0.04/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.rGWPHlYjt2 true 0.12/0.33 % Computer : n016.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 960 0.12/0.33 % WCLimit : 120 0.12/0.33 % DateTime : Tue Aug 9 08:22:12 EDT 2022 0.12/0.33 % CPUTime : 0.12/0.33 % Running portfolio for 960 s 0.12/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.12/0.33 % Number of cores: 8 0.12/0.33 % Python version: Python 3.6.8 0.12/0.33 % Running in HO mode 0.45/0.60 % Total configuration time : 828 0.45/0.60 % Estimated wc time : 1656 0.45/0.60 % Estimated cpu time (8 cpus) : 207.0 0.47/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.47/0.68 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.47/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.47/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.47/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.47/0.69 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.47/0.69 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.47/0.69 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 97.43/12.84 % Solved by lams/40_b.comb.sh. 97.43/12.84 % done 331 iterations in 12.081s 97.43/12.84 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 97.43/12.84 % SZS output start Refutation 97.43/12.84 thf(n_2t_type, type, n_2t: $i). 97.43/12.84 thf('#sk5_type', type, '#sk5': $i). 97.43/12.84 thf('#ty_enc6_type', type, '#ty_enc6': ($i > $i > $o) > $i > $i > $o). 97.43/12.84 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 97.43/12.84 thf(moref_type, type, moref: $i > $i > $o). 97.43/12.84 thf(d_not_type, type, d_not: $o > $o). 97.43/12.84 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 97.43/12.84 thf(in_type, type, in: $i > $i > $o). 97.43/12.84 thf(den_type, type, den: $i > $i). 97.43/12.84 thf(n_1t_type, type, n_1t: $i). 97.43/12.84 thf(first1_type, type, first1: $i > $i > $i). 97.43/12.84 thf(ap_type, type, ap: $i > $i > $i). 97.43/12.84 thf(nat_type, type, nat: $i). 97.43/12.84 thf(iii_type, type, iii: $i > $i > $o). 97.43/12.84 thf(l_or_type, type, l_or: $o > $o > $o). 97.43/12.84 thf('#sk4_type', type, '#sk4': $i). 97.43/12.84 thf(second1_type, type, second1: $i > $i > $i). 97.43/12.84 thf(lessf_type, type, lessf: $i > $i > $o). 97.43/12.84 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 97.43/12.84 thf('#sk2_type', type, '#sk2': $i). 97.43/12.84 thf(frac_type, type, frac: $i). 97.43/12.84 thf(n_ts_type, type, n_ts: $i > $i > $i). 97.43/12.84 thf(imp_type, type, imp: $o > $o > $o). 97.43/12.84 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 97.43/12.84 thf(n_eq_type, type, n_eq: $i > $i > $o). 97.43/12.84 thf(n_is_type, type, n_is: $i > $i > $o). 97.43/12.84 thf(n_some_type, type, n_some: ($i > $o) > $o). 97.43/12.84 thf(moreq_type, type, moreq: $i > $i > $o). 97.43/12.84 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o). 97.43/12.84 thf('#sk3_type', type, '#sk3': $i). 97.43/12.84 thf(num_type, type, num: $i > $i). 97.43/12.84 thf(pair1type_type, type, pair1type: $i > $i). 97.43/12.84 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 97.43/12.84 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 97.43/12.84 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 97.43/12.84 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 97.43/12.84 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 97.43/12.84 thf(satz46, conjecture, 97.43/12.84 (all_of @ 97.43/12.84 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.43/12.84 ( ^[X0:$i]: 97.43/12.84 ( all_of @ 97.43/12.84 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.43/12.84 ( ^[X1:$i]: 97.43/12.84 ( all_of @ 97.43/12.84 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 97.43/12.84 ( ^[X2:$i]: 97.43/12.84 ( all_of @ 97.43/12.84 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 97.43/12.84 ( ^[X3:$i]: 97.43/12.84 ( ( moreq @ X0 @ X1 ) => 97.43/12.84 ( ( n_eq @ X0 @ X2 ) => 97.43/12.84 ( ( n_eq @ X1 @ X3 ) => ( moreq @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 97.43/12.84 thf(zf_stmt_0, negated_conjecture, 97.43/12.84 (~( all_of @ 97.43/12.84 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.43/12.84 ( ^[X0:$i]: 97.43/12.84 ( all_of @ 97.43/12.84 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.43/12.84 ( ^[X1:$i]: 97.43/12.84 ( all_of @ 97.43/12.84 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 97.43/12.84 ( ^[X2:$i]: 97.43/12.84 ( all_of @ 97.43/12.84 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 97.43/12.84 ( ^[X3:$i]: 97.43/12.84 ( ( moreq @ X0 @ X1 ) => 97.43/12.84 ( ( n_eq @ X0 @ X2 ) => 97.43/12.84 ( ( n_eq @ X1 @ X3 ) => ( moreq @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) )), 97.43/12.84 inference('cnf.neg', [status(esa)], [satz46])). 97.43/12.84 thf(zip_derived_cl282, plain, 97.43/12.84 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 97.43/12.84 (^[Y0 : $i]: 97.43/12.84 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 97.43/12.84 (^[Y1 : $i]: 97.43/12.84 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 97.43/12.84 (^[Y2 : $i]: 97.43/12.84 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 97.43/12.84 (^[Y3 : $i]: 97.43/12.84 (((moreq @ Y0 @ Y1) => 97.43/12.84 (((n_eq @ Y0 @ Y2) => 97.43/12.84 (((n_eq @ Y1 @ Y3) => (moreq @ Y2 @ Y3)))))))))))))))), 97.43/12.84 inference('cnf', [status(esa)], [zf_stmt_0])). 97.43/12.84 thf(zip_derived_cl283, plain, 97.43/12.84 (~ (all_of @ ((('#C') @ in @ frac)) @ 97.43/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 97.43/12.84 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 97.43/12.84 ((('#S') @ ((('#B') @ ('#S') @ 97.43/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @ 97.43/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ ('#S') @ 97.43/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 97.43/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ ('#S') @ 97.43/12.84 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.43/12.84 moreq)))))))))))))), 97.43/12.84 inference('lams2combs', [status(thm)], [zip_derived_cl282])). 97.43/12.84 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))). 97.43/12.84 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])). 97.43/12.84 thf(zip_derived_cl1352, plain, 97.43/12.84 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 97.43/12.84 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 97.43/12.84 ((('#C') @ in @ 97.43/12.84 (pair1type @ nat)))))))) @ 97.43/12.84 ((('#S') @ ((('#B') @ ('#S') @ 97.43/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @ 97.43/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ ('#S') @ 97.43/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 97.43/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ ('#S') @ 97.43/12.84 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.43/12.84 moreq)))))))))))))), 97.43/12.84 inference('rw', [status(thm)], [zip_derived_cl283, '0'])). 97.43/12.84 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 97.43/12.84 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 97.43/12.84 thf('1', plain, 97.43/12.84 (![X0:( $i > $o ),X1:( $i > $o )]: 97.43/12.84 ( ( ~( all_of @ X0 @ X1 ) ) <=> 97.43/12.84 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 97.43/12.84 inference('rw.lit', [status(esa)], [def_all_of])). 97.43/12.84 thf(zip_derived_cl1353, plain, 97.43/12.84 (~ (((!!) @ (^[Y0 : $i]: 97.43/12.84 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (all_of @ 97.43/12.84 ((('#C') @ in @ 97.43/12.84 (pair1type @ nat)))))) @ 97.43/12.84 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 97.43/12.84 ((('#C') @ in @ 97.43/12.84 (pair1type @ nat)))))))) @ 97.43/12.84 ((('#S') @ ((('#B') @ ('#S') @ 97.43/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (=>))) @ 97.43/12.84 moreq)))))))) @ 97.43/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ ('#S') @ 97.43/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (=>))) @ 97.43/12.84 n_eq)))))))) @ 97.43/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ ('#S') @ 97.43/12.84 ((('#B') @ ((('#B') @ (=>))) @ 97.43/12.84 n_eq)))))) @ 97.43/12.84 moreq)))))))))) @ 97.43/12.84 Y0)))))))), 97.43/12.84 inference('rw_clause', [status(thm)], [zip_derived_cl1352, '1'])). 97.43/12.84 thf(zip_derived_cl1354, plain, 97.43/12.84 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.43/12.84 ((('#C') @ is_of @ 97.43/12.84 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.43/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (all_of @ 97.43/12.84 ((('#C') @ in @ (pair1type @ nat)))))) @ 97.43/12.84 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 97.43/12.84 ((('#C') @ in @ 97.43/12.84 (pair1type @ nat)))))))) @ 97.43/12.84 ((('#S') @ ((('#B') @ ('#S') @ 97.43/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @ 97.43/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ ('#S') @ 97.43/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (=>))) @ 97.43/12.84 n_eq)))))))) @ 97.43/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ ('#S') @ 97.43/12.84 ((('#B') @ ((('#B') @ (=>))) @ 97.43/12.84 n_eq)))))) @ 97.43/12.84 moreq))))))))))))))))), 97.43/12.84 inference('comb-normalize', [status(thm)], [zip_derived_cl1353])). 97.43/12.84 thf(zip_derived_cl1355, plain, 97.43/12.84 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.43/12.84 ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (all_of @ 97.43/12.84 ((('#C') @ in @ (pair1type @ nat)))))) @ 97.43/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @ 97.43/12.84 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))))) @ 97.43/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ ('#S') @ 97.43/12.84 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.43/12.84 moreq)))))))))))))), 97.43/12.84 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1354])). 97.43/12.84 thf(zip_derived_cl1357, plain, 97.43/12.84 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 97.43/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @ 97.43/12.84 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))))) @ 97.43/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ ('#S') @ 97.43/12.84 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.43/12.84 moreq)))))))))))), 97.43/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1355])). 97.43/12.84 thf(zip_derived_cl1358, plain, 97.43/12.84 (~ (((!!) @ (^[Y0 : $i]: 97.43/12.84 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (all_of @ 97.43/12.84 ((('#C') @ in @ 97.43/12.84 (pair1type @ nat)))))) @ 97.43/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @ 97.43/12.84 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ (=>) @ 97.43/12.84 (n_eq @ '#sk2'))))))) @ 97.43/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ ('#S') @ 97.43/12.84 ((('#B') @ ((('#B') @ (=>))) @ 97.43/12.84 n_eq)))))) @ 97.43/12.84 moreq)))))))) @ 97.43/12.84 Y0)))))))), 97.43/12.84 inference('rw_clause', [status(thm)], [zip_derived_cl1357, '1'])). 97.43/12.84 thf(zip_derived_cl1359, plain, 97.43/12.84 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.43/12.84 ((('#C') @ is_of @ 97.43/12.84 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.43/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (all_of @ 97.43/12.84 ((('#C') @ in @ (pair1type @ nat)))))) @ 97.43/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @ 97.43/12.84 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ (=>) @ 97.43/12.84 (n_eq @ '#sk2'))))))) @ 97.43/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ ('#S') @ 97.43/12.84 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.43/12.84 moreq))))))))))))))), 97.43/12.84 inference('comb-normalize', [status(thm)], [zip_derived_cl1358])). 97.43/12.84 thf(zip_derived_cl1360, plain, 97.43/12.84 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.43/12.84 ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (((=>) @ (moreq @ '#sk2' @ '#sk3'))))) @ 97.43/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @ 97.43/12.84 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))))) @ 97.43/12.84 moreq)))))))))))), 97.43/12.84 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1359])). 97.43/12.84 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 97.43/12.84 thf('2', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 97.43/12.84 define([status(thm)])). 97.43/12.84 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 97.43/12.84 thf('3', plain, 97.43/12.84 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 97.43/12.84 define([status(thm)])). 97.43/12.84 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))). 97.43/12.84 thf('4', plain, 97.43/12.84 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )), 97.43/12.84 define([status(thm)])). 97.43/12.84 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) = 97.43/12.84 ((n_some @ (diffprop @ X0 @ X1))))). 97.43/12.84 thf('5', plain, 97.43/12.84 (![X1:$i,X0:$i]: 97.43/12.84 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 97.43/12.84 define([status(thm)])). 97.43/12.84 thf(def_first1, axiom,(( first1 @ (X1)@ (X0)) = ((ap @ X0 @ n_1t)))). 97.43/12.84 thf('6', plain, 97.43/12.84 (![X1:$i,X0:$i]: ( ( first1 @ X1 @ X0 ) = ( ap @ X0 @ n_1t ) )), 97.43/12.84 define([status(thm)])). 97.43/12.84 thf(def_second1, axiom,(( second1 @ (X1)@ (X0)) = ((ap @ X0 @ n_2t)))). 97.43/12.84 thf('7', plain, 97.43/12.84 (![X1:$i,X0:$i]: ( ( second1 @ X1 @ X0 ) = ( ap @ X0 @ n_2t ) )), 97.43/12.84 define([status(thm)])). 97.43/12.84 thf(def_num, axiom,(( num @ (X0)) = ((first1 @ nat @ X0)))). 97.43/12.84 thf('8', plain, (![X0:$i]: ( ( num @ X0 ) = ( first1 @ nat @ X0 ) )), 97.43/12.84 define([status(thm)])). 97.43/12.84 thf(def_den, axiom,(( den @ (X0)) = ((second1 @ nat @ X0)))). 97.43/12.84 thf('9', plain, (![X0:$i]: ( ( den @ X0 ) = ( second1 @ nat @ X0 ) )), 97.43/12.84 define([status(thm)])). 97.43/12.84 thf(def_n_eq, axiom,(( n_eq @ (X0)@ (X1)) = 97.43/12.84 ((n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @ 97.43/12.84 (n_ts @ (num @ X1) @ (den @ X0)))))). 97.43/12.84 thf('10', plain, 97.43/12.84 (![X1:$i,X0:$i]: 97.43/12.84 ( ( n_eq @ X0 @ X1 ) = 97.43/12.84 ( n_is @ 97.43/12.84 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 97.43/12.84 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )), 97.43/12.84 define([status(thm)])). 97.43/12.84 thf(def_moref, axiom,(( moref @ (X0)@ (X1)) = 97.43/12.84 ((d_29_ii @ (n_ts @ (num @ X0) @ (den @ X1)) @ 97.43/12.84 (n_ts @ (num @ X1) @ (den @ X0)))))). 97.43/12.84 thf('11', plain, 97.43/12.84 (![X1:$i,X0:$i]: 97.43/12.84 ( ( moref @ X0 @ X1 ) = 97.43/12.84 ( d_29_ii @ 97.43/12.84 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 97.43/12.84 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )), 97.43/12.84 define([status(thm)])). 97.43/12.84 thf(def_moreq, axiom,(( moreq @ (X0)@ (X1)) = 97.43/12.84 ((l_or @ (moref @ X0 @ X1) @ (n_eq @ X0 @ X1))))). 97.43/12.84 thf('12', plain, 97.43/12.84 (![X1:$i,X0:$i]: 97.43/12.84 ( ( moreq @ X0 @ X1 ) = 97.43/12.84 ( l_or @ ( moref @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )), 97.43/12.84 define([status(thm)])). 97.43/12.84 thf(zip_derived_cl1361, plain, 97.43/12.84 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.43/12.84 ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 97.43/12.84 (imp @ 97.43/12.84 (l_some @ nat @ 97.43/12.84 (diffprop @ 97.43/12.84 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.84 (ap @ '#sk3' @ n_2t)) @ 97.43/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.43/12.84 (ap @ '#sk2' @ n_2t)))) @ 97.43/12.84 ($false)) @ 97.43/12.84 (n_is @ 97.43/12.84 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.84 (ap @ '#sk3' @ n_2t)) @ 97.43/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.43/12.84 (ap @ '#sk2' @ n_2t)))))))) @ 97.43/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @ 97.43/12.84 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))))) @ 97.43/12.84 moreq)))))))))))), 97.43/12.84 inference('rw', [status(thm)], 97.43/12.84 [zip_derived_cl1360, '2', '3', '4', '5', '6', '6', '7', '7', 97.43/12.84 '8', '8', '9', '9', '10', '11', '12'])). 97.43/12.84 thf(zip_derived_cl1363, plain, 97.43/12.84 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 97.43/12.84 (imp @ 97.43/12.84 (l_some @ nat @ 97.43/12.84 (diffprop @ 97.43/12.84 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.84 (ap @ '#sk3' @ n_2t)) @ 97.43/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.43/12.84 (ap @ '#sk2' @ n_2t)))) @ 97.43/12.84 ($false)) @ 97.43/12.84 (n_is @ 97.43/12.84 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.84 (ap @ '#sk3' @ n_2t)) @ 97.43/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.43/12.84 (ap @ '#sk2' @ n_2t)))))))) @ 97.43/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @ 97.43/12.84 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))))) @ 97.43/12.84 moreq)))))))))), 97.43/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])). 97.43/12.84 thf(zip_derived_cl1364, plain, 97.43/12.84 (~ (((!!) @ (^[Y0 : $i]: 97.43/12.84 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 97.43/12.84 (imp @ 97.43/12.84 (l_some @ nat @ 97.43/12.84 (diffprop @ 97.43/12.84 (n_ts @ 97.43/12.84 (ap @ '#sk2' @ 97.43/12.84 n_1t) @ 97.43/12.84 (ap @ '#sk3' @ 97.43/12.84 n_2t)) @ 97.43/12.84 (n_ts @ 97.43/12.84 (ap @ '#sk3' @ 97.43/12.84 n_1t) @ 97.43/12.84 (ap @ '#sk2' @ 97.43/12.84 n_2t)))) @ 97.43/12.84 ($false)) @ 97.43/12.84 (n_is @ 97.43/12.84 (n_ts @ 97.43/12.84 (ap @ '#sk2' @ n_1t) @ 97.43/12.84 (ap @ '#sk3' @ n_2t)) @ 97.43/12.84 (n_ts @ 97.43/12.84 (ap @ '#sk3' @ n_1t) @ 97.43/12.84 (ap @ '#sk2' @ n_2t)))))))) @ 97.43/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.84 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @ 97.43/12.84 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 97.43/12.84 (n_eq @ '#sk3'))))) @ 97.43/12.84 moreq)))))) @ 97.43/12.84 Y0)))))))), 97.43/12.84 inference('rw_clause', [status(thm)], [zip_derived_cl1363, '1'])). 97.43/12.84 thf(zip_derived_cl1365, plain, 97.43/12.84 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.43/12.84 ((('#C') @ is_of @ 97.43/12.84 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.43/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.84 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 97.43/12.84 (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ 97.43/12.85 (ap @ '#sk2' @ n_1t) @ 97.43/12.85 (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ 97.43/12.85 (ap @ '#sk3' @ n_1t) @ 97.43/12.85 (ap @ '#sk2' @ n_2t)))) @ 97.43/12.85 ($false)) @ 97.43/12.85 (n_is @ 97.43/12.85 (n_ts @ 97.43/12.85 (ap @ '#sk2' @ n_1t) @ 97.43/12.85 (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ 97.43/12.85 (ap @ '#sk3' @ n_1t) @ 97.43/12.85 (ap @ '#sk2' @ n_2t)))))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @ 97.43/12.85 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 97.43/12.85 (n_eq @ '#sk3'))))) @ 97.43/12.85 moreq))))))))))))), 97.43/12.85 inference('comb-normalize', [status(thm)], [zip_derived_cl1364])). 97.43/12.85 thf(zip_derived_cl1366, plain, 97.43/12.85 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (((=>) @ (imp @ 97.43/12.85 (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.85 (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.43/12.85 (ap @ '#sk2' @ n_2t)))) @ 97.43/12.85 ($false)) @ 97.43/12.85 (n_is @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.85 (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.43/12.85 (ap @ '#sk2' @ n_2t)))))) @ 97.43/12.85 ((('#B') @ (((=>) @ (n_eq @ '#sk2' @ '#sk4'))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @ 97.43/12.85 (moreq @ '#sk4'))))))))))), 97.43/12.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1365])). 97.43/12.85 thf(zip_derived_cl1367, plain, 97.43/12.85 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (((=>) @ (imp @ 97.43/12.85 (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.85 (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.43/12.85 (ap @ '#sk2' @ n_2t)))) @ 97.43/12.85 ($false)) @ 97.43/12.85 (n_is @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.85 (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.43/12.85 (ap @ '#sk2' @ n_2t)))))) @ 97.43/12.85 ((('#B') @ (((=>) @ (n_is @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.85 (ap @ '#sk4' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ 97.43/12.85 (ap @ '#sk2' @ n_2t))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @ 97.43/12.85 (moreq @ '#sk4'))))))))))), 97.43/12.85 inference('rw', [status(thm)], 97.43/12.85 [zip_derived_cl1366, '6', '6', '7', '7', '8', '8', '9', '9', 97.43/12.85 '10'])). 97.43/12.85 thf(zip_derived_cl1369, plain, 97.43/12.85 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (((=>) @ (imp @ 97.43/12.85 (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.85 (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.43/12.85 (ap @ '#sk2' @ n_2t)))) @ 97.43/12.85 ($false)) @ 97.43/12.85 (n_is @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.85 (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.43/12.85 (ap @ '#sk2' @ n_2t)))))) @ 97.43/12.85 ((('#B') @ (((=>) @ (n_is @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.85 (ap @ '#sk4' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ 97.43/12.85 (ap @ '#sk2' @ n_2t))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @ (moreq @ '#sk4'))))))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1367])). 97.43/12.85 thf(zip_derived_cl1370, plain, 97.43/12.85 (~ (((!!) @ (^[Y0 : $i]: 97.43/12.85 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 ((('#B') @ (((=>) @ (imp @ 97.43/12.85 (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.85 (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.43/12.85 (ap @ '#sk2' @ n_2t)))) @ 97.43/12.85 ($false)) @ 97.43/12.85 (n_is @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.85 (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.43/12.85 (ap @ '#sk2' @ n_2t)))))) @ 97.43/12.85 ((('#B') @ (((=>) @ (n_is @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.85 (ap @ '#sk4' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ 97.43/12.85 (ap @ '#sk2' @ n_2t))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @ 97.43/12.85 (moreq @ '#sk4'))))) @ 97.43/12.85 Y0)))))))), 97.43/12.85 inference('rw_clause', [status(thm)], [zip_derived_cl1369, '1'])). 97.43/12.85 thf(zip_derived_cl1371, plain, 97.43/12.85 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.43/12.85 ((('#C') @ is_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.43/12.85 ((('#B') @ (((=>) @ (imp @ 97.43/12.85 (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.85 (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.43/12.85 (ap @ '#sk2' @ n_2t)))) @ 97.43/12.85 ($false)) @ 97.43/12.85 (n_is @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.85 (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.43/12.85 (ap @ '#sk2' @ n_2t)))))) @ 97.43/12.85 ((('#B') @ (((=>) @ (n_is @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.43/12.85 (ap @ '#sk4' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ 97.43/12.85 (ap @ '#sk2' @ n_2t))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @ 97.43/12.85 (moreq @ '#sk4')))))))))))), 97.43/12.85 inference('comb-normalize', [status(thm)], [zip_derived_cl1370])). 97.43/12.85 thf(zip_derived_cl1372, plain, 97.43/12.85 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 (((imp @ 97.43/12.85 (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @ 97.43/12.85 ($false)) @ 97.43/12.85 (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) => 97.43/12.85 (((n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t))) => 97.43/12.85 (((n_eq @ '#sk3' @ '#sk5') => (moreq @ '#sk4' @ '#sk5')))))))))), 97.43/12.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1371])). 97.43/12.85 thf(zip_derived_cl1373, plain, 97.43/12.85 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 (((imp @ 97.43/12.85 (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @ 97.43/12.85 ($false)) @ 97.43/12.85 (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) => 97.43/12.85 (((n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t))) => 97.43/12.85 (((n_is @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t))) => 97.43/12.85 (imp @ 97.43/12.85 (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 97.43/12.85 ($false)) @ 97.43/12.85 (n_is @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))))))))), 97.43/12.85 inference('rw', [status(thm)], 97.43/12.85 [zip_derived_cl1372, '2', '3', '4', '5', '6', '6', '6', '7', 97.43/12.85 '7', '7', '8', '8', '8', '9', '9', '9', '10', '10', '11', '12'])). 97.43/12.85 thf(zip_derived_cl1375, plain, 97.43/12.85 (~ (((imp @ 97.43/12.85 (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @ 97.43/12.85 ($false)) @ 97.43/12.85 (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) => 97.43/12.85 (((n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t))) => 97.43/12.85 (((n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t))) => (imp @ 97.43/12.85 (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 97.43/12.85 ($false)) @ 97.43/12.85 (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1373])). 97.43/12.85 thf(zip_derived_cl1377, plain, 97.43/12.85 (~ (((n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t))) => 97.43/12.85 (((n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t))) => (imp @ 97.43/12.85 (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 97.43/12.85 ($false)) @ 97.43/12.85 (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1375])). 97.43/12.85 thf(zip_derived_cl1380, plain, 97.43/12.85 (~ (((n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t))) => (imp @ 97.43/12.85 (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 97.43/12.85 ($false)) @ 97.43/12.85 (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1377])). 97.43/12.85 thf(zip_derived_cl1383, plain, 97.43/12.85 (~ (imp @ 97.43/12.85 (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 97.43/12.85 ($false)) @ 97.43/12.85 (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1380])). 97.43/12.85 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 97.43/12.85 thf('13', plain, 97.43/12.85 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 97.43/12.85 inference('rw.lit', [status(esa)], [def_imp])). 97.43/12.85 thf(zip_derived_cl1385, plain, 97.43/12.85 (~ (((imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 97.43/12.85 ($false)) => (n_is @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))))), 97.43/12.85 inference('rw_clause', [status(thm)], [zip_derived_cl1383, '13'])). 97.43/12.85 thf(zip_derived_cl1389, plain, 97.43/12.85 (~ (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1385])). 97.43/12.85 thf(satz38, axiom, 97.43/12.85 (all_of @ 97.43/12.85 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.43/12.85 ( ^[X0:$i]: 97.43/12.85 ( all_of @ 97.43/12.85 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.43/12.85 ( ^[X1:$i]: ( ( n_eq @ X0 @ X1 ) => ( n_eq @ X1 @ X0 ) ) ) ) ))). 97.43/12.85 thf(zip_derived_cl92, plain, 97.43/12.85 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 97.43/12.85 (^[Y0 : $i]: 97.43/12.85 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 97.43/12.85 (^[Y1 : $i]: (((n_eq @ Y0 @ Y1) => (n_eq @ Y1 @ Y0)))))))), 97.43/12.85 inference('cnf', [status(esa)], [satz38])). 97.43/12.85 thf(zip_derived_cl93, plain, 97.43/12.85 ( (all_of @ ((('#C') @ in @ frac)) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#S') @ ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 97.43/12.85 ((('#C') @ n_eq)))))))), 97.43/12.85 inference('lams2combs', [status(thm)], [zip_derived_cl92])). 97.43/12.85 thf(zip_derived_cl403, plain, 97.43/12.85 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#S') @ ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 97.43/12.85 ((('#C') @ n_eq)))))))), 97.43/12.85 inference('rw', [status(thm)], [zip_derived_cl93, '0'])). 97.43/12.85 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 97.43/12.85 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 97.43/12.85 thf('14', plain, 97.43/12.85 (![X0:( $i > $o ),X1:( $i > $o )]: 97.43/12.85 ( ( all_of @ X0 @ X1 ) <=> 97.43/12.85 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 97.43/12.85 inference('rw.lit', [status(esa)], [def_all_of])). 97.43/12.85 thf(zip_derived_cl404, plain, 97.43/12.85 ( (((!!) @ (^[Y0 : $i]: 97.43/12.85 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 97.43/12.85 ((('#C') @ n_eq)))) @ 97.43/12.85 Y0)))))))), 97.43/12.85 inference('rw_clause', [status(thm)], [zip_derived_cl403, '14'])). 97.43/12.85 thf(zip_derived_cl405, plain, 97.43/12.85 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.43/12.85 ((('#C') @ is_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 97.43/12.85 ((('#C') @ n_eq))))))))))), 97.43/12.85 inference('comb-normalize', [status(thm)], [zip_derived_cl404])). 97.43/12.85 thf(zip_derived_cl406, plain, 97.43/12.85 (![X2 : $i]: 97.43/12.85 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ ((('#C') @ n_eq @ X2)))))))), 97.43/12.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl405])). 97.43/12.85 thf(zip_derived_cl407, plain, 97.43/12.85 (![X2 : $i]: 97.43/12.85 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ 97.43/12.85 ((('#C') @ n_eq @ X2))))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl406])). 97.43/12.85 thf(zip_derived_cl408, plain, 97.43/12.85 (![X0 : $i]: 97.43/12.85 ( (((!!) @ (^[Y0 : $i]: 97.43/12.85 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @ 97.43/12.85 ((('#C') @ n_eq @ X0)) @ Y0))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('rw_clause', [status(thm)], [zip_derived_cl407, '14'])). 97.43/12.85 thf(zip_derived_cl409, plain, 97.43/12.85 (![X0 : $i]: 97.43/12.85 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.43/12.85 ((('#C') @ is_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @ 97.43/12.85 ((('#C') @ n_eq @ X0)))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('comb-normalize', [status(thm)], [zip_derived_cl408])). 97.43/12.85 thf(zip_derived_cl410, plain, 97.43/12.85 (![X0 : $i, X2 : $i]: 97.43/12.85 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 (((n_eq @ X0 @ X2) => (n_eq @ X2 @ X0))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl409])). 97.43/12.85 thf(zip_derived_cl411, plain, 97.43/12.85 (![X0 : $i, X2 : $i]: 97.43/12.85 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) => (n_is @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('rw', [status(thm)], 97.43/12.85 [zip_derived_cl410, '6', '6', '7', '7', '8', '8', '9', '9', 97.43/12.85 '10', '10'])). 97.43/12.85 thf(zip_derived_cl412, plain, 97.43/12.85 (![X0 : $i, X2 : $i]: 97.43/12.85 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) => (n_is @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl411])). 97.43/12.85 thf(zip_derived_cl413, plain, 97.43/12.85 (![X0 : $i, X2 : $i]: 97.43/12.85 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) 97.43/12.85 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl412])). 97.43/12.85 thf(zip_derived_cl3377, plain, 97.43/12.85 ((~ (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (n_is @ (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t))))), 97.43/12.85 inference('sup+', [status(thm)], [zip_derived_cl1389, zip_derived_cl413])). 97.43/12.85 thf(zip_derived_cl1368, plain, 97.43/12.85 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1367])). 97.43/12.85 thf(zip_derived_cl1374, plain, 97.43/12.85 ( (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1373])). 97.43/12.85 thf(zip_derived_cl3397, plain, 97.43/12.85 (~ (n_is @ (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)))), 97.43/12.85 inference('demod', [status(thm)], 97.43/12.85 [zip_derived_cl3377, zip_derived_cl1368, zip_derived_cl1374])). 97.43/12.85 thf(zip_derived_cl1382, plain, 97.43/12.85 ( (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t)))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1380])). 97.43/12.85 thf(zip_derived_cl413, plain, 97.43/12.85 (![X0 : $i, X2 : $i]: 97.43/12.85 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) 97.43/12.85 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl412])). 97.43/12.85 thf(zip_derived_cl3359, plain, 97.43/12.85 ((~ (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | (n_is @ (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t))))), 97.43/12.85 inference('sup-', [status(thm)], [zip_derived_cl1382, zip_derived_cl413])). 97.43/12.85 thf(zip_derived_cl1374, plain, 97.43/12.85 ( (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1373])). 97.43/12.85 thf(zip_derived_cl1362, plain, 97.43/12.85 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])). 97.43/12.85 thf(zip_derived_cl3395, plain, 97.43/12.85 ( (n_is @ (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)))), 97.43/12.85 inference('demod', [status(thm)], 97.43/12.85 [zip_derived_cl3359, zip_derived_cl1374, zip_derived_cl1362])). 97.43/12.85 thf(zip_derived_cl1374, plain, 97.43/12.85 ( (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1373])). 97.43/12.85 thf(zip_derived_cl8757, plain, 97.43/12.85 ( (is_of @ '#sk5' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 97.43/12.85 inference('remove_ty_args', [status(thm)], [zip_derived_cl1374])). 97.43/12.85 thf(zip_derived_cl1379, plain, 97.43/12.85 ( (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1377])). 97.43/12.85 thf(zip_derived_cl1382, plain, 97.43/12.85 ( (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t)))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1380])). 97.43/12.85 thf(zip_derived_cl1368, plain, 97.43/12.85 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1367])). 97.43/12.85 thf(zip_derived_cl8756, plain, 97.43/12.85 ( (is_of @ '#sk4' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 97.43/12.85 inference('remove_ty_args', [status(thm)], [zip_derived_cl1368])). 97.43/12.85 thf(zip_derived_cl1379, plain, 97.43/12.85 ( (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1377])). 97.43/12.85 thf(zip_derived_cl413, plain, 97.43/12.85 (![X0 : $i, X2 : $i]: 97.43/12.85 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) 97.43/12.85 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl412])). 97.43/12.85 thf(zip_derived_cl3358, plain, 97.43/12.85 ((~ (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t))))), 97.43/12.85 inference('sup-', [status(thm)], [zip_derived_cl1379, zip_derived_cl413])). 97.43/12.85 thf(zip_derived_cl1368, plain, 97.43/12.85 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1367])). 97.43/12.85 thf(zip_derived_cl1356, plain, 97.43/12.85 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1355])). 97.43/12.85 thf(zip_derived_cl3394, plain, 97.43/12.85 ( (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)))), 97.43/12.85 inference('demod', [status(thm)], 97.43/12.85 [zip_derived_cl3358, zip_derived_cl1368, zip_derived_cl1356])). 97.43/12.85 thf(zip_derived_cl413, plain, 97.43/12.85 (![X0 : $i, X2 : $i]: 97.43/12.85 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) 97.43/12.85 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl412])). 97.43/12.85 thf(zip_derived_cl8708, plain, 97.43/12.85 (![X0 : $i, X2 : $i]: 97.43/12.85 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) 97.43/12.85 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t))) 97.43/12.85 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 97.43/12.85 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat))))), 97.43/12.85 inference('remove_ty_args', [status(thm)], [zip_derived_cl413])). 97.43/12.85 thf(zip_derived_cl1356, plain, 97.43/12.85 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1355])). 97.43/12.85 thf(zip_derived_cl8754, plain, 97.43/12.85 ( (is_of @ '#sk2' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 97.43/12.85 inference('remove_ty_args', [status(thm)], [zip_derived_cl1356])). 97.43/12.85 thf(zip_derived_cl1362, plain, 97.43/12.85 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])). 97.43/12.85 thf(zip_derived_cl8755, plain, 97.43/12.85 ( (is_of @ '#sk3' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 97.43/12.85 inference('remove_ty_args', [status(thm)], [zip_derived_cl1362])). 97.43/12.85 thf(zip_derived_cl1376, plain, 97.43/12.85 ( (imp @ 97.43/12.85 (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @ 97.43/12.85 ($false)) @ 97.43/12.85 (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1375])). 97.43/12.85 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 97.43/12.85 thf('15', plain, 97.43/12.85 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 97.43/12.85 inference('rw.lit', [status(esa)], [def_imp])). 97.43/12.85 thf(zip_derived_cl1378, plain, 97.43/12.85 ( (((imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @ 97.43/12.85 ($false)) => (n_is @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))))), 97.43/12.85 inference('rw_clause', [status(thm)], [zip_derived_cl1376, '15'])). 97.43/12.85 thf(zip_derived_cl1381, plain, 97.43/12.85 ((~ (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @ 97.43/12.85 ($false)) 97.43/12.85 | (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1378])). 97.43/12.85 thf(zip_derived_cl1384, plain, 97.43/12.85 ((~ (((l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) => 97.43/12.85 ($false))) 97.43/12.85 | (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))), 97.43/12.85 inference('rw_clause', [status(thm)], [zip_derived_cl1381, '13'])). 97.43/12.85 thf(zip_derived_cl1386, plain, 97.43/12.85 ((~ (((~) @ (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))))) 97.43/12.85 | (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))), 97.43/12.85 inference('simplify boolean subterms', [status(thm)], 97.43/12.85 [zip_derived_cl1384])). 97.43/12.85 thf(zip_derived_cl1387, plain, 97.43/12.85 (( (l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) 97.43/12.85 | (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))), 97.43/12.85 inference('simplify nested equalities', [status(thm)], 97.43/12.85 [zip_derived_cl1386])). 97.43/12.85 thf(zip_derived_cl1388, plain, 97.43/12.85 ( (imp @ 97.43/12.85 (l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 97.43/12.85 ($false))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1385])). 97.43/12.85 thf(zip_derived_cl1390, plain, 97.43/12.85 ( (((l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) => 97.43/12.85 ($false)))), 97.43/12.85 inference('rw_clause', [status(thm)], [zip_derived_cl1388, '15'])). 97.43/12.85 thf(zip_derived_cl1391, plain, 97.43/12.85 ( (((~) @ (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))), 97.43/12.85 inference('simplify boolean subterms', [status(thm)], 97.43/12.85 [zip_derived_cl1390])). 97.43/12.85 thf(zip_derived_cl1392, plain, 97.43/12.85 (~ (l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))), 97.43/12.85 inference('simplify nested equalities', [status(thm)], 97.43/12.85 [zip_derived_cl1391])). 97.43/12.85 thf(satz39, axiom, 97.43/12.85 (all_of @ 97.43/12.85 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.43/12.85 ( ^[X0:$i]: 97.43/12.85 ( all_of @ 97.43/12.85 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.43/12.85 ( ^[X1:$i]: 97.43/12.85 ( all_of @ 97.43/12.85 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 97.43/12.85 ( ^[X2:$i]: 97.43/12.85 ( ( n_eq @ X0 @ X1 ) => 97.43/12.85 ( ( n_eq @ X1 @ X2 ) => ( n_eq @ X0 @ X2 ) ) ) ) ) ) ) ))). 97.43/12.85 thf(zip_derived_cl122, plain, 97.43/12.85 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 97.43/12.85 (^[Y0 : $i]: 97.43/12.85 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 97.43/12.85 (^[Y1 : $i]: 97.43/12.85 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 97.43/12.85 (^[Y2 : $i]: 97.43/12.85 (((n_eq @ Y0 @ Y1) => 97.43/12.85 (((n_eq @ Y1 @ Y2) => (n_eq @ Y0 @ Y2)))))))))))), 97.43/12.85 inference('cnf', [status(esa)], [satz39])). 97.43/12.85 thf(zip_derived_cl123, plain, 97.43/12.85 ( (all_of @ ((('#C') @ in @ frac)) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.43/12.85 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.43/12.85 n_eq)))))))))), 97.43/12.85 inference('lams2combs', [status(thm)], [zip_derived_cl122])). 97.43/12.85 thf(zip_derived_cl1171, plain, 97.43/12.85 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.43/12.85 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.43/12.85 n_eq)))))))))), 97.43/12.85 inference('rw', [status(thm)], [zip_derived_cl123, '0'])). 97.43/12.85 thf(zip_derived_cl1172, plain, 97.43/12.85 ( (((!!) @ (^[Y0 : $i]: 97.43/12.85 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (all_of @ 97.43/12.85 ((('#C') @ in @ 97.43/12.85 (pair1type @ nat)))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.43/12.85 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ 97.43/12.85 n_eq)))))) @ 97.43/12.85 n_eq)))))) @ 97.43/12.85 Y0)))))))), 97.43/12.85 inference('rw_clause', [status(thm)], [zip_derived_cl1171, '14'])). 97.43/12.85 thf(zip_derived_cl1173, plain, 97.43/12.85 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.43/12.85 ((('#C') @ is_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat)))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.43/12.85 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ 97.43/12.85 n_eq)))))) @ 97.43/12.85 n_eq))))))))))))), 97.43/12.85 inference('comb-normalize', [status(thm)], [zip_derived_cl1172])). 97.43/12.85 thf(zip_derived_cl1174, plain, 97.43/12.85 (![X2 : $i]: 97.43/12.85 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 97.43/12.85 ((('#C') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 97.43/12.85 (n_eq @ X2))))))))))), 97.43/12.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1173])). 97.43/12.85 thf(zip_derived_cl1175, plain, 97.43/12.85 (![X2 : $i]: 97.43/12.85 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 97.43/12.85 ((('#C') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 97.43/12.85 (n_eq @ X2)))))))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1174])). 97.43/12.85 thf(zip_derived_cl1176, plain, 97.43/12.85 (![X0 : $i]: 97.43/12.85 ( (((!!) @ (^[Y0 : $i]: 97.43/12.85 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 ((('#B') @ (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 97.43/12.85 ((('#C') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 97.43/12.85 (n_eq @ X0))))) @ 97.43/12.85 Y0))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('rw_clause', [status(thm)], [zip_derived_cl1175, '14'])). 97.43/12.85 thf(zip_derived_cl1177, plain, 97.43/12.85 (![X0 : $i]: 97.43/12.85 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.43/12.85 ((('#C') @ is_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 97.43/12.85 ((('#C') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 97.43/12.85 (n_eq @ X0))))))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('comb-normalize', [status(thm)], [zip_derived_cl1176])). 97.43/12.85 thf(zip_derived_cl1178, plain, 97.43/12.85 (![X0 : $i, X2 : $i]: 97.43/12.85 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ (n_eq @ X0)))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1177])). 97.43/12.85 thf(zip_derived_cl1179, plain, 97.43/12.85 (![X0 : $i, X2 : $i]: 97.43/12.85 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (((=>) @ (n_is @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ (n_eq @ X0)))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('rw', [status(thm)], 97.43/12.85 [zip_derived_cl1178, '6', '6', '7', '7', '8', '8', '9', '9', 97.43/12.85 '10'])). 97.43/12.85 thf(zip_derived_cl1180, plain, 97.43/12.85 (![X0 : $i, X2 : $i]: 97.43/12.85 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (((=>) @ (n_is @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ (n_eq @ X0)))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1179])). 97.43/12.85 thf(zip_derived_cl1181, plain, 97.43/12.85 (![X0 : $i, X1 : $i]: 97.43/12.85 ( (((!!) @ (^[Y0 : $i]: 97.43/12.85 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 ((('#B') @ (((=>) @ (n_is @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ 97.43/12.85 (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ 97.43/12.85 (ap @ X0 @ n_2t))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ 97.43/12.85 (n_eq @ X0))) @ 97.43/12.85 Y0))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('rw_clause', [status(thm)], [zip_derived_cl1180, '14'])). 97.43/12.85 thf(zip_derived_cl1182, plain, 97.43/12.85 (![X0 : $i, X1 : $i]: 97.43/12.85 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.43/12.85 ((('#C') @ is_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.43/12.85 ((('#B') @ (((=>) @ (n_is @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ 97.43/12.85 (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ 97.43/12.85 (ap @ X0 @ n_2t))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ 97.43/12.85 (n_eq @ X0))))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('comb-normalize', [status(thm)], [zip_derived_cl1181])). 97.43/12.85 thf(zip_derived_cl1183, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X3 : $i]: 97.43/12.85 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))) => 97.43/12.85 (((n_eq @ X1 @ X3) => (n_eq @ X0 @ X3))))))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1182])). 97.43/12.85 thf(zip_derived_cl1184, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X3 : $i]: 97.43/12.85 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))) => 97.43/12.85 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t))) => (n_is @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t))))))))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('rw', [status(thm)], 97.43/12.85 [zip_derived_cl1183, '6', '6', '6', '7', '7', '7', '8', '8', 97.43/12.85 '8', '9', '9', '9', '10', '10'])). 97.43/12.85 thf(zip_derived_cl1185, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X3 : $i]: 97.43/12.85 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))) => 97.43/12.85 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t))) => (n_is @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1184])). 97.43/12.85 thf(zip_derived_cl1186, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X3 : $i]: 97.43/12.85 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))) 97.43/12.85 | (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t))) => (n_is @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t))))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1185])). 97.43/12.85 thf(zip_derived_cl1187, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X3 : $i]: 97.43/12.85 (~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t))) 97.43/12.85 | (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t))) 97.43/12.85 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1186])). 97.43/12.85 thf(zip_derived_cl8746, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X3 : $i]: 97.43/12.85 (~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t))) 97.43/12.85 | (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t))) 97.43/12.85 | ~ (is_of @ X3 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 97.43/12.85 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 97.43/12.85 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 97.43/12.85 | ~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))))), 97.43/12.85 inference('remove_ty_args', [status(thm)], [zip_derived_cl1187])). 97.43/12.85 thf(satz45, axiom, 97.43/12.85 (all_of @ 97.43/12.85 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.43/12.85 ( ^[X0:$i]: 97.43/12.85 ( all_of @ 97.43/12.85 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.43/12.85 ( ^[X1:$i]: 97.43/12.85 ( all_of @ 97.43/12.85 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 97.43/12.85 ( ^[X2:$i]: 97.43/12.85 ( all_of @ 97.43/12.85 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 97.43/12.85 ( ^[X3:$i]: 97.43/12.85 ( ( lessf @ X0 @ X1 ) => 97.43/12.85 ( ( n_eq @ X0 @ X2 ) => 97.43/12.85 ( ( n_eq @ X1 @ X3 ) => ( lessf @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 97.43/12.85 thf(zip_derived_cl192, plain, 97.43/12.85 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 97.43/12.85 (^[Y0 : $i]: 97.43/12.85 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 97.43/12.85 (^[Y1 : $i]: 97.43/12.85 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 97.43/12.85 (^[Y2 : $i]: 97.43/12.85 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 97.43/12.85 (^[Y3 : $i]: 97.43/12.85 (((lessf @ Y0 @ Y1) => 97.43/12.85 (((n_eq @ Y0 @ Y2) => 97.43/12.85 (((n_eq @ Y1 @ Y3) => (lessf @ Y2 @ Y3)))))))))))))))), 97.43/12.85 inference('cnf', [status(esa)], [satz45])). 97.43/12.85 thf(zip_derived_cl193, plain, 97.43/12.85 ( (all_of @ ((('#C') @ in @ frac)) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 97.43/12.85 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.85 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @ 97.43/12.85 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 97.43/12.85 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.43/12.85 lessf)))))))))))))), 97.43/12.85 inference('lams2combs', [status(thm)], [zip_derived_cl192])). 97.43/12.85 thf(zip_derived_cl2543, plain, 97.43/12.85 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 97.43/12.85 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 97.43/12.85 ((('#C') @ in @ 97.43/12.85 (pair1type @ nat)))))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.85 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @ 97.43/12.85 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 97.43/12.85 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.43/12.85 lessf)))))))))))))), 97.43/12.85 inference('rw', [status(thm)], [zip_derived_cl193, '0'])). 97.43/12.85 thf(zip_derived_cl2544, plain, 97.43/12.85 ( (((!!) @ (^[Y0 : $i]: 97.43/12.85 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (all_of @ 97.43/12.85 ((('#C') @ in @ 97.43/12.85 (pair1type @ nat)))))) @ 97.43/12.85 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 97.43/12.85 ((('#C') @ in @ 97.43/12.85 (pair1type @ nat)))))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.85 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ 97.43/12.85 lessf)))))))) @ 97.43/12.85 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ 97.43/12.85 n_eq)))))))) @ 97.43/12.85 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ 97.43/12.85 n_eq)))))) @ 97.43/12.85 lessf)))))))))) @ 97.43/12.85 Y0)))))))), 97.43/12.85 inference('rw_clause', [status(thm)], [zip_derived_cl2543, '14'])). 97.43/12.85 thf(zip_derived_cl2545, plain, 97.43/12.85 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.43/12.85 ((('#C') @ is_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat)))))) @ 97.43/12.85 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 97.43/12.85 ((('#C') @ in @ 97.43/12.85 (pair1type @ nat)))))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.85 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @ 97.43/12.85 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ ('#B'))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 97.43/12.85 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.43/12.85 lessf))))))))))))))))), 97.43/12.85 inference('comb-normalize', [status(thm)], [zip_derived_cl2544])). 97.43/12.85 thf(zip_derived_cl2546, plain, 97.43/12.85 (![X2 : $i]: 97.43/12.85 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat)))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ (=>) @ (lessf @ X2))))))) @ 97.43/12.85 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ (=>) @ (n_eq @ X2))))))) @ 97.43/12.85 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.43/12.85 lessf)))))))))))))), 97.43/12.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2545])). 97.43/12.85 thf(zip_derived_cl2547, plain, 97.43/12.85 (![X2 : $i]: 97.43/12.85 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat)))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ (=>) @ (lessf @ X2))))))) @ 97.43/12.85 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ (=>) @ (n_eq @ X2))))))) @ 97.43/12.85 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.43/12.85 lessf))))))))))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2546])). 97.43/12.85 thf(zip_derived_cl2548, plain, 97.43/12.85 (![X0 : $i]: 97.43/12.85 ( (((!!) @ (^[Y0 : $i]: 97.43/12.85 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 ((('#B') @ (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (all_of @ 97.43/12.85 ((('#C') @ in @ 97.43/12.85 (pair1type @ nat)))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ (=>) @ (lessf @ X0))))))) @ 97.43/12.85 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ (=>) @ 97.43/12.85 (n_eq @ X0))))))) @ 97.43/12.85 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ 97.43/12.85 n_eq)))))) @ 97.43/12.85 lessf)))))))) @ 97.43/12.85 Y0))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('rw_clause', [status(thm)], [zip_derived_cl2547, '14'])). 97.43/12.85 thf(zip_derived_cl2549, plain, 97.43/12.85 (![X0 : $i]: 97.43/12.85 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.43/12.85 ((('#C') @ is_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (all_of @ 97.43/12.85 ((('#C') @ in @ 97.43/12.85 (pair1type @ nat)))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ (=>) @ (lessf @ X0))))))) @ 97.43/12.85 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ (=>) @ 97.43/12.85 (n_eq @ X0))))))) @ 97.43/12.85 ((('#C') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ ('#S') @ 97.43/12.85 ((('#B') @ ((('#B') @ (=>))) @ 97.43/12.85 n_eq)))))) @ 97.43/12.85 lessf)))))))))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('comb-normalize', [status(thm)], [zip_derived_cl2548])). 97.43/12.85 thf(zip_derived_cl2550, plain, 97.43/12.85 (![X0 : $i, X2 : $i]: 97.43/12.85 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (((=>) @ (lessf @ X0 @ X2))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X0))))) @ 97.43/12.85 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 97.43/12.85 lessf))))))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2549])). 97.43/12.85 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))). 97.43/12.85 thf('16', plain, 97.43/12.85 (![X1:$i,X0:$i]: 97.43/12.85 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 97.43/12.85 define([status(thm)])). 97.43/12.85 thf(def_lessf, axiom,(( lessf @ (X0)@ (X1)) = 97.43/12.85 ((iii @ (n_ts @ (num @ X0) @ (den @ X1)) @ (n_ts @ (num @ X1) @ (den @ X0)))))). 97.43/12.85 thf('17', plain, 97.43/12.85 (![X1:$i,X0:$i]: 97.43/12.85 ( ( lessf @ X0 @ X1 ) = 97.43/12.85 ( iii @ 97.43/12.85 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 97.43/12.85 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )), 97.43/12.85 define([status(thm)])). 97.43/12.85 thf(zip_derived_cl2551, plain, 97.43/12.85 (![X0 : $i, X2 : $i]: 97.43/12.85 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ 97.43/12.85 (ap @ X0 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ 97.43/12.85 (ap @ X2 @ n_2t)))))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X0))))) @ 97.43/12.85 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 97.43/12.85 lessf))))))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('rw', [status(thm)], 97.43/12.85 [zip_derived_cl2550, '4', '16', '6', '6', '7', '7', '8', '8', 97.43/12.85 '9', '9', '17'])). 97.43/12.85 thf(zip_derived_cl2552, plain, 97.43/12.85 (![X0 : $i, X2 : $i]: 97.43/12.85 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ 97.43/12.85 (ap @ X0 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ 97.43/12.85 (ap @ X2 @ n_2t)))))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 97.43/12.85 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 97.43/12.85 lessf))))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2551])). 97.43/12.85 thf(zip_derived_cl2553, plain, 97.43/12.85 (![X0 : $i, X1 : $i]: 97.43/12.85 ( (((!!) @ (^[Y0 : $i]: 97.43/12.85 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 ((('#B') @ (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ 97.43/12.85 (ap @ X1 @ n_1t) @ 97.43/12.85 (ap @ X0 @ n_2t)) @ 97.43/12.85 (n_ts @ 97.43/12.85 (ap @ X0 @ n_1t) @ 97.43/12.85 (ap @ X1 @ n_2t)))))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 97.43/12.85 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 97.43/12.85 (n_eq @ X1))))) @ 97.43/12.85 lessf)))))) @ 97.43/12.85 Y0))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('rw_clause', [status(thm)], [zip_derived_cl2552, '14'])). 97.43/12.85 thf(zip_derived_cl2554, plain, 97.43/12.85 (![X0 : $i, X1 : $i]: 97.43/12.85 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.43/12.85 ((('#C') @ is_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.43/12.85 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.43/12.85 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ 97.43/12.85 (ap @ X1 @ n_1t) @ 97.43/12.85 (ap @ X0 @ n_2t)) @ 97.43/12.85 (n_ts @ 97.43/12.85 (ap @ X0 @ n_1t) @ 97.43/12.85 (ap @ X1 @ n_2t)))))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ ('#B') @ 97.43/12.85 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 97.43/12.85 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))))) @ 97.43/12.85 lessf)))))))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('comb-normalize', [status(thm)], [zip_derived_cl2553])). 97.43/12.85 thf(zip_derived_cl2555, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X3 : $i]: 97.43/12.85 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (((=>) @ (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) @ 97.43/12.85 ((('#B') @ (((=>) @ (n_eq @ X0 @ X3))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (lessf @ X3)))))))))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2554])). 97.43/12.85 thf(zip_derived_cl2556, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X3 : $i]: 97.43/12.85 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (((=>) @ (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) @ 97.43/12.85 ((('#B') @ (((=>) @ (n_is @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (lessf @ X3)))))))))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('rw', [status(thm)], 97.43/12.85 [zip_derived_cl2555, '6', '6', '7', '7', '8', '8', '9', '9', 97.43/12.85 '10'])). 97.43/12.85 thf(zip_derived_cl2557, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X3 : $i]: 97.43/12.85 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.43/12.85 ((('#B') @ (((=>) @ (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) @ 97.43/12.85 ((('#B') @ (((=>) @ (n_is @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ 97.43/12.85 (ap @ X3 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X3 @ n_1t) @ 97.43/12.85 (ap @ X0 @ n_2t))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (lessf @ X3)))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2556])). 97.43/12.85 thf(zip_derived_cl2558, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X2 : $i]: 97.43/12.85 ( (((!!) @ (^[Y0 : $i]: 97.43/12.85 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 ((('#B') @ (((=>) @ (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ 97.43/12.85 (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ 97.43/12.85 (ap @ X0 @ n_2t)))))) @ 97.43/12.85 ((('#B') @ (((=>) @ (n_is @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ 97.43/12.85 (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ 97.43/12.85 (ap @ X1 @ n_2t))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @ 97.43/12.85 (lessf @ X2))))) @ 97.43/12.85 Y0))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('rw_clause', [status(thm)], [zip_derived_cl2557, '14'])). 97.43/12.85 thf(zip_derived_cl2559, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X2 : $i]: 97.43/12.85 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.43/12.85 ((('#C') @ is_of @ 97.43/12.85 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.43/12.85 ((('#B') @ (((=>) @ (l_some @ nat @ 97.43/12.85 (diffprop @ 97.43/12.85 (n_ts @ (ap @ X0 @ n_1t) @ 97.43/12.85 (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ 97.43/12.85 (ap @ X0 @ n_2t)))))) @ 97.43/12.85 ((('#B') @ (((=>) @ (n_is @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ 97.43/12.85 (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ 97.43/12.85 (ap @ X1 @ n_2t))))) @ 97.43/12.85 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @ 97.43/12.85 (lessf @ X2))))))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('comb-normalize', [status(thm)], [zip_derived_cl2558])). 97.43/12.85 thf(zip_derived_cl2560, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 97.43/12.85 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 (((l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) => 97.43/12.85 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) => 97.43/12.85 (((n_eq @ X0 @ X4) => (lessf @ X2 @ X4))))))))) 97.43/12.85 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2559])). 97.43/12.85 thf(zip_derived_cl2561, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 97.43/12.85 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.43/12.85 (((l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) => 97.43/12.85 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) => 97.43/12.85 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @ 97.43/12.85 nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))))))))))) 97.43/12.85 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('rw', [status(thm)], 97.43/12.85 [zip_derived_cl2560, '4', '16', '6', '6', '6', '7', '7', '7', 97.43/12.85 '8', '8', '8', '9', '9', '9', '10', '17'])). 97.43/12.85 thf(zip_derived_cl2562, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 97.43/12.85 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | (((l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) => 97.43/12.85 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) => 97.43/12.85 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @ 97.43/12.85 nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))))))))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2561])). 97.43/12.85 thf(zip_derived_cl2563, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 97.43/12.85 (~ (l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 97.43/12.85 | (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) => 97.43/12.85 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @ 97.43/12.85 nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))))))) 97.43/12.85 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2562])). 97.43/12.85 thf(zip_derived_cl2564, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 97.43/12.85 (~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) 97.43/12.85 | (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @ 97.43/12.85 nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))))) 97.43/12.85 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2563])). 97.43/12.85 thf(zip_derived_cl2565, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 97.43/12.85 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) 97.43/12.85 | (l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))) 97.43/12.85 | ~ (l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 97.43/12.85 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 97.43/12.85 | ~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))))), 97.43/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2564])). 97.43/12.85 thf(zip_derived_cl8789, plain, 97.43/12.85 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 97.43/12.85 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) 97.43/12.85 | (l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))) 97.43/12.85 | ~ (l_some @ nat @ 97.43/12.85 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 97.43/12.85 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 97.43/12.85 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 97.43/12.85 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 97.43/12.85 | ~ (is_of @ X4 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 97.43/12.85 | ~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.43/12.85 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))))), 97.43/12.85 inference('remove_ty_args', [status(thm)], [zip_derived_cl2565])). 97.43/12.85 thf(zip_derived_cl8809, plain, ($false), 97.43/12.85 inference('eprover', [status(thm)], 97.43/12.85 [zip_derived_cl3397, zip_derived_cl3395, zip_derived_cl8757, 97.43/12.85 zip_derived_cl1379, zip_derived_cl1382, zip_derived_cl8756, 97.43/12.85 zip_derived_cl3394, zip_derived_cl8708, zip_derived_cl8754, 97.43/12.85 zip_derived_cl8755, zip_derived_cl1387, zip_derived_cl1392, 97.43/12.85 zip_derived_cl8746, zip_derived_cl8789])). 97.43/12.85 97.43/12.85 % SZS output end Refutation 97.43/12.85 97.43/12.85 97.43/12.85 % Terminating... 97.68/12.95 % Runner terminated. 97.68/12.95 % Zipperpin 1.5 exiting 97.68/12.95 EOF