', '0', '7', '7', '1', '8', '9', '9', '10', '11'])). 158.55/27.18 thf(zip_derived_cl1815, plain, 158.55/27.18 (![X0 : $i, X2 : $i]: 158.55/27.18 (~ (is_of @ X2 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ (((X0) = (X2))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X0) = (X2))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1814])). 158.55/27.18 thf(zip_derived_cl1816, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (((imp @ 158.55/27.18 (imp @ (((X0) = (X1))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X0) = (X1))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) => 158.55/27.18 ($false))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1815, '13'])). 158.55/27.18 thf(zip_derived_cl1817, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (((~) @ (imp @ 158.55/27.18 (imp @ (((X0) = (X1))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X0) = (X1))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('simplify boolean subterms', [status(thm)], 158.55/27.18 [zip_derived_cl1816])). 158.55/27.18 thf(zip_derived_cl1818, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (imp @ 158.55/27.18 (imp @ (((X0) = (X1))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X0) = (X1))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('simplify nested equalities', [status(thm)], 158.55/27.18 [zip_derived_cl1817])). 158.55/27.18 thf(zip_derived_cl1819, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (((imp @ (((X1) = (X0))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) => 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X1) = (X0))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false)))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1818, '14'])). 158.55/27.18 thf(zip_derived_cl1821, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X1) = (X0))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false)) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1819])). 158.55/27.18 thf(zip_derived_cl1823, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (((imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X1) = (X0))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) => ($false))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1821, '14'])). 158.55/27.18 thf(zip_derived_cl1825, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (((~) @ (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X1) = (X0))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('simplify boolean subterms', [status(thm)], 158.55/27.18 [zip_derived_cl1823])). 158.55/27.18 thf(zip_derived_cl1826, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X1) = (X0))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('simplify nested equalities', [status(thm)], 158.55/27.18 [zip_derived_cl1825])). 158.55/27.18 thf(zip_derived_cl1827, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (((imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X0) = (X1))) @ ($false))) @ 158.55/27.18 ($false))) => 158.55/27.18 ($false))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1826, '13'])). 158.55/27.18 thf(zip_derived_cl1830, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (((~) @ (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X0) = (X1))) @ ($false))) @ 158.55/27.18 ($false))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('simplify boolean subterms', [status(thm)], 158.55/27.18 [zip_derived_cl1827])). 158.55/27.18 thf(zip_derived_cl1831, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X0) = (X1))) @ ($false))) @ 158.55/27.18 ($false))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('simplify nested equalities', [status(thm)], 158.55/27.18 [zip_derived_cl1830])). 158.55/27.18 thf(zip_derived_cl1832, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (((imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) => 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X1) = (X0))) @ ($false))) @ 158.55/27.18 ($false)))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1831, '14'])). 158.55/27.18 thf(zip_derived_cl1835, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1832])). 158.55/27.18 thf(zip_derived_cl1837, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (((l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) => 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false)))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1835, '13'])). 158.55/27.18 thf(zip_derived_cl1839, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) 158.55/27.18 | (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false)) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1837])). 158.55/27.18 thf(zip_derived_cl1843, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (((l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) => 158.55/27.18 ($false))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1839, '13'])). 158.55/27.18 thf(zip_derived_cl1845, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (((~) @ (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))))), 158.55/27.18 inference('simplify boolean subterms', [status(thm)], 158.55/27.18 [zip_derived_cl1843])). 158.55/27.18 thf(zip_derived_cl1846, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))))), 158.55/27.18 inference('simplify nested equalities', [status(thm)], 158.55/27.18 [zip_derived_cl1845])). 158.55/27.18 thf(zip_derived_cl10179, plain, 158.55/27.18 (((('#sk1') = ('#sk2')) 158.55/27.18 | ~ (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 moref))))) 158.55/27.18 | ~ (is_of @ '#sk1' @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ '#sk2' @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('sup-', [status(thm)], [zip_derived_cl657, zip_derived_cl1846])). 158.55/27.18 thf(zip_derived_cl648, plain, 158.55/27.18 (~ (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl646])). 158.55/27.18 thf(zip_derived_cl650, plain, 158.55/27.18 (~ (((l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 moref))))) => 158.55/27.18 ($false)))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl648, '14'])). 158.55/27.18 thf(zip_derived_cl652, plain, 158.55/27.18 (~ (((~) @ (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 moref)))))))), 158.55/27.18 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl650])). 158.55/27.18 thf(zip_derived_cl653, plain, 158.55/27.18 ( (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 moref)))))), 158.55/27.18 inference('simplify nested equalities', [status(thm)], 158.55/27.18 [zip_derived_cl652])). 158.55/27.18 thf(zip_derived_cl639, plain, 158.55/27.18 ( (is_of @ '#sk1' @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl638])). 158.55/27.18 thf(zip_derived_cl645, plain, 158.55/27.18 ( (is_of @ '#sk2' @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl644])). 158.55/27.18 thf(zip_derived_cl10213, plain, ((('#sk1') = ('#sk2'))), 158.55/27.18 inference('demod', [status(thm)], 158.55/27.18 [zip_derived_cl10179, zip_derived_cl653, zip_derived_cl639, 158.55/27.18 zip_derived_cl645])). 158.55/27.18 thf(zip_derived_cl653, plain, 158.55/27.18 ( (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ '#sk1')))))) @ 158.55/27.18 ((('#C') @ inf @ '#sk2')))))) @ 158.55/27.18 moref)))))), 158.55/27.18 inference('simplify nested equalities', [status(thm)], 158.55/27.18 [zip_derived_cl652])). 158.55/27.18 thf(satz81, axiom, 158.55/27.18 (all_of @ 158.55/27.18 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 158.55/27.18 ( ^[X0:$i]: 158.55/27.18 ( all_of @ 158.55/27.18 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 158.55/27.18 ( ^[X1:$i]: 158.55/27.18 ( orec3 @ 158.55/27.18 ( rt_is @ X0 @ X1 ) @ ( rt_more @ X0 @ X1 ) @ 158.55/27.18 ( rt_less @ X0 @ X1 ) ) ) ) ))). 158.55/27.18 thf(zip_derived_cl487, plain, 158.55/27.18 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @ 158.55/27.18 (^[Y0 : $i]: 158.55/27.18 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @ 158.55/27.18 (^[Y1 : $i]: 158.55/27.18 (orec3 @ (rt_is @ Y0 @ Y1) @ (rt_more @ Y0 @ Y1) @ 158.55/27.18 (rt_less @ Y0 @ Y1))))))), 158.55/27.18 inference('cnf', [status(esa)], [satz81])). 158.55/27.18 thf(zip_derived_cl488, plain, 158.55/27.18 ( (all_of @ ((('#C') @ in @ rat)) @ 158.55/27.18 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#B') @ ((('#B') @ orec3)) @ rt_is)))) @ 158.55/27.18 rt_more)))) @ 158.55/27.18 rt_less)))))), 158.55/27.18 inference('lams2combs', [status(thm)], [zip_derived_cl487])). 158.55/27.18 thf(zip_derived_cl1725, plain, 158.55/27.18 ( (all_of @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 158.55/27.18 ((('#B') @ (all_of @ 158.55/27.18 ((('#C') @ in @ 158.55/27.18 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#B') @ ((('#B') @ orec3)) @ rt_is)))) @ 158.55/27.18 rt_more)))) @ 158.55/27.18 rt_less)))))), 158.55/27.18 inference('rw', [status(thm)], [zip_derived_cl488, '0', '1'])). 158.55/27.18 thf(zip_derived_cl1726, plain, 158.55/27.18 ( (((!!) @ (^[Y0 : $i]: 158.55/27.18 (((is_of @ Y0 @ 158.55/27.18 ((('#C') @ in @ 158.55/27.18 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 158.55/27.18 ((('#B') @ (all_of @ 158.55/27.18 ((('#C') @ in @ 158.55/27.18 (d_Sep @ (power @ frac) @ 158.55/27.18 (anec @ frac @ n_eq))))) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#B') @ ((('#B') @ orec3)) @ 158.55/27.18 rt_is)))) @ 158.55/27.18 rt_more)))) @ 158.55/27.18 rt_less)) @ 158.55/27.18 Y0)))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1725, '15'])). 158.55/27.18 thf(zip_derived_cl1727, plain, 158.55/27.18 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 158.55/27.18 ((('#C') @ is_of @ 158.55/27.18 ((('#C') @ in @ 158.55/27.18 (d_Sep @ (power @ frac) @ 158.55/27.18 (anec @ frac @ n_eq)))))))) @ 158.55/27.18 ((('#B') @ (all_of @ 158.55/27.18 ((('#C') @ in @ 158.55/27.18 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#B') @ ((('#B') @ orec3)) @ 158.55/27.18 rt_is)))) @ 158.55/27.18 rt_more)))) @ 158.55/27.18 rt_less))))))))), 158.55/27.18 inference('comb-normalize', [status(thm)], [zip_derived_cl1726])). 158.55/27.18 thf(zip_derived_cl1728, plain, 158.55/27.18 (![X2 : $i]: 158.55/27.18 (((is_of @ X2 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 158.55/27.18 (all_of @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 158.55/27.18 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X2))) @ 158.55/27.18 (rt_more @ X2))) @ 158.55/27.18 (rt_less @ X2))))))), 158.55/27.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1727])). 158.55/27.18 thf(zip_derived_cl1729, plain, 158.55/27.18 (![X2 : $i]: 158.55/27.18 (~ (is_of @ X2 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | (all_of @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))) @ 158.55/27.18 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X2))) @ 158.55/27.18 (rt_more @ X2))) @ 158.55/27.18 (rt_less @ X2)))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1728])). 158.55/27.18 thf(zip_derived_cl1730, plain, 158.55/27.18 (![X0 : $i]: 158.55/27.18 ( (((!!) @ (^[Y0 : $i]: 158.55/27.18 (((is_of @ Y0 @ 158.55/27.18 ((('#C') @ in @ 158.55/27.18 (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 158.55/27.18 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X0))) @ 158.55/27.18 (rt_more @ X0))) @ 158.55/27.18 (rt_less @ X0) @ Y0))))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1729, '15'])). 158.55/27.18 thf(zip_derived_cl1731, plain, 158.55/27.18 (![X0 : $i]: 158.55/27.18 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 158.55/27.18 ((('#C') @ is_of @ 158.55/27.18 ((('#C') @ in @ 158.55/27.18 (d_Sep @ (power @ frac) @ 158.55/27.18 (anec @ frac @ n_eq)))))))) @ 158.55/27.18 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (rt_is @ X0))) @ 158.55/27.18 (rt_more @ X0))) @ 158.55/27.18 (rt_less @ X0))))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('comb-normalize', [status(thm)], [zip_derived_cl1730])). 158.55/27.18 thf(zip_derived_cl1732, plain, 158.55/27.18 (![X0 : $i, X2 : $i]: 158.55/27.18 ( (((is_of @ X2 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 158.55/27.18 (orec3 @ (rt_is @ X0 @ X2) @ (rt_more @ X0 @ X2) @ 158.55/27.18 (rt_less @ X0 @ X2)))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1731])). 158.55/27.18 thf(def_or3, axiom,(( or3 @ (X0)@ (X1)@ (X2)) = 158.55/27.18 ((l_or @ X0 @ (l_or @ X1 @ X2))))). 158.55/27.18 thf('20', plain, 158.55/27.18 (![X2:$o,X1:$o,X0:$o]: 158.55/27.18 ( ( or3 @ X0 @ X1 @ X2 ) = ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) )), 158.55/27.18 define([status(thm)])). 158.55/27.18 thf(def_orec3, axiom,(( orec3 @ (X0)@ (X1)@ (X2)) = 158.55/27.18 ((d_and @ (or3 @ X0 @ X1 @ X2) @ (ec3 @ X0 @ X1 @ X2))))). 158.55/27.18 thf('21', plain, 158.55/27.18 (![X2:$o,X1:$o,X0:$o]: 158.55/27.18 ( ( orec3 @ X0 @ X1 @ X2 ) = 158.55/27.18 ( d_and @ ( or3 @ X0 @ X1 @ X2 ) @ ( ec3 @ X0 @ X1 @ X2 ) ) )), 158.55/27.18 define([status(thm)])). 158.55/27.18 thf(zip_derived_cl1733, plain, 158.55/27.18 (![X0 : $i, X2 : $i]: 158.55/27.18 ( (((is_of @ X2 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) => 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ (imp @ (((X0) = (X2))) @ ($false)) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false)) @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 lessf))))))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ (((X0) = (X2))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X0) = (X2))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('rw', [status(thm)], 158.55/27.18 [zip_derived_cl1732, '3', '3', '3', '3', '3', '3', '3', '3', 158.55/27.18 '3', '16', '16', '16', '16', '16', '16', '17', '17', '17', 158.55/27.18 '4', '4', '20', '18', '19', '21', '5', '6', '6', '0', '7', 158.55/27.18 '7', '1', '8', '9', '9', '10', '11'])). 158.55/27.18 thf(zip_derived_cl1734, plain, 158.55/27.18 (![X0 : $i, X2 : $i]: 158.55/27.18 (~ (is_of @ X2 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ (imp @ (((X0) = (X2))) @ ($false)) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false)) @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 lessf))))))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ (((X0) = (X2))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X2)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X0) = (X2))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1733])). 158.55/27.18 thf(zip_derived_cl1735, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (((imp @ 158.55/27.18 (imp @ (imp @ (((X0) = (X1))) @ ($false)) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false)) @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ (((X0) = (X1))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X0) = (X1))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) => 158.55/27.18 ($false))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1734, '13'])). 158.55/27.18 thf(zip_derived_cl1736, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (((~) @ (imp @ 158.55/27.18 (imp @ (imp @ (((X0) = (X1))) @ ($false)) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false)) @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ (((X0) = (X1))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X0) = (X1))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('simplify boolean subterms', [status(thm)], 158.55/27.18 [zip_derived_cl1735])). 158.55/27.18 thf(zip_derived_cl1737, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (imp @ 158.55/27.18 (imp @ (imp @ (((X0) = (X1))) @ ($false)) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false)) @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ (((X0) = (X1))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X0) = (X1))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('simplify nested equalities', [status(thm)], 158.55/27.18 [zip_derived_cl1736])). 158.55/27.18 thf(zip_derived_cl1738, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (((imp @ (imp @ (((X1) = (X0))) @ ($false)) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false)) @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))))) => 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ (((X1) = (X0))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X1) = (X0))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false)))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1737, '14'])). 158.55/27.18 thf(zip_derived_cl1740, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ (((X1) = (X0))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X1) = (X0))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false)) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1738])). 158.55/27.18 thf(zip_derived_cl1742, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (((imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ (((X1) = (X0))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X1) = (X0))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) => ($false))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1740, '14'])). 158.55/27.18 thf(zip_derived_cl1744, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (((~) @ (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ (((X1) = (X0))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X1) = (X0))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('simplify boolean subterms', [status(thm)], 158.55/27.18 [zip_derived_cl1742])). 158.55/27.18 thf(zip_derived_cl1745, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ (((X1) = (X0))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X1) = (X0))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('simplify nested equalities', [status(thm)], 158.55/27.18 [zip_derived_cl1744])). 158.55/27.18 thf(zip_derived_cl1746, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (((imp @ 158.55/27.18 (imp @ (((X0) = (X1))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X0) = (X1))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) => 158.55/27.18 ($false))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1745, '13'])). 158.55/27.18 thf(zip_derived_cl1748, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (((~) @ (imp @ 158.55/27.18 (imp @ (((X0) = (X1))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X0) = (X1))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('simplify boolean subterms', [status(thm)], 158.55/27.18 [zip_derived_cl1746])). 158.55/27.18 thf(zip_derived_cl1749, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (imp @ 158.55/27.18 (imp @ (((X0) = (X1))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X0) = (X1))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('simplify nested equalities', [status(thm)], 158.55/27.18 [zip_derived_cl1748])). 158.55/27.18 thf(zip_derived_cl1750, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (((imp @ (((X1) = (X0))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) => 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 ($false))) @ 158.55/27.18 (imp @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 lessf))))) @ 158.55/27.18 (imp @ (((X1) = (X0))) @ ($false))) @ 158.55/27.18 ($false))) @ 158.55/27.18 ($false)) @ 158.55/27.18 ($false)))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1749, '14'])). 158.55/27.18 thf(zip_derived_cl1754, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (imp @ (((X1) = (X0))) @ 158.55/27.18 (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1750])). 158.55/27.18 thf(zip_derived_cl1757, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (((((X1) = (X0))) => (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false)))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1754, '13'])). 158.55/27.18 thf(zip_derived_cl1760, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (((X1) = (X0))) 158.55/27.18 | (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false)) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1757])). 158.55/27.18 thf(zip_derived_cl1766, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (((X1) != (X0)) 158.55/27.18 | (imp @ 158.55/27.18 (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) @ 158.55/27.18 ($false)) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('simplify nested equalities', [status(thm)], 158.55/27.18 [zip_derived_cl1760])). 158.55/27.18 thf(zip_derived_cl1767, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (((l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) => 158.55/27.18 ($false))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ((X1) != (X0)))), 158.55/27.18 inference('rw_clause', [status(thm)], [zip_derived_cl1766, '13'])). 158.55/27.18 thf(zip_derived_cl1771, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 ( (((~) @ (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ((X1) != (X0)))), 158.55/27.18 inference('simplify boolean subterms', [status(thm)], 158.55/27.18 [zip_derived_cl1767])). 158.55/27.18 thf(zip_derived_cl1772, plain, 158.55/27.18 (![X0 : $i, X1 : $i]: 158.55/27.18 (~ (l_some @ frac @ 158.55/27.18 ((('#B') @ (l_some @ frac) @ 158.55/27.18 ((('#S') @ ((('#B') @ ('#S') @ 158.55/27.18 ((('#C') @ ((('#B') @ ('#B') @ 158.55/27.18 ((('#B') @ and3 @ 158.55/27.18 ((('#C') @ inf @ X1)))))) @ 158.55/27.18 ((('#C') @ inf @ X0)))))) @ 158.55/27.18 moref))))) 158.55/27.18 | ~ (is_of @ X0 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ X1 @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ((X1) != (X0)))), 158.55/27.18 inference('simplify nested equalities', [status(thm)], 158.55/27.18 [zip_derived_cl1771])). 158.55/27.18 thf(zip_derived_cl9693, plain, 158.55/27.18 (((('#sk1') != ('#sk2')) 158.55/27.18 | ~ (is_of @ '#sk1' @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))) 158.55/27.18 | ~ (is_of @ '#sk2' @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq))))))), 158.55/27.18 inference('sup-', [status(thm)], [zip_derived_cl653, zip_derived_cl1772])). 158.55/27.18 thf(zip_derived_cl639, plain, 158.55/27.18 ( (is_of @ '#sk1' @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl638])). 158.55/27.18 thf(zip_derived_cl645, plain, 158.55/27.18 ( (is_of @ '#sk2' @ 158.55/27.18 ((('#C') @ in @ (d_Sep @ (power @ frac) @ (anec @ frac @ n_eq)))))), 158.55/27.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl644])). 158.55/27.18 thf(zip_derived_cl9726, plain, ((('#sk1') != ('#sk2'))), 158.55/27.18 inference('demod', [status(thm)], 158.55/27.18 [zip_derived_cl9693, zip_derived_cl639, zip_derived_cl645])). 158.55/27.18 thf(zip_derived_cl10214, plain, ($false), 158.55/27.18 inference('simplify_reflect-', [status(thm)], 158.55/27.18 [zip_derived_cl10213, zip_derived_cl9726])). 158.55/27.18 158.55/27.18 % SZS output end Refutation 158.55/27.18 158.55/27.18 158.55/27.18 % Terminating... 159.36/27.38 % Runner terminated. 159.40/27.40 % Zipperpin 1.5 exiting 159.40/27.42 EOF