0.00/0.05 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.xdJ8722c1T true 0.21/0.47 % Computer : n016.cluster.edu 0.21/0.47 % Model : x86_64 x86_64 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.21/0.47 % Memory : 8046.5625MB 0.21/0.47 % OS : Linux 6.8.0-71-generic 0.21/0.47 % CPULimit : 1440 0.21/0.47 % WCLimit : 180 0.21/0.47 % DateTime : Mon Jul 27 14:34:37 UTC 2026 0.21/0.48 % CPUTime : 0.21/0.48 % Running portfolio for 1440 s 0.21/0.48 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.21/0.48 % Number of cores: 8 0.21/0.48 % Python version: Python 3.12.3 0.21/0.49 % Running in HO mode 0.44/0.94 % Total configuration time : 828 0.44/0.94 % Estimated wc time : 1656 0.44/0.94 % Estimated cpu time (8 cpus) : 207.0 0.44/1.06 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 1.84/1.09 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 1.84/1.13 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 1.84/1.13 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 1.84/1.13 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 1.84/1.14 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 1.84/1.14 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 1.84/1.16 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 136.57/18.52 % Solved by lams/40_b.comb.sh. 136.57/18.52 % done 0 iterations in 17.264s 136.57/18.52 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 136.57/18.52 % SZS output start Refutation 136.57/18.52 thf(n_2t_type, type, n_2t: $i). 136.57/18.52 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 136.57/18.52 thf(lesseq_type, type, lesseq: $i > $i > $o). 136.57/18.52 thf(d_not_type, type, d_not: $o > $o). 136.57/18.52 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 136.57/18.52 thf(in_type, type, in: $i > $i > $o). 136.57/18.52 thf(den_type, type, den: $i > $i). 136.57/18.52 thf(n_1t_type, type, n_1t: $i). 136.57/18.52 thf(first1_type, type, first1: $i > $i > $i). 136.57/18.52 thf(ap_type, type, ap: $i > $i > $i). 136.57/18.52 thf('#sk4_type', type, '#sk4': $i). 136.57/18.52 thf(nat_type, type, nat: $i). 136.57/18.52 thf(iii_type, type, iii: $i > $i > $o). 136.57/18.52 thf(l_or_type, type, l_or: $o > $o > $o). 136.57/18.52 thf(second1_type, type, second1: $i > $i > $i). 136.57/18.52 thf(lessf_type, type, lessf: $i > $i > $o). 136.57/18.52 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 136.57/18.52 thf('#sk2_type', type, '#sk2': $i). 136.57/18.52 thf(frac_type, type, frac: $i). 136.57/18.52 thf(n_ts_type, type, n_ts: $i > $i > $i). 136.57/18.52 thf(imp_type, type, imp: $o > $o > $o). 136.57/18.52 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 136.57/18.52 thf(n_eq_type, type, n_eq: $i > $i > $o). 136.57/18.52 thf('#sk3_type', type, '#sk3': $i). 136.57/18.52 thf(n_is_type, type, n_is: $i > $i > $o). 136.57/18.52 thf('#ty_enc5_type', type, '#ty_enc5': ($i > $i > $o) > $i > $i > $o). 136.57/18.52 thf(n_some_type, type, n_some: ($i > $o) > $o). 136.57/18.52 thf(num_type, type, num: $i > $i). 136.57/18.52 thf(pair1type_type, type, pair1type: $i > $i). 136.57/18.52 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 136.57/18.52 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 136.57/18.52 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 136.57/18.52 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 136.57/18.52 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 136.57/18.52 thf(satz37, axiom, 136.57/18.52 (all_of @ 136.57/18.52 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ ( ^[X0:$i]: ( n_eq @ X0 @ X0 ) ))). 136.57/18.52 thf(zip_derived_cl12, plain, 136.57/18.52 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 136.57/18.52 (^[Y0 : $i]: (n_eq @ Y0 @ Y0)))), 136.57/18.52 inference('cnf', [status(esa)], [satz37])). 136.57/18.52 thf(zip_derived_cl13, plain, 136.57/18.52 ( (all_of @ ((('#C') @ in @ frac)) @ ((('#S') @ n_eq @ ('#I'))))), 136.57/18.52 inference('lams2combs', [status(thm)], [zip_derived_cl12])). 136.57/18.52 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))). 136.57/18.52 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])). 136.57/18.52 thf(zip_derived_cl307, plain, 136.57/18.52 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 136.57/18.52 ((('#S') @ n_eq @ ('#I'))))), 136.57/18.52 inference('rw', [status(thm)], [zip_derived_cl13, '0'])). 136.57/18.52 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 136.57/18.52 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 136.57/18.52 thf('1', plain, 136.57/18.52 (![X0:( $i > $o ),X1:( $i > $o )]: 136.57/18.52 ( ( all_of @ X0 @ X1 ) <=> 136.57/18.52 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 136.57/18.52 inference('rw.lit', [status(esa)], [def_all_of])). 136.57/18.52 thf(zip_derived_cl308, plain, 136.57/18.52 ( (((!!) @ (^[Y0 : $i]: 136.57/18.52 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 136.57/18.52 ((('#S') @ n_eq @ ('#I') @ Y0)))))))), 136.57/18.52 inference('rw_clause', [status(thm)], [zip_derived_cl307, '1'])). 136.57/18.52 thf(zip_derived_cl309, plain, 136.57/18.52 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 136.57/18.52 ((('#C') @ is_of @ 136.57/18.52 ((('#C') @ in @ (pair1type @ nat))))))) @ 136.57/18.52 ((('#S') @ n_eq @ ('#I')))))))), 136.57/18.52 inference('comb-normalize', [status(thm)], [zip_derived_cl308])). 136.57/18.52 thf(zip_derived_cl310, plain, 136.57/18.52 (![X2 : $i]: 136.57/18.52 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (n_eq @ X2 @ 136.57/18.52 X2)))), 136.57/18.52 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl309])). 136.57/18.52 thf(def_first1, axiom,(( first1 @ (X1)@ (X0)) = ((ap @ X0 @ n_1t)))). 136.57/18.52 thf('2', plain, 136.57/18.52 (![X1:$i,X0:$i]: ( ( first1 @ X1 @ X0 ) = ( ap @ X0 @ n_1t ) )), 136.57/18.52 define([status(thm)])). 136.57/18.52 thf(def_second1, axiom,(( second1 @ (X1)@ (X0)) = ((ap @ X0 @ n_2t)))). 136.57/18.52 thf('3', plain, 136.57/18.52 (![X1:$i,X0:$i]: ( ( second1 @ X1 @ X0 ) = ( ap @ X0 @ n_2t ) )), 136.57/18.52 define([status(thm)])). 136.57/18.52 thf(def_num, axiom,(( num @ (X0)) = ((first1 @ nat @ X0)))). 136.57/18.52 thf('4', plain, (![X0:$i]: ( ( num @ X0 ) = ( first1 @ nat @ X0 ) )), 136.57/18.52 define([status(thm)])). 136.57/18.52 thf(def_den, axiom,(( den @ (X0)) = ((second1 @ nat @ X0)))). 136.57/18.52 thf('5', plain, (![X0:$i]: ( ( den @ X0 ) = ( second1 @ nat @ X0 ) )), 136.57/18.52 define([status(thm)])). 136.57/18.52 thf(def_n_eq, axiom,(( n_eq @ (X0)@ (X1)) = 136.57/18.52 ((n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @ 136.57/18.52 (n_ts @ (num @ X1) @ (den @ X0)))))). 136.57/18.52 thf('6', plain, 136.57/18.52 (![X1:$i,X0:$i]: 136.57/18.52 ( ( n_eq @ X0 @ X1 ) = 136.57/18.52 ( n_is @ 136.57/18.52 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 136.57/18.52 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )), 136.57/18.52 define([status(thm)])). 136.57/18.52 thf(zip_derived_cl311, plain, 136.57/18.52 (![X2 : $i]: 136.57/18.52 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (n_is @ 136.57/18.52 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t)) @ 136.57/18.52 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t)))))), 136.57/18.52 inference('rw', [status(thm)], 136.57/18.52 [zip_derived_cl310, '2', '3', '4', '5', '6'])). 136.57/18.52 thf(zip_derived_cl312, plain, 136.57/18.52 (![X2 : $i]: 136.57/18.52 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 136.57/18.52 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t)) @ 136.57/18.52 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t))))), 136.57/18.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl311])). 136.57/18.52 thf(zip_derived_cl2810, plain, 136.57/18.52 (![X2 : $i]: 136.57/18.52 (~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 136.57/18.52 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t)) @ 136.57/18.52 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t))))), 136.57/18.52 inference('remove_ty_args', [status(thm)], [zip_derived_cl312])). 136.57/18.52 thf(satz51b, conjecture, 136.57/18.52 (all_of @ 136.57/18.52 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 136.57/18.52 ( ^[X0:$i]: 136.57/18.52 ( all_of @ 136.57/18.52 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 136.57/18.52 ( ^[X1:$i]: 136.57/18.52 ( all_of @ 136.57/18.52 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 136.57/18.52 ( ^[X2:$i]: 136.57/18.52 ( ( lessf @ X0 @ X1 ) => 136.57/18.52 ( ( lesseq @ X1 @ X2 ) => ( lessf @ X0 @ X2 ) ) ) ) ) ) ) ))). 136.57/18.52 thf(zf_stmt_0, negated_conjecture, 136.57/18.52 (~( all_of @ 136.57/18.52 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 136.57/18.52 ( ^[X0:$i]: 136.57/18.52 ( all_of @ 136.57/18.52 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 136.57/18.52 ( ^[X1:$i]: 136.57/18.52 ( all_of @ 136.57/18.52 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 136.57/18.52 ( ^[X2:$i]: 136.57/18.52 ( ( lessf @ X0 @ X1 ) => 136.57/18.52 ( ( lesseq @ X1 @ X2 ) => ( lessf @ X0 @ X2 ) ) ) ) ) ) ) ) )), 136.57/18.52 inference('cnf.neg', [status(esa)], [satz51b])). 136.57/18.52 thf(zip_derived_cl294, plain, 136.57/18.52 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 136.57/18.52 (^[Y0 : $i]: 136.57/18.52 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 136.57/18.52 (^[Y1 : $i]: 136.57/18.52 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 136.57/18.52 (^[Y2 : $i]: 136.57/18.52 (((lessf @ Y0 @ Y1) => 136.57/18.52 (((lesseq @ Y1 @ Y2) => (lessf @ Y0 @ Y2)))))))))))), 136.57/18.52 inference('cnf', [status(esa)], [zf_stmt_0])). 136.57/18.52 thf(zip_derived_cl295, plain, 136.57/18.52 (~ (all_of @ ((('#C') @ in @ frac)) @ 136.57/18.52 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 136.57/18.52 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 136.57/18.52 ((('#S') @ ((('#B') @ ('#S') @ 139.11/18.52 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.52 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 139.11/18.52 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 139.11/18.52 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @ 139.11/18.52 lessf)))))))))), 139.11/18.52 inference('lams2combs', [status(thm)], [zip_derived_cl294])). 139.11/18.52 thf(zip_derived_cl470, plain, 139.11/18.52 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.52 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.52 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 139.11/18.52 ((('#S') @ ((('#B') @ ('#S') @ 139.11/18.52 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.52 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 139.11/18.52 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 139.11/18.52 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @ 139.11/18.52 lessf)))))))))), 139.11/18.52 inference('rw', [status(thm)], [zip_derived_cl295, '0'])). 139.11/18.52 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 139.11/18.52 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 139.11/18.52 thf('7', plain, 139.11/18.52 (![X0:( $i > $o ),X1:( $i > $o )]: 139.11/18.52 ( ( ~( all_of @ X0 @ X1 ) ) <=> 139.11/18.52 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 139.11/18.52 inference('rw.lit', [status(esa)], [def_all_of])). 139.11/18.52 thf(zip_derived_cl471, plain, 139.11/18.52 (~ (((!!) @ (^[Y0 : $i]: 139.11/18.52 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 139.11/18.52 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.52 ((('#B') @ ((('#B') @ (all_of @ 139.11/18.52 ((('#C') @ in @ 139.11/18.52 (pair1type @ nat)))))) @ 139.11/18.52 ((('#S') @ ((('#B') @ ('#S') @ 139.11/18.52 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.52 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 139.11/18.52 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 139.11/18.52 ((('#B') @ ((('#B') @ (=>))) @ 139.11/18.52 lesseq)))))) @ 139.11/18.52 lessf)))))) @ 139.11/18.52 Y0)))))))), 139.11/18.52 inference('rw_clause', [status(thm)], [zip_derived_cl470, '7'])). 139.11/18.52 thf(zip_derived_cl472, plain, 139.11/18.52 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 139.11/18.52 ((('#C') @ is_of @ 139.11/18.52 ((('#C') @ in @ (pair1type @ nat))))))) @ 139.11/18.52 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.52 ((('#B') @ ((('#B') @ (all_of @ 139.11/18.52 ((('#C') @ in @ (pair1type @ nat)))))) @ 139.11/18.52 ((('#S') @ ((('#B') @ ('#S') @ 139.11/18.52 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.52 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 139.11/18.52 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 139.11/18.52 ((('#B') @ ((('#B') @ (=>))) @ 139.11/18.52 lesseq)))))) @ 139.11/18.52 lessf))))))))))))), 139.11/18.52 inference('comb-normalize', [status(thm)], [zip_derived_cl471])). 139.11/18.52 thf(zip_derived_cl473, plain, 139.11/18.52 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 139.11/18.52 ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.52 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.52 ((('#S') @ ((('#B') @ ('#B') @ 139.11/18.52 ((('#B') @ (=>) @ (lessf @ '#sk2'))))) @ 139.11/18.52 ((('#C') @ ((('#B') @ ('#S') @ 139.11/18.52 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 139.11/18.52 (lessf @ '#sk2'))))))))))), 139.11/18.52 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl472])). 139.11/18.52 thf(zip_derived_cl475, plain, 139.11/18.52 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.52 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.52 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (lessf @ '#sk2'))))) @ 139.11/18.52 ((('#C') @ ((('#B') @ ('#S') @ 139.11/18.52 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 139.11/18.52 (lessf @ '#sk2'))))))))), 139.11/18.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl473])). 139.11/18.52 thf(zip_derived_cl476, plain, 139.11/18.52 (~ (((!!) @ (^[Y0 : $i]: 139.11/18.52 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 139.11/18.52 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.52 ((('#S') @ ((('#B') @ ('#B') @ 139.11/18.52 ((('#B') @ (=>) @ (lessf @ '#sk2'))))) @ 139.11/18.52 ((('#C') @ ((('#B') @ ('#S') @ 139.11/18.52 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 139.11/18.52 (lessf @ '#sk2'))))) @ 139.11/18.52 Y0)))))))), 139.11/18.52 inference('rw_clause', [status(thm)], [zip_derived_cl475, '7'])). 139.11/18.52 thf(zip_derived_cl477, plain, 139.11/18.52 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 139.11/18.52 ((('#C') @ is_of @ 139.11/18.52 ((('#C') @ in @ (pair1type @ nat))))))) @ 139.11/18.52 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.52 ((('#S') @ ((('#B') @ ('#B') @ 139.11/18.52 ((('#B') @ (=>) @ (lessf @ '#sk2'))))) @ 139.11/18.52 ((('#C') @ ((('#B') @ ('#S') @ 139.11/18.52 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 139.11/18.52 (lessf @ '#sk2')))))))))))), 139.11/18.52 inference('comb-normalize', [status(thm)], [zip_derived_cl476])). 139.11/18.52 thf(zip_derived_cl478, plain, 139.11/18.52 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 139.11/18.52 ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.52 ((('#B') @ (((=>) @ (lessf @ '#sk2' @ '#sk3'))) @ 139.11/18.52 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 139.11/18.52 (lessf @ '#sk2'))))))))), 139.11/18.52 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl477])). 139.11/18.52 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))). 139.11/18.52 thf('8', plain, 139.11/18.52 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )), 139.11/18.52 define([status(thm)])). 139.11/18.52 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))). 139.11/18.52 thf('9', plain, 139.11/18.52 (![X1:$i,X0:$i]: 139.11/18.52 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 139.11/18.52 define([status(thm)])). 139.11/18.52 thf(def_lessf, axiom,(( lessf @ (X0)@ (X1)) = 139.11/18.52 ((iii @ (n_ts @ (num @ X0) @ (den @ X1)) @ (n_ts @ (num @ X1) @ (den @ X0)))))). 139.11/18.52 thf('10', plain, 139.11/18.52 (![X1:$i,X0:$i]: 139.11/18.52 ( ( lessf @ X0 @ X1 ) = 139.11/18.52 ( iii @ 139.11/18.52 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 139.11/18.52 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )), 139.11/18.52 define([status(thm)])). 139.11/18.52 thf(zip_derived_cl479, plain, 139.11/18.52 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 139.11/18.52 ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.52 ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.52 (diffprop @ 139.11/18.52 (n_ts @ (ap @ '#sk3' @ n_1t) @ 139.11/18.52 (ap @ '#sk2' @ n_2t)) @ 139.11/18.52 (n_ts @ (ap @ '#sk2' @ n_1t) @ 139.11/18.52 (ap @ '#sk3' @ n_2t)))))) @ 139.11/18.52 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 139.11/18.52 (lessf @ '#sk2'))))))))), 139.11/18.52 inference('rw', [status(thm)], 139.11/18.52 [zip_derived_cl478, '8', '9', '2', '2', '3', '3', '4', '4', 139.11/18.52 '5', '5', '10'])). 139.11/18.52 thf(zip_derived_cl481, plain, 139.11/18.52 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.52 ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.52 (diffprop @ 139.11/18.52 (n_ts @ (ap @ '#sk3' @ n_1t) @ 139.11/18.52 (ap @ '#sk2' @ n_2t)) @ 139.11/18.52 (n_ts @ (ap @ '#sk2' @ n_1t) @ 139.11/18.52 (ap @ '#sk3' @ n_2t)))))) @ 139.11/18.52 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ (lessf @ '#sk2'))))))), 139.11/18.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl479])). 139.11/18.52 thf(zip_derived_cl482, plain, 139.11/18.52 (~ (((!!) @ (^[Y0 : $i]: 139.11/18.52 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 139.11/18.52 ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.52 (diffprop @ 139.11/18.52 (n_ts @ (ap @ '#sk3' @ n_1t) @ 139.11/18.52 (ap @ '#sk2' @ n_2t)) @ 139.11/18.52 (n_ts @ (ap @ '#sk2' @ n_1t) @ 139.11/18.52 (ap @ '#sk3' @ n_2t)))))) @ 139.11/18.52 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 139.11/18.52 (lessf @ '#sk2'))) @ 139.11/18.52 Y0)))))))), 139.11/18.52 inference('rw_clause', [status(thm)], [zip_derived_cl481, '7'])). 139.11/18.52 thf(zip_derived_cl483, plain, 139.11/18.52 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 139.11/18.52 ((('#C') @ is_of @ 139.11/18.52 ((('#C') @ in @ (pair1type @ nat))))))) @ 139.11/18.52 ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.52 (diffprop @ 139.11/18.52 (n_ts @ (ap @ '#sk3' @ n_1t) @ 139.11/18.53 (ap @ '#sk2' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk2' @ n_1t) @ 139.11/18.53 (ap @ '#sk3' @ n_2t)))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 139.11/18.53 (lessf @ '#sk2')))))))))), 139.11/18.53 inference('comb-normalize', [status(thm)], [zip_derived_cl482])). 139.11/18.53 thf(zip_derived_cl484, plain, 139.11/18.53 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => 139.11/18.53 (((l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) => 139.11/18.53 (((lesseq @ '#sk3' @ '#sk4') => (lessf @ '#sk2' @ '#sk4')))))))), 139.11/18.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl483])). 139.11/18.53 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 139.11/18.53 thf('11', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 139.11/18.53 define([status(thm)])). 139.11/18.53 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 139.11/18.53 thf('12', plain, 139.11/18.53 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 139.11/18.53 define([status(thm)])). 139.11/18.53 thf(def_lesseq, axiom,(( lesseq @ (X0)@ (X1)) = 139.11/18.53 ((l_or @ (lessf @ X0 @ X1) @ (n_eq @ X0 @ X1))))). 139.11/18.53 thf('13', plain, 139.11/18.53 (![X1:$i,X0:$i]: 139.11/18.53 ( ( lesseq @ X0 @ X1 ) = 139.11/18.53 ( l_or @ ( lessf @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )), 139.11/18.53 define([status(thm)])). 139.11/18.53 thf(zip_derived_cl485, plain, 139.11/18.53 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => 139.11/18.53 (((l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) => 139.11/18.53 (((imp @ 139.11/18.53 (imp @ 139.11/18.53 (l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 139.11/18.53 ($false)) @ 139.11/18.53 (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) => 139.11/18.53 (l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))))))), 139.11/18.53 inference('rw', [status(thm)], 139.11/18.53 [zip_derived_cl484, '11', '12', '8', '8', '9', '9', '2', '2', 139.11/18.53 '2', '3', '3', '3', '4', '4', '4', '5', '5', '5', '6', '10', 139.11/18.53 '10', '13'])). 139.11/18.53 thf(zip_derived_cl487, plain, 139.11/18.53 (~ (((l_some @ nat @ 139.11/18.53 (diffprop @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) => 139.11/18.53 (((imp @ 139.11/18.53 (imp @ 139.11/18.53 (l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 139.11/18.53 ($false)) @ 139.11/18.53 (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) => 139.11/18.53 (l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))))), 139.11/18.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])). 139.11/18.53 thf(zip_derived_cl489, plain, 139.11/18.53 (~ (((imp @ 139.11/18.53 (imp @ 139.11/18.53 (l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 139.11/18.53 ($false)) @ 139.11/18.53 (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) => 139.11/18.53 (l_some @ nat @ 139.11/18.53 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))), 139.11/18.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl487])). 139.11/18.53 thf(zip_derived_cl490, plain, 139.11/18.53 ( (imp @ 139.11/18.53 (imp @ 139.11/18.53 (l_some @ nat @ 139.11/18.53 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 139.11/18.53 ($false)) @ 139.11/18.53 (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t))))), 139.11/18.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl489])). 139.11/18.53 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 139.11/18.53 thf('14', plain, 139.11/18.53 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 139.11/18.53 inference('rw.lit', [status(esa)], [def_imp])). 139.11/18.53 thf(zip_derived_cl492, plain, 139.11/18.53 ( (((imp @ 139.11/18.53 (l_some @ nat @ 139.11/18.53 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 139.11/18.53 ($false)) => (n_is @ 139.11/18.53 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)))))), 139.11/18.53 inference('rw_clause', [status(thm)], [zip_derived_cl490, '14'])). 139.11/18.53 thf(zip_derived_cl493, plain, 139.11/18.53 ((~ (imp @ 139.11/18.53 (l_some @ nat @ 139.11/18.53 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 139.11/18.53 ($false)) 139.11/18.53 | (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t))))), 139.11/18.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl492])). 139.11/18.53 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 139.11/18.53 thf('15', plain, 139.11/18.53 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 139.11/18.53 inference('rw.lit', [status(esa)], [def_imp])). 139.11/18.53 thf(zip_derived_cl494, plain, 139.11/18.53 ((~ (((l_some @ nat @ 139.11/18.53 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) => 139.11/18.53 ($false))) 139.11/18.53 | (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t))))), 139.11/18.53 inference('rw_clause', [status(thm)], [zip_derived_cl493, '15'])). 139.11/18.53 thf(zip_derived_cl495, plain, 139.11/18.53 ((~ (((~) @ (l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))))) 139.11/18.53 | (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t))))), 139.11/18.53 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl494])). 139.11/18.53 thf(zip_derived_cl496, plain, 139.11/18.53 (( (l_some @ nat @ 139.11/18.53 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) 139.11/18.53 | (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t))))), 139.11/18.53 inference('simplify nested equalities', [status(thm)], 139.11/18.53 [zip_derived_cl495])). 139.11/18.53 thf(zip_derived_cl486, plain, 139.11/18.53 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))), 139.11/18.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])). 139.11/18.53 thf(zip_derived_cl2828, plain, 139.11/18.53 ( (is_of @ '#sk4' @ ('#ty_enc5' @ in @ (pair1type @ nat)))), 139.11/18.53 inference('remove_ty_args', [status(thm)], [zip_derived_cl486])). 139.11/18.53 thf(zip_derived_cl480, plain, 139.11/18.53 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))), 139.11/18.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl479])). 139.11/18.53 thf(zip_derived_cl2827, plain, 139.11/18.53 ( (is_of @ '#sk3' @ ('#ty_enc5' @ in @ (pair1type @ nat)))), 139.11/18.53 inference('remove_ty_args', [status(thm)], [zip_derived_cl480])). 139.11/18.53 thf(zip_derived_cl474, plain, 139.11/18.53 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))), 139.11/18.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl473])). 139.11/18.53 thf(zip_derived_cl2826, plain, 139.11/18.53 ( (is_of @ '#sk2' @ ('#ty_enc5' @ in @ (pair1type @ nat)))), 139.11/18.53 inference('remove_ty_args', [status(thm)], [zip_derived_cl474])). 139.11/18.53 thf(zip_derived_cl488, plain, 139.11/18.53 ( (l_some @ nat @ 139.11/18.53 (diffprop @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t))))), 139.11/18.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl487])). 139.11/18.53 thf(zip_derived_cl491, plain, 139.11/18.53 (~ (l_some @ nat @ 139.11/18.53 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t))))), 139.11/18.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl489])). 139.11/18.53 thf(satz45, axiom, 139.11/18.53 (all_of @ 139.11/18.53 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 139.11/18.53 ( ^[X0:$i]: 139.11/18.53 ( all_of @ 139.11/18.53 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 139.11/18.53 ( ^[X1:$i]: 139.11/18.53 ( all_of @ 139.11/18.53 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 139.11/18.53 ( ^[X2:$i]: 139.11/18.53 ( all_of @ 139.11/18.53 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 139.11/18.53 ( ^[X3:$i]: 139.11/18.53 ( ( lessf @ X0 @ X1 ) => 139.11/18.53 ( ( n_eq @ X0 @ X2 ) => 139.11/18.53 ( ( n_eq @ X1 @ X3 ) => ( lessf @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 139.11/18.53 thf(zip_derived_cl250, plain, 139.11/18.53 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 139.11/18.53 (^[Y0 : $i]: 139.11/18.53 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 139.11/18.53 (^[Y1 : $i]: 139.11/18.53 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 139.11/18.53 (^[Y2 : $i]: 139.11/18.53 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 139.11/18.53 (^[Y3 : $i]: 139.11/18.53 (((lessf @ Y0 @ Y1) => 139.11/18.53 (((n_eq @ Y0 @ Y2) => 139.11/18.53 (((n_eq @ Y1 @ Y3) => (lessf @ Y2 @ Y3)))))))))))))))), 139.11/18.53 inference('cnf', [status(esa)], [satz45])). 139.11/18.53 thf(zip_derived_cl251, plain, 139.11/18.53 ( (all_of @ ((('#C') @ in @ frac)) @ 139.11/18.53 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 139.11/18.53 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ ('#S') @ 139.11/18.53 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.53 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @ 139.11/18.53 ((('#C') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ ('#S') @ 139.11/18.53 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 139.11/18.53 ((('#C') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ ('#S') @ 139.11/18.53 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 139.11/18.53 lessf)))))))))))))), 139.11/18.53 inference('lams2combs', [status(thm)], [zip_derived_cl250])). 139.11/18.53 thf(zip_derived_cl2589, plain, 139.11/18.53 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.53 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 139.11/18.53 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 139.11/18.53 ((('#C') @ in @ 139.11/18.53 (pair1type @ nat)))))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ ('#S') @ 139.11/18.53 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.53 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @ 139.11/18.53 ((('#C') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ ('#S') @ 139.11/18.53 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 139.11/18.53 ((('#C') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ ('#S') @ 139.11/18.53 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 139.11/18.53 lessf)))))))))))))), 139.11/18.53 inference('rw', [status(thm)], [zip_derived_cl251, '0'])). 139.11/18.53 thf(zip_derived_cl2590, plain, 139.11/18.53 ( (((!!) @ (^[Y0 : $i]: 139.11/18.53 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 139.11/18.53 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (all_of @ 139.11/18.53 ((('#C') @ in @ 139.11/18.53 (pair1type @ nat)))))) @ 139.11/18.53 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 139.11/18.53 ((('#C') @ in @ 139.11/18.53 (pair1type @ nat)))))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ ('#S') @ 139.11/18.53 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.53 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (=>))) @ 139.11/18.53 lessf)))))))) @ 139.11/18.53 ((('#C') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ ('#S') @ 139.11/18.53 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (=>))) @ 139.11/18.53 n_eq)))))))) @ 139.11/18.53 ((('#C') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ ('#S') @ 139.11/18.53 ((('#B') @ ((('#B') @ (=>))) @ 139.11/18.53 n_eq)))))) @ 139.11/18.53 lessf)))))))))) @ 139.11/18.53 Y0)))))))), 139.11/18.53 inference('rw_clause', [status(thm)], [zip_derived_cl2589, '1'])). 139.11/18.53 thf(zip_derived_cl2591, plain, 139.11/18.53 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 139.11/18.53 ((('#C') @ is_of @ 139.11/18.53 ((('#C') @ in @ (pair1type @ nat))))))) @ 139.11/18.53 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (all_of @ 139.11/18.53 ((('#C') @ in @ (pair1type @ nat)))))) @ 139.11/18.53 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 139.11/18.53 ((('#C') @ in @ 139.11/18.53 (pair1type @ nat)))))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ ('#S') @ 139.11/18.53 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.53 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @ 139.11/18.53 ((('#C') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ ('#S') @ 139.11/18.53 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 139.11/18.53 ((('#C') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ ('#S') @ 139.11/18.53 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 139.11/18.53 lessf))))))))))))))))), 139.11/18.53 inference('comb-normalize', [status(thm)], [zip_derived_cl2590])). 139.11/18.53 thf(zip_derived_cl2592, plain, 139.11/18.53 (![X2 : $i]: 139.11/18.53 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 139.11/18.53 ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.53 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (all_of @ 139.11/18.53 ((('#C') @ in @ (pair1type @ nat)))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ (=>) @ (lessf @ X2))))))) @ 139.11/18.53 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ (=>) @ (n_eq @ X2))))))) @ 139.11/18.53 ((('#C') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ ('#S') @ 139.11/18.53 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 139.11/18.53 lessf)))))))))))))), 139.11/18.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2591])). 139.11/18.53 thf(zip_derived_cl2593, plain, 139.11/18.53 (![X2 : $i]: 139.11/18.53 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.53 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.53 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (all_of @ 139.11/18.53 ((('#C') @ in @ (pair1type @ nat)))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ (=>) @ (lessf @ X2))))))) @ 139.11/18.53 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ (=>) @ (n_eq @ X2))))))) @ 139.11/18.53 ((('#C') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ ('#S') @ 139.11/18.53 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 139.11/18.53 lessf))))))))))))), 139.11/18.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2592])). 139.11/18.53 thf(zip_derived_cl2594, plain, 139.11/18.53 (![X0 : $i]: 139.11/18.53 ( (((!!) @ (^[Y0 : $i]: 139.11/18.53 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 139.11/18.53 ((('#B') @ (all_of @ 139.11/18.53 ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (all_of @ 139.11/18.53 ((('#C') @ in @ 139.11/18.53 (pair1type @ nat)))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ (=>) @ (lessf @ X0))))))) @ 139.11/18.53 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ (=>) @ 139.11/18.53 (n_eq @ X0))))))) @ 139.11/18.53 ((('#C') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ ('#S') @ 139.11/18.53 ((('#B') @ ((('#B') @ (=>))) @ 139.11/18.53 n_eq)))))) @ 139.11/18.53 lessf)))))))) @ 139.11/18.53 Y0))))))) 139.11/18.53 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.53 inference('rw_clause', [status(thm)], [zip_derived_cl2593, '1'])). 139.11/18.53 thf(zip_derived_cl2595, plain, 139.11/18.53 (![X0 : $i]: 139.11/18.53 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 139.11/18.53 ((('#C') @ is_of @ 139.11/18.53 ((('#C') @ in @ (pair1type @ nat))))))) @ 139.11/18.53 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (all_of @ 139.11/18.53 ((('#C') @ in @ 139.11/18.53 (pair1type @ nat)))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ (=>) @ (lessf @ X0))))))) @ 139.11/18.53 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ (=>) @ 139.11/18.53 (n_eq @ X0))))))) @ 139.11/18.53 ((('#C') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ ('#S') @ 139.11/18.53 ((('#B') @ ((('#B') @ (=>))) @ 139.11/18.53 n_eq)))))) @ 139.11/18.53 lessf)))))))))))))) 139.11/18.53 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.53 inference('comb-normalize', [status(thm)], [zip_derived_cl2594])). 139.11/18.53 thf(zip_derived_cl2596, plain, 139.11/18.53 (![X0 : $i, X2 : $i]: 139.11/18.53 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 139.11/18.53 ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.53 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (((=>) @ (lessf @ X0 @ X2))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X0))))) @ 139.11/18.53 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 139.11/18.53 lessf))))))))))) 139.11/18.53 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2595])). 139.11/18.53 thf(zip_derived_cl2597, plain, 139.11/18.53 (![X0 : $i, X2 : $i]: 139.11/18.53 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 139.11/18.53 ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.53 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ (ap @ X2 @ n_1t) @ 139.11/18.53 (ap @ X0 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X0 @ n_1t) @ 139.11/18.53 (ap @ X2 @ n_2t)))))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X0))))) @ 139.11/18.53 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 139.11/18.53 lessf))))))))))) 139.11/18.53 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.53 inference('rw', [status(thm)], 139.11/18.53 [zip_derived_cl2596, '8', '9', '2', '2', '3', '3', '4', '4', 139.11/18.53 '5', '5', '10'])). 139.11/18.53 thf(zip_derived_cl2598, plain, 139.11/18.53 (![X0 : $i, X2 : $i]: 139.11/18.53 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.53 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.53 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ (ap @ X2 @ n_1t) @ 139.11/18.53 (ap @ X0 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X0 @ n_1t) @ 139.11/18.53 (ap @ X2 @ n_2t)))))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 139.11/18.53 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 139.11/18.53 lessf))))))))) 139.11/18.53 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2597])). 139.11/18.53 thf(zip_derived_cl2599, plain, 139.11/18.53 (![X0 : $i, X1 : $i]: 139.11/18.53 ( (((!!) @ (^[Y0 : $i]: 139.11/18.53 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 139.11/18.53 ((('#B') @ (all_of @ 139.11/18.53 ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ 139.11/18.53 (ap @ X1 @ n_1t) @ 139.11/18.53 (ap @ X0 @ n_2t)) @ 139.11/18.53 (n_ts @ 139.11/18.53 (ap @ X0 @ n_1t) @ 139.11/18.53 (ap @ X1 @ n_2t)))))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 139.11/18.53 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 139.11/18.53 (n_eq @ X1))))) @ 139.11/18.53 lessf)))))) @ 139.11/18.53 Y0))))))) 139.11/18.53 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.53 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.53 inference('rw_clause', [status(thm)], [zip_derived_cl2598, '1'])). 139.11/18.53 thf(zip_derived_cl2600, plain, 139.11/18.53 (![X0 : $i, X1 : $i]: 139.11/18.53 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 139.11/18.53 ((('#C') @ is_of @ 139.11/18.53 ((('#C') @ in @ (pair1type @ nat))))))) @ 139.11/18.53 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.53 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ 139.11/18.53 (ap @ X1 @ n_1t) @ 139.11/18.53 (ap @ X0 @ n_2t)) @ 139.11/18.53 (n_ts @ 139.11/18.53 (ap @ X0 @ n_1t) @ 139.11/18.53 (ap @ X1 @ n_2t)))))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ ('#B') @ 139.11/18.53 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 139.11/18.53 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))))) @ 139.11/18.53 lessf)))))))))))) 139.11/18.53 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.53 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.53 inference('comb-normalize', [status(thm)], [zip_derived_cl2599])). 139.11/18.53 thf(zip_derived_cl2601, plain, 139.11/18.53 (![X0 : $i, X1 : $i, X3 : $i]: 139.11/18.53 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 139.11/18.53 ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.53 ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) @ 139.11/18.53 ((('#B') @ (((=>) @ (n_eq @ X0 @ X3))) @ 139.11/18.53 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (lessf @ X3)))))))))) 139.11/18.53 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.53 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2600])). 139.11/18.53 thf(zip_derived_cl2602, plain, 139.11/18.53 (![X0 : $i, X1 : $i, X3 : $i]: 139.11/18.53 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 139.11/18.53 ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.53 ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) @ 139.11/18.53 ((('#B') @ (((=>) @ (n_is @ 139.11/18.53 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (lessf @ X3)))))))))) 139.11/18.53 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.53 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.53 inference('rw', [status(thm)], 139.11/18.53 [zip_derived_cl2601, '2', '2', '3', '3', '4', '4', '5', '5', 139.11/18.53 '6'])). 139.11/18.53 thf(zip_derived_cl2603, plain, 139.11/18.53 (![X0 : $i, X1 : $i, X3 : $i]: 139.11/18.53 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.53 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.53 ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) @ 139.11/18.53 ((('#B') @ (((=>) @ (n_is @ 139.11/18.53 (n_ts @ (ap @ X0 @ n_1t) @ 139.11/18.53 (ap @ X3 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X3 @ n_1t) @ 139.11/18.53 (ap @ X0 @ n_2t))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (lessf @ X3)))))))) 139.11/18.53 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.53 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2602])). 139.11/18.53 thf(zip_derived_cl2604, plain, 139.11/18.53 (![X0 : $i, X1 : $i, X2 : $i]: 139.11/18.53 ( (((!!) @ (^[Y0 : $i]: 139.11/18.53 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 139.11/18.53 ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ (ap @ X0 @ n_1t) @ 139.11/18.53 (ap @ X1 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X1 @ n_1t) @ 139.11/18.53 (ap @ X0 @ n_2t)))))) @ 139.11/18.53 ((('#B') @ (((=>) @ (n_is @ 139.11/18.53 (n_ts @ (ap @ X1 @ n_1t) @ 139.11/18.53 (ap @ X2 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X2 @ n_1t) @ 139.11/18.53 (ap @ X1 @ n_2t))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @ 139.11/18.53 (lessf @ X2))))) @ 139.11/18.53 Y0))))))) 139.11/18.53 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.53 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.53 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.53 inference('rw_clause', [status(thm)], [zip_derived_cl2603, '1'])). 139.11/18.53 thf(zip_derived_cl2605, plain, 139.11/18.53 (![X0 : $i, X1 : $i, X2 : $i]: 139.11/18.53 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 139.11/18.53 ((('#C') @ is_of @ 139.11/18.53 ((('#C') @ in @ (pair1type @ nat))))))) @ 139.11/18.53 ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.53 (diffprop @ 139.11/18.53 (n_ts @ (ap @ X0 @ n_1t) @ 139.11/18.53 (ap @ X1 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X1 @ n_1t) @ 139.11/18.53 (ap @ X0 @ n_2t)))))) @ 139.11/18.53 ((('#B') @ (((=>) @ (n_is @ 139.11/18.53 (n_ts @ (ap @ X1 @ n_1t) @ 139.11/18.53 (ap @ X2 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X2 @ n_1t) @ 139.11/18.53 (ap @ X1 @ n_2t))))) @ 139.11/18.53 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @ 139.11/18.53 (lessf @ X2))))))))))) 139.11/18.53 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.53 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.53 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.53 inference('comb-normalize', [status(thm)], [zip_derived_cl2604])). 139.11/18.53 thf(zip_derived_cl2606, plain, 139.11/18.53 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 139.11/18.53 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 139.11/18.53 (((l_some @ nat @ 139.11/18.53 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) => 139.11/18.53 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) => 139.11/18.53 (((n_eq @ X0 @ X4) => (lessf @ X2 @ X4))))))))) 139.11/18.53 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.53 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.53 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2605])). 139.11/18.53 thf(zip_derived_cl2607, plain, 139.11/18.53 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 139.11/18.53 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 139.11/18.53 (((l_some @ nat @ 139.11/18.53 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) => 139.11/18.53 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) => 139.11/18.53 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @ 139.11/18.53 nat @ 139.11/18.53 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 139.11/18.53 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))))))))))) 139.11/18.53 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.53 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.53 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.54 inference('rw', [status(thm)], 139.11/18.54 [zip_derived_cl2606, '8', '9', '2', '2', '2', '3', '3', '3', 139.11/18.54 '4', '4', '4', '5', '5', '5', '6', '10'])). 139.11/18.54 thf(zip_derived_cl2608, plain, 139.11/18.54 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 139.11/18.54 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | (((l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) => 139.11/18.54 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) => 139.11/18.54 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @ 139.11/18.54 nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))))))))) 139.11/18.54 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2607])). 139.11/18.54 thf(zip_derived_cl2609, plain, 139.11/18.54 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 139.11/18.54 (~ (l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 139.11/18.54 | (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) => 139.11/18.54 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @ 139.11/18.54 nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))))))) 139.11/18.54 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2608])). 139.11/18.54 thf(zip_derived_cl2610, plain, 139.11/18.54 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 139.11/18.54 (~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) 139.11/18.54 | (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @ 139.11/18.54 nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))))) 139.11/18.54 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))), 139.11/18.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2609])). 139.11/18.54 thf(zip_derived_cl2611, plain, 139.11/18.54 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 139.11/18.54 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) 139.11/18.54 | (l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))) 139.11/18.54 | ~ (l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 139.11/18.54 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))))), 139.11/18.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2610])). 139.11/18.54 thf(zip_derived_cl2906, plain, 139.11/18.54 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 139.11/18.54 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) 139.11/18.54 | (l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))) 139.11/18.54 | ~ (l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 139.11/18.54 | ~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 139.11/18.54 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 139.11/18.54 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 139.11/18.54 | ~ (is_of @ X4 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 139.11/18.54 | ~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))))), 139.11/18.54 inference('remove_ty_args', [status(thm)], [zip_derived_cl2611])). 139.11/18.54 thf(satz50, axiom, 139.11/18.54 (all_of @ 139.11/18.54 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 139.11/18.54 ( ^[X0:$i]: 139.11/18.54 ( all_of @ 139.11/18.54 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 139.11/18.54 ( ^[X1:$i]: 139.11/18.54 ( all_of @ 139.11/18.54 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 139.11/18.54 ( ^[X2:$i]: 139.11/18.54 ( ( lessf @ X0 @ X1 ) => 139.11/18.54 ( ( lessf @ X1 @ X2 ) => ( lessf @ X0 @ X2 ) ) ) ) ) ) ) ))). 139.11/18.54 thf(zip_derived_cl152, plain, 139.11/18.54 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 139.11/18.54 (^[Y0 : $i]: 139.11/18.54 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 139.11/18.54 (^[Y1 : $i]: 139.11/18.54 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 139.11/18.54 (^[Y2 : $i]: 139.11/18.54 (((lessf @ Y0 @ Y1) => 139.11/18.54 (((lessf @ Y1 @ Y2) => (lessf @ Y0 @ Y2)))))))))))), 139.11/18.54 inference('cnf', [status(esa)], [satz50])). 139.11/18.54 thf(zip_derived_cl153, plain, 139.11/18.54 ( (all_of @ ((('#C') @ in @ frac)) @ 139.11/18.54 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 139.11/18.54 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 139.11/18.54 ((('#S') @ ((('#B') @ ('#S') @ 139.11/18.54 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.54 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 139.11/18.54 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 139.11/18.54 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 139.11/18.54 lessf)))))))))), 139.11/18.54 inference('lams2combs', [status(thm)], [zip_derived_cl152])). 139.11/18.54 thf(zip_derived_cl1444, plain, 139.11/18.54 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.54 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.54 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 139.11/18.54 ((('#S') @ ((('#B') @ ('#S') @ 139.11/18.54 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.54 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 139.11/18.54 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 139.11/18.54 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 139.11/18.54 lessf)))))))))), 139.11/18.54 inference('rw', [status(thm)], [zip_derived_cl153, '0'])). 139.11/18.54 thf(zip_derived_cl1445, plain, 139.11/18.54 ( (((!!) @ (^[Y0 : $i]: 139.11/18.54 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 139.11/18.54 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.54 ((('#B') @ ((('#B') @ (all_of @ 139.11/18.54 ((('#C') @ in @ 139.11/18.54 (pair1type @ nat)))))) @ 139.11/18.54 ((('#S') @ ((('#B') @ ('#S') @ 139.11/18.54 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.54 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 139.11/18.54 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 139.11/18.54 ((('#B') @ ((('#B') @ (=>))) @ 139.11/18.54 lessf)))))) @ 139.11/18.54 lessf)))))) @ 139.11/18.54 Y0)))))))), 139.11/18.54 inference('rw_clause', [status(thm)], [zip_derived_cl1444, '1'])). 139.11/18.54 thf(zip_derived_cl1446, plain, 139.11/18.54 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 139.11/18.54 ((('#C') @ is_of @ 139.11/18.54 ((('#C') @ in @ (pair1type @ nat))))))) @ 139.11/18.54 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.54 ((('#B') @ ((('#B') @ (all_of @ 139.11/18.54 ((('#C') @ in @ (pair1type @ nat)))))) @ 139.11/18.54 ((('#S') @ ((('#B') @ ('#S') @ 139.11/18.54 ((('#B') @ ((('#B') @ ('#B'))) @ 139.11/18.54 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 139.11/18.54 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 139.11/18.54 ((('#B') @ ((('#B') @ (=>))) @ 139.11/18.54 lessf)))))) @ 139.11/18.54 lessf))))))))))))), 139.11/18.54 inference('comb-normalize', [status(thm)], [zip_derived_cl1445])). 139.11/18.54 thf(zip_derived_cl1447, plain, 139.11/18.54 (![X2 : $i]: 139.11/18.54 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 139.11/18.54 ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.54 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.54 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (lessf @ X2))))) @ 139.11/18.54 ((('#C') @ ((('#B') @ ('#S') @ 139.11/18.54 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 139.11/18.54 (lessf @ X2))))))))))), 139.11/18.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1446])). 139.11/18.54 thf(zip_derived_cl1448, plain, 139.11/18.54 (![X2 : $i]: 139.11/18.54 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.54 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.54 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (lessf @ X2))))) @ 139.11/18.54 ((('#C') @ ((('#B') @ ('#S') @ 139.11/18.54 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 139.11/18.54 (lessf @ X2)))))))))), 139.11/18.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1447])). 139.11/18.54 thf(zip_derived_cl1449, plain, 139.11/18.54 (![X0 : $i]: 139.11/18.54 ( (((!!) @ (^[Y0 : $i]: 139.11/18.54 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 139.11/18.54 ((('#B') @ (all_of @ 139.11/18.54 ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.54 ((('#S') @ ((('#B') @ ('#B') @ 139.11/18.54 ((('#B') @ (=>) @ (lessf @ X0))))) @ 139.11/18.54 ((('#C') @ ((('#B') @ ('#S') @ 139.11/18.54 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 139.11/18.54 (lessf @ X0))))) @ 139.11/18.54 Y0))))))) 139.11/18.54 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.54 inference('rw_clause', [status(thm)], [zip_derived_cl1448, '1'])). 139.11/18.54 thf(zip_derived_cl1450, plain, 139.11/18.54 (![X0 : $i]: 139.11/18.54 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 139.11/18.54 ((('#C') @ is_of @ 139.11/18.54 ((('#C') @ in @ (pair1type @ nat))))))) @ 139.11/18.54 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 139.11/18.54 ((('#S') @ ((('#B') @ ('#B') @ 139.11/18.54 ((('#B') @ (=>) @ (lessf @ X0))))) @ 139.11/18.54 ((('#C') @ ((('#B') @ ('#S') @ 139.11/18.54 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 139.11/18.54 (lessf @ X0))))))))))) 139.11/18.54 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.54 inference('comb-normalize', [status(thm)], [zip_derived_cl1449])). 139.11/18.54 thf(zip_derived_cl1451, plain, 139.11/18.54 (![X0 : $i, X2 : $i]: 139.11/18.54 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 139.11/18.54 ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.54 ((('#B') @ (((=>) @ (lessf @ X0 @ X2))) @ 139.11/18.54 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @ (lessf @ X0)))))))) 139.11/18.54 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1450])). 139.11/18.54 thf(zip_derived_cl1452, plain, 139.11/18.54 (![X0 : $i, X2 : $i]: 139.11/18.54 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 139.11/18.54 ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.54 ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.54 (diffprop @ 139.11/18.54 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))))) @ 139.11/18.54 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @ (lessf @ X0)))))))) 139.11/18.54 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.54 inference('rw', [status(thm)], 139.11/18.54 [zip_derived_cl1451, '8', '9', '2', '2', '3', '3', '4', '4', 139.11/18.54 '5', '5', '10'])). 139.11/18.54 thf(zip_derived_cl1453, plain, 139.11/18.54 (![X0 : $i, X2 : $i]: 139.11/18.54 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 139.11/18.54 ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.54 (diffprop @ 139.11/18.54 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))))) @ 139.11/18.54 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @ (lessf @ X0)))))) 139.11/18.54 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1452])). 139.11/18.54 thf(zip_derived_cl1454, plain, 139.11/18.54 (![X0 : $i, X1 : $i]: 139.11/18.54 ( (((!!) @ (^[Y0 : $i]: 139.11/18.54 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 139.11/18.54 ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.54 (diffprop @ 139.11/18.54 (n_ts @ (ap @ X1 @ n_1t) @ 139.11/18.54 (ap @ X0 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X0 @ n_1t) @ 139.11/18.54 (ap @ X1 @ n_2t)))))) @ 139.11/18.54 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X1))) @ 139.11/18.54 (lessf @ X0))) @ 139.11/18.54 Y0))))))) 139.11/18.54 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.54 inference('rw_clause', [status(thm)], [zip_derived_cl1453, '1'])). 139.11/18.54 thf(zip_derived_cl1455, plain, 139.11/18.54 (![X0 : $i, X1 : $i]: 139.11/18.54 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 139.11/18.54 ((('#C') @ is_of @ 139.11/18.54 ((('#C') @ in @ (pair1type @ nat))))))) @ 139.11/18.54 ((('#B') @ (((=>) @ (l_some @ nat @ 139.11/18.54 (diffprop @ 139.11/18.54 (n_ts @ (ap @ X1 @ n_1t) @ 139.11/18.54 (ap @ X0 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X0 @ n_1t) @ 139.11/18.54 (ap @ X1 @ n_2t)))))) @ 139.11/18.54 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X1))) @ 139.11/18.54 (lessf @ X0))))))))) 139.11/18.54 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.54 inference('comb-normalize', [status(thm)], [zip_derived_cl1454])). 139.11/18.54 thf(zip_derived_cl1456, plain, 139.11/18.54 (![X0 : $i, X1 : $i, X3 : $i]: 139.11/18.54 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => 139.11/18.54 (((l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) => 139.11/18.54 (((lessf @ X1 @ X3) => (lessf @ X0 @ X3))))))) 139.11/18.54 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.54 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1455])). 139.11/18.54 thf(zip_derived_cl1457, plain, 139.11/18.54 (![X0 : $i, X1 : $i, X3 : $i]: 139.11/18.54 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => 139.11/18.54 (((l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) => 139.11/18.54 (((l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)))) => 139.11/18.54 (l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)))))))))) 139.11/18.54 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.54 inference('rw', [status(thm)], 139.11/18.54 [zip_derived_cl1456, '8', '8', '9', '9', '2', '2', '2', '3', 139.11/18.54 '3', '3', '4', '4', '4', '5', '5', '5', '10', '10'])). 139.11/18.54 thf(zip_derived_cl1458, plain, 139.11/18.54 (![X0 : $i, X1 : $i, X3 : $i]: 139.11/18.54 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | (((l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) => 139.11/18.54 (((l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)))) => 139.11/18.54 (l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)))))))) 139.11/18.54 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1457])). 139.11/18.54 thf(zip_derived_cl1459, plain, 139.11/18.54 (![X0 : $i, X1 : $i, X3 : $i]: 139.11/18.54 (~ (l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) 139.11/18.54 | (((l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)))) => 139.11/18.54 (l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)))))) 139.11/18.54 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))))), 139.11/18.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1458])). 139.11/18.54 thf(zip_derived_cl1460, plain, 139.11/18.54 (![X0 : $i, X1 : $i, X3 : $i]: 139.11/18.54 (~ (l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)))) 139.11/18.54 | (l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)))) 139.11/18.54 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 139.11/18.54 | ~ (l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))), 139.11/18.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1459])). 139.11/18.54 thf(zip_derived_cl2874, plain, 139.11/18.54 (![X0 : $i, X1 : $i, X3 : $i]: 139.11/18.54 (~ (l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)))) 139.11/18.54 | (l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)))) 139.11/18.54 | ~ (is_of @ X3 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 139.11/18.54 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 139.11/18.54 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 139.11/18.54 | ~ (l_some @ nat @ 139.11/18.54 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 139.11/18.54 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))), 139.11/18.54 inference('remove_ty_args', [status(thm)], [zip_derived_cl1460])). 139.11/18.54 thf(zip_derived_cl2909, plain, ($false), 139.11/18.54 inference('eprover', [status(thm)], 139.11/18.54 [zip_derived_cl2810, zip_derived_cl496, zip_derived_cl2828, 139.11/18.54 zip_derived_cl2827, zip_derived_cl2826, zip_derived_cl488, 139.11/18.54 zip_derived_cl491, zip_derived_cl2906, zip_derived_cl2874])). 139.11/18.54 139.11/18.54 % SZS output end Refutation 139.11/18.54 139.11/18.54 139.11/18.54 % Terminating... 19.75/18.62 % Runner terminated. 19.75/18.65 % Zipperpin 1.5 exiting 19.75/18.67 EOF