0.05/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.16 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.3OGp5HabmX true 0.15/0.36 % Computer : n028.cluster.edu 0.15/0.36 % Model : x86_64 x86_64 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.36 % Memory : 8042.1875MB 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.36 % CPULimit : 960 0.15/0.36 % WCLimit : 120 0.15/0.36 % DateTime : Tue Aug 9 08:06:35 EDT 2022 0.15/0.36 % CPUTime : 0.15/0.36 % Running portfolio for 960 s 0.15/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.15/0.36 % Number of cores: 8 0.15/0.36 % Python version: Python 3.6.8 0.15/0.36 % Running in HO mode 0.51/0.64 % Total configuration time : 828 0.51/0.64 % Estimated wc time : 1656 0.51/0.64 % Estimated cpu time (8 cpus) : 207.0 0.51/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.51/0.73 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.51/0.73 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.51/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.51/0.73 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.51/0.74 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.51/0.74 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.51/0.74 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 130.15/17.07 % Solved by lams/40_b.comb.sh. 130.15/17.07 % done 0 iterations in 16.262s 130.15/17.07 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 130.15/17.07 % SZS output start Refutation 130.15/17.07 thf(rt_is_type, type, rt_is: $i > $i > $o). 130.15/17.07 thf('#ty_enc10_type', type, '#ty_enc10': (($i > $o) > $o) > ($i > $i > $o) > 130.15/17.07 $i > $o). 130.15/17.07 thf(inf_type, type, inf: $i > $i > $o). 130.15/17.07 thf('#ty_enc9_type', type, '#ty_enc9': ($i > $i > $o) > $i > $i > $o). 130.15/17.07 thf(plusfrt_type, type, plusfrt: $i). 130.15/17.07 thf('#ty_enc13_type', type, '#ty_enc13': ($i > ($i > $o) > $i > $o > $o) > 130.15/17.07 ($i > $o) > $i > $i > $o > $o). 130.15/17.07 thf(rt_lessis_type, type, rt_lessis: $i > $i > $o). 130.15/17.07 thf(d_not_type, type, d_not: $o > $o). 130.15/17.07 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 130.15/17.07 thf(in_type, type, in: $i > $i > $o). 130.15/17.07 thf('#ty_enc16_type', type, '#ty_enc16': ($o > $o > $o) > ($i > $o) > $i > $o > $o). 130.15/17.07 thf('#sk5_type', type, '#sk5': $i). 130.15/17.07 thf('#sk7_type', type, '#sk7': $i). 130.15/17.07 thf(and3_type, type, and3: $o > $o > $o > $o). 130.15/17.07 thf(e_is_type, type, e_is: $i > $i > $i > $o). 130.15/17.07 thf(l_or_type, type, l_or: $o > $o > $o). 130.15/17.07 thf('#ty_enc12_type', type, '#ty_enc12': (($i > $o > $o) > ($i > $o) > $i > $o) > 130.15/17.07 ($i > $i > $o > $o) > $i > 130.15/17.07 ($i > $o) > $i > $o). 130.15/17.07 thf('#ty_enc11_type', type, '#ty_enc11': ($i > ($i > $o) > $i > $o) > 130.15/17.07 ($i > $i > $o) > $i > $i > $o). 130.15/17.07 thf('#ty_enc17_type', type, '#ty_enc17': ($i > $o > $o) > ($i > $o) > $i > $o). 130.15/17.07 thf('#ty_enc15_type', type, '#ty_enc15': ($o > $o > $o > $o) > ($i > $o) > 130.15/17.07 $i > $o > $o > $o). 130.15/17.07 thf(rat_type, type, rat: $i). 130.15/17.07 thf(lessf_type, type, lessf: $i > $i > $o). 130.15/17.07 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 130.15/17.07 thf(rt_pl_type, type, rt_pl: $i > $i > $i). 130.15/17.07 thf(frac_type, type, frac: $i). 130.15/17.07 thf(imp_type, type, imp: $o > $o > $o). 130.15/17.07 thf('#sk6_type', type, '#sk6': $i). 130.15/17.07 thf('#sk8_type', type, '#sk8': $i). 130.15/17.07 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 130.15/17.07 thf(indrat_type, type, indrat: $i > $i > $i > $i > $i). 130.15/17.07 thf(rt_less_type, type, rt_less: $i > $i > $o). 130.15/17.07 thf(n_eq_type, type, n_eq: $i > $i > $o). 130.15/17.07 thf(class_type, type, class: $i > $i). 130.15/17.07 thf('#ty_enc14_type', type, '#ty_enc14': (($o > $o > $o) > ($i > $o) > $i > 130.15/17.07 $o > $o) > 130.15/17.07 ($i > $o > $o > $o) > $i > 130.15/17.07 ($i > $o) > $i > $o > $o). 130.15/17.07 thf(ect_type, type, ect: $i > ($i > $i > $o) > $i). 130.15/17.07 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 130.15/17.07 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 130.15/17.07 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 130.15/17.07 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 130.15/17.07 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 130.15/17.07 thf(satz96f, axiom, 130.15/17.07 (all_of @ 130.15/17.07 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 130.15/17.07 ( ^[X0:$i]: 130.15/17.07 ( all_of @ 130.15/17.07 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 130.15/17.07 ( ^[X1:$i]: 130.15/17.07 ( all_of @ 130.15/17.07 ( ^[X2:$i]: ( in @ X2 @ rat ) ) @ 130.15/17.07 ( ^[X2:$i]: 130.15/17.07 ( ( rt_less @ X0 @ X1 ) => 130.15/17.07 ( rt_less @ ( rt_pl @ X2 @ X0 ) @ ( rt_pl @ X2 @ X1 ) ) ) ) ) ) ) ))). 130.15/17.07 thf(zip_derived_cl472, plain, 130.15/17.07 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @ 130.15/17.07 (^[Y0 : $i]: 130.15/17.07 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @ 130.15/17.07 (^[Y1 : $i]: 130.15/17.07 (all_of @ (^[Y2 : $i]: (in @ Y2 @ rat)) @ 130.15/17.07 (^[Y2 : $i]: 130.15/17.07 (((rt_less @ Y0 @ Y1) => (rt_less @ (rt_pl @ Y2 @ Y0) @ 130.15/17.07 (rt_pl @ Y2 @ Y1))))))))))), 130.15/17.07 inference('cnf', [status(esa)], [satz96f])). 130.15/17.07 thf(zip_derived_cl473, plain, 130.15/17.07 ( (all_of @ ((('#C') @ in @ rat)) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ rat))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ rt_less)) @ 130.15/17.07 ((('#C') @ rt_pl)))))))) @ 130.15/17.07 ((('#C') @ rt_pl)))))))))))), 130.15/17.07 inference('lams2combs', [status(thm)], [zip_derived_cl472])). 130.15/17.07 thf(def_rat, axiom,(( rat ) = ((ect @ frac @ n_eq)))). 130.15/17.07 thf('0', plain, (( rat ) = ( ect @ frac @ n_eq )), define([status(thm)])). 130.15/17.07 thf(zip_derived_cl3270, plain, 130.15/17.07 ( (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ rt_less)) @ 130.15/17.07 ((('#C') @ rt_pl)))))))) @ 130.15/17.07 ((('#C') @ rt_pl)))))))))))), 130.15/17.07 inference('rw', [status(thm)], [zip_derived_cl473, '0'])). 130.15/17.07 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 130.15/17.07 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 130.15/17.07 thf('1', plain, 130.15/17.07 (![X0:( $i > $o ),X1:( $i > $o )]: 130.15/17.07 ( ( all_of @ X0 @ X1 ) <=> 130.15/17.07 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 130.15/17.07 inference('rw.lit', [status(esa)], [def_all_of])). 130.15/17.07 thf(zip_derived_cl3271, plain, 130.15/17.07 ( (((!!) @ (^[Y0 : $i]: 130.15/17.07 (((is_of @ Y0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ 130.15/17.07 (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ rt_less)) @ 130.15/17.07 ((('#C') @ rt_pl)))))))) @ 130.15/17.07 ((('#C') @ rt_pl)))))))) @ 130.15/17.07 Y0)))))))), 130.15/17.07 inference('rw_clause', [status(thm)], [zip_derived_cl3270, '1'])). 130.15/17.07 thf(zip_derived_cl3272, plain, 130.15/17.07 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 130.15/17.07 ((('#C') @ is_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))))))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ rt_less)) @ 130.15/17.07 ((('#C') @ rt_pl)))))))) @ 130.15/17.07 ((('#C') @ rt_pl))))))))))))))), 130.15/17.07 inference('comb-normalize', [status(thm)], [zip_derived_cl3271])). 130.15/17.07 thf(zip_derived_cl3273, plain, 130.15/17.07 (![X2 : $i]: 130.15/17.07 (((is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (rt_less @ X2))))) @ 130.15/17.07 ((('#B') @ ((('#S') @ ((('#B') @ rt_less @ 130.15/17.07 ((('#C') @ rt_pl @ X2)))))) @ 130.15/17.07 ((('#C') @ rt_pl)))))))))))), 130.15/17.07 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3272])). 130.15/17.07 thf(zip_derived_cl3274, plain, 130.15/17.07 (![X2 : $i]: 130.15/17.07 (~ (is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ (=>) @ (rt_less @ X2))))) @ 130.15/17.07 ((('#B') @ ((('#S') @ ((('#B') @ rt_less @ 130.15/17.07 ((('#C') @ rt_pl @ X2)))))) @ 130.15/17.07 ((('#C') @ rt_pl))))))))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3273])). 130.15/17.07 thf(zip_derived_cl3275, plain, 130.15/17.07 (![X0 : $i]: 130.15/17.07 ( (((!!) @ (^[Y0 : $i]: 130.15/17.07 (((is_of @ Y0 @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ (=>) @ (rt_less @ X0))))) @ 130.15/17.07 ((('#B') @ ((('#S') @ ((('#B') @ rt_less @ 130.15/17.07 ((('#C') @ rt_pl @ X0)))))) @ 130.15/17.07 ((('#C') @ rt_pl)))))) @ 130.15/17.07 Y0))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('rw_clause', [status(thm)], [zip_derived_cl3274, '1'])). 130.15/17.07 thf(zip_derived_cl3276, plain, 130.15/17.07 (![X0 : $i]: 130.15/17.07 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 130.15/17.07 ((('#C') @ is_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))))))) @ 130.15/17.07 ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ (=>) @ (rt_less @ X0))))) @ 130.15/17.07 ((('#B') @ ((('#S') @ ((('#B') @ rt_less @ 130.15/17.07 ((('#C') @ rt_pl @ X0)))))) @ 130.15/17.07 ((('#C') @ rt_pl)))))))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('comb-normalize', [status(thm)], [zip_derived_cl3275])). 130.15/17.07 thf(zip_derived_cl3277, plain, 130.15/17.07 (![X0 : $i, X2 : $i]: 130.15/17.07 ( (((is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (((=>) @ (rt_less @ X0 @ X2))) @ 130.15/17.07 ((('#S') @ ((('#B') @ rt_less @ ((('#C') @ rt_pl @ X0)))) @ 130.15/17.07 ((('#C') @ rt_pl @ X2))))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3276])). 130.15/17.07 thf(def_rt_less, axiom,(( rt_less @ (X0)@ (X1)) = 130.15/17.07 ((l_some @ frac @ 130.15/17.07 (^[Y0 : $i]: 130.15/17.07 (l_some @ frac @ 130.15/17.07 (^[Y1 : $i]: 130.15/17.07 (and3 @ (inf @ Y0 @ (class @ X0)) @ (inf @ Y1 @ (class @ X1)) @ 130.15/17.07 (lessf @ Y0 @ Y1))))))))). 130.15/17.07 thf('2', plain, 130.15/17.07 (![X1:$i,X0:$i]: 130.15/17.07 ( ( rt_less @ X0 @ X1 ) = 130.15/17.07 ( l_some @ 130.15/17.07 frac @ 130.15/17.07 ( ^[V_1:$i]: 130.15/17.07 ( l_some @ 130.15/17.07 frac @ 130.15/17.07 ( ^[V_2:$i]: 130.15/17.07 ( and3 @ 130.15/17.07 ( inf @ V_1 @ ( class @ X0 ) ) @ 130.15/17.07 ( inf @ V_2 @ ( class @ X1 ) ) @ ( lessf @ V_1 @ V_2 ) ) ) ) ) ) )), 130.15/17.07 define([status(thm)])). 130.15/17.07 thf(zip_derived_cl3278, plain, 130.15/17.07 (![X0 : $i, X2 : $i]: 130.15/17.07 ( (((is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (((=>) @ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X0))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X2))))))) @ 130.15/17.07 lessf))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ rt_less @ ((('#C') @ rt_pl @ X0)))) @ 130.15/17.07 ((('#C') @ rt_pl @ X2))))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('rw', [status(thm)], [zip_derived_cl3277, '2'])). 130.15/17.07 thf(zip_derived_cl3279, plain, 130.15/17.07 (![X0 : $i, X2 : $i]: 130.15/17.07 (~ (is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (((=>) @ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X0))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X2))))))) @ 130.15/17.07 lessf))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ rt_less @ ((('#C') @ rt_pl @ X0)))) @ 130.15/17.07 ((('#C') @ rt_pl @ X2))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3278])). 130.15/17.07 thf(zip_derived_cl3280, plain, 130.15/17.07 (![X0 : $i, X1 : $i]: 130.15/17.07 ( (((!!) @ (^[Y0 : $i]: 130.15/17.07 (((is_of @ Y0 @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 ((('#B') @ (((=>) @ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ( 130.15/17.07 '#S') @ 130.15/17.07 ((('#C') @ ( 130.15/17.07 (('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X0))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X1))))))) @ 130.15/17.07 lessf))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ rt_less @ 130.15/17.07 ((('#C') @ rt_pl @ X0)))) @ 130.15/17.07 ((('#C') @ rt_pl @ X1)))) @ 130.15/17.07 Y0))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('rw_clause', [status(thm)], [zip_derived_cl3279, '1'])). 130.15/17.07 thf(zip_derived_cl3281, plain, 130.15/17.07 (![X0 : $i, X1 : $i]: 130.15/17.07 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 130.15/17.07 ((('#C') @ is_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))))))) @ 130.15/17.07 ((('#B') @ (((=>) @ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ (( 130.15/17.07 ('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ( 130.15/17.07 ( 130.15/17.07 ('#B') @ and3 @ 130.15/17.07 ( 130.15/17.07 ( 130.15/17.07 ('#C') @ inf @ 130.15/17.07 ( 130.15/17.07 class @ 130.15/17.07 X0))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X1))))))) @ 130.15/17.07 lessf))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ rt_less @ ((('#C') @ rt_pl @ X0)))) @ 130.15/17.07 ((('#C') @ rt_pl @ X1)))))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('comb-normalize', [status(thm)], [zip_derived_cl3280])). 130.15/17.07 thf(zip_derived_cl3282, plain, 130.15/17.07 (![X0 : $i, X1 : $i, X3 : $i]: 130.15/17.07 ( (((is_of @ X3 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 (((l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ X0))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ X1))))))) @ 130.15/17.07 lessf))))) => 130.15/17.07 (rt_less @ (rt_pl @ X3 @ X0) @ (rt_pl @ X3 @ X1)))))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3281])). 130.15/17.07 thf(def_rt_pl, axiom,(( rt_pl @ (X0)@ (X1)) = 130.15/17.07 ((indrat @ X0 @ X1 @ rat @ plusfrt)))). 130.15/17.07 thf('3', plain, 130.15/17.07 (![X1:$i,X0:$i]: 130.15/17.07 ( ( rt_pl @ X0 @ X1 ) = ( indrat @ X0 @ X1 @ rat @ plusfrt ) )), 130.15/17.07 define([status(thm)])). 130.15/17.07 thf(zip_derived_cl3283, plain, 130.15/17.07 (![X0 : $i, X1 : $i, X3 : $i]: 130.15/17.07 ( (((is_of @ X3 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 (((l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ X0))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ X1))))))) @ 130.15/17.07 lessf))))) => 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ X3 @ X0 @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ X3 @ X1 @ (ect @ frac @ n_eq) @ 130.15/17.07 plusfrt)))))))) @ 130.15/17.07 lessf))))))))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('rw', [status(thm)], [zip_derived_cl3282, '0', '2', '3', '3'])). 130.15/17.07 thf(zip_derived_cl3284, plain, 130.15/17.07 (![X0 : $i, X1 : $i, X3 : $i]: 130.15/17.07 (~ (is_of @ X3 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | (((l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ X0))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ X1))))))) @ 130.15/17.07 lessf))))) => 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ X3 @ X0 @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ X3 @ X1 @ (ect @ frac @ n_eq) @ 130.15/17.07 plusfrt)))))))) @ 130.15/17.07 lessf))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3283])). 130.15/17.07 thf(zip_derived_cl3285, plain, 130.15/17.07 (![X0 : $i, X1 : $i, X3 : $i]: 130.15/17.07 (~ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ X0))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ X1))))))) @ 130.15/17.07 lessf))))) 130.15/17.07 | (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ X3 @ X0 @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ X3 @ X1 @ (ect @ frac @ n_eq) @ 130.15/17.07 plusfrt)))))))) @ 130.15/17.07 lessf))))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X3 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3284])). 130.15/17.07 thf(zip_derived_cl5290, plain, 130.15/17.07 (![X0 : $i, X1 : $i, X3 : $i]: 130.15/17.07 (~ (l_some @ frac @ 130.15/17.07 ('#ty_enc10' @ (l_some @ frac) @ 130.15/17.07 ('#ty_enc11' @ 130.15/17.07 ('#ty_enc12' @ '#ty_enc17' @ 130.15/17.07 ('#ty_enc13' @ 130.15/17.07 ('#ty_enc14' @ '#ty_enc16' @ 130.15/17.07 ('#ty_enc15' @ and3 @ ('#ty_enc9' @ inf @ (class @ X0)))) @ 130.15/17.07 ('#ty_enc9' @ inf @ (class @ X1)))) @ 130.15/17.07 lessf))) 130.15/17.07 | (l_some @ frac @ 130.15/17.07 ('#ty_enc10' @ (l_some @ frac) @ 130.15/17.07 ('#ty_enc11' @ 130.15/17.07 ('#ty_enc12' @ '#ty_enc17' @ 130.15/17.07 ('#ty_enc13' @ 130.15/17.07 ('#ty_enc14' @ '#ty_enc16' @ 130.15/17.07 ('#ty_enc15' @ and3 @ 130.15/17.07 ('#ty_enc9' @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ X3 @ X0 @ (ect @ frac @ n_eq) @ plusfrt))))) @ 130.15/17.07 ('#ty_enc9' @ inf @ 130.15/17.07 (class @ (indrat @ X3 @ X1 @ (ect @ frac @ n_eq) @ plusfrt))))) @ 130.15/17.07 lessf))) 130.15/17.07 | ~ (is_of @ X1 @ ('#ty_enc9' @ in @ (ect @ frac @ n_eq))) 130.15/17.07 | ~ (is_of @ X0 @ ('#ty_enc9' @ in @ (ect @ frac @ n_eq))) 130.15/17.07 | ~ (is_of @ X3 @ ('#ty_enc9' @ in @ (ect @ frac @ n_eq))))), 130.15/17.07 inference('remove_ty_args', [status(thm)], [zip_derived_cl3285])). 130.15/17.07 thf(satz99c, conjecture, 130.15/17.07 (all_of @ 130.15/17.07 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 130.15/17.07 ( ^[X0:$i]: 130.15/17.07 ( all_of @ 130.15/17.07 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 130.15/17.07 ( ^[X1:$i]: 130.15/17.07 ( all_of @ 130.15/17.07 ( ^[X2:$i]: ( in @ X2 @ rat ) ) @ 130.15/17.07 ( ^[X2:$i]: 130.15/17.07 ( all_of @ 130.15/17.07 ( ^[X3:$i]: ( in @ X3 @ rat ) ) @ 130.15/17.07 ( ^[X3:$i]: 130.15/17.07 ( ( rt_lessis @ X0 @ X1 ) => 130.15/17.07 ( ( rt_less @ X2 @ X3 ) => 130.15/17.07 ( rt_less @ ( rt_pl @ X0 @ X2 ) @ ( rt_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 130.15/17.07 thf(zf_stmt_0, negated_conjecture, 130.15/17.07 (~( all_of @ 130.15/17.07 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 130.15/17.07 ( ^[X0:$i]: 130.15/17.07 ( all_of @ 130.15/17.07 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 130.15/17.07 ( ^[X1:$i]: 130.15/17.07 ( all_of @ 130.15/17.07 ( ^[X2:$i]: ( in @ X2 @ rat ) ) @ 130.15/17.07 ( ^[X2:$i]: 130.15/17.07 ( all_of @ 130.15/17.07 ( ^[X3:$i]: ( in @ X3 @ rat ) ) @ 130.15/17.07 ( ^[X3:$i]: 130.15/17.07 ( ( rt_lessis @ X0 @ X1 ) => 130.15/17.07 ( ( rt_less @ X2 @ X3 ) => 130.15/17.07 ( rt_less @ ( rt_pl @ X0 @ X2 ) @ ( rt_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) )), 130.15/17.07 inference('cnf.neg', [status(esa)], [satz99c])). 130.15/17.07 thf(zip_derived_cl516, plain, 130.15/17.07 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @ 130.15/17.07 (^[Y0 : $i]: 130.15/17.07 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @ 130.15/17.07 (^[Y1 : $i]: 130.15/17.07 (all_of @ (^[Y2 : $i]: (in @ Y2 @ rat)) @ 130.15/17.07 (^[Y2 : $i]: 130.15/17.07 (all_of @ (^[Y3 : $i]: (in @ Y3 @ rat)) @ 130.15/17.07 (^[Y3 : $i]: 130.15/17.07 (((rt_lessis @ Y0 @ Y1) => 130.15/17.07 (((rt_less @ Y2 @ Y3) => (rt_less @ 130.15/17.07 (rt_pl @ Y0 @ Y2) @ (rt_pl @ Y1 @ Y3))))))))))))))), 130.15/17.07 inference('cnf', [status(esa)], [zf_stmt_0])). 130.15/17.07 thf(zip_derived_cl517, plain, 130.15/17.07 (~ (all_of @ ((('#C') @ in @ rat)) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ rat))))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ rat))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))))))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ 130.15/17.07 rt_less)))))))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#C') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ rt_less)) @ rt_pl)))))))) @ 130.15/17.07 rt_pl)))))))))))))), 130.15/17.07 inference('lams2combs', [status(thm)], [zip_derived_cl516])). 130.15/17.07 thf(zip_derived_cl2047, plain, 130.15/17.07 (~ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ 130.15/17.07 (ect @ frac @ n_eq)))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_lessis)))))))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ 130.15/17.07 rt_less)))))))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#C') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ rt_less)) @ rt_pl)))))))) @ 130.15/17.07 rt_pl)))))))))))))), 130.15/17.07 inference('rw', [status(thm)], [zip_derived_cl517, '0'])). 130.15/17.07 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 130.15/17.07 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 130.15/17.07 thf('4', plain, 130.15/17.07 (![X0:( $i > $o ),X1:( $i > $o )]: 130.15/17.07 ( ( ~( all_of @ X0 @ X1 ) ) <=> 130.15/17.07 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 130.15/17.07 inference('rw.lit', [status(esa)], [def_all_of])). 130.15/17.07 thf(zip_derived_cl2048, plain, 130.15/17.07 (~ (((!!) @ (^[Y0 : $i]: 130.15/17.07 (((is_of @ Y0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ 130.15/17.07 (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ 130.15/17.07 (ect @ frac @ 130.15/17.07 n_eq)))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ 130.15/17.07 rt_lessis)))))))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 130.15/17.07 '#S') @ 130.15/17.07 ((('#B') @ ( 130.15/17.07 (('#B') @ ( 130.15/17.07 =>))) @ 130.15/17.07 rt_less)))))))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#C') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ rt_less)) @ 130.15/17.07 rt_pl)))))))) @ 130.15/17.07 rt_pl)))))))))) @ 130.15/17.07 Y0)))))))), 130.15/17.07 inference('rw_clause', [status(thm)], [zip_derived_cl2047, '4'])). 130.15/17.07 thf(zip_derived_cl2049, plain, 130.15/17.07 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 130.15/17.07 ((('#C') @ is_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))))))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ 130.15/17.07 (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ 130.15/17.07 (ect @ frac @ n_eq)))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ 130.15/17.07 rt_lessis)))))))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 130.15/17.07 '#S') @ 130.15/17.07 ((('#B') @ ( 130.15/17.07 (('#B') @ (=>))) @ 130.15/17.07 rt_less)))))))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#C') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ rt_less)) @ 130.15/17.07 rt_pl)))))))) @ 130.15/17.07 rt_pl))))))))))))))))), 130.15/17.07 inference('comb-normalize', [status(thm)], [zip_derived_cl2048])). 130.15/17.07 thf(zip_derived_cl2050, plain, 130.15/17.07 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ (=>) @ (rt_lessis @ '#sk5'))))))) @ 130.15/17.07 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))))) @ 130.15/17.07 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ 130.15/17.07 (rt_pl @ '#sk5'))))))) @ 130.15/17.07 rt_pl)))))))))))))), 130.15/17.07 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2049])). 130.15/17.07 thf(zip_derived_cl2052, plain, 130.15/17.07 (~ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ (=>) @ (rt_lessis @ '#sk5'))))))) @ 130.15/17.07 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))))) @ 130.15/17.07 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ (rt_pl @ '#sk5'))))))) @ 130.15/17.07 rt_pl)))))))))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2050])). 130.15/17.07 thf(zip_derived_cl2053, plain, 130.15/17.07 (~ (((!!) @ (^[Y0 : $i]: 130.15/17.07 (((is_of @ Y0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ 130.15/17.07 (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ (=>) @ 130.15/17.07 (rt_lessis @ '#sk5'))))))) @ 130.15/17.07 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ 130.15/17.07 rt_less)))))) @ 130.15/17.07 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ 130.15/17.07 (rt_pl @ '#sk5'))))))) @ 130.15/17.07 rt_pl)))))))) @ 130.15/17.07 Y0)))))))), 130.15/17.07 inference('rw_clause', [status(thm)], [zip_derived_cl2052, '4'])). 130.15/17.07 thf(zip_derived_cl2054, plain, 130.15/17.07 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 130.15/17.07 ((('#C') @ is_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))))))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ 130.15/17.07 (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ (=>) @ (rt_lessis @ '#sk5'))))))) @ 130.15/17.07 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ 130.15/17.07 rt_less)))))) @ 130.15/17.07 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ 130.15/17.07 (rt_pl @ '#sk5'))))))) @ 130.15/17.07 rt_pl))))))))))))))), 130.15/17.07 inference('comb-normalize', [status(thm)], [zip_derived_cl2053])). 130.15/17.07 thf(zip_derived_cl2055, plain, 130.15/17.07 (~ (((is_of @ '#sk6' @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (((=>) @ (rt_lessis @ '#sk5' @ '#sk6'))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ (rt_pl @ '#sk5'))))) @ 130.15/17.07 (rt_pl @ '#sk6'))))))))))))), 130.15/17.07 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2054])). 130.15/17.07 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 130.15/17.07 thf('5', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 130.15/17.07 define([status(thm)])). 130.15/17.07 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 130.15/17.07 thf('6', plain, 130.15/17.07 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 130.15/17.07 define([status(thm)])). 130.15/17.07 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))). 130.15/17.07 thf('7', plain, 130.15/17.07 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )), 130.15/17.07 define([status(thm)])). 130.15/17.07 thf(def_rt_is, axiom,(( rt_is @ (X0)@ (X1)) = ((e_is @ rat @ X0 @ X1)))). 130.15/17.07 thf('8', plain, 130.15/17.07 (![X1:$i,X0:$i]: ( ( rt_is @ X0 @ X1 ) = ( e_is @ rat @ X0 @ X1 ) )), 130.15/17.07 define([status(thm)])). 130.15/17.07 thf(def_rt_lessis, axiom,(( rt_lessis @ (X0)@ (X1)) = 130.15/17.07 ((l_or @ (rt_less @ X0 @ X1) @ (rt_is @ X0 @ X1))))). 130.15/17.07 thf('9', plain, 130.15/17.07 (![X1:$i,X0:$i]: 130.15/17.07 ( ( rt_lessis @ X0 @ X1 ) = 130.15/17.07 ( l_or @ ( rt_less @ X0 @ X1 ) @ ( rt_is @ X0 @ X1 ) ) )), 130.15/17.07 define([status(thm)])). 130.15/17.07 thf(zip_derived_cl2056, plain, 130.15/17.07 (~ (((is_of @ '#sk6' @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 130.15/17.07 (imp @ 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ( 130.15/17.07 '#S') @ 130.15/17.07 ((('#C') @ ( 130.15/17.07 (('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 '#sk6'))))))) @ 130.15/17.07 lessf))))) @ 130.15/17.07 ($false)) @ 130.15/17.07 ((('#sk5') = ('#sk6')))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ (rt_pl @ '#sk5'))))) @ 130.15/17.07 (rt_pl @ '#sk6'))))))))))))), 130.15/17.07 inference('rw', [status(thm)], 130.15/17.07 [zip_derived_cl2055, '5', '6', '7', '0', '8', '2', '9'])). 130.15/17.07 thf(zip_derived_cl2058, plain, 130.15/17.07 (~ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 130.15/17.07 (imp @ 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ( 130.15/17.07 '#S') @ 130.15/17.07 ((('#C') @ ( 130.15/17.07 (('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 '#sk6'))))))) @ 130.15/17.07 lessf))))) @ 130.15/17.07 ($false)) @ 130.15/17.07 ((('#sk5') = ('#sk6')))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ (rt_pl @ '#sk5'))))) @ 130.15/17.07 (rt_pl @ '#sk6'))))))))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2056])). 130.15/17.07 thf(zip_derived_cl2059, plain, 130.15/17.07 (~ (((!!) @ (^[Y0 : $i]: 130.15/17.07 (((is_of @ Y0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 130.15/17.07 (imp @ 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ ( 130.15/17.07 l_some @ frac) @ 130.15/17.07 ((('#S') @ ( 130.15/17.07 (('#B') @ ( 130.15/17.07 '#S') @ 130.15/17.07 ((('#C') @ ( 130.15/17.07 (('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 (( 130.15/17.07 ('#C') @ inf @ 130.15/17.07 ( 130.15/17.07 class @ 130.15/17.07 '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 '#sk6'))))))) @ 130.15/17.07 lessf))))) @ 130.15/17.07 ($false)) @ 130.15/17.07 ((('#sk5') = ('#sk6')))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ (rt_pl @ '#sk5'))))) @ 130.15/17.07 (rt_pl @ '#sk6'))))))) @ 130.15/17.07 Y0)))))))), 130.15/17.07 inference('rw_clause', [status(thm)], [zip_derived_cl2058, '4'])). 130.15/17.07 thf(zip_derived_cl2060, plain, 130.15/17.07 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 130.15/17.07 ((('#C') @ is_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))))))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 130.15/17.07 (imp @ 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ 130.15/17.07 frac) @ 130.15/17.07 ((('#S') @ (( 130.15/17.07 ('#B') @ ( 130.15/17.07 '#S') @ 130.15/17.07 ( 130.15/17.07 ( 130.15/17.07 ('#C') @ ( 130.15/17.07 ( 130.15/17.07 ('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ( 130.15/17.07 ( 130.15/17.07 ('#B') @ and3 @ 130.15/17.07 ( 130.15/17.07 ( 130.15/17.07 ('#C') @ inf @ 130.15/17.07 ( 130.15/17.07 class @ 130.15/17.07 '#sk5'))))))) @ 130.15/17.07 ( 130.15/17.07 ( 130.15/17.07 ('#C') @ inf @ 130.15/17.07 ( 130.15/17.07 class @ 130.15/17.07 '#sk6'))))))) @ 130.15/17.07 lessf))))) @ 130.15/17.07 ($false)) @ 130.15/17.07 ((('#sk5') = ('#sk6')))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ (rt_pl @ '#sk5'))))) @ 130.15/17.07 (rt_pl @ '#sk6')))))))))))))), 130.15/17.07 inference('comb-normalize', [status(thm)], [zip_derived_cl2059])). 130.15/17.07 thf(zip_derived_cl2061, plain, 130.15/17.07 (~ (((is_of @ '#sk7' @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (((=>) @ (imp @ 130.15/17.07 (imp @ 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ '#sk6'))))))) @ 130.15/17.07 lessf))))) @ 130.15/17.07 ($false)) @ 130.15/17.07 ((('#sk5') = ('#sk6')))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ (=>) @ (rt_less @ '#sk7'))) @ 130.15/17.07 ((('#B') @ (rt_less @ (rt_pl @ '#sk5' @ '#sk7')) @ 130.15/17.07 (rt_pl @ '#sk6'))))))))))), 130.15/17.07 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2060])). 130.15/17.07 thf(zip_derived_cl2062, plain, 130.15/17.07 (~ (((is_of @ '#sk7' @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (((=>) @ (imp @ 130.15/17.07 (imp @ 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ '#sk6'))))))) @ 130.15/17.07 lessf))))) @ 130.15/17.07 ($false)) @ 130.15/17.07 ((('#sk5') = ('#sk6')))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ (=>) @ (rt_less @ '#sk7'))) @ 130.15/17.07 ((('#B') @ (rt_less @ 130.15/17.07 (indrat @ '#sk5' @ '#sk7' @ (ect @ frac @ n_eq) @ 130.15/17.07 plusfrt)) @ 130.15/17.07 (rt_pl @ '#sk6'))))))))))), 130.15/17.07 inference('rw', [status(thm)], [zip_derived_cl2061, '0', '3'])). 130.15/17.07 thf(zip_derived_cl2064, plain, 130.15/17.07 (~ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (((=>) @ (imp @ 130.15/17.07 (imp @ 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ '#sk6'))))))) @ 130.15/17.07 lessf))))) @ 130.15/17.07 ($false)) @ 130.15/17.07 ((('#sk5') = ('#sk6')))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ (=>) @ (rt_less @ '#sk7'))) @ 130.15/17.07 ((('#B') @ (rt_less @ 130.15/17.07 (indrat @ '#sk5' @ '#sk7' @ (ect @ frac @ n_eq) @ 130.15/17.07 plusfrt)) @ 130.15/17.07 (rt_pl @ '#sk6'))))))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2062])). 130.15/17.07 thf(zip_derived_cl2065, plain, 130.15/17.07 (~ (((!!) @ (^[Y0 : $i]: 130.15/17.07 (((is_of @ Y0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 ((('#B') @ (((=>) @ (imp @ 130.15/17.07 (imp @ 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ( 130.15/17.07 '#S') @ 130.15/17.07 ((('#C') @ ( 130.15/17.07 (('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 '#sk6'))))))) @ 130.15/17.07 lessf))))) @ 130.15/17.07 ($false)) @ 130.15/17.07 ((('#sk5') = ('#sk6')))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ (=>) @ (rt_less @ '#sk7'))) @ 130.15/17.07 ((('#B') @ (rt_less @ 130.15/17.07 (indrat @ '#sk5' @ '#sk7' @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)) @ 130.15/17.07 (rt_pl @ '#sk6'))))) @ 130.15/17.07 Y0)))))))), 130.15/17.07 inference('rw_clause', [status(thm)], [zip_derived_cl2064, '4'])). 130.15/17.07 thf(zip_derived_cl2066, plain, 130.15/17.07 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 130.15/17.07 ((('#C') @ is_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))))))) @ 130.15/17.07 ((('#B') @ (((=>) @ (imp @ 130.15/17.07 (imp @ 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ (( 130.15/17.07 ('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ( 130.15/17.07 ( 130.15/17.07 ('#B') @ and3 @ 130.15/17.07 ( 130.15/17.07 ( 130.15/17.07 ('#C') @ inf @ 130.15/17.07 ( 130.15/17.07 class @ 130.15/17.07 '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ '#sk6'))))))) @ 130.15/17.07 lessf))))) @ 130.15/17.07 ($false)) @ 130.15/17.07 ((('#sk5') = ('#sk6')))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ (=>) @ (rt_less @ '#sk7'))) @ 130.15/17.07 ((('#B') @ (rt_less @ 130.15/17.07 (indrat @ '#sk5' @ '#sk7' @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)) @ 130.15/17.07 (rt_pl @ '#sk6')))))))))))), 130.15/17.07 inference('comb-normalize', [status(thm)], [zip_derived_cl2065])). 130.15/17.07 thf(zip_derived_cl2067, plain, 130.15/17.07 (~ (((is_of @ '#sk8' @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 (((imp @ 130.15/17.07 (imp @ 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk6'))))))) @ 130.15/17.07 lessf))))) @ 130.15/17.07 ($false)) @ 130.15/17.07 ((('#sk5') = ('#sk6')))) => 130.15/17.07 (((rt_less @ '#sk7' @ '#sk8') => (rt_less @ 130.15/17.07 (indrat @ '#sk5' @ '#sk7' @ (ect @ frac @ n_eq) @ plusfrt) @ 130.15/17.07 (rt_pl @ '#sk6' @ '#sk8'))))))))), 130.15/17.07 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2066])). 130.15/17.07 thf(zip_derived_cl2068, plain, 130.15/17.07 (~ (((is_of @ '#sk8' @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 (((imp @ 130.15/17.07 (imp @ 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk6'))))))) @ 130.15/17.07 lessf))))) @ 130.15/17.07 ($false)) @ 130.15/17.07 ((('#sk5') = ('#sk6')))) => 130.15/17.07 (((l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk7'))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk8'))))))) @ 130.15/17.07 lessf))))) => 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ '#sk5' @ '#sk7' @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ '#sk6' @ '#sk8' @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)))))))) @ 130.15/17.07 lessf)))))))))))), 130.15/17.07 inference('rw', [status(thm)], [zip_derived_cl2067, '0', '2', '2', '3'])). 130.15/17.07 thf(zip_derived_cl2070, plain, 130.15/17.07 (~ (((imp @ 130.15/17.07 (imp @ 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk6'))))))) @ 130.15/17.07 lessf))))) @ 130.15/17.07 ($false)) @ 130.15/17.07 ((('#sk5') = ('#sk6')))) => 130.15/17.07 (((l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk7'))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk8'))))))) @ 130.15/17.07 lessf))))) => 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ '#sk5' @ '#sk7' @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ '#sk6' @ '#sk8' @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)))))))) @ 130.15/17.07 lessf)))))))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2068])). 130.15/17.07 thf(zip_derived_cl2071, plain, 130.15/17.07 ( (imp @ 130.15/17.07 (imp @ 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk6'))))))) @ 130.15/17.07 lessf))))) @ 130.15/17.07 ($false)) @ 130.15/17.07 ((('#sk5') = ('#sk6'))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2070])). 130.15/17.07 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 130.15/17.07 thf('10', plain, 130.15/17.07 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 130.15/17.07 inference('rw.lit', [status(esa)], [def_imp])). 130.15/17.07 thf(zip_derived_cl2073, plain, 130.15/17.07 ( (((imp @ 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk6'))))))) @ 130.15/17.07 lessf))))) @ 130.15/17.07 ($false)) => ((('#sk5') = ('#sk6')))))), 130.15/17.07 inference('rw_clause', [status(thm)], [zip_derived_cl2071, '10'])). 130.15/17.07 thf(zip_derived_cl2076, plain, 130.15/17.07 ((~ (imp @ 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk6'))))))) @ 130.15/17.07 lessf))))) @ 130.15/17.07 ($false)) 130.15/17.07 | ((('#sk5') = ('#sk6'))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2073])). 130.15/17.07 thf(zip_derived_cl2077, plain, 130.15/17.07 ((~ (imp @ 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk6'))))))) @ 130.15/17.07 lessf))))) @ 130.15/17.07 ($false)) 130.15/17.07 | (('#sk5') = ('#sk6')))), 130.15/17.07 inference('simplify nested equalities', [status(thm)], 130.15/17.07 [zip_derived_cl2076])). 130.15/17.07 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 130.15/17.07 thf('11', plain, 130.15/17.07 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 130.15/17.07 inference('rw.lit', [status(esa)], [def_imp])). 130.15/17.07 thf(zip_derived_cl2078, plain, 130.15/17.07 ((~ (((l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk6'))))))) @ 130.15/17.07 lessf))))) => 130.15/17.07 ($false))) 130.15/17.07 | (('#sk5') = ('#sk6')))), 130.15/17.07 inference('rw_clause', [status(thm)], [zip_derived_cl2077, '11'])). 130.15/17.07 thf(zip_derived_cl2079, plain, 130.15/17.07 ((~ (((~) @ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk6'))))))) @ 130.15/17.07 lessf))))))) 130.15/17.07 | (('#sk5') = ('#sk6')))), 130.15/17.07 inference('simplify boolean subterms', [status(thm)], 130.15/17.07 [zip_derived_cl2078])). 130.15/17.07 thf(zip_derived_cl2080, plain, 130.15/17.07 (( (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk5'))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk6'))))))) @ 130.15/17.07 lessf))))) 130.15/17.07 | (('#sk5') = ('#sk6')))), 130.15/17.07 inference('simplify nested equalities', [status(thm)], 130.15/17.07 [zip_derived_cl2079])). 130.15/17.07 thf(zip_derived_cl5245, plain, 130.15/17.07 (( (l_some @ frac @ 130.15/17.07 ('#ty_enc10' @ (l_some @ frac) @ 130.15/17.07 ('#ty_enc11' @ 130.15/17.07 ('#ty_enc12' @ '#ty_enc17' @ 130.15/17.07 ('#ty_enc13' @ 130.15/17.07 ('#ty_enc14' @ '#ty_enc16' @ 130.15/17.07 ('#ty_enc15' @ and3 @ ('#ty_enc9' @ inf @ (class @ '#sk5')))) @ 130.15/17.07 ('#ty_enc9' @ inf @ (class @ '#sk6')))) @ 130.15/17.07 lessf))) 130.15/17.07 | (('#sk5') = ('#sk6')))), 130.15/17.07 inference('remove_ty_args', [status(thm)], [zip_derived_cl2080])). 130.15/17.07 thf(zip_derived_cl2063, plain, 130.15/17.07 ( (is_of @ '#sk7' @ ((('#C') @ in @ (ect @ frac @ n_eq))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2062])). 130.15/17.07 thf(zip_derived_cl5241, plain, 130.15/17.07 ( (is_of @ '#sk7' @ ('#ty_enc9' @ in @ (ect @ frac @ n_eq)))), 130.15/17.07 inference('remove_ty_args', [status(thm)], [zip_derived_cl2063])). 130.15/17.07 thf(zip_derived_cl2069, plain, 130.15/17.07 ( (is_of @ '#sk8' @ ((('#C') @ in @ (ect @ frac @ n_eq))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2068])). 130.15/17.07 thf(zip_derived_cl5242, plain, 130.15/17.07 ( (is_of @ '#sk8' @ ('#ty_enc9' @ in @ (ect @ frac @ n_eq)))), 130.15/17.07 inference('remove_ty_args', [status(thm)], [zip_derived_cl2069])). 130.15/17.07 thf(zip_derived_cl2051, plain, 130.15/17.07 ( (is_of @ '#sk5' @ ((('#C') @ in @ (ect @ frac @ n_eq))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2050])). 130.15/17.07 thf(zip_derived_cl5239, plain, 130.15/17.07 ( (is_of @ '#sk5' @ ('#ty_enc9' @ in @ (ect @ frac @ n_eq)))), 130.15/17.07 inference('remove_ty_args', [status(thm)], [zip_derived_cl2051])). 130.15/17.07 thf(zip_derived_cl2057, plain, 130.15/17.07 ( (is_of @ '#sk6' @ ((('#C') @ in @ (ect @ frac @ n_eq))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2056])). 130.15/17.07 thf(zip_derived_cl5240, plain, 130.15/17.07 ( (is_of @ '#sk6' @ ('#ty_enc9' @ in @ (ect @ frac @ n_eq)))), 130.15/17.07 inference('remove_ty_args', [status(thm)], [zip_derived_cl2057])). 130.15/17.07 thf(zip_derived_cl2072, plain, 130.15/17.07 (~ (((l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk7'))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk8'))))))) @ 130.15/17.07 lessf))))) => 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ '#sk5' @ '#sk7' @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ '#sk6' @ '#sk8' @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)))))))) @ 130.15/17.07 lessf)))))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2070])). 130.15/17.07 thf(zip_derived_cl2074, plain, 130.15/17.07 ( (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk7'))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ '#sk8'))))))) @ 130.15/17.07 lessf)))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2072])). 130.15/17.07 thf(zip_derived_cl5243, plain, 130.15/17.07 ( (l_some @ frac @ 130.15/17.07 ('#ty_enc10' @ (l_some @ frac) @ 130.15/17.07 ('#ty_enc11' @ 130.15/17.07 ('#ty_enc12' @ '#ty_enc17' @ 130.15/17.07 ('#ty_enc13' @ 130.15/17.07 ('#ty_enc14' @ '#ty_enc16' @ 130.15/17.07 ('#ty_enc15' @ and3 @ ('#ty_enc9' @ inf @ (class @ '#sk7')))) @ 130.15/17.07 ('#ty_enc9' @ inf @ (class @ '#sk8')))) @ 130.15/17.07 lessf)))), 130.15/17.07 inference('remove_ty_args', [status(thm)], [zip_derived_cl2074])). 130.15/17.07 thf(zip_derived_cl2075, plain, 130.15/17.07 (~ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ '#sk5' @ '#sk7' @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ '#sk6' @ '#sk8' @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)))))))) @ 130.15/17.07 lessf)))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2072])). 130.15/17.07 thf(zip_derived_cl5244, plain, 130.15/17.07 (~ (l_some @ frac @ 130.15/17.07 ('#ty_enc10' @ (l_some @ frac) @ 130.15/17.07 ('#ty_enc11' @ 130.15/17.07 ('#ty_enc12' @ '#ty_enc17' @ 130.15/17.07 ('#ty_enc13' @ 130.15/17.07 ('#ty_enc14' @ '#ty_enc16' @ 130.15/17.07 ('#ty_enc15' @ and3 @ 130.15/17.07 ('#ty_enc9' @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ '#sk5' @ '#sk7' @ (ect @ frac @ n_eq) @ plusfrt))))) @ 130.15/17.07 ('#ty_enc9' @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ '#sk6' @ '#sk8' @ (ect @ frac @ n_eq) @ plusfrt))))) @ 130.15/17.07 lessf)))), 130.15/17.07 inference('remove_ty_args', [status(thm)], [zip_derived_cl2075])). 130.15/17.07 thf(satz98a, axiom, 130.15/17.07 (all_of @ 130.15/17.07 ( ^[X0:$i]: ( in @ X0 @ rat ) ) @ 130.15/17.07 ( ^[X0:$i]: 130.15/17.07 ( all_of @ 130.15/17.07 ( ^[X1:$i]: ( in @ X1 @ rat ) ) @ 130.15/17.07 ( ^[X1:$i]: 130.15/17.07 ( all_of @ 130.15/17.07 ( ^[X2:$i]: ( in @ X2 @ rat ) ) @ 130.15/17.07 ( ^[X2:$i]: 130.15/17.07 ( all_of @ 130.15/17.07 ( ^[X3:$i]: ( in @ X3 @ rat ) ) @ 130.15/17.07 ( ^[X3:$i]: 130.15/17.07 ( ( rt_less @ X0 @ X1 ) => 130.15/17.07 ( ( rt_less @ X2 @ X3 ) => 130.15/17.07 ( rt_less @ ( rt_pl @ X0 @ X2 ) @ ( rt_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 130.15/17.07 thf(zip_derived_cl486, plain, 130.15/17.07 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @ 130.15/17.07 (^[Y0 : $i]: 130.15/17.07 (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @ 130.15/17.07 (^[Y1 : $i]: 130.15/17.07 (all_of @ (^[Y2 : $i]: (in @ Y2 @ rat)) @ 130.15/17.07 (^[Y2 : $i]: 130.15/17.07 (all_of @ (^[Y3 : $i]: (in @ Y3 @ rat)) @ 130.15/17.07 (^[Y3 : $i]: 130.15/17.07 (((rt_less @ Y0 @ Y1) => 130.15/17.07 (((rt_less @ Y2 @ Y3) => (rt_less @ 130.15/17.07 (rt_pl @ Y0 @ Y2) @ (rt_pl @ Y1 @ Y3))))))))))))))), 130.15/17.07 inference('cnf', [status(esa)], [satz98a])). 130.15/17.07 thf(zip_derived_cl487, plain, 130.15/17.07 ( (all_of @ ((('#C') @ in @ rat)) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ rat))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ rat))))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ rat))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))))))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ 130.15/17.07 rt_less)))))))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#C') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ rt_less)) @ rt_pl)))))))) @ 130.15/17.07 rt_pl)))))))))))))), 130.15/17.07 inference('lams2combs', [status(thm)], [zip_derived_cl486])). 130.15/17.07 thf(zip_derived_cl3656, plain, 130.15/17.07 ( (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ 130.15/17.07 (ect @ frac @ n_eq)))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))))))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ 130.15/17.07 rt_less)))))))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#C') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ rt_less)) @ rt_pl)))))))) @ 130.15/17.07 rt_pl)))))))))))))), 130.15/17.07 inference('rw', [status(thm)], [zip_derived_cl487, '0'])). 130.15/17.07 thf(zip_derived_cl3657, plain, 130.15/17.07 ( (((!!) @ (^[Y0 : $i]: 130.15/17.07 (((is_of @ Y0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ 130.15/17.07 (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ 130.15/17.07 (ect @ frac @ 130.15/17.07 n_eq)))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ 130.15/17.07 rt_less)))))))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 130.15/17.07 '#S') @ 130.15/17.07 ((('#B') @ ( 130.15/17.07 (('#B') @ ( 130.15/17.07 =>))) @ 130.15/17.07 rt_less)))))))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#C') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ rt_less)) @ 130.15/17.07 rt_pl)))))))) @ 130.15/17.07 rt_pl)))))))))) @ 130.15/17.07 Y0)))))))), 130.15/17.07 inference('rw_clause', [status(thm)], [zip_derived_cl3656, '1'])). 130.15/17.07 thf(zip_derived_cl3658, plain, 130.15/17.07 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 130.15/17.07 ((('#C') @ is_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))))))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ 130.15/17.07 (ect @ frac @ n_eq)))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ 130.15/17.07 rt_less)))))))) @ 130.15/17.07 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 130.15/17.07 '#S') @ 130.15/17.07 ((('#B') @ ( 130.15/17.07 (('#B') @ (=>))) @ 130.15/17.07 rt_less)))))))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#C') @ 130.15/17.07 ((('#B') @ ((('#B') @ ('#B'))) @ 130.15/17.07 ((('#B') @ ((('#B') @ rt_less)) @ 130.15/17.07 rt_pl)))))))) @ 130.15/17.07 rt_pl))))))))))))))))), 130.15/17.07 inference('comb-normalize', [status(thm)], [zip_derived_cl3657])). 130.15/17.07 thf(zip_derived_cl3659, plain, 130.15/17.07 (![X2 : $i]: 130.15/17.07 (((is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ (=>) @ (rt_less @ X2))))))) @ 130.15/17.07 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ 130.15/17.07 rt_less)))))) @ 130.15/17.07 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ (rt_pl @ X2))))))) @ 130.15/17.07 rt_pl)))))))))))))), 130.15/17.07 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3658])). 130.15/17.07 thf(zip_derived_cl3660, plain, 130.15/17.07 (![X2 : $i]: 130.15/17.07 (~ (is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ (=>) @ (rt_less @ X2))))))) @ 130.15/17.07 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ 130.15/17.07 rt_less)))))) @ 130.15/17.07 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ (rt_pl @ X2))))))) @ 130.15/17.07 rt_pl))))))))))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3659])). 130.15/17.07 thf(zip_derived_cl3661, plain, 130.15/17.07 (![X0 : $i]: 130.15/17.07 ( (((!!) @ (^[Y0 : $i]: 130.15/17.07 (((is_of @ Y0 @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ 130.15/17.07 (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ (=>) @ (rt_less @ X0))))))) @ 130.15/17.07 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ ( 130.15/17.07 =>))) @ 130.15/17.07 rt_less)))))) @ 130.15/17.07 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ 130.15/17.07 (rt_pl @ X0))))))) @ 130.15/17.07 rt_pl)))))))) @ 130.15/17.07 Y0))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('rw_clause', [status(thm)], [zip_derived_cl3660, '1'])). 130.15/17.07 thf(zip_derived_cl3662, plain, 130.15/17.07 (![X0 : $i]: 130.15/17.07 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 130.15/17.07 ((('#C') @ is_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))))))) @ 130.15/17.07 ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ 130.15/17.07 (ect @ frac @ n_eq)))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ (=>) @ (rt_less @ X0))))))) @ 130.15/17.07 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ 130.15/17.07 rt_less)))))) @ 130.15/17.07 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ 130.15/17.07 (rt_pl @ X0))))))) @ 130.15/17.07 rt_pl)))))))))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('comb-normalize', [status(thm)], [zip_derived_cl3661])). 130.15/17.07 thf(zip_derived_cl3663, plain, 130.15/17.07 (![X0 : $i, X2 : $i]: 130.15/17.07 ( (((is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (((=>) @ (rt_less @ X0 @ X2))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ (rt_pl @ X0))))) @ 130.15/17.07 (rt_pl @ X2)))))))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3662])). 130.15/17.07 thf(zip_derived_cl3664, plain, 130.15/17.07 (![X0 : $i, X2 : $i]: 130.15/17.07 ( (((is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ( 130.15/17.07 '#S') @ 130.15/17.07 ((('#C') @ ( 130.15/17.07 (('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 X0))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X2))))))) @ 130.15/17.07 lessf))))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ (rt_pl @ X0))))) @ 130.15/17.07 (rt_pl @ X2)))))))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('rw', [status(thm)], [zip_derived_cl3663, '2'])). 130.15/17.07 thf(zip_derived_cl3665, plain, 130.15/17.07 (![X0 : $i, X2 : $i]: 130.15/17.07 (~ (is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ( 130.15/17.07 '#S') @ 130.15/17.07 ((('#C') @ ( 130.15/17.07 (('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 ( 130.15/17.07 class @ 130.15/17.07 X0))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X2))))))) @ 130.15/17.07 lessf))))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ (rt_pl @ X0))))) @ 130.15/17.07 (rt_pl @ X2)))))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3664])). 130.15/17.07 thf(zip_derived_cl3666, plain, 130.15/17.07 (![X0 : $i, X1 : $i]: 130.15/17.07 ( (((!!) @ (^[Y0 : $i]: 130.15/17.07 (((is_of @ Y0 @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ frac @ 130.15/17.07 ((('#B') @ ( 130.15/17.07 l_some @ frac) @ 130.15/17.07 ((('#S') @ ( 130.15/17.07 (('#B') @ ( 130.15/17.07 '#S') @ 130.15/17.07 ((('#C') @ ( 130.15/17.07 (('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 (( 130.15/17.07 ('#C') @ inf @ 130.15/17.07 ( 130.15/17.07 class @ 130.15/17.07 X0))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X1))))))) @ 130.15/17.07 lessf))))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ 130.15/17.07 rt_less)))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ (rt_pl @ X0))))) @ 130.15/17.07 (rt_pl @ X1))))))) @ 130.15/17.07 Y0))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('rw_clause', [status(thm)], [zip_derived_cl3665, '1'])). 130.15/17.07 thf(zip_derived_cl3667, plain, 130.15/17.07 (![X0 : $i, X1 : $i]: 130.15/17.07 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 130.15/17.07 ((('#C') @ is_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))))))) @ 130.15/17.07 ((('#B') @ (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))) @ 130.15/17.07 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ 130.15/17.07 frac) @ 130.15/17.07 ((('#S') @ (( 130.15/17.07 ('#B') @ ( 130.15/17.07 '#S') @ 130.15/17.07 ( 130.15/17.07 ( 130.15/17.07 ('#C') @ ( 130.15/17.07 ( 130.15/17.07 ('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ( 130.15/17.07 ( 130.15/17.07 ('#B') @ and3 @ 130.15/17.07 ( 130.15/17.07 ( 130.15/17.07 ('#C') @ inf @ 130.15/17.07 ( 130.15/17.07 class @ 130.15/17.07 X0))))))) @ 130.15/17.07 ( 130.15/17.07 ( 130.15/17.07 ('#C') @ inf @ 130.15/17.07 ( 130.15/17.07 class @ 130.15/17.07 X1))))))) @ 130.15/17.07 lessf))))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#B') @ ((('#B') @ (=>))) @ rt_less)))) @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ rt_less @ (rt_pl @ X0))))) @ 130.15/17.07 (rt_pl @ X1))))))))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('comb-normalize', [status(thm)], [zip_derived_cl3666])). 130.15/17.07 thf(zip_derived_cl3668, plain, 130.15/17.07 (![X0 : $i, X1 : $i, X3 : $i]: 130.15/17.07 ( (((is_of @ X3 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (((=>) @ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X0))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X1))))))) @ 130.15/17.07 lessf))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ (=>) @ (rt_less @ X3))) @ 130.15/17.07 ((('#B') @ (rt_less @ (rt_pl @ X0 @ X3)) @ (rt_pl @ X1)))))))))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3667])). 130.15/17.07 thf(zip_derived_cl3669, plain, 130.15/17.07 (![X0 : $i, X1 : $i, X3 : $i]: 130.15/17.07 ( (((is_of @ X3 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => (all_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (((=>) @ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X0))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X1))))))) @ 130.15/17.07 lessf))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ (=>) @ (rt_less @ X3))) @ 130.15/17.07 ((('#B') @ (rt_less @ 130.15/17.07 (indrat @ X0 @ X3 @ (ect @ frac @ n_eq) @ plusfrt)) @ 130.15/17.07 (rt_pl @ X1)))))))))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('rw', [status(thm)], [zip_derived_cl3668, '0', '3'])). 130.15/17.07 thf(zip_derived_cl3670, plain, 130.15/17.07 (![X0 : $i, X1 : $i, X3 : $i]: 130.15/17.07 (~ (is_of @ X3 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | (all_of @ ((('#C') @ in @ (ect @ frac @ n_eq))) @ 130.15/17.07 ((('#B') @ (((=>) @ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X0))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X1))))))) @ 130.15/17.07 lessf))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ (=>) @ (rt_less @ X3))) @ 130.15/17.07 ((('#B') @ (rt_less @ 130.15/17.07 (indrat @ X0 @ X3 @ (ect @ frac @ n_eq) @ plusfrt)) @ 130.15/17.07 (rt_pl @ X1)))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3669])). 130.15/17.07 thf(zip_derived_cl3671, plain, 130.15/17.07 (![X0 : $i, X1 : $i, X2 : $i]: 130.15/17.07 ( (((!!) @ (^[Y0 : $i]: 130.15/17.07 (((is_of @ Y0 @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 ((('#B') @ (((=>) @ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ( 130.15/17.07 '#S') @ 130.15/17.07 ((('#C') @ ( 130.15/17.07 (('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X1))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X0))))))) @ 130.15/17.07 lessf))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ (=>) @ (rt_less @ X2))) @ 130.15/17.07 ((('#B') @ (rt_less @ 130.15/17.07 (indrat @ X1 @ X2 @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)) @ 130.15/17.07 (rt_pl @ X0))))) @ 130.15/17.07 Y0))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('rw_clause', [status(thm)], [zip_derived_cl3670, '1'])). 130.15/17.07 thf(zip_derived_cl3672, plain, 130.15/17.07 (![X0 : $i, X1 : $i, X2 : $i]: 130.15/17.07 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 130.15/17.07 ((('#C') @ is_of @ 130.15/17.07 ((('#C') @ in @ (ect @ frac @ n_eq))))))) @ 130.15/17.07 ((('#B') @ (((=>) @ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ (( 130.15/17.07 ('#B') @ ( 130.15/17.07 '#B') @ 130.15/17.07 ( 130.15/17.07 ( 130.15/17.07 ('#B') @ and3 @ 130.15/17.07 ( 130.15/17.07 ( 130.15/17.07 ('#C') @ inf @ 130.15/17.07 ( 130.15/17.07 class @ 130.15/17.07 X1))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ X0))))))) @ 130.15/17.07 lessf))))))) @ 130.15/17.07 ((('#S') @ ((('#B') @ (=>) @ (rt_less @ X2))) @ 130.15/17.07 ((('#B') @ (rt_less @ 130.15/17.07 (indrat @ X1 @ X2 @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)) @ 130.15/17.07 (rt_pl @ X0))))))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('comb-normalize', [status(thm)], [zip_derived_cl3671])). 130.15/17.07 thf(zip_derived_cl3673, plain, 130.15/17.07 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 130.15/17.07 ( (((is_of @ X4 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 (((l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ X1))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ X0))))))) @ 130.15/17.07 lessf))))) => 130.15/17.07 (((rt_less @ X2 @ X4) => (rt_less @ 130.15/17.07 (indrat @ X1 @ X2 @ (ect @ frac @ n_eq) @ plusfrt) @ 130.15/17.07 (rt_pl @ X0 @ X4)))))))) 130.15/17.07 | ~ (is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3672])). 130.15/17.07 thf(zip_derived_cl3674, plain, 130.15/17.07 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 130.15/17.07 ( (((is_of @ X4 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) => 130.15/17.07 (((l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ X1))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ X0))))))) @ 130.15/17.07 lessf))))) => 130.15/17.07 (((l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ X2))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ X4))))))) @ 130.15/17.07 lessf))))) => 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ X1 @ X2 @ 130.15/17.07 (ect @ frac @ n_eq) @ 130.15/17.07 plusfrt)))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ X0 @ X4 @ (ect @ frac @ n_eq) @ 130.15/17.07 plusfrt)))))))) @ 130.15/17.07 lessf))))))))))) 130.15/17.07 | ~ (is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('rw', [status(thm)], [zip_derived_cl3673, '0', '2', '2', '3'])). 130.15/17.07 thf(zip_derived_cl3675, plain, 130.15/17.07 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 130.15/17.07 (~ (is_of @ X4 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | (((l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ X1))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ X0))))))) @ 130.15/17.07 lessf))))) => 130.15/17.07 (((l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ X2))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ X4))))))) @ 130.15/17.07 lessf))))) => 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ X1 @ X2 @ 130.15/17.07 (ect @ frac @ n_eq) @ 130.15/17.07 plusfrt)))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ X0 @ X4 @ (ect @ frac @ n_eq) @ 130.15/17.07 plusfrt)))))))) @ 130.15/17.07 lessf))))))))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3674])). 130.15/17.07 thf(zip_derived_cl3676, plain, 130.15/17.07 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 130.15/17.07 (~ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ X1))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ X0))))))) @ 130.15/17.07 lessf))))) 130.15/17.07 | (((l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ X2))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ X4))))))) @ 130.15/17.07 lessf))))) => 130.15/17.07 (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ X1 @ X2 @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ X0 @ X4 @ (ect @ frac @ n_eq) @ 130.15/17.07 plusfrt)))))))) @ 130.15/17.07 lessf))))))) 130.15/17.07 | ~ (is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X4 @ ((('#C') @ in @ (ect @ frac @ n_eq)))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3675])). 130.15/17.07 thf(zip_derived_cl3677, plain, 130.15/17.07 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 130.15/17.07 (~ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ X2))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ X4))))))) @ 130.15/17.07 lessf))))) 130.15/17.07 | (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ X1 @ X2 @ 130.15/17.07 (ect @ frac @ n_eq) @ plusfrt)))))))) @ 130.15/17.07 ((('#C') @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ X0 @ X4 @ (ect @ frac @ n_eq) @ 130.15/17.07 plusfrt)))))))) @ 130.15/17.07 lessf))))) 130.15/17.07 | ~ (is_of @ X4 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X0 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X1 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (is_of @ X2 @ ((('#C') @ in @ (ect @ frac @ n_eq)))) 130.15/17.07 | ~ (l_some @ frac @ 130.15/17.07 ((('#B') @ (l_some @ frac) @ 130.15/17.07 ((('#S') @ ((('#B') @ ('#S') @ 130.15/17.07 ((('#C') @ ((('#B') @ ('#B') @ 130.15/17.07 ((('#B') @ and3 @ 130.15/17.07 ((('#C') @ inf @ (class @ X1))))))) @ 130.15/17.07 ((('#C') @ inf @ (class @ X0))))))) @ 130.15/17.07 lessf))))))), 130.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3676])). 130.15/17.07 thf(zip_derived_cl5306, plain, 130.15/17.07 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 130.15/17.07 (~ (l_some @ frac @ 130.15/17.07 ('#ty_enc10' @ (l_some @ frac) @ 130.15/17.07 ('#ty_enc11' @ 130.15/17.07 ('#ty_enc12' @ '#ty_enc17' @ 130.15/17.07 ('#ty_enc13' @ 130.15/17.07 ('#ty_enc14' @ '#ty_enc16' @ 130.15/17.07 ('#ty_enc15' @ and3 @ ('#ty_enc9' @ inf @ (class @ X2)))) @ 130.15/17.07 ('#ty_enc9' @ inf @ (class @ X4)))) @ 130.15/17.07 lessf))) 130.15/17.07 | (l_some @ frac @ 130.15/17.07 ('#ty_enc10' @ (l_some @ frac) @ 130.15/17.07 ('#ty_enc11' @ 130.15/17.07 ('#ty_enc12' @ '#ty_enc17' @ 130.15/17.07 ('#ty_enc13' @ 130.15/17.07 ('#ty_enc14' @ '#ty_enc16' @ 130.15/17.07 ('#ty_enc15' @ and3 @ 130.15/17.07 ('#ty_enc9' @ inf @ 130.15/17.07 (class @ 130.15/17.07 (indrat @ X1 @ X2 @ (ect @ frac @ n_eq) @ plusfrt))))) @ 130.15/17.07 ('#ty_enc9' @ inf @ 130.15/17.07 (class @ (indrat @ X0 @ X4 @ (ect @ frac @ n_eq) @ plusfrt))))) @ 130.15/17.07 lessf))) 130.15/17.07 | ~ (is_of @ X4 @ ('#ty_enc9' @ in @ (ect @ frac @ n_eq))) 130.15/17.07 | ~ (is_of @ X0 @ ('#ty_enc9' @ in @ (ect @ frac @ n_eq))) 130.15/17.07 | ~ (is_of @ X1 @ ('#ty_enc9' @ in @ (ect @ frac @ n_eq))) 130.15/17.07 | ~ (is_of @ X2 @ ('#ty_enc9' @ in @ (ect @ frac @ n_eq))) 130.15/17.07 | ~ (l_some @ frac @ 130.15/17.07 ('#ty_enc10' @ (l_some @ frac) @ 130.15/17.07 ('#ty_enc11' @ 130.15/17.07 ('#ty_enc12' @ '#ty_enc17' @ 130.15/17.07 ('#ty_enc13' @ 130.15/17.07 ('#ty_enc14' @ '#ty_enc16' @ 130.15/17.07 ('#ty_enc15' @ and3 @ ('#ty_enc9' @ inf @ (class @ X1)))) @ 130.15/17.07 ('#ty_enc9' @ inf @ (class @ X0)))) @ 130.15/17.07 lessf))))), 130.15/17.07 inference('remove_ty_args', [status(thm)], [zip_derived_cl3677])). 130.15/17.07 thf(zip_derived_cl5331, plain, ($false), 130.15/17.07 inference('eprover', [status(thm)], 130.15/17.07 [zip_derived_cl5290, zip_derived_cl5245, zip_derived_cl5241, 130.15/17.07 zip_derived_cl5242, zip_derived_cl5239, zip_derived_cl5240, 130.15/17.07 zip_derived_cl5243, zip_derived_cl5244, zip_derived_cl5306])). 130.15/17.07 130.15/17.07 % SZS output end Refutation 130.15/17.07 130.15/17.07 130.25/17.07 % Terminating... 130.71/17.20 % Runner terminated. 130.71/17.20 % Zipperpin 1.5 exiting 130.71/17.20 EOF