0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.16 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.F6irU2wBch true 0.16/0.37 % Computer : n014.cluster.edu 0.16/0.37 % Model : x86_64 x86_64 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.37 % Memory : 8042.1875MB 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.37 % CPULimit : 960 0.16/0.37 % WCLimit : 120 0.16/0.37 % DateTime : Tue Aug 9 07:55:31 EDT 2022 0.16/0.37 % CPUTime : 0.16/0.37 % Running portfolio for 960 s 0.16/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.16/0.37 % Number of cores: 8 0.16/0.37 % Python version: Python 3.6.8 0.16/0.37 % Running in HO mode 0.21/0.54 % Total configuration time : 828 0.21/0.54 % Estimated wc time : 1656 0.21/0.54 % Estimated cpu time (8 cpus) : 207.0 0.21/0.57 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.21/0.57 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.94/0.59 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.94/0.59 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.94/0.60 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.94/0.60 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 1.05/0.61 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 1.05/0.61 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 91.33/12.01 % Solved by lams/40_b.comb.sh. 91.33/12.01 % done 755 iterations in 11.340s 91.33/12.01 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 91.33/12.01 % SZS output start Refutation 91.33/12.01 thf('#sk2_type', type, '#sk2': $i). 91.33/12.01 thf(moref_type, type, moref: $i > $i > $o). 91.33/12.01 thf(lesseq_type, type, lesseq: $i > $i > $o). 91.33/12.01 thf(d_not_type, type, d_not: $o > $o). 91.33/12.01 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 91.33/12.01 thf(in_type, type, in: $i > $i > $o). 91.33/12.01 thf(nat_type, type, nat: $i). 91.33/12.01 thf(l_or_type, type, l_or: $o > $o > $o). 91.33/12.01 thf(lessf_type, type, lessf: $i > $i > $o). 91.33/12.01 thf('#sk3_type', type, '#sk3': $i). 91.33/12.01 thf(frac_type, type, frac: $i). 91.33/12.01 thf(imp_type, type, imp: $o > $o > $o). 91.33/12.01 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 91.33/12.01 thf(n_eq_type, type, n_eq: $i > $i > $o). 91.33/12.01 thf('#ty_enc5_type', type, '#ty_enc5': ($i > $i > $o) > $i > $i > $o). 91.33/12.01 thf('#sk4_type', type, '#sk4': $i). 91.33/12.01 thf(moreq_type, type, moreq: $i > $i > $o). 91.33/12.01 thf(pair1type_type, type, pair1type: $i > $i). 91.33/12.01 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 91.33/12.01 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 91.33/12.01 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 91.33/12.01 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 91.33/12.01 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 91.33/12.01 thf(satz52, conjecture, 91.33/12.01 (all_of @ 91.33/12.01 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 91.33/12.01 ( ^[X0:$i]: 91.33/12.01 ( all_of @ 91.33/12.01 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 91.33/12.01 ( ^[X1:$i]: 91.33/12.01 ( all_of @ 91.33/12.01 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 91.33/12.01 ( ^[X2:$i]: 91.33/12.01 ( ( lesseq @ X0 @ X1 ) => 91.33/12.01 ( ( lesseq @ X1 @ X2 ) => ( lesseq @ X0 @ X2 ) ) ) ) ) ) ) ))). 91.33/12.01 thf(zf_stmt_0, negated_conjecture, 91.33/12.01 (~( all_of @ 91.33/12.01 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 91.33/12.01 ( ^[X0:$i]: 91.33/12.01 ( all_of @ 91.33/12.01 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 91.33/12.01 ( ^[X1:$i]: 91.33/12.01 ( all_of @ 91.33/12.01 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 91.33/12.01 ( ^[X2:$i]: 91.33/12.01 ( ( lesseq @ X0 @ X1 ) => 91.33/12.01 ( ( lesseq @ X1 @ X2 ) => ( lesseq @ X0 @ X2 ) ) ) ) ) ) ) ) )), 91.33/12.01 inference('cnf.neg', [status(esa)], [satz52])). 91.33/12.01 thf(zip_derived_cl292, plain, 91.33/12.01 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 91.33/12.01 (^[Y0 : $i]: 91.33/12.01 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 91.33/12.01 (^[Y1 : $i]: 91.33/12.01 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 91.33/12.01 (^[Y2 : $i]: 91.33/12.01 (((lesseq @ Y0 @ Y1) => 91.33/12.01 (((lesseq @ Y1 @ Y2) => (lesseq @ Y0 @ Y2)))))))))))), 91.33/12.01 inference('cnf', [status(esa)], [zf_stmt_0])). 91.33/12.01 thf(zip_derived_cl293, plain, 91.33/12.01 (~ (all_of @ ((('#C') @ in @ frac)) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ ('#B'))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @ 91.33/12.01 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @ 91.33/12.01 lesseq)))))))))), 91.33/12.01 inference('lams2combs', [status(thm)], [zip_derived_cl292])). 91.33/12.01 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))). 91.33/12.01 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])). 91.33/12.01 thf(zip_derived_cl480, plain, 91.33/12.01 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ ('#B'))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @ 91.33/12.01 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @ 91.33/12.01 lesseq)))))))))), 91.33/12.01 inference('rw', [status(thm)], [zip_derived_cl293, '0'])). 91.33/12.01 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 91.33/12.01 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 91.33/12.01 thf('1', plain, 91.33/12.01 (![X0:( $i > $o ),X1:( $i > $o )]: 91.33/12.01 ( ( ~( all_of @ X0 @ X1 ) ) <=> 91.33/12.01 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 91.33/12.01 inference('rw.lit', [status(esa)], [def_all_of])). 91.33/12.01 thf(zip_derived_cl481, plain, 91.33/12.01 (~ (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (all_of @ 91.33/12.01 ((('#C') @ in @ 91.33/12.01 (pair1type @ nat)))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ ('#B'))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @ 91.33/12.01 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ 91.33/12.01 lesseq)))))) @ 91.33/12.01 lesseq)))))) @ 91.33/12.01 Y0)))))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl480, '1'])). 91.33/12.01 thf(zip_derived_cl482, plain, 91.33/12.01 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat)))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ ('#B'))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @ 91.33/12.01 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ 91.33/12.01 lesseq)))))) @ 91.33/12.01 lesseq))))))))))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl481])). 91.33/12.01 thf(zip_derived_cl483, plain, 91.33/12.01 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#B') @ 91.33/12.01 ((('#B') @ (=>) @ (lesseq @ '#sk2'))))) @ 91.33/12.01 ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 91.33/12.01 (lesseq @ '#sk2'))))))))))), 91.33/12.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl482])). 91.33/12.01 thf(zip_derived_cl485, plain, 91.33/12.01 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#B') @ 91.33/12.01 ((('#B') @ (=>) @ (lesseq @ '#sk2'))))) @ 91.33/12.01 ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 91.33/12.01 (lesseq @ '#sk2'))))))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl483])). 91.33/12.01 thf(zip_derived_cl486, plain, 91.33/12.01 (~ (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#B') @ 91.33/12.01 ((('#B') @ (=>) @ (lesseq @ '#sk2'))))) @ 91.33/12.01 ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 91.33/12.01 (lesseq @ '#sk2'))))) @ 91.33/12.01 Y0)))))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl485, '1'])). 91.33/12.01 thf(zip_derived_cl487, plain, 91.33/12.01 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#B') @ 91.33/12.01 ((('#B') @ (=>) @ (lesseq @ '#sk2'))))) @ 91.33/12.01 ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 91.33/12.01 (lesseq @ '#sk2')))))))))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl486])). 91.33/12.01 thf(zip_derived_cl488, plain, 91.33/12.01 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (((=>) @ (lesseq @ '#sk2' @ '#sk3'))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 91.33/12.01 (lesseq @ '#sk2'))))))))), 91.33/12.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl487])). 91.33/12.01 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 91.33/12.01 thf('2', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 91.33/12.01 define([status(thm)])). 91.33/12.01 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 91.33/12.01 thf('3', plain, 91.33/12.01 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 91.33/12.01 define([status(thm)])). 91.33/12.01 thf(def_lesseq, axiom,(( lesseq @ (X0)@ (X1)) = 91.33/12.01 ((l_or @ (lessf @ X0 @ X1) @ (n_eq @ X0 @ X1))))). 91.33/12.01 thf('4', plain, 91.33/12.01 (![X1:$i,X0:$i]: 91.33/12.01 ( ( lesseq @ X0 @ X1 ) = 91.33/12.01 ( l_or @ ( lessf @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )), 91.33/12.01 define([status(thm)])). 91.33/12.01 thf(zip_derived_cl489, plain, 91.33/12.01 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (((=>) @ (imp @ 91.33/12.01 (imp @ (lessf @ '#sk2' @ '#sk3') @ ($false)) @ 91.33/12.01 (n_eq @ '#sk2' @ '#sk3')))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 91.33/12.01 (lesseq @ '#sk2'))))))))), 91.33/12.01 inference('rw', [status(thm)], [zip_derived_cl488, '2', '3', '4'])). 91.33/12.01 thf(zip_derived_cl491, plain, 91.33/12.01 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (((=>) @ (imp @ 91.33/12.01 (imp @ (lessf @ '#sk2' @ '#sk3') @ ($false)) @ 91.33/12.01 (n_eq @ '#sk2' @ '#sk3')))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 91.33/12.01 (lesseq @ '#sk2'))))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl489])). 91.33/12.01 thf(zip_derived_cl492, plain, 91.33/12.01 (~ (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (((=>) @ (imp @ 91.33/12.01 (imp @ (lessf @ '#sk2' @ '#sk3') @ 91.33/12.01 ($false)) @ 91.33/12.01 (n_eq @ '#sk2' @ '#sk3')))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 91.33/12.01 (lesseq @ '#sk2'))) @ 91.33/12.01 Y0)))))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl491, '1'])). 91.33/12.01 thf(zip_derived_cl493, plain, 91.33/12.01 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (((=>) @ (imp @ 91.33/12.01 (imp @ (lessf @ '#sk2' @ '#sk3') @ 91.33/12.01 ($false)) @ 91.33/12.01 (n_eq @ '#sk2' @ '#sk3')))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 91.33/12.01 (lesseq @ '#sk2')))))))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl492])). 91.33/12.01 thf(zip_derived_cl494, plain, 91.33/12.01 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 (((imp @ (imp @ (lessf @ '#sk2' @ '#sk3') @ ($false)) @ 91.33/12.01 (n_eq @ '#sk2' @ '#sk3')) => 91.33/12.01 (((lesseq @ '#sk3' @ '#sk4') => (lesseq @ '#sk2' @ '#sk4')))))))), 91.33/12.01 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl493])). 91.33/12.01 thf(zip_derived_cl495, plain, 91.33/12.01 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 (((imp @ (imp @ (lessf @ '#sk2' @ '#sk3') @ ($false)) @ 91.33/12.01 (n_eq @ '#sk2' @ '#sk3')) => 91.33/12.01 (((imp @ (imp @ (lessf @ '#sk3' @ '#sk4') @ ($false)) @ 91.33/12.01 (n_eq @ '#sk3' @ '#sk4')) => (imp @ 91.33/12.01 (imp @ (lessf @ '#sk2' @ '#sk4') @ ($false)) @ 91.33/12.01 (n_eq @ '#sk2' @ '#sk4'))))))))), 91.33/12.01 inference('rw', [status(thm)], 91.33/12.01 [zip_derived_cl494, '2', '2', '3', '3', '4', '4'])). 91.33/12.01 thf(zip_derived_cl497, plain, 91.33/12.01 (~ (((imp @ (imp @ (lessf @ '#sk2' @ '#sk3') @ ($false)) @ 91.33/12.01 (n_eq @ '#sk2' @ '#sk3')) => 91.33/12.01 (((imp @ (imp @ (lessf @ '#sk3' @ '#sk4') @ ($false)) @ 91.33/12.01 (n_eq @ '#sk3' @ '#sk4')) => (imp @ 91.33/12.01 (imp @ (lessf @ '#sk2' @ '#sk4') @ ($false)) @ 91.33/12.01 (n_eq @ '#sk2' @ '#sk4'))))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl495])). 91.33/12.01 thf(zip_derived_cl499, plain, 91.33/12.01 (~ (((imp @ (imp @ (lessf @ '#sk3' @ '#sk4') @ ($false)) @ 91.33/12.01 (n_eq @ '#sk3' @ '#sk4')) => (imp @ 91.33/12.01 (imp @ (lessf @ '#sk2' @ '#sk4') @ ($false)) @ 91.33/12.01 (n_eq @ '#sk2' @ '#sk4'))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl497])). 91.33/12.01 thf(zip_derived_cl501, plain, 91.33/12.01 ( (imp @ (imp @ (lessf @ '#sk3' @ '#sk4') @ ($false)) @ 91.33/12.01 (n_eq @ '#sk3' @ '#sk4'))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl499])). 91.33/12.01 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 91.33/12.01 thf('5', plain, 91.33/12.01 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 91.33/12.01 inference('rw.lit', [status(esa)], [def_imp])). 91.33/12.01 thf(zip_derived_cl504, plain, 91.33/12.01 ( (((imp @ (lessf @ '#sk3' @ '#sk4') @ ($false)) => (n_eq @ '#sk3' @ 91.33/12.01 '#sk4')))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl501, '5'])). 91.33/12.01 thf(zip_derived_cl507, plain, 91.33/12.01 ((~ (imp @ (lessf @ '#sk3' @ '#sk4') @ ($false)) 91.33/12.01 | (n_eq @ '#sk3' @ '#sk4'))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl504])). 91.33/12.01 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 91.33/12.01 thf('6', plain, 91.33/12.01 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 91.33/12.01 inference('rw.lit', [status(esa)], [def_imp])). 91.33/12.01 thf(zip_derived_cl512, plain, 91.33/12.01 ((~ (((lessf @ '#sk3' @ '#sk4') => ($false))) | (n_eq @ '#sk3' @ '#sk4'))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl507, '6'])). 91.33/12.01 thf(zip_derived_cl514, plain, 91.33/12.01 ((~ (((~) @ (lessf @ '#sk3' @ '#sk4'))) | (n_eq @ '#sk3' @ '#sk4'))), 91.33/12.01 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl512])). 91.33/12.01 thf(zip_derived_cl515, plain, 91.33/12.01 (( (lessf @ '#sk3' @ '#sk4') | (n_eq @ '#sk3' @ '#sk4'))), 91.33/12.01 inference('simplify nested equalities', [status(thm)], 91.33/12.01 [zip_derived_cl514])). 91.33/12.01 thf(satz51d, axiom, 91.33/12.01 (all_of @ 91.33/12.01 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 91.33/12.01 ( ^[X0:$i]: 91.33/12.01 ( all_of @ 91.33/12.01 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 91.33/12.01 ( ^[X1:$i]: 91.33/12.01 ( all_of @ 91.33/12.01 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 91.33/12.01 ( ^[X2:$i]: 91.33/12.01 ( ( moref @ X0 @ X1 ) => 91.33/12.01 ( ( moreq @ X1 @ X2 ) => ( moref @ X0 @ X2 ) ) ) ) ) ) ) ))). 91.33/12.01 thf(zip_derived_cl12, plain, 91.33/12.01 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 91.33/12.01 (^[Y0 : $i]: 91.33/12.01 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 91.33/12.01 (^[Y1 : $i]: 91.33/12.01 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 91.33/12.01 (^[Y2 : $i]: 91.33/12.01 (((moref @ Y0 @ Y1) => 91.33/12.01 (((moreq @ Y1 @ Y2) => (moref @ Y0 @ Y2)))))))))))), 91.33/12.01 inference('cnf', [status(esa)], [satz51d])). 91.33/12.01 thf(zip_derived_cl13, plain, 91.33/12.01 ( (all_of @ ((('#C') @ in @ frac)) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ ('#B'))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 91.33/12.01 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 91.33/12.01 moref)))))))))), 91.33/12.01 inference('lams2combs', [status(thm)], [zip_derived_cl12])). 91.33/12.01 thf(zip_derived_cl1217, plain, 91.33/12.01 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ ('#B'))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 91.33/12.01 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 91.33/12.01 moref)))))))))), 91.33/12.01 inference('rw', [status(thm)], [zip_derived_cl13, '0'])). 91.33/12.01 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 91.33/12.01 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 91.33/12.01 thf('7', plain, 91.33/12.01 (![X0:( $i > $o ),X1:( $i > $o )]: 91.33/12.01 ( ( all_of @ X0 @ X1 ) <=> 91.33/12.01 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 91.33/12.01 inference('rw.lit', [status(esa)], [def_all_of])). 91.33/12.01 thf(zip_derived_cl1218, plain, 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (all_of @ 91.33/12.01 ((('#C') @ in @ 91.33/12.01 (pair1type @ nat)))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ ('#B'))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 91.33/12.01 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ 91.33/12.01 moreq)))))) @ 91.33/12.01 moref)))))) @ 91.33/12.01 Y0)))))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl1217, '7'])). 91.33/12.01 thf(zip_derived_cl1219, plain, 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat)))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ ('#B'))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 91.33/12.01 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ 91.33/12.01 moreq)))))) @ 91.33/12.01 moref))))))))))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl1218])). 91.33/12.01 thf(zip_derived_cl1220, plain, 91.33/12.01 (![X2 : $i]: 91.33/12.01 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (moref @ X2))))) @ 91.33/12.01 ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 91.33/12.01 (moref @ X2))))))))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1219])). 91.33/12.01 thf(zip_derived_cl1221, plain, 91.33/12.01 (![X2 : $i]: 91.33/12.01 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (moref @ X2))))) @ 91.33/12.01 ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 91.33/12.01 (moref @ X2)))))))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1220])). 91.33/12.01 thf(zip_derived_cl1222, plain, 91.33/12.01 (![X0 : $i]: 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#B') @ 91.33/12.01 ((('#B') @ (=>) @ (moref @ X0))))) @ 91.33/12.01 ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 91.33/12.01 (moref @ X0))))) @ 91.33/12.01 Y0))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl1221, '7'])). 91.33/12.01 thf(zip_derived_cl1223, plain, 91.33/12.01 (![X0 : $i]: 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#B') @ 91.33/12.01 ((('#B') @ (=>) @ (moref @ X0))))) @ 91.33/12.01 ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 91.33/12.01 (moref @ X0))))))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl1222])). 91.33/12.01 thf(zip_derived_cl1224, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (((=>) @ (moref @ X0 @ X2))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X2))) @ (moref @ X0)))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1223])). 91.33/12.01 thf(zip_derived_cl1225, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (((=>) @ (moref @ X0 @ X2))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X2))) @ (moref @ X0)))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1224])). 91.33/12.01 thf(zip_derived_cl1226, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (((=>) @ (moref @ X0 @ X1))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X1))) @ 91.33/12.01 (moref @ X0))) @ 91.33/12.01 Y0))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl1225, '7'])). 91.33/12.01 thf(zip_derived_cl1227, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (((=>) @ (moref @ X0 @ X1))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X1))) @ 91.33/12.01 (moref @ X0))))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl1226])). 91.33/12.01 thf(zip_derived_cl1228, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X3 : $i]: 91.33/12.01 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 (((moref @ X0 @ X1) => (((moreq @ X1 @ X3) => (moref @ X0 @ X3))))))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1227])). 91.33/12.01 thf(def_moreq, axiom,(( moreq @ (X0)@ (X1)) = 91.33/12.01 ((l_or @ (moref @ X0 @ X1) @ (n_eq @ X0 @ X1))))). 91.33/12.01 thf('8', plain, 91.33/12.01 (![X1:$i,X0:$i]: 91.33/12.01 ( ( moreq @ X0 @ X1 ) = 91.33/12.01 ( l_or @ ( moref @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )), 91.33/12.01 define([status(thm)])). 91.33/12.01 thf(zip_derived_cl1229, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X3 : $i]: 91.33/12.01 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 (((moref @ X0 @ X1) => 91.33/12.01 (((imp @ (imp @ (moref @ X1 @ X3) @ ($false)) @ 91.33/12.01 (n_eq @ X1 @ X3)) => (moref @ X0 @ X3))))))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw', [status(thm)], [zip_derived_cl1228, '2', '3', '8'])). 91.33/12.01 thf(zip_derived_cl1230, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X3 : $i]: 91.33/12.01 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (((moref @ X0 @ X1) => 91.33/12.01 (((imp @ (imp @ (moref @ X1 @ X3) @ ($false)) @ 91.33/12.01 (n_eq @ X1 @ X3)) => (moref @ X0 @ X3))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1229])). 91.33/12.01 thf(zip_derived_cl1231, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X3 : $i]: 91.33/12.01 (~ (moref @ X0 @ X1) 91.33/12.01 | (((imp @ (imp @ (moref @ X1 @ X3) @ ($false)) @ 91.33/12.01 (n_eq @ X1 @ X3)) => (moref @ X0 @ X3))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1230])). 91.33/12.01 thf(zip_derived_cl1232, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X3 : $i]: 91.33/12.01 (~ (imp @ (imp @ (moref @ X1 @ X3) @ ($false)) @ (n_eq @ X1 @ X3)) 91.33/12.01 | (moref @ X0 @ X3) 91.33/12.01 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (moref @ X0 @ X1))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1231])). 91.33/12.01 thf(zip_derived_cl1233, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X2 : $i]: 91.33/12.01 (~ (((imp @ (moref @ X0 @ X2) @ ($false)) => (n_eq @ X0 @ X2))) 91.33/12.01 | ~ (moref @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (moref @ X1 @ X2))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl1232, '6'])). 91.33/12.01 thf(zip_derived_cl1234, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X2 : $i]: 91.33/12.01 ( (imp @ (moref @ X0 @ X2) @ ($false)) 91.33/12.01 | (moref @ X1 @ X2) 91.33/12.01 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (moref @ X1 @ X0))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1233])). 91.33/12.01 thf(zip_derived_cl1236, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X2 : $i]: 91.33/12.01 ( (((moref @ X0 @ X2) => ($false))) 91.33/12.01 | ~ (moref @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (moref @ X1 @ X2))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl1234, '5'])). 91.33/12.01 thf(zip_derived_cl1237, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X2 : $i]: 91.33/12.01 ( (((~) @ (moref @ X0 @ X2))) 91.33/12.01 | ~ (moref @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (moref @ X1 @ X2))), 91.33/12.01 inference('simplify boolean subterms', [status(thm)], 91.33/12.01 [zip_derived_cl1236])). 91.33/12.01 thf(zip_derived_cl1238, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X2 : $i]: 91.33/12.01 (~ (moref @ X0 @ X2) 91.33/12.01 | ~ (moref @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (moref @ X1 @ X2))), 91.33/12.01 inference('simplify nested equalities', [status(thm)], 91.33/12.01 [zip_derived_cl1237])). 91.33/12.01 thf(zip_derived_cl20204, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X2 : $i]: 91.33/12.01 (~ (moref @ X0 @ X2) 91.33/12.01 | ~ (moref @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | (moref @ X1 @ X2))), 91.33/12.01 inference('remove_ty_args', [status(thm)], [zip_derived_cl1238])). 91.33/12.01 thf(zip_derived_cl1235, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X2 : $i]: 91.33/12.01 (~ (n_eq @ X0 @ X2) 91.33/12.01 | (moref @ X1 @ X2) 91.33/12.01 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (moref @ X1 @ X0))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1233])). 91.33/12.01 thf(zip_derived_cl20203, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X2 : $i]: 91.33/12.01 (~ (n_eq @ X0 @ X2) 91.33/12.01 | (moref @ X1 @ X2) 91.33/12.01 | ~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (moref @ X1 @ X0))), 91.33/12.01 inference('remove_ty_args', [status(thm)], [zip_derived_cl1235])). 91.33/12.01 thf(zip_derived_cl498, plain, 91.33/12.01 ( (imp @ (imp @ (lessf @ '#sk2' @ '#sk3') @ ($false)) @ 91.33/12.01 (n_eq @ '#sk2' @ '#sk3'))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl497])). 91.33/12.01 thf(zip_derived_cl500, plain, 91.33/12.01 ( (((imp @ (lessf @ '#sk2' @ '#sk3') @ ($false)) => (n_eq @ '#sk2' @ 91.33/12.01 '#sk3')))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl498, '5'])). 91.33/12.01 thf(zip_derived_cl503, plain, 91.33/12.01 ((~ (imp @ (lessf @ '#sk2' @ '#sk3') @ ($false)) 91.33/12.01 | (n_eq @ '#sk2' @ '#sk3'))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl500])). 91.33/12.01 thf(zip_derived_cl506, plain, 91.33/12.01 ((~ (((lessf @ '#sk2' @ '#sk3') => ($false))) | (n_eq @ '#sk2' @ '#sk3'))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl503, '6'])). 91.33/12.01 thf(zip_derived_cl510, plain, 91.33/12.01 ((~ (((~) @ (lessf @ '#sk2' @ '#sk3'))) | (n_eq @ '#sk2' @ '#sk3'))), 91.33/12.01 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl506])). 91.33/12.01 thf(zip_derived_cl511, plain, 91.33/12.01 (( (lessf @ '#sk2' @ '#sk3') | (n_eq @ '#sk2' @ '#sk3'))), 91.33/12.01 inference('simplify nested equalities', [status(thm)], 91.33/12.01 [zip_derived_cl510])). 91.33/12.01 thf(zip_derived_cl496, plain, 91.33/12.01 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl495])). 91.33/12.01 thf(zip_derived_cl20165, plain, 91.33/12.01 ( (is_of @ '#sk4' @ ('#ty_enc5' @ in @ (pair1type @ nat)))), 91.33/12.01 inference('remove_ty_args', [status(thm)], [zip_derived_cl496])). 91.33/12.01 thf(zip_derived_cl502, plain, 91.33/12.01 (~ (imp @ (imp @ (lessf @ '#sk2' @ '#sk4') @ ($false)) @ 91.33/12.01 (n_eq @ '#sk2' @ '#sk4'))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl499])). 91.33/12.01 thf(zip_derived_cl505, plain, 91.33/12.01 (~ (((imp @ (lessf @ '#sk2' @ '#sk4') @ ($false)) => (n_eq @ '#sk2' @ 91.33/12.01 '#sk4')))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl502, '6'])). 91.33/12.01 thf(zip_derived_cl509, plain, (~ (n_eq @ '#sk2' @ '#sk4')), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl505])). 91.33/12.01 thf(satz41j, axiom, 91.33/12.01 (all_of @ 91.33/12.01 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 91.33/12.01 ( ^[X0:$i]: 91.33/12.01 ( all_of @ 91.33/12.01 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 91.33/12.01 ( ^[X1:$i]: ( ( d_not @ ( moreq @ X0 @ X1 ) ) => ( lessf @ X0 @ X1 ) ) ) ) ))). 91.33/12.01 thf(zip_derived_cl96, plain, 91.33/12.01 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 91.33/12.01 (^[Y0 : $i]: 91.33/12.01 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 91.33/12.01 (^[Y1 : $i]: (((d_not @ (moreq @ Y0 @ Y1)) => (lessf @ Y0 @ Y1)))))))), 91.33/12.01 inference('cnf', [status(esa)], [satz41j])). 91.33/12.01 thf(zip_derived_cl97, plain, 91.33/12.01 ( (all_of @ ((('#C') @ in @ frac)) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ 91.33/12.01 ((('#B') @ ((('#B') @ d_not)) @ moreq)))))) @ 91.33/12.01 lessf)))))), 91.33/12.01 inference('lams2combs', [status(thm)], [zip_derived_cl96])). 91.33/12.01 thf(zip_derived_cl692, plain, 91.33/12.01 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ 91.33/12.01 ((('#B') @ ((('#B') @ d_not)) @ moreq)))))) @ 91.33/12.01 lessf)))))), 91.33/12.01 inference('rw', [status(thm)], [zip_derived_cl97, '0'])). 91.33/12.01 thf(zip_derived_cl693, plain, 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ 91.33/12.01 ((('#B') @ ((('#B') @ d_not)) @ moreq)))))) @ 91.33/12.01 lessf)) @ 91.33/12.01 Y0)))))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl692, '7'])). 91.33/12.01 thf(zip_derived_cl694, plain, 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ 91.33/12.01 ((('#B') @ ((('#B') @ d_not)) @ moreq)))))) @ 91.33/12.01 lessf))))))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl693])). 91.33/12.01 thf(zip_derived_cl695, plain, 91.33/12.01 (![X2 : $i]: 91.33/12.01 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (moreq @ X2))))) @ 91.33/12.01 (lessf @ X2))))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl694])). 91.33/12.01 thf(zip_derived_cl696, plain, 91.33/12.01 (![X2 : $i]: 91.33/12.01 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (moreq @ X2))))) @ 91.33/12.01 (lessf @ X2)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl695])). 91.33/12.01 thf(zip_derived_cl697, plain, 91.33/12.01 (![X0 : $i]: 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#B') @ d_not @ (moreq @ X0))))) @ 91.33/12.01 (lessf @ X0) @ Y0))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl696, '7'])). 91.33/12.01 thf(zip_derived_cl698, plain, 91.33/12.01 (![X0 : $i]: 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#B') @ d_not @ (moreq @ X0))))) @ 91.33/12.01 (lessf @ X0))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl697])). 91.33/12.01 thf(zip_derived_cl699, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 (((d_not @ (moreq @ X0 @ X2)) => (lessf @ X0 @ X2))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl698])). 91.33/12.01 thf(zip_derived_cl700, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 (((imp @ 91.33/12.01 (imp @ (imp @ (moref @ X0 @ X2) @ ($false)) @ (n_eq @ X0 @ X2)) @ 91.33/12.01 ($false)) => (lessf @ X0 @ X2))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw', [status(thm)], [zip_derived_cl699, '2', '2', '3', '8'])). 91.33/12.01 thf(zip_derived_cl701, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (((imp @ 91.33/12.01 (imp @ (imp @ (moref @ X0 @ X2) @ ($false)) @ (n_eq @ X0 @ X2)) @ 91.33/12.01 ($false)) => (lessf @ X0 @ X2))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl700])). 91.33/12.01 thf(zip_derived_cl702, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 (~ (imp @ 91.33/12.01 (imp @ (imp @ (moref @ X0 @ X2) @ ($false)) @ (n_eq @ X0 @ X2)) @ 91.33/12.01 ($false)) 91.33/12.01 | (lessf @ X0 @ X2) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl701])). 91.33/12.01 thf(zip_derived_cl703, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 (~ (((imp @ (imp @ (moref @ X1 @ X0) @ ($false)) @ 91.33/12.01 (n_eq @ X1 @ X0)) => ($false))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (lessf @ X1 @ X0))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl702, '6'])). 91.33/12.01 thf(zip_derived_cl704, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 (~ (((~) @ (imp @ (imp @ (moref @ X1 @ X0) @ ($false)) @ 91.33/12.01 (n_eq @ X1 @ X0)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (lessf @ X1 @ X0))), 91.33/12.01 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl703])). 91.33/12.01 thf(zip_derived_cl705, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 ( (imp @ (imp @ (moref @ X1 @ X0) @ ($false)) @ (n_eq @ X1 @ X0)) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (lessf @ X1 @ X0))), 91.33/12.01 inference('simplify nested equalities', [status(thm)], 91.33/12.01 [zip_derived_cl704])). 91.33/12.01 thf(zip_derived_cl706, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 ( (((imp @ (moref @ X1 @ X0) @ ($false)) => (n_eq @ X1 @ X0))) 91.33/12.01 | (lessf @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl705, '5'])). 91.33/12.01 thf(zip_derived_cl707, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 (~ (imp @ (moref @ X1 @ X0) @ ($false)) 91.33/12.01 | (n_eq @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (lessf @ X1 @ X0))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl706])). 91.33/12.01 thf(zip_derived_cl708, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 (~ (((moref @ X1 @ X0) => ($false))) 91.33/12.01 | (lessf @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (n_eq @ X1 @ X0))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl707, '6'])). 91.33/12.01 thf(zip_derived_cl709, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 (~ (((~) @ (moref @ X1 @ X0))) 91.33/12.01 | (lessf @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (n_eq @ X1 @ X0))), 91.33/12.01 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl708])). 91.33/12.01 thf(zip_derived_cl710, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 ( (moref @ X1 @ X0) 91.33/12.01 | (lessf @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (n_eq @ X1 @ X0))), 91.33/12.01 inference('simplify nested equalities', [status(thm)], 91.33/12.01 [zip_derived_cl709])). 91.33/12.01 thf(zip_derived_cl20178, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 ( (moref @ X1 @ X0) 91.33/12.01 | (lessf @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | (n_eq @ X1 @ X0))), 91.33/12.01 inference('remove_ty_args', [status(thm)], [zip_derived_cl710])). 91.33/12.01 thf(zip_derived_cl508, plain, 91.33/12.01 ( (imp @ (lessf @ '#sk2' @ '#sk4') @ ($false))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl505])). 91.33/12.01 thf(zip_derived_cl513, plain, ( (((lessf @ '#sk2' @ '#sk4') => ($false)))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl508, '5'])). 91.33/12.01 thf(zip_derived_cl516, plain, ( (((~) @ (lessf @ '#sk2' @ '#sk4')))), 91.33/12.01 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl513])). 91.33/12.01 thf(zip_derived_cl517, plain, (~ (lessf @ '#sk2' @ '#sk4')), 91.33/12.01 inference('simplify nested equalities', [status(thm)], 91.33/12.01 [zip_derived_cl516])). 91.33/12.01 thf(satz39, axiom, 91.33/12.01 (all_of @ 91.33/12.01 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 91.33/12.01 ( ^[X0:$i]: 91.33/12.01 ( all_of @ 91.33/12.01 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 91.33/12.01 ( ^[X1:$i]: 91.33/12.01 ( all_of @ 91.33/12.01 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 91.33/12.01 ( ^[X2:$i]: 91.33/12.01 ( ( n_eq @ X0 @ X1 ) => 91.33/12.01 ( ( n_eq @ X1 @ X2 ) => ( n_eq @ X0 @ X2 ) ) ) ) ) ) ) ))). 91.33/12.01 thf(zip_derived_cl132, plain, 91.33/12.01 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 91.33/12.01 (^[Y0 : $i]: 91.33/12.01 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 91.33/12.01 (^[Y1 : $i]: 91.33/12.01 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 91.33/12.01 (^[Y2 : $i]: 91.33/12.01 (((n_eq @ Y0 @ Y1) => 91.33/12.01 (((n_eq @ Y1 @ Y2) => (n_eq @ Y0 @ Y2)))))))))))), 91.33/12.01 inference('cnf', [status(esa)], [satz39])). 91.33/12.01 thf(zip_derived_cl133, plain, 91.33/12.01 ( (all_of @ ((('#C') @ in @ frac)) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ ('#B'))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 91.33/12.01 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 91.33/12.01 n_eq)))))))))), 91.33/12.01 inference('lams2combs', [status(thm)], [zip_derived_cl132])). 91.33/12.01 thf(zip_derived_cl1417, plain, 91.33/12.01 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ ('#B'))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 91.33/12.01 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 91.33/12.01 n_eq)))))))))), 91.33/12.01 inference('rw', [status(thm)], [zip_derived_cl133, '0'])). 91.33/12.01 thf(zip_derived_cl1418, plain, 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (all_of @ 91.33/12.01 ((('#C') @ in @ 91.33/12.01 (pair1type @ nat)))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ ('#B'))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 91.33/12.01 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ 91.33/12.01 n_eq)))))) @ 91.33/12.01 n_eq)))))) @ 91.33/12.01 Y0)))))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl1417, '7'])). 91.33/12.01 thf(zip_derived_cl1419, plain, 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat)))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ ('#B'))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 91.33/12.01 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ 91.33/12.01 n_eq)))))) @ 91.33/12.01 n_eq))))))))))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl1418])). 91.33/12.01 thf(zip_derived_cl1420, plain, 91.33/12.01 (![X2 : $i]: 91.33/12.01 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 91.33/12.01 ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 91.33/12.01 (n_eq @ X2))))))))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1419])). 91.33/12.01 thf(zip_derived_cl1421, plain, 91.33/12.01 (![X2 : $i]: 91.33/12.01 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 91.33/12.01 ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 91.33/12.01 (n_eq @ X2)))))))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1420])). 91.33/12.01 thf(zip_derived_cl1422, plain, 91.33/12.01 (![X0 : $i]: 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#B') @ 91.33/12.01 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 91.33/12.01 ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 91.33/12.01 (n_eq @ X0))))) @ 91.33/12.01 Y0))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl1421, '7'])). 91.33/12.01 thf(zip_derived_cl1423, plain, 91.33/12.01 (![X0 : $i]: 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#B') @ 91.33/12.01 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 91.33/12.01 ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 91.33/12.01 (n_eq @ X0))))))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl1422])). 91.33/12.01 thf(zip_derived_cl1424, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ (n_eq @ X0)))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1423])). 91.33/12.01 thf(zip_derived_cl1425, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ (n_eq @ X0)))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1424])). 91.33/12.01 thf(zip_derived_cl1426, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ 91.33/12.01 (n_eq @ X0))) @ 91.33/12.01 Y0))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl1425, '7'])). 91.33/12.01 thf(zip_derived_cl1427, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ 91.33/12.01 (n_eq @ X0))))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl1426])). 91.33/12.01 thf(zip_derived_cl1428, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X3 : $i]: 91.33/12.01 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 (((n_eq @ X0 @ X1) => (((n_eq @ X1 @ X3) => (n_eq @ X0 @ X3))))))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1427])). 91.33/12.01 thf(zip_derived_cl1429, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X3 : $i]: 91.33/12.01 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (((n_eq @ X0 @ X1) => (((n_eq @ X1 @ X3) => (n_eq @ X0 @ X3))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1428])). 91.33/12.01 thf(zip_derived_cl1430, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X3 : $i]: 91.33/12.01 (~ (n_eq @ X0 @ X1) 91.33/12.01 | (((n_eq @ X1 @ X3) => (n_eq @ X0 @ X3))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1429])). 91.33/12.01 thf(zip_derived_cl1431, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X3 : $i]: 91.33/12.01 (~ (n_eq @ X1 @ X3) 91.33/12.01 | (n_eq @ X0 @ X3) 91.33/12.01 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (n_eq @ X0 @ X1))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1430])). 91.33/12.01 thf(zip_derived_cl20214, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X3 : $i]: 91.33/12.01 (~ (n_eq @ X1 @ X3) 91.33/12.01 | (n_eq @ X0 @ X3) 91.33/12.01 | ~ (is_of @ X3 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (n_eq @ X0 @ X1))), 91.33/12.01 inference('remove_ty_args', [status(thm)], [zip_derived_cl1431])). 91.33/12.01 thf(zip_derived_cl490, plain, 91.33/12.01 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl489])). 91.33/12.01 thf(zip_derived_cl20164, plain, 91.33/12.01 ( (is_of @ '#sk3' @ ('#ty_enc5' @ in @ (pair1type @ nat)))), 91.33/12.01 inference('remove_ty_args', [status(thm)], [zip_derived_cl490])). 91.33/12.01 thf(zip_derived_cl484, plain, 91.33/12.01 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl483])). 91.33/12.01 thf(zip_derived_cl20163, plain, 91.33/12.01 ( (is_of @ '#sk2' @ ('#ty_enc5' @ in @ (pair1type @ nat)))), 91.33/12.01 inference('remove_ty_args', [status(thm)], [zip_derived_cl484])). 91.33/12.01 thf(satz51c, axiom, 91.33/12.01 (all_of @ 91.33/12.01 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 91.33/12.01 ( ^[X0:$i]: 91.33/12.01 ( all_of @ 91.33/12.01 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 91.33/12.01 ( ^[X1:$i]: 91.33/12.01 ( all_of @ 91.33/12.01 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 91.33/12.01 ( ^[X2:$i]: 91.33/12.01 ( ( moreq @ X0 @ X1 ) => 91.33/12.01 ( ( moref @ X1 @ X2 ) => ( moref @ X0 @ X2 ) ) ) ) ) ) ) ))). 91.33/12.01 thf(zip_derived_cl130, plain, 91.33/12.01 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 91.33/12.01 (^[Y0 : $i]: 91.33/12.01 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 91.33/12.01 (^[Y1 : $i]: 91.33/12.01 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 91.33/12.01 (^[Y2 : $i]: 91.33/12.01 (((moreq @ Y0 @ Y1) => 91.33/12.01 (((moref @ Y1 @ Y2) => (moref @ Y0 @ Y2)))))))))))), 91.33/12.01 inference('cnf', [status(esa)], [satz51c])). 91.33/12.01 thf(zip_derived_cl131, plain, 91.33/12.01 ( (all_of @ ((('#C') @ in @ frac)) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ ('#B'))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 91.33/12.01 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 91.33/12.01 moref)))))))))), 91.33/12.01 inference('lams2combs', [status(thm)], [zip_derived_cl130])). 91.33/12.01 thf(zip_derived_cl1381, plain, 91.33/12.01 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ ('#B'))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 91.33/12.01 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 91.33/12.01 moref)))))))))), 91.33/12.01 inference('rw', [status(thm)], [zip_derived_cl131, '0'])). 91.33/12.01 thf(zip_derived_cl1382, plain, 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (all_of @ 91.33/12.01 ((('#C') @ in @ 91.33/12.01 (pair1type @ nat)))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ ('#B'))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 91.33/12.01 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ 91.33/12.01 moref)))))) @ 91.33/12.01 moref)))))) @ 91.33/12.01 Y0)))))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl1381, '7'])). 91.33/12.01 thf(zip_derived_cl1383, plain, 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat)))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ ('#B'))) @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 91.33/12.01 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ 91.33/12.01 moref)))))) @ 91.33/12.01 moref))))))))))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl1382])). 91.33/12.01 thf(zip_derived_cl1384, plain, 91.33/12.01 (![X2 : $i]: 91.33/12.01 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (moreq @ X2))))) @ 91.33/12.01 ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 91.33/12.01 (moref @ X2))))))))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1383])). 91.33/12.01 thf(zip_derived_cl1385, plain, 91.33/12.01 (![X2 : $i]: 91.33/12.01 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (moreq @ X2))))) @ 91.33/12.01 ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 91.33/12.01 (moref @ X2)))))))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1384])). 91.33/12.01 thf(zip_derived_cl1386, plain, 91.33/12.01 (![X0 : $i]: 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#B') @ 91.33/12.01 ((('#B') @ (=>) @ (moreq @ X0))))) @ 91.33/12.01 ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 91.33/12.01 (moref @ X0))))) @ 91.33/12.01 Y0))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl1385, '7'])). 91.33/12.01 thf(zip_derived_cl1387, plain, 91.33/12.01 (![X0 : $i]: 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#B') @ 91.33/12.01 ((('#B') @ (=>) @ (moreq @ X0))))) @ 91.33/12.01 ((('#C') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 91.33/12.01 (moref @ X0))))))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl1386])). 91.33/12.01 thf(zip_derived_cl1388, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (((=>) @ (moreq @ X0 @ X2))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ (moref @ X0)))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1387])). 91.33/12.01 thf(zip_derived_cl1389, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (((=>) @ (imp @ (imp @ (moref @ X0 @ X2) @ ($false)) @ 91.33/12.01 (n_eq @ X0 @ X2)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ (moref @ X0)))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw', [status(thm)], [zip_derived_cl1388, '2', '3', '8'])). 91.33/12.01 thf(zip_derived_cl1390, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (((=>) @ (imp @ 91.33/12.01 (imp @ (moref @ X0 @ X2) @ ($false)) @ 91.33/12.01 (n_eq @ X0 @ X2)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ (moref @ X0)))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1389])). 91.33/12.01 thf(zip_derived_cl1391, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (((=>) @ (imp @ 91.33/12.01 (imp @ (moref @ X0 @ X1) @ 91.33/12.01 ($false)) @ 91.33/12.01 (n_eq @ X0 @ X1)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moref @ X1))) @ 91.33/12.01 (moref @ X0))) @ 91.33/12.01 Y0))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl1390, '7'])). 91.33/12.01 thf(zip_derived_cl1392, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (((=>) @ (imp @ 91.33/12.01 (imp @ (moref @ X0 @ X1) @ ($false)) @ 91.33/12.01 (n_eq @ X0 @ X1)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moref @ X1))) @ 91.33/12.01 (moref @ X0))))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl1391])). 91.33/12.01 thf(zip_derived_cl1393, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X3 : $i]: 91.33/12.01 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 (((imp @ (imp @ (moref @ X0 @ X1) @ ($false)) @ 91.33/12.01 (n_eq @ X0 @ X1)) => (((moref @ X1 @ X3) => (moref @ X0 @ X3))))))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1392])). 91.33/12.01 thf(zip_derived_cl1394, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X3 : $i]: 91.33/12.01 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (((imp @ (imp @ (moref @ X0 @ X1) @ ($false)) @ 91.33/12.01 (n_eq @ X0 @ X1)) => (((moref @ X1 @ X3) => (moref @ X0 @ X3))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1393])). 91.33/12.01 thf(zip_derived_cl1395, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X3 : $i]: 91.33/12.01 (~ (imp @ (imp @ (moref @ X0 @ X1) @ ($false)) @ (n_eq @ X0 @ X1)) 91.33/12.01 | (((moref @ X1 @ X3) => (moref @ X0 @ X3))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1394])). 91.33/12.01 thf(zip_derived_cl1396, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X2 : $i]: 91.33/12.01 (~ (((imp @ (moref @ X1 @ X2) @ ($false)) => (n_eq @ X1 @ X2))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (((moref @ X2 @ X0) => (moref @ X1 @ X0))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl1395, '6'])). 91.33/12.01 thf(zip_derived_cl1398, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X2 : $i]: 91.33/12.01 (~ (n_eq @ X1 @ X2) 91.33/12.01 | (((moref @ X2 @ X0) => (moref @ X1 @ X0))) 91.33/12.01 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])). 91.33/12.01 thf(zip_derived_cl1400, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X2 : $i]: 91.33/12.01 (~ (moref @ X2 @ X0) 91.33/12.01 | (moref @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (n_eq @ X1 @ X2))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1398])). 91.33/12.01 thf(zip_derived_cl20212, plain, 91.33/12.01 (![X0 : $i, X1 : $i, X2 : $i]: 91.33/12.01 (~ (moref @ X2 @ X0) 91.33/12.01 | (moref @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (n_eq @ X1 @ X2))), 91.33/12.01 inference('remove_ty_args', [status(thm)], [zip_derived_cl1400])). 91.33/12.01 thf(satz38, axiom, 91.33/12.01 (all_of @ 91.33/12.01 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 91.33/12.01 ( ^[X0:$i]: 91.33/12.01 ( all_of @ 91.33/12.01 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 91.33/12.01 ( ^[X1:$i]: ( ( n_eq @ X0 @ X1 ) => ( n_eq @ X1 @ X0 ) ) ) ) ))). 91.33/12.01 thf(zip_derived_cl208, plain, 91.33/12.01 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 91.33/12.01 (^[Y0 : $i]: 91.33/12.01 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 91.33/12.01 (^[Y1 : $i]: (((n_eq @ Y0 @ Y1) => (n_eq @ Y1 @ Y0)))))))), 91.33/12.01 inference('cnf', [status(esa)], [satz38])). 91.33/12.01 thf(zip_derived_cl209, plain, 91.33/12.01 ( (all_of @ ((('#C') @ in @ frac)) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 91.33/12.01 ((('#C') @ n_eq)))))))), 91.33/12.01 inference('lams2combs', [status(thm)], [zip_derived_cl208])). 91.33/12.01 thf(zip_derived_cl536, plain, 91.33/12.01 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 91.33/12.01 ((('#C') @ n_eq)))))))), 91.33/12.01 inference('rw', [status(thm)], [zip_derived_cl209, '0'])). 91.33/12.01 thf(zip_derived_cl537, plain, 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 91.33/12.01 ((('#C') @ n_eq)))) @ 91.33/12.01 Y0)))))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl536, '7'])). 91.33/12.01 thf(zip_derived_cl538, plain, 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 91.33/12.01 ((('#C') @ n_eq))))))))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl537])). 91.33/12.01 thf(zip_derived_cl539, plain, 91.33/12.01 (![X2 : $i]: 91.33/12.01 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ ((('#C') @ n_eq @ X2)))))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl538])). 91.33/12.01 thf(zip_derived_cl540, plain, 91.33/12.01 (![X2 : $i]: 91.33/12.01 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ 91.33/12.01 ((('#C') @ n_eq @ X2))))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl539])). 91.33/12.01 thf(zip_derived_cl541, plain, 91.33/12.01 (![X0 : $i]: 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @ 91.33/12.01 ((('#C') @ n_eq @ X0)) @ Y0))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl540, '7'])). 91.33/12.01 thf(zip_derived_cl542, plain, 91.33/12.01 (![X0 : $i]: 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @ 91.33/12.01 ((('#C') @ n_eq @ X0)))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl541])). 91.33/12.01 thf(zip_derived_cl543, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 (((n_eq @ X0 @ X2) => (n_eq @ X2 @ X0))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl542])). 91.33/12.01 thf(zip_derived_cl544, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (((n_eq @ X0 @ X2) => (n_eq @ X2 @ X0))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl543])). 91.33/12.01 thf(zip_derived_cl545, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 (~ (n_eq @ X0 @ X2) 91.33/12.01 | (n_eq @ X2 @ X0) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl544])). 91.33/12.01 thf(zip_derived_cl20168, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 (~ (n_eq @ X0 @ X2) 91.33/12.01 | (n_eq @ X2 @ X0) 91.33/12.01 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat))))), 91.33/12.01 inference('remove_ty_args', [status(thm)], [zip_derived_cl545])). 91.33/12.01 thf(satz42, axiom, 91.33/12.01 (all_of @ 91.33/12.01 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 91.33/12.01 ( ^[X0:$i]: 91.33/12.01 ( all_of @ 91.33/12.01 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 91.33/12.01 ( ^[X1:$i]: ( ( moref @ X0 @ X1 ) => ( lessf @ X1 @ X0 ) ) ) ) ))). 91.33/12.01 thf(zip_derived_cl288, plain, 91.33/12.01 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 91.33/12.01 (^[Y0 : $i]: 91.33/12.01 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 91.33/12.01 (^[Y1 : $i]: (((moref @ Y0 @ Y1) => (lessf @ Y1 @ Y0)))))))), 91.33/12.01 inference('cnf', [status(esa)], [satz42])). 91.33/12.01 thf(zip_derived_cl289, plain, 91.33/12.01 ( (all_of @ ((('#C') @ in @ frac)) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 91.33/12.01 ((('#C') @ lessf)))))))), 91.33/12.01 inference('lams2combs', [status(thm)], [zip_derived_cl288])). 91.33/12.01 thf(zip_derived_cl604, plain, 91.33/12.01 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 91.33/12.01 ((('#C') @ lessf)))))))), 91.33/12.01 inference('rw', [status(thm)], [zip_derived_cl289, '0'])). 91.33/12.01 thf(zip_derived_cl605, plain, 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 91.33/12.01 ((('#C') @ lessf)))) @ 91.33/12.01 Y0)))))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl604, '7'])). 91.33/12.01 thf(zip_derived_cl606, plain, 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 91.33/12.01 ((('#C') @ lessf))))))))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl605])). 91.33/12.01 thf(zip_derived_cl607, plain, 91.33/12.01 (![X2 : $i]: 91.33/12.01 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 91.33/12.01 ((('#C') @ lessf @ X2)))))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl606])). 91.33/12.01 thf(zip_derived_cl608, plain, 91.33/12.01 (![X2 : $i]: 91.33/12.01 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 91.33/12.01 ((('#C') @ lessf @ X2))))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl607])). 91.33/12.01 thf(zip_derived_cl609, plain, 91.33/12.01 (![X0 : $i]: 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moref @ X0))) @ 91.33/12.01 ((('#C') @ lessf @ X0)) @ Y0))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl608, '7'])). 91.33/12.01 thf(zip_derived_cl610, plain, 91.33/12.01 (![X0 : $i]: 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moref @ X0))) @ 91.33/12.01 ((('#C') @ lessf @ X0)))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl609])). 91.33/12.01 thf(zip_derived_cl611, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 (((moref @ X0 @ X2) => (lessf @ X2 @ X0))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl610])). 91.33/12.01 thf(zip_derived_cl612, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (((moref @ X0 @ X2) => (lessf @ X2 @ X0))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl611])). 91.33/12.01 thf(zip_derived_cl613, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 (~ (moref @ X0 @ X2) 91.33/12.01 | (lessf @ X2 @ X0) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl612])). 91.33/12.01 thf(zip_derived_cl20172, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 (~ (moref @ X0 @ X2) 91.33/12.01 | (lessf @ X2 @ X0) 91.33/12.01 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat))))), 91.33/12.01 inference('remove_ty_args', [status(thm)], [zip_derived_cl613])). 91.33/12.01 thf(satz41g, axiom, 91.33/12.01 (all_of @ 91.33/12.01 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 91.33/12.01 ( ^[X0:$i]: 91.33/12.01 ( all_of @ 91.33/12.01 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 91.33/12.01 ( ^[X1:$i]: 91.33/12.01 ( ( moref @ X0 @ X1 ) => ( d_not @ ( lesseq @ X0 @ X1 ) ) ) ) ) ))). 91.33/12.01 thf(zip_derived_cl54, plain, 91.33/12.01 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 91.33/12.01 (^[Y0 : $i]: 91.33/12.01 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 91.33/12.01 (^[Y1 : $i]: (((moref @ Y0 @ Y1) => (d_not @ (lesseq @ Y0 @ Y1))))))))), 91.33/12.01 inference('cnf', [status(esa)], [satz41g])). 91.33/12.01 thf(zip_derived_cl55, plain, 91.33/12.01 ( (all_of @ ((('#C') @ in @ frac)) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 91.33/12.01 ((('#B') @ ((('#B') @ d_not)) @ lesseq)))))))), 91.33/12.01 inference('lams2combs', [status(thm)], [zip_derived_cl54])). 91.33/12.01 thf(zip_derived_cl615, plain, 91.33/12.01 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 91.33/12.01 ((('#B') @ ((('#B') @ d_not)) @ lesseq)))))))), 91.33/12.01 inference('rw', [status(thm)], [zip_derived_cl55, '0'])). 91.33/12.01 thf(zip_derived_cl616, plain, 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 91.33/12.01 ((('#B') @ ((('#B') @ d_not)) @ lesseq)))) @ 91.33/12.01 Y0)))))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl615, '7'])). 91.33/12.01 thf(zip_derived_cl617, plain, 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 91.33/12.01 ((('#B') @ ((('#B') @ d_not)) @ lesseq))))))))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl616])). 91.33/12.01 thf(zip_derived_cl618, plain, 91.33/12.01 (![X2 : $i]: 91.33/12.01 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 91.33/12.01 ((('#B') @ d_not @ (lesseq @ X2))))))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl617])). 91.33/12.01 thf(zip_derived_cl619, plain, 91.33/12.01 (![X2 : $i]: 91.33/12.01 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 91.33/12.01 ((('#B') @ d_not @ (lesseq @ X2)))))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl618])). 91.33/12.01 thf(zip_derived_cl620, plain, 91.33/12.01 (![X0 : $i]: 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moref @ X0))) @ 91.33/12.01 ((('#B') @ d_not @ (lesseq @ X0))) @ Y0))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl619, '7'])). 91.33/12.01 thf(zip_derived_cl621, plain, 91.33/12.01 (![X0 : $i]: 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (moref @ X0))) @ 91.33/12.01 ((('#B') @ d_not @ (lesseq @ X0))))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl620])). 91.33/12.01 thf(zip_derived_cl622, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 (((moref @ X0 @ X2) => (d_not @ (lesseq @ X0 @ X2)))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl621])). 91.33/12.01 thf(zip_derived_cl623, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 (((moref @ X0 @ X2) => (imp @ 91.33/12.01 (imp @ (imp @ (lessf @ X0 @ X2) @ ($false)) @ (n_eq @ X0 @ X2)) @ 91.33/12.01 ($false)))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw', [status(thm)], [zip_derived_cl622, '2', '2', '3', '4'])). 91.33/12.01 thf(zip_derived_cl624, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (((moref @ X0 @ X2) => (imp @ 91.33/12.01 (imp @ (imp @ (lessf @ X0 @ X2) @ ($false)) @ (n_eq @ X0 @ X2)) @ 91.33/12.01 ($false)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl623])). 91.33/12.01 thf(zip_derived_cl625, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 (~ (moref @ X0 @ X2) 91.33/12.01 | (imp @ 91.33/12.01 (imp @ (imp @ (lessf @ X0 @ X2) @ ($false)) @ (n_eq @ X0 @ X2)) @ 91.33/12.01 ($false)) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl624])). 91.33/12.01 thf(zip_derived_cl626, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 ( (((imp @ (imp @ (lessf @ X1 @ X0) @ ($false)) @ (n_eq @ X1 @ X0)) => 91.33/12.01 ($false))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (moref @ X1 @ X0))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl625, '5'])). 91.33/12.01 thf(zip_derived_cl627, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 ( (((~) @ (imp @ (imp @ (lessf @ X1 @ X0) @ ($false)) @ 91.33/12.01 (n_eq @ X1 @ X0)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (moref @ X1 @ X0))), 91.33/12.01 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl626])). 91.33/12.01 thf(zip_derived_cl628, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 (~ (imp @ (imp @ (lessf @ X1 @ X0) @ ($false)) @ (n_eq @ X1 @ X0)) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (moref @ X1 @ X0))), 91.33/12.01 inference('simplify nested equalities', [status(thm)], 91.33/12.01 [zip_derived_cl627])). 91.33/12.01 thf(zip_derived_cl629, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 (~ (((imp @ (lessf @ X1 @ X0) @ ($false)) => (n_eq @ X1 @ X0))) 91.33/12.01 | ~ (moref @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl628, '6'])). 91.33/12.01 thf(zip_derived_cl631, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 (~ (n_eq @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (moref @ X1 @ X0))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl629])). 91.33/12.01 thf(zip_derived_cl20173, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 (~ (n_eq @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (moref @ X1 @ X0))), 91.33/12.01 inference('remove_ty_args', [status(thm)], [zip_derived_cl631])). 91.33/12.01 thf(satz43, axiom, 91.33/12.01 (all_of @ 91.33/12.01 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 91.33/12.01 ( ^[X0:$i]: 91.33/12.01 ( all_of @ 91.33/12.01 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 91.33/12.01 ( ^[X1:$i]: ( ( lessf @ X0 @ X1 ) => ( moref @ X1 @ X0 ) ) ) ) ))). 91.33/12.01 thf(zip_derived_cl180, plain, 91.33/12.01 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 91.33/12.01 (^[Y0 : $i]: 91.33/12.01 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 91.33/12.01 (^[Y1 : $i]: (((lessf @ Y0 @ Y1) => (moref @ Y1 @ Y0)))))))), 91.33/12.01 inference('cnf', [status(esa)], [satz43])). 91.33/12.01 thf(zip_derived_cl181, plain, 91.33/12.01 ( (all_of @ ((('#C') @ in @ frac)) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 91.33/12.01 ((('#C') @ moref)))))))), 91.33/12.01 inference('lams2combs', [status(thm)], [zip_derived_cl180])). 91.33/12.01 thf(zip_derived_cl518, plain, 91.33/12.01 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 91.33/12.01 ((('#C') @ moref)))))))), 91.33/12.01 inference('rw', [status(thm)], [zip_derived_cl181, '0'])). 91.33/12.01 thf(zip_derived_cl519, plain, 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 91.33/12.01 ((('#C') @ moref)))) @ 91.33/12.01 Y0)))))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl518, '7'])). 91.33/12.01 thf(zip_derived_cl520, plain, 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 91.33/12.01 ((('#S') @ ((('#B') @ ('#S') @ 91.33/12.01 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 91.33/12.01 ((('#C') @ moref))))))))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl519])). 91.33/12.01 thf(zip_derived_cl521, plain, 91.33/12.01 (![X2 : $i]: 91.33/12.01 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @ 91.33/12.01 ((('#C') @ moref @ X2)))))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl520])). 91.33/12.01 thf(zip_derived_cl522, plain, 91.33/12.01 (![X2 : $i]: 91.33/12.01 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @ 91.33/12.01 ((('#C') @ moref @ X2))))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl521])). 91.33/12.01 thf(zip_derived_cl523, plain, 91.33/12.01 (![X0 : $i]: 91.33/12.01 ( (((!!) @ (^[Y0 : $i]: 91.33/12.01 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X0))) @ 91.33/12.01 ((('#C') @ moref @ X0)) @ Y0))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl522, '7'])). 91.33/12.01 thf(zip_derived_cl524, plain, 91.33/12.01 (![X0 : $i]: 91.33/12.01 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 91.33/12.01 ((('#C') @ is_of @ 91.33/12.01 ((('#C') @ in @ (pair1type @ nat))))))) @ 91.33/12.01 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X0))) @ 91.33/12.01 ((('#C') @ moref @ X0)))))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('comb-normalize', [status(thm)], [zip_derived_cl523])). 91.33/12.01 thf(zip_derived_cl525, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 91.33/12.01 (((lessf @ X0 @ X2) => (moref @ X2 @ X0))))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl524])). 91.33/12.01 thf(zip_derived_cl526, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | (((lessf @ X0 @ X2) => (moref @ X2 @ X0))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl525])). 91.33/12.01 thf(zip_derived_cl527, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 (~ (lessf @ X0 @ X2) 91.33/12.01 | (moref @ X2 @ X0) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl526])). 91.33/12.01 thf(zip_derived_cl20166, plain, 91.33/12.01 (![X0 : $i, X2 : $i]: 91.33/12.01 (~ (lessf @ X0 @ X2) 91.33/12.01 | (moref @ X2 @ X0) 91.33/12.01 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat))))), 91.33/12.01 inference('remove_ty_args', [status(thm)], [zip_derived_cl527])). 91.33/12.01 thf(zip_derived_cl630, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 ( (imp @ (lessf @ X1 @ X0) @ ($false)) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (moref @ X1 @ X0))), 91.33/12.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl629])). 91.33/12.01 thf(zip_derived_cl632, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 ( (((lessf @ X1 @ X0) => ($false))) 91.33/12.01 | ~ (moref @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('rw_clause', [status(thm)], [zip_derived_cl630, '5'])). 91.33/12.01 thf(zip_derived_cl633, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 ( (((~) @ (lessf @ X1 @ X0))) 91.33/12.01 | ~ (moref @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl632])). 91.33/12.01 thf(zip_derived_cl634, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 (~ (lessf @ X1 @ X0) 91.33/12.01 | ~ (moref @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 91.33/12.01 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 91.33/12.01 inference('simplify nested equalities', [status(thm)], 91.33/12.01 [zip_derived_cl633])). 91.33/12.01 thf(zip_derived_cl20174, plain, 91.33/12.01 (![X0 : $i, X1 : $i]: 91.33/12.01 (~ (lessf @ X1 @ X0) 91.33/12.01 | ~ (moref @ X1 @ X0) 91.33/12.01 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 91.33/12.01 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))))), 91.33/12.01 inference('remove_ty_args', [status(thm)], [zip_derived_cl634])). 91.33/12.01 thf(zip_derived_cl20271, plain, ($false), 91.33/12.01 inference('eprover', [status(thm)], 91.33/12.01 [zip_derived_cl515, zip_derived_cl20204, zip_derived_cl20203, 91.33/12.01 zip_derived_cl511, zip_derived_cl20165, zip_derived_cl509, 91.33/12.01 zip_derived_cl20178, zip_derived_cl517, zip_derived_cl20214, 91.33/12.01 zip_derived_cl20164, zip_derived_cl20163, 91.33/12.01 zip_derived_cl20212, zip_derived_cl20168, 91.33/12.01 zip_derived_cl20172, zip_derived_cl20173, 91.33/12.01 zip_derived_cl20166, zip_derived_cl20174])). 91.33/12.01 91.33/12.01 % SZS output end Refutation 91.33/12.01 91.33/12.01 91.33/12.01 % Terminating... 91.33/12.08 % Runner terminated. 91.33/12.08 % Zipperpin 1.5 exiting 91.33/12.08 EOF