0.04/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.GyHe9GCzNu true 0.13/0.34 % Computer : n009.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1440 0.13/0.34 % WCLimit : 180 0.13/0.34 % DateTime : Mon Jul 3 10:57:41 EDT 2023 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 1440 s 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.34 % Python version: Python 3.6.8 0.13/0.34 % Running in HO mode 0.45/0.62 % Total configuration time : 828 0.45/0.62 % Estimated wc time : 1656 0.45/0.62 % Estimated cpu time (8 cpus) : 207.0 0.49/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.49/0.69 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.49/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.49/0.70 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.49/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.49/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.49/0.70 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.49/0.70 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 97.13/12.84 % Solved by lams/40_b.comb.sh. 97.13/12.84 % done 306 iterations in 12.058s 97.13/12.84 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 97.13/12.84 % SZS output start Refutation 97.13/12.84 thf(n_2t_type, type, n_2t: $i). 97.13/12.84 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 97.13/12.84 thf(lesseq_type, type, lesseq: $i > $i > $o). 97.13/12.84 thf(d_not_type, type, d_not: $o > $o). 97.13/12.84 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 97.13/12.84 thf(in_type, type, in: $i > $i > $o). 97.13/12.84 thf(den_type, type, den: $i > $i). 97.13/12.84 thf(n_1t_type, type, n_1t: $i). 97.13/12.84 thf(first1_type, type, first1: $i > $i > $i). 97.13/12.84 thf(ap_type, type, ap: $i > $i > $i). 97.13/12.84 thf('#sk4_type', type, '#sk4': $i). 97.13/12.84 thf(nat_type, type, nat: $i). 97.13/12.84 thf(iii_type, type, iii: $i > $i > $o). 97.13/12.84 thf(l_or_type, type, l_or: $o > $o > $o). 97.13/12.84 thf(second1_type, type, second1: $i > $i > $i). 97.13/12.84 thf(lessf_type, type, lessf: $i > $i > $o). 97.13/12.84 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 97.13/12.84 thf('#sk2_type', type, '#sk2': $i). 97.13/12.84 thf(frac_type, type, frac: $i). 97.13/12.84 thf(n_ts_type, type, n_ts: $i > $i > $i). 97.13/12.84 thf(imp_type, type, imp: $o > $o > $o). 97.13/12.84 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 97.13/12.84 thf(n_eq_type, type, n_eq: $i > $i > $o). 97.13/12.84 thf('#sk3_type', type, '#sk3': $i). 97.13/12.84 thf(n_is_type, type, n_is: $i > $i > $o). 97.13/12.84 thf('#ty_enc5_type', type, '#ty_enc5': ($i > $i > $o) > $i > $i > $o). 97.13/12.84 thf(n_some_type, type, n_some: ($i > $o) > $o). 97.13/12.84 thf(num_type, type, num: $i > $i). 97.13/12.84 thf(pair1type_type, type, pair1type: $i > $i). 97.13/12.84 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 97.13/12.84 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 97.13/12.84 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 97.13/12.84 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 97.13/12.84 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 97.13/12.84 thf(satz37, axiom, 97.13/12.84 (all_of @ 97.13/12.84 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ ( ^[X0:$i]: ( n_eq @ X0 @ X0 ) ))). 97.13/12.84 thf(zip_derived_cl136, plain, 97.13/12.84 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 97.13/12.84 (^[Y0 : $i]: (n_eq @ Y0 @ Y0)))), 97.13/12.84 inference('cnf', [status(esa)], [satz37])). 97.13/12.84 thf(zip_derived_cl137, plain, 97.13/12.84 ( (all_of @ ((('#C') @ in @ frac)) @ ((('#S') @ n_eq @ ('#I'))))), 97.13/12.84 inference('lams2combs', [status(thm)], [zip_derived_cl136])). 97.13/12.84 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))). 97.13/12.84 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])). 97.13/12.84 thf(zip_derived_cl307, plain, 97.13/12.84 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#S') @ n_eq @ ('#I'))))), 97.13/12.84 inference('rw', [status(thm)], [zip_derived_cl137, '0'])). 97.13/12.84 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 97.13/12.84 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 97.13/12.84 thf('1', plain, 97.13/12.84 (![X0:( $i > $o ),X1:( $i > $o )]: 97.13/12.84 ( ( all_of @ X0 @ X1 ) <=> 97.13/12.84 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 97.13/12.84 inference('rw.lit', [status(esa)], [def_all_of])). 97.13/12.84 thf(zip_derived_cl308, plain, 97.13/12.84 ( (((!!) @ (^[Y0 : $i]: 97.13/12.84 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 ((('#S') @ n_eq @ ('#I') @ Y0)))))))), 97.13/12.84 inference('rw_clause', [status(thm)], [zip_derived_cl307, '1'])). 97.13/12.84 thf(zip_derived_cl309, plain, 97.13/12.84 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.13/12.84 ((('#C') @ is_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.13/12.84 ((('#S') @ n_eq @ ('#I')))))))), 97.13/12.84 inference('comb-normalize', [status(thm)], [zip_derived_cl308])). 97.13/12.84 thf(zip_derived_cl310, plain, 97.13/12.84 (![X2 : $i]: 97.13/12.84 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (n_eq @ X2 @ 97.13/12.84 X2)))), 97.13/12.84 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl309])). 97.13/12.84 thf(def_first1, axiom,(( first1 @ (X1)@ (X0)) = ((ap @ X0 @ n_1t)))). 97.13/12.84 thf('2', plain, 97.13/12.84 (![X1:$i,X0:$i]: ( ( first1 @ X1 @ X0 ) = ( ap @ X0 @ n_1t ) )), 97.13/12.84 define([status(thm)])). 97.13/12.84 thf(def_second1, axiom,(( second1 @ (X1)@ (X0)) = ((ap @ X0 @ n_2t)))). 97.13/12.84 thf('3', plain, 97.13/12.84 (![X1:$i,X0:$i]: ( ( second1 @ X1 @ X0 ) = ( ap @ X0 @ n_2t ) )), 97.13/12.84 define([status(thm)])). 97.13/12.84 thf(def_num, axiom,(( num @ (X0)) = ((first1 @ nat @ X0)))). 97.13/12.84 thf('4', plain, (![X0:$i]: ( ( num @ X0 ) = ( first1 @ nat @ X0 ) )), 97.13/12.84 define([status(thm)])). 97.13/12.84 thf(def_den, axiom,(( den @ (X0)) = ((second1 @ nat @ X0)))). 97.13/12.84 thf('5', plain, (![X0:$i]: ( ( den @ X0 ) = ( second1 @ nat @ X0 ) )), 97.13/12.84 define([status(thm)])). 97.13/12.84 thf(def_n_eq, axiom,(( n_eq @ (X0)@ (X1)) = 97.13/12.84 ((n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @ 97.13/12.84 (n_ts @ (num @ X1) @ (den @ X0)))))). 97.13/12.84 thf('6', plain, 97.13/12.84 (![X1:$i,X0:$i]: 97.13/12.84 ( ( n_eq @ X0 @ X1 ) = 97.13/12.84 ( n_is @ 97.13/12.84 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 97.13/12.84 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )), 97.13/12.84 define([status(thm)])). 97.13/12.84 thf(zip_derived_cl311, plain, 97.13/12.84 (![X2 : $i]: 97.13/12.84 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (n_is @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t)))))), 97.13/12.84 inference('rw', [status(thm)], 97.13/12.84 [zip_derived_cl310, '2', '3', '4', '5', '6'])). 97.13/12.84 thf(zip_derived_cl312, plain, 97.13/12.84 (![X2 : $i]: 97.13/12.84 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl311])). 97.13/12.84 thf(zip_derived_cl8169, plain, 97.13/12.84 (![X2 : $i]: 97.13/12.84 (~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.13/12.84 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X2 @ n_2t))))), 97.13/12.84 inference('remove_ty_args', [status(thm)], [zip_derived_cl312])). 97.13/12.84 thf(satz51b, conjecture, 97.13/12.84 (all_of @ 97.13/12.84 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.13/12.84 ( ^[X0:$i]: 97.13/12.84 ( all_of @ 97.13/12.84 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.13/12.84 ( ^[X1:$i]: 97.13/12.84 ( all_of @ 97.13/12.84 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 97.13/12.84 ( ^[X2:$i]: 97.13/12.84 ( ( lessf @ X0 @ X1 ) => 97.13/12.84 ( ( lesseq @ X1 @ X2 ) => ( lessf @ X0 @ X2 ) ) ) ) ) ) ) ))). 97.13/12.84 thf(zf_stmt_0, negated_conjecture, 97.13/12.84 (~( all_of @ 97.13/12.84 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.13/12.84 ( ^[X0:$i]: 97.13/12.84 ( all_of @ 97.13/12.84 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.13/12.84 ( ^[X1:$i]: 97.13/12.84 ( all_of @ 97.13/12.84 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 97.13/12.84 ( ^[X2:$i]: 97.13/12.84 ( ( lessf @ X0 @ X1 ) => 97.13/12.84 ( ( lesseq @ X1 @ X2 ) => ( lessf @ X0 @ X2 ) ) ) ) ) ) ) ) )), 97.13/12.84 inference('cnf.neg', [status(esa)], [satz51b])). 97.13/12.84 thf(zip_derived_cl294, plain, 97.13/12.84 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 97.13/12.84 (^[Y0 : $i]: 97.13/12.84 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 97.13/12.84 (^[Y1 : $i]: 97.13/12.84 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 97.13/12.84 (^[Y2 : $i]: 97.13/12.84 (((lessf @ Y0 @ Y1) => 97.13/12.84 (((lesseq @ Y1 @ Y2) => (lessf @ Y0 @ Y2)))))))))))), 97.13/12.84 inference('cnf', [status(esa)], [zf_stmt_0])). 97.13/12.84 thf(zip_derived_cl295, plain, 97.13/12.84 (~ (all_of @ ((('#C') @ in @ frac)) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 97.13/12.84 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @ 97.13/12.84 lessf)))))))))), 97.13/12.84 inference('lams2combs', [status(thm)], [zip_derived_cl294])). 97.13/12.84 thf(zip_derived_cl474, plain, 97.13/12.84 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 97.13/12.84 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @ 97.13/12.84 lessf)))))))))), 97.13/12.84 inference('rw', [status(thm)], [zip_derived_cl295, '0'])). 97.13/12.84 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 97.13/12.84 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 97.13/12.84 thf('7', plain, 97.13/12.84 (![X0:( $i > $o ),X1:( $i > $o )]: 97.13/12.84 ( ( ~( all_of @ X0 @ X1 ) ) <=> 97.13/12.84 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 97.13/12.84 inference('rw.lit', [status(esa)], [def_all_of])). 97.13/12.84 thf(zip_derived_cl475, plain, 97.13/12.84 (~ (((!!) @ (^[Y0 : $i]: 97.13/12.84 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (all_of @ 97.13/12.84 ((('#C') @ in @ 97.13/12.84 (pair1type @ nat)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 97.13/12.84 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ 97.13/12.84 lesseq)))))) @ 97.13/12.84 lessf)))))) @ 97.13/12.84 Y0)))))))), 97.13/12.84 inference('rw_clause', [status(thm)], [zip_derived_cl474, '7'])). 97.13/12.84 thf(zip_derived_cl476, plain, 97.13/12.84 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.13/12.84 ((('#C') @ is_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 97.13/12.84 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ 97.13/12.84 lesseq)))))) @ 97.13/12.84 lessf))))))))))))), 97.13/12.84 inference('comb-normalize', [status(thm)], [zip_derived_cl475])). 97.13/12.84 thf(zip_derived_cl477, plain, 97.13/12.84 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ (=>) @ (lessf @ '#sk2'))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 97.13/12.84 (lessf @ '#sk2'))))))))))), 97.13/12.84 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl476])). 97.13/12.84 thf(zip_derived_cl479, plain, 97.13/12.84 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (lessf @ '#sk2'))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 97.13/12.84 (lessf @ '#sk2'))))))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl477])). 97.13/12.84 thf(zip_derived_cl480, plain, 97.13/12.84 (~ (((!!) @ (^[Y0 : $i]: 97.13/12.84 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ (=>) @ (lessf @ '#sk2'))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 97.13/12.84 (lessf @ '#sk2'))))) @ 97.13/12.84 Y0)))))))), 97.13/12.84 inference('rw_clause', [status(thm)], [zip_derived_cl479, '7'])). 97.13/12.84 thf(zip_derived_cl481, plain, 97.13/12.84 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.13/12.84 ((('#C') @ is_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ (=>) @ (lessf @ '#sk2'))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 97.13/12.84 (lessf @ '#sk2')))))))))))), 97.13/12.84 inference('comb-normalize', [status(thm)], [zip_derived_cl480])). 97.13/12.84 thf(zip_derived_cl482, plain, 97.13/12.84 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (((=>) @ (lessf @ '#sk2' @ '#sk3'))) @ 97.13/12.84 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 97.13/12.84 (lessf @ '#sk2'))))))))), 97.13/12.84 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl481])). 97.13/12.84 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))). 97.13/12.84 thf('8', plain, 97.13/12.84 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )), 97.13/12.84 define([status(thm)])). 97.13/12.84 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))). 97.13/12.84 thf('9', plain, 97.13/12.84 (![X1:$i,X0:$i]: 97.13/12.84 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 97.13/12.84 define([status(thm)])). 97.13/12.84 thf(def_lessf, axiom,(( lessf @ (X0)@ (X1)) = 97.13/12.84 ((iii @ (n_ts @ (num @ X0) @ (den @ X1)) @ (n_ts @ (num @ X1) @ (den @ X0)))))). 97.13/12.84 thf('10', plain, 97.13/12.84 (![X1:$i,X0:$i]: 97.13/12.84 ( ( lessf @ X0 @ X1 ) = 97.13/12.84 ( iii @ 97.13/12.84 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 97.13/12.84 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )), 97.13/12.84 define([status(thm)])). 97.13/12.84 thf(zip_derived_cl483, plain, 97.13/12.84 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.13/12.84 (ap @ '#sk2' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.13/12.84 (ap @ '#sk3' @ n_2t)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 97.13/12.84 (lessf @ '#sk2'))))))))), 97.13/12.84 inference('rw', [status(thm)], 97.13/12.84 [zip_derived_cl482, '8', '9', '2', '2', '3', '3', '4', '4', 97.13/12.84 '5', '5', '10'])). 97.13/12.84 thf(zip_derived_cl485, plain, 97.13/12.84 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.13/12.84 (ap @ '#sk2' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.13/12.84 (ap @ '#sk3' @ n_2t)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ (lessf @ '#sk2'))))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl483])). 97.13/12.84 thf(zip_derived_cl486, plain, 97.13/12.84 (~ (((!!) @ (^[Y0 : $i]: 97.13/12.84 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.13/12.84 (ap @ '#sk2' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.13/12.84 (ap @ '#sk3' @ n_2t)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 97.13/12.84 (lessf @ '#sk2'))) @ 97.13/12.84 Y0)))))))), 97.13/12.84 inference('rw_clause', [status(thm)], [zip_derived_cl485, '7'])). 97.13/12.84 thf(zip_derived_cl487, plain, 97.13/12.84 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.13/12.84 ((('#C') @ is_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.13/12.84 ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ 97.13/12.84 (ap @ '#sk2' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk2' @ n_1t) @ 97.13/12.84 (ap @ '#sk3' @ n_2t)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 97.13/12.84 (lessf @ '#sk2')))))))))), 97.13/12.84 inference('comb-normalize', [status(thm)], [zip_derived_cl486])). 97.13/12.84 thf(zip_derived_cl488, plain, 97.13/12.84 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 (((l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) => 97.13/12.84 (((lesseq @ '#sk3' @ '#sk4') => (lessf @ '#sk2' @ '#sk4')))))))), 97.13/12.84 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl487])). 97.13/12.84 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 97.13/12.84 thf('11', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 97.13/12.84 define([status(thm)])). 97.13/12.84 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 97.13/12.84 thf('12', plain, 97.13/12.84 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 97.13/12.84 define([status(thm)])). 97.13/12.84 thf(def_lesseq, axiom,(( lesseq @ (X0)@ (X1)) = 97.13/12.84 ((l_or @ (lessf @ X0 @ X1) @ (n_eq @ X0 @ X1))))). 97.13/12.84 thf('13', plain, 97.13/12.84 (![X1:$i,X0:$i]: 97.13/12.84 ( ( lesseq @ X0 @ X1 ) = 97.13/12.84 ( l_or @ ( lessf @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )), 97.13/12.84 define([status(thm)])). 97.13/12.84 thf(zip_derived_cl489, plain, 97.13/12.84 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 (((l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) => 97.13/12.84 (((imp @ 97.13/12.84 (imp @ 97.13/12.84 (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 97.13/12.84 ($false)) @ 97.13/12.84 (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) => 97.13/12.84 (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))))))), 97.13/12.84 inference('rw', [status(thm)], 97.13/12.84 [zip_derived_cl488, '11', '12', '8', '8', '9', '9', '2', '2', 97.13/12.84 '2', '3', '3', '3', '4', '4', '4', '5', '5', '5', '6', '10', 97.13/12.84 '10', '13'])). 97.13/12.84 thf(zip_derived_cl491, plain, 97.13/12.84 (~ (((l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) => 97.13/12.84 (((imp @ 97.13/12.84 (imp @ 97.13/12.84 (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 97.13/12.84 ($false)) @ 97.13/12.84 (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) => 97.13/12.84 (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl489])). 97.13/12.84 thf(zip_derived_cl493, plain, 97.13/12.84 (~ (((imp @ 97.13/12.84 (imp @ 97.13/12.84 (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 97.13/12.84 ($false)) @ 97.13/12.84 (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)))) => 97.13/12.84 (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl491])). 97.13/12.84 thf(zip_derived_cl494, plain, 97.13/12.84 ( (imp @ 97.13/12.84 (imp @ 97.13/12.84 (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 97.13/12.84 ($false)) @ 97.13/12.84 (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl493])). 97.13/12.84 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 97.13/12.84 thf('14', plain, 97.13/12.84 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 97.13/12.84 inference('rw.lit', [status(esa)], [def_imp])). 97.13/12.84 thf(zip_derived_cl496, plain, 97.13/12.84 ( (((imp @ 97.13/12.84 (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 97.13/12.84 ($false)) => (n_is @ 97.13/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)))))), 97.13/12.84 inference('rw_clause', [status(thm)], [zip_derived_cl494, '14'])). 97.13/12.84 thf(zip_derived_cl497, plain, 97.13/12.84 ((~ (imp @ 97.13/12.84 (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 97.13/12.84 ($false)) 97.13/12.84 | (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl496])). 97.13/12.84 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 97.13/12.84 thf('15', plain, 97.13/12.84 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 97.13/12.84 inference('rw.lit', [status(esa)], [def_imp])). 97.13/12.84 thf(zip_derived_cl498, plain, 97.13/12.84 ((~ (((l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) => 97.13/12.84 ($false))) 97.13/12.84 | (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t))))), 97.13/12.84 inference('rw_clause', [status(thm)], [zip_derived_cl497, '15'])). 97.13/12.84 thf(zip_derived_cl499, plain, 97.13/12.84 ((~ (((~) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))))) 97.13/12.84 | (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t))))), 97.13/12.84 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl498])). 97.13/12.84 thf(zip_derived_cl500, plain, 97.13/12.84 (( (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) 97.13/12.84 | (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk3' @ n_2t))))), 97.13/12.84 inference('simplify nested equalities', [status(thm)], 97.13/12.84 [zip_derived_cl499])). 97.13/12.84 thf(zip_derived_cl490, plain, 97.13/12.84 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl489])). 97.13/12.84 thf(zip_derived_cl8186, plain, 97.13/12.84 ( (is_of @ '#sk4' @ ('#ty_enc5' @ in @ (pair1type @ nat)))), 97.13/12.84 inference('remove_ty_args', [status(thm)], [zip_derived_cl490])). 97.13/12.84 thf(zip_derived_cl484, plain, 97.13/12.84 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl483])). 97.13/12.84 thf(zip_derived_cl8185, plain, 97.13/12.84 ( (is_of @ '#sk3' @ ('#ty_enc5' @ in @ (pair1type @ nat)))), 97.13/12.84 inference('remove_ty_args', [status(thm)], [zip_derived_cl484])). 97.13/12.84 thf(zip_derived_cl478, plain, 97.13/12.84 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl477])). 97.13/12.84 thf(zip_derived_cl8184, plain, 97.13/12.84 ( (is_of @ '#sk2' @ ('#ty_enc5' @ in @ (pair1type @ nat)))), 97.13/12.84 inference('remove_ty_args', [status(thm)], [zip_derived_cl478])). 97.13/12.84 thf(zip_derived_cl492, plain, 97.13/12.84 ( (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl491])). 97.13/12.84 thf(zip_derived_cl495, plain, 97.13/12.84 (~ (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl493])). 97.13/12.84 thf(satz45, axiom, 97.13/12.84 (all_of @ 97.13/12.84 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.13/12.84 ( ^[X0:$i]: 97.13/12.84 ( all_of @ 97.13/12.84 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.13/12.84 ( ^[X1:$i]: 97.13/12.84 ( all_of @ 97.13/12.84 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 97.13/12.84 ( ^[X2:$i]: 97.13/12.84 ( all_of @ 97.13/12.84 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 97.13/12.84 ( ^[X3:$i]: 97.13/12.84 ( ( lessf @ X0 @ X1 ) => 97.13/12.84 ( ( n_eq @ X0 @ X2 ) => 97.13/12.84 ( ( n_eq @ X1 @ X3 ) => ( lessf @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 97.13/12.84 thf(zip_derived_cl224, plain, 97.13/12.84 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 97.13/12.84 (^[Y0 : $i]: 97.13/12.84 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 97.13/12.84 (^[Y1 : $i]: 97.13/12.84 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 97.13/12.84 (^[Y2 : $i]: 97.13/12.84 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 97.13/12.84 (^[Y3 : $i]: 97.13/12.84 (((lessf @ Y0 @ Y1) => 97.13/12.84 (((n_eq @ Y0 @ Y2) => 97.13/12.84 (((n_eq @ Y1 @ Y3) => (lessf @ Y2 @ Y3)))))))))))))))), 97.13/12.84 inference('cnf', [status(esa)], [satz45])). 97.13/12.84 thf(zip_derived_cl225, plain, 97.13/12.84 ( (all_of @ ((('#C') @ in @ frac)) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 97.13/12.84 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.13/12.84 lessf)))))))))))))), 97.13/12.84 inference('lams2combs', [status(thm)], [zip_derived_cl224])). 97.13/12.84 thf(zip_derived_cl2677, plain, 97.13/12.84 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 97.13/12.84 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 97.13/12.84 ((('#C') @ in @ 97.13/12.84 (pair1type @ nat)))))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.13/12.84 lessf)))))))))))))), 97.13/12.84 inference('rw', [status(thm)], [zip_derived_cl225, '0'])). 97.13/12.84 thf(zip_derived_cl2678, plain, 97.13/12.84 ( (((!!) @ (^[Y0 : $i]: 97.13/12.84 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (all_of @ 97.13/12.84 ((('#C') @ in @ 97.13/12.84 (pair1type @ nat)))))) @ 97.13/12.84 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 97.13/12.84 ((('#C') @ in @ 97.13/12.84 (pair1type @ nat)))))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ 97.13/12.84 lessf)))))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ 97.13/12.84 n_eq)))))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ 97.13/12.84 n_eq)))))) @ 97.13/12.84 lessf)))))))))) @ 97.13/12.84 Y0)))))))), 97.13/12.84 inference('rw_clause', [status(thm)], [zip_derived_cl2677, '1'])). 97.13/12.84 thf(zip_derived_cl2679, plain, 97.13/12.84 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.13/12.84 ((('#C') @ is_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat)))))) @ 97.13/12.84 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 97.13/12.84 ((('#C') @ in @ 97.13/12.84 (pair1type @ nat)))))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.13/12.84 lessf))))))))))))))))), 97.13/12.84 inference('comb-normalize', [status(thm)], [zip_derived_cl2678])). 97.13/12.84 thf(zip_derived_cl2680, plain, 97.13/12.84 (![X2 : $i]: 97.13/12.84 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ (=>) @ (lessf @ X2))))))) @ 97.13/12.84 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ (=>) @ (n_eq @ X2))))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.13/12.84 lessf)))))))))))))), 97.13/12.84 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2679])). 97.13/12.84 thf(zip_derived_cl2681, plain, 97.13/12.84 (![X2 : $i]: 97.13/12.84 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ (=>) @ (lessf @ X2))))))) @ 97.13/12.84 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ (=>) @ (n_eq @ X2))))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 97.13/12.84 lessf))))))))))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2680])). 97.13/12.84 thf(zip_derived_cl2682, plain, 97.13/12.84 (![X0 : $i]: 97.13/12.84 ( (((!!) @ (^[Y0 : $i]: 97.13/12.84 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 ((('#B') @ (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (all_of @ 97.13/12.84 ((('#C') @ in @ 97.13/12.84 (pair1type @ nat)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ (=>) @ (lessf @ X0))))))) @ 97.13/12.84 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ (=>) @ 97.13/12.84 (n_eq @ X0))))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ 97.13/12.84 n_eq)))))) @ 97.13/12.84 lessf)))))))) @ 97.13/12.84 Y0))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('rw_clause', [status(thm)], [zip_derived_cl2681, '1'])). 97.13/12.84 thf(zip_derived_cl2683, plain, 97.13/12.84 (![X0 : $i]: 97.13/12.84 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.13/12.84 ((('#C') @ is_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (all_of @ 97.13/12.84 ((('#C') @ in @ 97.13/12.84 (pair1type @ nat)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ (=>) @ (lessf @ X0))))))) @ 97.13/12.84 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ (=>) @ 97.13/12.84 (n_eq @ X0))))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ 97.13/12.84 n_eq)))))) @ 97.13/12.84 lessf)))))))))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('comb-normalize', [status(thm)], [zip_derived_cl2682])). 97.13/12.84 thf(zip_derived_cl2684, plain, 97.13/12.84 (![X0 : $i, X2 : $i]: 97.13/12.84 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (((=>) @ (lessf @ X0 @ X2))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X0))))) @ 97.13/12.84 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 97.13/12.84 lessf))))))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2683])). 97.13/12.84 thf(zip_derived_cl2685, plain, 97.13/12.84 (![X0 : $i, X2 : $i]: 97.13/12.84 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ 97.13/12.84 (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ 97.13/12.84 (ap @ X2 @ n_2t)))))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X0))))) @ 97.13/12.84 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 97.13/12.84 lessf))))))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('rw', [status(thm)], 97.13/12.84 [zip_derived_cl2684, '8', '9', '2', '2', '3', '3', '4', '4', 97.13/12.84 '5', '5', '10'])). 97.13/12.84 thf(zip_derived_cl2686, plain, 97.13/12.84 (![X0 : $i, X2 : $i]: 97.13/12.84 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ 97.13/12.84 (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ 97.13/12.84 (ap @ X2 @ n_2t)))))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 97.13/12.84 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 97.13/12.84 lessf))))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2685])). 97.13/12.84 thf(zip_derived_cl2687, plain, 97.13/12.84 (![X0 : $i, X1 : $i]: 97.13/12.84 ( (((!!) @ (^[Y0 : $i]: 97.13/12.84 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 ((('#B') @ (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ 97.13/12.84 (ap @ X1 @ n_1t) @ 97.13/12.84 (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ 97.13/12.84 (ap @ X0 @ n_1t) @ 97.13/12.84 (ap @ X1 @ n_2t)))))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 97.13/12.84 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 97.13/12.84 (n_eq @ X1))))) @ 97.13/12.84 lessf)))))) @ 97.13/12.84 Y0))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('rw_clause', [status(thm)], [zip_derived_cl2686, '1'])). 97.13/12.84 thf(zip_derived_cl2688, plain, 97.13/12.84 (![X0 : $i, X1 : $i]: 97.13/12.84 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.13/12.84 ((('#C') @ is_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ 97.13/12.84 (ap @ X1 @ n_1t) @ 97.13/12.84 (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ 97.13/12.84 (ap @ X0 @ n_1t) @ 97.13/12.84 (ap @ X1 @ n_2t)))))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 97.13/12.84 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))))) @ 97.13/12.84 lessf)))))))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('comb-normalize', [status(thm)], [zip_derived_cl2687])). 97.13/12.84 thf(zip_derived_cl2689, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X3 : $i]: 97.13/12.84 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) @ 97.13/12.84 ((('#B') @ (((=>) @ (n_eq @ X0 @ X3))) @ 97.13/12.84 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (lessf @ X3)))))))))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2688])). 97.13/12.84 thf(zip_derived_cl2690, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X3 : $i]: 97.13/12.84 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) @ 97.13/12.84 ((('#B') @ (((=>) @ (n_is @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (lessf @ X3)))))))))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('rw', [status(thm)], 97.13/12.84 [zip_derived_cl2689, '2', '2', '3', '3', '4', '4', '5', '5', 97.13/12.84 '6'])). 97.13/12.84 thf(zip_derived_cl2691, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X3 : $i]: 97.13/12.84 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) @ 97.13/12.84 ((('#B') @ (((=>) @ (n_is @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ 97.13/12.84 (ap @ X3 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X3 @ n_1t) @ 97.13/12.84 (ap @ X0 @ n_2t))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (lessf @ X3)))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2690])). 97.13/12.84 thf(zip_derived_cl2692, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X2 : $i]: 97.13/12.84 ( (((!!) @ (^[Y0 : $i]: 97.13/12.84 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ 97.13/12.84 (ap @ X1 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ 97.13/12.84 (ap @ X0 @ n_2t)))))) @ 97.13/12.84 ((('#B') @ (((=>) @ (n_is @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ 97.13/12.84 (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ 97.13/12.84 (ap @ X1 @ n_2t))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @ 97.13/12.84 (lessf @ X2))))) @ 97.13/12.84 Y0))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('rw_clause', [status(thm)], [zip_derived_cl2691, '1'])). 97.13/12.84 thf(zip_derived_cl2693, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X2 : $i]: 97.13/12.84 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.13/12.84 ((('#C') @ is_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.13/12.84 ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ 97.13/12.84 (ap @ X1 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ 97.13/12.84 (ap @ X0 @ n_2t)))))) @ 97.13/12.84 ((('#B') @ (((=>) @ (n_is @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ 97.13/12.84 (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ 97.13/12.84 (ap @ X1 @ n_2t))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @ 97.13/12.84 (lessf @ X2))))))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('comb-normalize', [status(thm)], [zip_derived_cl2692])). 97.13/12.84 thf(zip_derived_cl2694, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 97.13/12.84 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 (((l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) => 97.13/12.84 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) => 97.13/12.84 (((n_eq @ X0 @ X4) => (lessf @ X2 @ X4))))))))) 97.13/12.84 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2693])). 97.13/12.84 thf(zip_derived_cl2695, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 97.13/12.84 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 (((l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) => 97.13/12.84 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) => 97.13/12.84 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @ 97.13/12.84 nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))))))))))) 97.13/12.84 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('rw', [status(thm)], 97.13/12.84 [zip_derived_cl2694, '8', '9', '2', '2', '2', '3', '3', '3', 97.13/12.84 '4', '4', '4', '5', '5', '5', '6', '10'])). 97.13/12.84 thf(zip_derived_cl2696, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 97.13/12.84 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | (((l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) => 97.13/12.84 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) => 97.13/12.84 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @ 97.13/12.84 nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2695])). 97.13/12.84 thf(zip_derived_cl2697, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 97.13/12.84 (~ (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 97.13/12.84 | (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) => 97.13/12.84 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @ 97.13/12.84 nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))))))) 97.13/12.84 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2696])). 97.13/12.84 thf(zip_derived_cl2698, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 97.13/12.84 (~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) 97.13/12.84 | (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @ 97.13/12.84 nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))))) 97.13/12.84 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2697])). 97.13/12.84 thf(zip_derived_cl2699, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 97.13/12.84 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) 97.13/12.84 | (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))) 97.13/12.84 | ~ (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 97.13/12.84 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2698])). 97.13/12.84 thf(zip_derived_cl8267, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 97.13/12.84 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) 97.13/12.84 | (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))) 97.13/12.84 | ~ (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 97.13/12.84 | ~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.13/12.84 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.13/12.84 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.13/12.84 | ~ (is_of @ X4 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.13/12.84 | ~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))))), 97.13/12.84 inference('remove_ty_args', [status(thm)], [zip_derived_cl2699])). 97.13/12.84 thf(satz50, axiom, 97.13/12.84 (all_of @ 97.13/12.84 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.13/12.84 ( ^[X0:$i]: 97.13/12.84 ( all_of @ 97.13/12.84 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.13/12.84 ( ^[X1:$i]: 97.13/12.84 ( all_of @ 97.13/12.84 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 97.13/12.84 ( ^[X2:$i]: 97.13/12.84 ( ( lessf @ X0 @ X1 ) => 97.13/12.84 ( ( lessf @ X1 @ X2 ) => ( lessf @ X0 @ X2 ) ) ) ) ) ) ) ))). 97.13/12.84 thf(zip_derived_cl16, plain, 97.13/12.84 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 97.13/12.84 (^[Y0 : $i]: 97.13/12.84 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 97.13/12.84 (^[Y1 : $i]: 97.13/12.84 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 97.13/12.84 (^[Y2 : $i]: 97.13/12.84 (((lessf @ Y0 @ Y1) => 97.13/12.84 (((lessf @ Y1 @ Y2) => (lessf @ Y0 @ Y2)))))))))))), 97.13/12.84 inference('cnf', [status(esa)], [satz50])). 97.13/12.84 thf(zip_derived_cl17, plain, 97.13/12.84 ( (all_of @ ((('#C') @ in @ frac)) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 97.13/12.84 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 97.13/12.84 lessf)))))))))), 97.13/12.84 inference('lams2combs', [status(thm)], [zip_derived_cl16])). 97.13/12.84 thf(zip_derived_cl915, plain, 97.13/12.84 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 97.13/12.84 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 97.13/12.84 lessf)))))))))), 97.13/12.84 inference('rw', [status(thm)], [zip_derived_cl17, '0'])). 97.13/12.84 thf(zip_derived_cl916, plain, 97.13/12.84 ( (((!!) @ (^[Y0 : $i]: 97.13/12.84 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (all_of @ 97.13/12.84 ((('#C') @ in @ 97.13/12.84 (pair1type @ nat)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 97.13/12.84 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ 97.13/12.84 lessf)))))) @ 97.13/12.84 lessf)))))) @ 97.13/12.84 Y0)))))))), 97.13/12.84 inference('rw_clause', [status(thm)], [zip_derived_cl915, '1'])). 97.13/12.84 thf(zip_derived_cl917, plain, 97.13/12.84 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.13/12.84 ((('#C') @ is_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ ('#B'))) @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))) @ 97.13/12.84 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ 97.13/12.84 lessf)))))) @ 97.13/12.84 lessf))))))))))))), 97.13/12.84 inference('comb-normalize', [status(thm)], [zip_derived_cl916])). 97.13/12.84 thf(zip_derived_cl918, plain, 97.13/12.84 (![X2 : $i]: 97.13/12.84 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (lessf @ X2))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 97.13/12.84 (lessf @ X2))))))))))), 97.13/12.84 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl917])). 97.13/12.84 thf(zip_derived_cl919, plain, 97.13/12.84 (![X2 : $i]: 97.13/12.84 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (lessf @ X2))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 97.13/12.84 (lessf @ X2)))))))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl918])). 97.13/12.84 thf(zip_derived_cl920, plain, 97.13/12.84 (![X0 : $i]: 97.13/12.84 ( (((!!) @ (^[Y0 : $i]: 97.13/12.84 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 ((('#B') @ (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ (=>) @ (lessf @ X0))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 97.13/12.84 (lessf @ X0))))) @ 97.13/12.84 Y0))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('rw_clause', [status(thm)], [zip_derived_cl919, '1'])). 97.13/12.84 thf(zip_derived_cl921, plain, 97.13/12.84 (![X0 : $i]: 97.13/12.84 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.13/12.84 ((('#C') @ is_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.13/12.84 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.13/12.84 ((('#S') @ ((('#B') @ ('#B') @ 97.13/12.84 ((('#B') @ (=>) @ (lessf @ X0))))) @ 97.13/12.84 ((('#C') @ ((('#B') @ ('#S') @ 97.13/12.84 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 97.13/12.84 (lessf @ X0))))))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('comb-normalize', [status(thm)], [zip_derived_cl920])). 97.13/12.84 thf(zip_derived_cl922, plain, 97.13/12.84 (![X0 : $i, X2 : $i]: 97.13/12.84 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (((=>) @ (lessf @ X0 @ X2))) @ 97.13/12.84 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @ (lessf @ X0)))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl921])). 97.13/12.84 thf(zip_derived_cl923, plain, 97.13/12.84 (![X0 : $i, X2 : $i]: 97.13/12.84 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @ (lessf @ X0)))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('rw', [status(thm)], 97.13/12.84 [zip_derived_cl922, '8', '9', '2', '2', '3', '3', '4', '4', 97.13/12.84 '5', '5', '10'])). 97.13/12.84 thf(zip_derived_cl924, plain, 97.13/12.84 (![X0 : $i, X2 : $i]: 97.13/12.84 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.13/12.84 ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @ (lessf @ X0)))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl923])). 97.13/12.84 thf(zip_derived_cl925, plain, 97.13/12.84 (![X0 : $i, X1 : $i]: 97.13/12.84 ( (((!!) @ (^[Y0 : $i]: 97.13/12.84 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ 97.13/12.84 (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ 97.13/12.84 (ap @ X1 @ n_2t)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X1))) @ 97.13/12.84 (lessf @ X0))) @ 97.13/12.84 Y0))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('rw_clause', [status(thm)], [zip_derived_cl924, '1'])). 97.13/12.84 thf(zip_derived_cl926, plain, 97.13/12.84 (![X0 : $i, X1 : $i]: 97.13/12.84 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.13/12.84 ((('#C') @ is_of @ 97.13/12.84 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.13/12.84 ((('#B') @ (((=>) @ (l_some @ nat @ 97.13/12.84 (diffprop @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ 97.13/12.84 (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ 97.13/12.84 (ap @ X1 @ n_2t)))))) @ 97.13/12.84 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X1))) @ 97.13/12.84 (lessf @ X0))))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('comb-normalize', [status(thm)], [zip_derived_cl925])). 97.13/12.84 thf(zip_derived_cl927, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X3 : $i]: 97.13/12.84 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 (((l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) => 97.13/12.84 (((lessf @ X1 @ X3) => (lessf @ X0 @ X3))))))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl926])). 97.13/12.84 thf(zip_derived_cl928, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X3 : $i]: 97.13/12.84 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.13/12.84 (((l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) => 97.13/12.84 (((l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)))) => 97.13/12.84 (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)))))))))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('rw', [status(thm)], 97.13/12.84 [zip_derived_cl927, '8', '8', '9', '9', '2', '2', '2', '3', 97.13/12.84 '3', '3', '4', '4', '4', '5', '5', '5', '10', '10'])). 97.13/12.84 thf(zip_derived_cl929, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X3 : $i]: 97.13/12.84 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | (((l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) => 97.13/12.84 (((l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)))) => 97.13/12.84 (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)))))))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl928])). 97.13/12.84 thf(zip_derived_cl930, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X3 : $i]: 97.13/12.84 (~ (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) 97.13/12.84 | (((l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)))) => 97.13/12.84 (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)))))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl929])). 97.13/12.84 thf(zip_derived_cl931, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X3 : $i]: 97.13/12.84 (~ (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)))) 97.13/12.84 | (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)))) 97.13/12.84 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.13/12.84 | ~ (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))), 97.13/12.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl930])). 97.13/12.84 thf(zip_derived_cl8201, plain, 97.13/12.84 (![X0 : $i, X1 : $i, X3 : $i]: 97.13/12.84 (~ (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)))) 97.13/12.84 | (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)))) 97.13/12.84 | ~ (is_of @ X3 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.13/12.84 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.13/12.84 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.13/12.84 | ~ (l_some @ nat @ 97.13/12.84 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 97.13/12.84 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))), 97.13/12.84 inference('remove_ty_args', [status(thm)], [zip_derived_cl931])). 97.13/12.84 thf(zip_derived_cl8288, plain, ($false), 97.13/12.84 inference('eprover', [status(thm)], 97.13/12.84 [zip_derived_cl8169, zip_derived_cl500, zip_derived_cl8186, 97.13/12.84 zip_derived_cl8185, zip_derived_cl8184, zip_derived_cl492, 97.13/12.84 zip_derived_cl495, zip_derived_cl8267, zip_derived_cl8201])). 97.13/12.84 97.13/12.84 % SZS output end Refutation 97.13/12.84 97.13/12.84 97.13/12.84 % Terminating... 97.52/12.95 % Runner terminated. 97.52/12.97 % Zipperpin 1.5 exiting 97.52/12.97 EOF