0.02/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.6YRdsufxwQ true 0.14/0.35 % Computer : n008.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 960 0.14/0.35 % WCLimit : 120 0.14/0.35 % DateTime : Tue Aug 9 07:53:24 EDT 2022 0.14/0.35 % CPUTime : 0.14/0.35 % Running portfolio for 960 s 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.35 % Number of cores: 8 0.20/0.36 % Python version: Python 3.6.8 0.20/0.36 % Running in HO mode 0.53/0.65 % Total configuration time : 828 0.53/0.65 % Estimated wc time : 1656 0.53/0.65 % Estimated cpu time (8 cpus) : 207.0 0.53/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.53/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.53/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.53/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.53/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.53/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.53/0.74 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.53/0.75 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 108.97/14.38 % Solved by lams/40_b.comb.sh. 108.97/14.38 % done 60 iterations in 13.544s 108.97/14.38 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 108.97/14.38 % SZS output start Refutation 108.97/14.38 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 108.97/14.38 thf(moref_type, type, moref: $i > $i > $o). 108.97/14.38 thf('#sk3_type', type, '#sk3': $i). 108.97/14.38 thf(d_not_type, type, d_not: $o > $o). 108.97/14.38 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 108.97/14.38 thf(in_type, type, in: $i > $i > $o). 108.97/14.38 thf(den_type, type, den: $i > $i). 108.97/14.38 thf(n_fr_type, type, n_fr: $i > $i > $i). 108.97/14.38 thf(nat_type, type, nat: $i). 108.97/14.38 thf(l_or_type, type, l_or: $o > $o > $o). 108.97/14.38 thf('#sk5_type', type, '#sk5': $i). 108.97/14.38 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 108.97/14.38 thf(frac_type, type, frac: $i). 108.97/14.38 thf(n_ts_type, type, n_ts: $i > $i > $i). 108.97/14.38 thf(imp_type, type, imp: $o > $o > $o). 108.97/14.38 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 108.97/14.38 thf(n_eq_type, type, n_eq: $i > $i > $o). 108.97/14.38 thf('#sk4_type', type, '#sk4': $i). 108.97/14.38 thf('#ty_enc6_type', type, '#ty_enc6': ($i > $i > $o) > $i > $i > $o). 108.97/14.38 thf(n_some_type, type, n_some: ($i > $o) > $o). 108.97/14.38 thf(moreq_type, type, moreq: $i > $i > $o). 108.97/14.38 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o). 108.97/14.38 thf(n_pl_type, type, n_pl: $i > $i > $i). 108.97/14.38 thf(n_pf_type, type, n_pf: $i > $i > $i). 108.97/14.38 thf(num_type, type, num: $i > $i). 108.97/14.38 thf('#sk2_type', type, '#sk2': $i). 108.97/14.38 thf(pair1type_type, type, pair1type: $i > $i). 108.97/14.38 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 108.97/14.38 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 108.97/14.38 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 108.97/14.38 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 108.97/14.38 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 108.97/14.38 thf(satz65b, conjecture, 108.97/14.38 (all_of @ 108.97/14.38 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 108.97/14.38 ( ^[X0:$i]: 108.97/14.38 ( all_of @ 108.97/14.38 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 108.97/14.38 ( ^[X1:$i]: 108.97/14.38 ( all_of @ 108.97/14.38 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 108.97/14.38 ( ^[X2:$i]: 108.97/14.38 ( all_of @ 108.97/14.38 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 108.97/14.38 ( ^[X3:$i]: 108.97/14.38 ( ( moref @ X0 @ X1 ) => 108.97/14.38 ( ( moreq @ X2 @ X3 ) => 108.97/14.38 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 108.97/14.38 thf(zf_stmt_0, negated_conjecture, 108.97/14.38 (~( all_of @ 108.97/14.38 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 108.97/14.38 ( ^[X0:$i]: 108.97/14.38 ( all_of @ 108.97/14.38 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 108.97/14.38 ( ^[X1:$i]: 108.97/14.38 ( all_of @ 108.97/14.38 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 108.97/14.38 ( ^[X2:$i]: 108.97/14.38 ( all_of @ 108.97/14.38 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 108.97/14.38 ( ^[X3:$i]: 108.97/14.38 ( ( moref @ X0 @ X1 ) => 108.97/14.38 ( ( moreq @ X2 @ X3 ) => 108.97/14.38 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) )), 108.97/14.38 inference('cnf.neg', [status(esa)], [satz65b])). 108.97/14.38 thf(zip_derived_cl358, plain, 108.97/14.38 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 108.97/14.38 (^[Y0 : $i]: 108.97/14.38 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 108.97/14.38 (^[Y1 : $i]: 108.97/14.38 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 108.97/14.38 (^[Y2 : $i]: 108.97/14.38 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 108.97/14.38 (^[Y3 : $i]: 108.97/14.38 (((moref @ Y0 @ Y1) => 108.97/14.38 (((moreq @ Y2 @ Y3) => (moref @ (n_pf @ Y0 @ Y2) @ 108.97/14.38 (n_pf @ Y1 @ Y3))))))))))))))), 108.97/14.38 inference('cnf', [status(esa)], [zf_stmt_0])). 108.97/14.38 thf(zip_derived_cl359, plain, 108.97/14.38 (~ (all_of @ ((('#C') @ in @ frac)) @ 108.97/14.38 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 108.97/14.38 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 108.97/14.38 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.38 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.38 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @ 108.97/14.38 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.38 ((('#B') @ ((('#B') @ (=>))) @ 108.97/14.38 moreq)))))))) @ 108.97/14.38 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ ('#C') @ 108.97/14.38 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.38 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @ 108.97/14.38 n_pf)))))))))))))), 108.97/14.38 inference('lams2combs', [status(thm)], [zip_derived_cl358])). 108.97/14.38 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))). 108.97/14.38 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])). 108.97/14.38 thf(zip_derived_cl1512, plain, 108.97/14.38 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.38 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 108.97/14.38 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 108.97/14.38 ((('#C') @ in @ 108.97/14.38 (pair1type @ nat)))))))) @ 108.97/14.38 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.38 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.38 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @ 108.97/14.38 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.38 ((('#B') @ ((('#B') @ (=>))) @ 108.97/14.38 moreq)))))))) @ 108.97/14.38 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ ('#C') @ 108.97/14.38 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.38 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @ 108.97/14.38 n_pf)))))))))))))), 108.97/14.38 inference('rw', [status(thm)], [zip_derived_cl359, '0'])). 108.97/14.38 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 108.97/14.38 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 108.97/14.38 thf('1', plain, 108.97/14.38 (![X0:( $i > $o ),X1:( $i > $o )]: 108.97/14.38 ( ( ~( all_of @ X0 @ X1 ) ) <=> 108.97/14.38 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 108.97/14.38 inference('rw.lit', [status(esa)], [def_all_of])). 108.97/14.38 thf(zip_derived_cl1513, plain, 108.97/14.38 (~ (((!!) @ (^[Y0 : $i]: 108.97/14.38 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.38 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.38 ((('#C') @ in @ 108.97/14.38 (pair1type @ nat)))))) @ 108.97/14.38 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 108.97/14.38 ((('#C') @ in @ 108.97/14.38 (pair1type @ nat)))))))) @ 108.97/14.38 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.38 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.38 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (=>))) @ 108.97/14.38 moref)))))))) @ 108.97/14.38 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 108.97/14.38 '#S') @ 108.97/14.38 ((('#B') @ ( 108.97/14.38 (('#B') @ ( 108.97/14.38 =>))) @ 108.97/14.38 moreq)))))))) @ 108.97/14.38 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ ('#C') @ 108.97/14.38 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.38 ((('#B') @ ((('#B') @ moref)) @ 108.97/14.38 n_pf)))))))) @ 108.97/14.38 n_pf)))))))))) @ 108.97/14.38 Y0)))))))), 108.97/14.38 inference('rw_clause', [status(thm)], [zip_derived_cl1512, '1'])). 108.97/14.38 thf(zip_derived_cl1514, plain, 108.97/14.38 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 108.97/14.38 ((('#C') @ is_of @ 108.97/14.38 ((('#C') @ in @ (pair1type @ nat))))))) @ 108.97/14.38 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.38 ((('#C') @ in @ (pair1type @ nat)))))) @ 108.97/14.38 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 108.97/14.38 ((('#C') @ in @ 108.97/14.38 (pair1type @ nat)))))))) @ 108.97/14.38 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.38 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.38 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @ 108.97/14.38 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 108.97/14.38 '#S') @ 108.97/14.38 ((('#B') @ ( 108.97/14.38 (('#B') @ (=>))) @ 108.97/14.38 moreq)))))))) @ 108.97/14.38 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ ('#C') @ 108.97/14.38 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.38 ((('#B') @ ((('#B') @ moref)) @ 108.97/14.38 n_pf)))))))) @ 108.97/14.38 n_pf))))))))))))))))), 108.97/14.38 inference('comb-normalize', [status(thm)], [zip_derived_cl1513])). 108.97/14.38 thf(zip_derived_cl1515, plain, 108.97/14.38 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 108.97/14.38 ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.38 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.38 ((('#C') @ in @ (pair1type @ nat)))))) @ 108.97/14.38 ((('#S') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ (=>) @ (moref @ '#sk2'))))))) @ 108.97/14.38 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.38 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 108.97/14.38 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ moref @ (n_pf @ '#sk2'))))))) @ 108.97/14.38 n_pf)))))))))))))), 108.97/14.38 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1514])). 108.97/14.38 thf(zip_derived_cl1517, plain, 108.97/14.38 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.38 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 108.97/14.38 ((('#S') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ (=>) @ (moref @ '#sk2'))))))) @ 108.97/14.38 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.38 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 108.97/14.38 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ moref @ (n_pf @ '#sk2'))))))) @ 108.97/14.38 n_pf)))))))))))), 108.97/14.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1515])). 108.97/14.38 thf(zip_derived_cl1518, plain, 108.97/14.38 (~ (((!!) @ (^[Y0 : $i]: 108.97/14.38 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.38 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.38 ((('#C') @ in @ 108.97/14.38 (pair1type @ nat)))))) @ 108.97/14.38 ((('#S') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ (=>) @ (moref @ '#sk2'))))))) @ 108.97/14.38 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.38 ((('#B') @ ((('#B') @ (=>))) @ 108.97/14.38 moreq)))))) @ 108.97/14.38 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ moref @ 108.97/14.38 (n_pf @ '#sk2'))))))) @ 108.97/14.38 n_pf)))))))) @ 108.97/14.38 Y0)))))))), 108.97/14.38 inference('rw_clause', [status(thm)], [zip_derived_cl1517, '1'])). 108.97/14.38 thf(zip_derived_cl1519, plain, 108.97/14.38 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 108.97/14.38 ((('#C') @ is_of @ 108.97/14.38 ((('#C') @ in @ (pair1type @ nat))))))) @ 108.97/14.38 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.38 ((('#C') @ in @ (pair1type @ nat)))))) @ 108.97/14.38 ((('#S') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ (=>) @ (moref @ '#sk2'))))))) @ 108.97/14.38 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.38 ((('#B') @ ((('#B') @ (=>))) @ 108.97/14.38 moreq)))))) @ 108.97/14.38 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ moref @ 108.97/14.38 (n_pf @ '#sk2'))))))) @ 108.97/14.38 n_pf))))))))))))))), 108.97/14.38 inference('comb-normalize', [status(thm)], [zip_derived_cl1518])). 108.97/14.38 thf(zip_derived_cl1520, plain, 108.97/14.38 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 108.97/14.38 ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.38 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (((=>) @ (moref @ '#sk2' @ '#sk3'))))) @ 108.97/14.38 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.38 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 108.97/14.38 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @ 108.97/14.38 (n_pf @ '#sk3'))))))))))))), 108.97/14.38 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1519])). 108.97/14.38 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))). 108.97/14.38 thf('2', plain, 108.97/14.38 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )), 108.97/14.38 define([status(thm)])). 108.97/14.38 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) = 108.97/14.38 ((n_some @ (diffprop @ X0 @ X1))))). 108.97/14.38 thf('3', plain, 108.97/14.38 (![X1:$i,X0:$i]: 108.97/14.38 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 108.97/14.38 define([status(thm)])). 108.97/14.38 thf(def_moref, axiom,(( moref @ (X0)@ (X1)) = 108.97/14.38 ((d_29_ii @ (n_ts @ (num @ X0) @ (den @ X1)) @ 108.97/14.38 (n_ts @ (num @ X1) @ (den @ X0)))))). 108.97/14.38 thf('4', plain, 108.97/14.38 (![X1:$i,X0:$i]: 108.97/14.38 ( ( moref @ X0 @ X1 ) = 108.97/14.38 ( d_29_ii @ 108.97/14.38 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 108.97/14.38 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )), 108.97/14.38 define([status(thm)])). 108.97/14.38 thf(zip_derived_cl1521, plain, 108.97/14.38 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 108.97/14.38 ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.38 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.38 (diffprop @ 108.97/14.38 (n_ts @ (num @ '#sk2') @ 108.97/14.38 (den @ '#sk3')) @ 108.97/14.38 (n_ts @ (num @ '#sk3') @ 108.97/14.38 (den @ '#sk2')))))))) @ 108.97/14.38 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.38 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 108.97/14.38 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @ 108.97/14.38 (n_pf @ '#sk3'))))))))))))), 108.97/14.38 inference('rw', [status(thm)], [zip_derived_cl1520, '2', '3', '4'])). 108.97/14.38 thf(zip_derived_cl1523, plain, 108.97/14.38 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.38 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.38 (diffprop @ 108.97/14.38 (n_ts @ (num @ '#sk2') @ 108.97/14.38 (den @ '#sk3')) @ 108.97/14.38 (n_ts @ (num @ '#sk3') @ 108.97/14.38 (den @ '#sk2')))))))) @ 108.97/14.38 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.38 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 108.97/14.38 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @ 108.97/14.38 (n_pf @ '#sk3'))))))))))), 108.97/14.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1521])). 108.97/14.38 thf(zip_derived_cl1524, plain, 108.97/14.38 (~ (((!!) @ (^[Y0 : $i]: 108.97/14.38 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.38 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.38 (diffprop @ 108.97/14.38 (n_ts @ 108.97/14.38 (num @ '#sk2') @ 108.97/14.38 (den @ '#sk3')) @ 108.97/14.38 (n_ts @ 108.97/14.38 (num @ '#sk3') @ 108.97/14.38 (den @ '#sk2')))))))) @ 108.97/14.38 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.38 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 108.97/14.38 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @ 108.97/14.38 (n_pf @ '#sk3'))))))) @ 108.97/14.38 Y0)))))))), 108.97/14.38 inference('rw_clause', [status(thm)], [zip_derived_cl1523, '1'])). 108.97/14.38 thf(zip_derived_cl1525, plain, 108.97/14.38 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 108.97/14.38 ((('#C') @ is_of @ 108.97/14.38 ((('#C') @ in @ (pair1type @ nat))))))) @ 108.97/14.38 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.38 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.38 (diffprop @ 108.97/14.38 (n_ts @ 108.97/14.38 (num @ '#sk2') @ 108.97/14.38 (den @ '#sk3')) @ 108.97/14.38 (n_ts @ 108.97/14.38 (num @ '#sk3') @ 108.97/14.38 (den @ '#sk2')))))))) @ 108.97/14.38 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.38 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 108.97/14.38 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.38 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @ 108.97/14.38 (n_pf @ '#sk3')))))))))))))), 108.97/14.38 inference('comb-normalize', [status(thm)], [zip_derived_cl1524])). 108.97/14.38 thf(zip_derived_cl1526, plain, 108.97/14.38 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 108.97/14.38 ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.38 ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.38 (diffprop @ 108.97/14.38 (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 108.97/14.38 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))))) @ 108.97/14.38 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @ 108.97/14.38 ((('#B') @ (moref @ (n_pf @ '#sk2' @ '#sk4')) @ (n_pf @ '#sk3'))))))))))), 108.97/14.38 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1525])). 108.97/14.39 thf(def_n_pf, axiom,(( n_pf @ (X0)@ (X1)) = 108.97/14.39 ((n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X0) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X0))) @ 108.97/14.39 (n_ts @ (den @ X0) @ (den @ X1)))))). 108.97/14.39 thf('5', plain, 108.97/14.39 (![X1:$i,X0:$i]: 108.97/14.39 ( ( n_pf @ X0 @ X1 ) = 108.97/14.39 ( n_fr @ 108.97/14.39 ( n_pl @ 108.97/14.39 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 108.97/14.39 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) @ 108.97/14.39 ( n_ts @ ( den @ X0 ) @ ( den @ X1 ) ) ) )), 108.97/14.39 define([status(thm)])). 108.97/14.39 thf(zip_derived_cl1527, plain, 108.97/14.39 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 108.97/14.39 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @ 108.97/14.39 ((('#B') @ (moref @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 108.97/14.39 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 108.97/14.39 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 108.97/14.39 (n_pf @ '#sk3'))))))))))), 108.97/14.39 inference('rw', [status(thm)], [zip_derived_cl1526, '5'])). 108.97/14.39 thf(zip_derived_cl1529, plain, 108.97/14.39 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 108.97/14.39 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @ 108.97/14.39 ((('#B') @ (moref @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 108.97/14.39 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 108.97/14.39 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 108.97/14.39 (n_pf @ '#sk3'))))))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1527])). 108.97/14.39 thf(zip_derived_cl1530, plain, 108.97/14.39 (~ (((!!) @ (^[Y0 : $i]: 108.97/14.39 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.39 ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ (num @ '#sk2') @ 108.97/14.39 (den @ '#sk3')) @ 108.97/14.39 (n_ts @ (num @ '#sk3') @ 108.97/14.39 (den @ '#sk2')))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @ 108.97/14.39 ((('#B') @ (moref @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ 108.97/14.39 (n_ts @ (num @ '#sk2') @ 108.97/14.39 (den @ '#sk4')) @ 108.97/14.39 (n_ts @ (num @ '#sk4') @ 108.97/14.39 (den @ '#sk2'))) @ 108.97/14.39 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 108.97/14.39 (n_pf @ '#sk3'))))) @ 108.97/14.39 Y0)))))))), 108.97/14.39 inference('rw_clause', [status(thm)], [zip_derived_cl1529, '1'])). 108.97/14.39 thf(zip_derived_cl1531, plain, 108.97/14.39 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 108.97/14.39 ((('#C') @ is_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))))))) @ 108.97/14.39 ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ (num @ '#sk2') @ 108.97/14.39 (den @ '#sk3')) @ 108.97/14.39 (n_ts @ (num @ '#sk3') @ 108.97/14.39 (den @ '#sk2')))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @ 108.97/14.39 ((('#B') @ (moref @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ 108.97/14.39 (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 108.97/14.39 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 108.97/14.39 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 108.97/14.39 (n_pf @ '#sk3')))))))))))), 108.97/14.39 inference('comb-normalize', [status(thm)], [zip_derived_cl1530])). 108.97/14.39 thf(zip_derived_cl1532, plain, 108.97/14.39 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.39 (((l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 108.97/14.39 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) => 108.97/14.39 (((moreq @ '#sk4' @ '#sk5') => (moref @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 108.97/14.39 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 108.97/14.39 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 108.97/14.39 (n_pf @ '#sk3' @ '#sk5'))))))))), 108.97/14.39 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1531])). 108.97/14.39 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 108.97/14.39 thf('6', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 108.97/14.39 define([status(thm)])). 108.97/14.39 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 108.97/14.39 thf('7', plain, 108.97/14.39 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 108.97/14.39 define([status(thm)])). 108.97/14.39 thf(def_moreq, axiom,(( moreq @ (X0)@ (X1)) = 108.97/14.39 ((l_or @ (moref @ X0 @ X1) @ (n_eq @ X0 @ X1))))). 108.97/14.39 thf('8', plain, 108.97/14.39 (![X1:$i,X0:$i]: 108.97/14.39 ( ( moreq @ X0 @ X1 ) = 108.97/14.39 ( l_or @ ( moref @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )), 108.97/14.39 define([status(thm)])). 108.97/14.39 thf(zip_derived_cl1533, plain, 108.97/14.39 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.39 (((l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 108.97/14.39 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) => 108.97/14.39 (((imp @ 108.97/14.39 (imp @ 108.97/14.39 (l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) @ 108.97/14.39 ($false)) @ 108.97/14.39 (n_eq @ '#sk4' @ '#sk5')) => (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 108.97/14.39 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 108.97/14.39 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 108.97/14.39 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))) @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 108.97/14.39 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 108.97/14.39 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 108.97/14.39 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))))))))))))), 108.97/14.39 inference('rw', [status(thm)], 108.97/14.39 [zip_derived_cl1532, '6', '7', '2', '2', '3', '3', '4', '4', 108.97/14.39 '8', '5'])). 108.97/14.39 thf(zip_derived_cl1535, plain, 108.97/14.39 (~ (((l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 108.97/14.39 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) => 108.97/14.39 (((imp @ 108.97/14.39 (imp @ 108.97/14.39 (l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) @ 108.97/14.39 ($false)) @ 108.97/14.39 (n_eq @ '#sk4' @ '#sk5')) => (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 108.97/14.39 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 108.97/14.39 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 108.97/14.39 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))) @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 108.97/14.39 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 108.97/14.39 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 108.97/14.39 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))))))))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1533])). 108.97/14.39 thf(zip_derived_cl1537, plain, 108.97/14.39 (~ (((imp @ 108.97/14.39 (imp @ 108.97/14.39 (l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) @ 108.97/14.39 ($false)) @ 108.97/14.39 (n_eq @ '#sk4' @ '#sk5')) => (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 108.97/14.39 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 108.97/14.39 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 108.97/14.39 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))) @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 108.97/14.39 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 108.97/14.39 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 108.97/14.39 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))))))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1535])). 108.97/14.39 thf(zip_derived_cl1538, plain, 108.97/14.39 ( (imp @ 108.97/14.39 (imp @ 108.97/14.39 (l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) @ 108.97/14.39 ($false)) @ 108.97/14.39 (n_eq @ '#sk4' @ '#sk5'))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1537])). 108.97/14.39 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 108.97/14.39 thf('9', plain, 108.97/14.39 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 108.97/14.39 inference('rw.lit', [status(esa)], [def_imp])). 108.97/14.39 thf(zip_derived_cl1540, plain, 108.97/14.39 ( (((imp @ 108.97/14.39 (l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) @ 108.97/14.39 ($false)) => (n_eq @ '#sk4' @ '#sk5')))), 108.97/14.39 inference('rw_clause', [status(thm)], [zip_derived_cl1538, '9'])). 108.97/14.39 thf(zip_derived_cl1541, plain, 108.97/14.39 ((~ (imp @ 108.97/14.39 (l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) @ 108.97/14.39 ($false)) 108.97/14.39 | (n_eq @ '#sk4' @ '#sk5'))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1540])). 108.97/14.39 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 108.97/14.39 thf('10', plain, 108.97/14.39 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 108.97/14.39 inference('rw.lit', [status(esa)], [def_imp])). 108.97/14.39 thf(zip_derived_cl1542, plain, 108.97/14.39 ((~ (((l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) => 108.97/14.39 ($false))) 108.97/14.39 | (n_eq @ '#sk4' @ '#sk5'))), 108.97/14.39 inference('rw_clause', [status(thm)], [zip_derived_cl1541, '10'])). 108.97/14.39 thf(zip_derived_cl1543, plain, 108.97/14.39 ((~ (((~) @ (l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))))) 108.97/14.39 | (n_eq @ '#sk4' @ '#sk5'))), 108.97/14.39 inference('simplify boolean subterms', [status(thm)], 108.97/14.39 [zip_derived_cl1542])). 108.97/14.39 thf(zip_derived_cl1544, plain, 108.97/14.39 (( (l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) 108.97/14.39 | (n_eq @ '#sk4' @ '#sk5'))), 108.97/14.39 inference('simplify nested equalities', [status(thm)], 108.97/14.39 [zip_derived_cl1543])). 108.97/14.39 thf(zip_derived_cl1516, plain, 108.97/14.39 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1515])). 108.97/14.39 thf(zip_derived_cl4021, plain, 108.97/14.39 ( (is_of @ '#sk2' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 108.97/14.39 inference('remove_ty_args', [status(thm)], [zip_derived_cl1516])). 108.97/14.39 thf(zip_derived_cl1522, plain, 108.97/14.39 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1521])). 108.97/14.39 thf(zip_derived_cl4022, plain, 108.97/14.39 ( (is_of @ '#sk3' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 108.97/14.39 inference('remove_ty_args', [status(thm)], [zip_derived_cl1522])). 108.97/14.39 thf(zip_derived_cl1528, plain, 108.97/14.39 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1527])). 108.97/14.39 thf(zip_derived_cl4023, plain, 108.97/14.39 ( (is_of @ '#sk4' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 108.97/14.39 inference('remove_ty_args', [status(thm)], [zip_derived_cl1528])). 108.97/14.39 thf(zip_derived_cl1534, plain, 108.97/14.39 ( (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1533])). 108.97/14.39 thf(zip_derived_cl4024, plain, 108.97/14.39 ( (is_of @ '#sk5' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 108.97/14.39 inference('remove_ty_args', [status(thm)], [zip_derived_cl1534])). 108.97/14.39 thf(zip_derived_cl1536, plain, 108.97/14.39 ( (l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 108.97/14.39 (n_ts @ (num @ '#sk3') @ (den @ '#sk2'))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1535])). 108.97/14.39 thf(satz64, axiom, 108.97/14.39 (all_of @ 108.97/14.39 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 108.97/14.39 ( ^[X0:$i]: 108.97/14.39 ( all_of @ 108.97/14.39 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 108.97/14.39 ( ^[X1:$i]: 108.97/14.39 ( all_of @ 108.97/14.39 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 108.97/14.39 ( ^[X2:$i]: 108.97/14.39 ( all_of @ 108.97/14.39 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 108.97/14.39 ( ^[X3:$i]: 108.97/14.39 ( ( moref @ X0 @ X1 ) => 108.97/14.39 ( ( moref @ X2 @ X3 ) => 108.97/14.39 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 108.97/14.39 thf(zip_derived_cl64, plain, 108.97/14.39 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 108.97/14.39 (^[Y0 : $i]: 108.97/14.39 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 108.97/14.39 (^[Y1 : $i]: 108.97/14.39 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 108.97/14.39 (^[Y2 : $i]: 108.97/14.39 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 108.97/14.39 (^[Y3 : $i]: 108.97/14.39 (((moref @ Y0 @ Y1) => 108.97/14.39 (((moref @ Y2 @ Y3) => (moref @ (n_pf @ Y0 @ Y2) @ 108.97/14.39 (n_pf @ Y1 @ Y3))))))))))))))), 108.97/14.39 inference('cnf', [status(esa)], [satz64])). 108.97/14.39 thf(zip_derived_cl65, plain, 108.97/14.39 ( (all_of @ ((('#C') @ in @ frac)) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ 108.97/14.39 moref)))))))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ ('#C') @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @ 108.97/14.39 n_pf)))))))))))))), 108.97/14.39 inference('lams2combs', [status(thm)], [zip_derived_cl64])). 108.97/14.39 thf(zip_derived_cl2578, plain, 108.97/14.39 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ 108.97/14.39 (pair1type @ nat)))))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ 108.97/14.39 moref)))))))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ ('#C') @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @ 108.97/14.39 n_pf)))))))))))))), 108.97/14.39 inference('rw', [status(thm)], [zip_derived_cl65, '0'])). 108.97/14.39 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 108.97/14.39 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 108.97/14.39 thf('11', plain, 108.97/14.39 (![X0:( $i > $o ),X1:( $i > $o )]: 108.97/14.39 ( ( all_of @ X0 @ X1 ) <=> 108.97/14.39 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 108.97/14.39 inference('rw.lit', [status(esa)], [def_all_of])). 108.97/14.39 thf(zip_derived_cl2579, plain, 108.97/14.39 ( (((!!) @ (^[Y0 : $i]: 108.97/14.39 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ 108.97/14.39 (pair1type @ nat)))))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ 108.97/14.39 (pair1type @ nat)))))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ 108.97/14.39 moref)))))))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 108.97/14.39 '#S') @ 108.97/14.39 ((('#B') @ ( 108.97/14.39 (('#B') @ ( 108.97/14.39 =>))) @ 108.97/14.39 moref)))))))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ ('#C') @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ moref)) @ 108.97/14.39 n_pf)))))))) @ 108.97/14.39 n_pf)))))))))) @ 108.97/14.39 Y0)))))))), 108.97/14.39 inference('rw_clause', [status(thm)], [zip_derived_cl2578, '11'])). 108.97/14.39 thf(zip_derived_cl2580, plain, 108.97/14.39 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 108.97/14.39 ((('#C') @ is_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))))))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat)))))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ 108.97/14.39 (pair1type @ nat)))))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 108.97/14.39 '#S') @ 108.97/14.39 ((('#B') @ ( 108.97/14.39 (('#B') @ (=>))) @ 108.97/14.39 moref)))))))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ ('#C') @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ moref)) @ 108.97/14.39 n_pf)))))))) @ 108.97/14.39 n_pf))))))))))))))))), 108.97/14.39 inference('comb-normalize', [status(thm)], [zip_derived_cl2579])). 108.97/14.39 thf(zip_derived_cl2581, plain, 108.97/14.39 (![X2 : $i]: 108.97/14.39 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat)))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ (=>) @ (moref @ X2))))))) @ 108.97/14.39 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 108.97/14.39 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ (n_pf @ X2))))))) @ 108.97/14.39 n_pf)))))))))))))), 108.97/14.39 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2580])). 108.97/14.39 thf(zip_derived_cl2582, plain, 108.97/14.39 (![X2 : $i]: 108.97/14.39 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat)))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ (=>) @ (moref @ X2))))))) @ 108.97/14.39 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ 108.97/14.39 moref)))))) @ 108.97/14.39 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ (n_pf @ X2))))))) @ 108.97/14.39 n_pf))))))))))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2581])). 108.97/14.39 thf(zip_derived_cl2583, plain, 108.97/14.39 (![X0 : $i]: 108.97/14.39 ( (((!!) @ (^[Y0 : $i]: 108.97/14.39 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.39 ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ 108.97/14.39 (pair1type @ nat)))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ (=>) @ (moref @ X0))))))) @ 108.97/14.39 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ ( 108.97/14.39 =>))) @ 108.97/14.39 moref)))))) @ 108.97/14.39 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ 108.97/14.39 (n_pf @ X0))))))) @ 108.97/14.39 n_pf)))))))) @ 108.97/14.39 Y0))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('rw_clause', [status(thm)], [zip_derived_cl2582, '11'])). 108.97/14.39 thf(zip_derived_cl2584, plain, 108.97/14.39 (![X0 : $i]: 108.97/14.39 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 108.97/14.39 ((('#C') @ is_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))))))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ 108.97/14.39 (pair1type @ nat)))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ (=>) @ (moref @ X0))))))) @ 108.97/14.39 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ 108.97/14.39 moref)))))) @ 108.97/14.39 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ 108.97/14.39 (n_pf @ X0))))))) @ 108.97/14.39 n_pf)))))))))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('comb-normalize', [status(thm)], [zip_derived_cl2583])). 108.97/14.39 thf(zip_derived_cl2585, plain, 108.97/14.39 (![X0 : $i, X2 : $i]: 108.97/14.39 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X2))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ (n_pf @ X0))))) @ 108.97/14.39 (n_pf @ X2)))))))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2584])). 108.97/14.39 thf(zip_derived_cl2586, plain, 108.97/14.39 (![X0 : $i, X2 : $i]: 108.97/14.39 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X2)) @ 108.97/14.39 (n_ts @ (num @ X2) @ (den @ X0)))))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ (n_pf @ X0))))) @ 108.97/14.39 (n_pf @ X2)))))))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('rw', [status(thm)], [zip_derived_cl2585, '2', '3', '4'])). 108.97/14.39 thf(zip_derived_cl2587, plain, 108.97/14.39 (![X0 : $i, X2 : $i]: 108.97/14.39 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ (num @ X0) @ 108.97/14.39 (den @ X2)) @ 108.97/14.39 (n_ts @ (num @ X2) @ 108.97/14.39 (den @ X0)))))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ (n_pf @ X0))))) @ 108.97/14.39 (n_pf @ X2)))))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2586])). 108.97/14.39 thf(zip_derived_cl2588, plain, 108.97/14.39 (![X0 : $i, X1 : $i]: 108.97/14.39 ( (((!!) @ (^[Y0 : $i]: 108.97/14.39 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.39 ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ X0) @ 108.97/14.39 (den @ X1)) @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ X1) @ 108.97/14.39 (den @ X0)))))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ (n_pf @ X0))))) @ 108.97/14.39 (n_pf @ X1))))))) @ 108.97/14.39 Y0))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('rw_clause', [status(thm)], [zip_derived_cl2587, '11'])). 108.97/14.39 thf(zip_derived_cl2589, plain, 108.97/14.39 (![X0 : $i, X1 : $i]: 108.97/14.39 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 108.97/14.39 ((('#C') @ is_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))))))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ (num @ X0) @ 108.97/14.39 (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ 108.97/14.39 (den @ X0)))))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ (n_pf @ X0))))) @ 108.97/14.39 (n_pf @ X1))))))))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('comb-normalize', [status(thm)], [zip_derived_cl2588])). 108.97/14.39 thf(zip_derived_cl2590, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X3 : $i]: 108.97/14.39 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X0)))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 108.97/14.39 ((('#B') @ (moref @ (n_pf @ X0 @ X3)) @ (n_pf @ X1)))))))))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2589])). 108.97/14.39 thf(zip_derived_cl2591, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X3 : $i]: 108.97/14.39 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X0)))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 108.97/14.39 ((('#B') @ (moref @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 108.97/14.39 (n_ts @ (num @ X3) @ (den @ X0))) @ 108.97/14.39 (n_ts @ (den @ X0) @ (den @ X3)))) @ 108.97/14.39 (n_pf @ X1)))))))))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('rw', [status(thm)], [zip_derived_cl2590, '5'])). 108.97/14.39 thf(zip_derived_cl2592, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X3 : $i]: 108.97/14.39 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X0)))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 108.97/14.39 ((('#B') @ (moref @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 108.97/14.39 (n_ts @ (num @ X3) @ (den @ X0))) @ 108.97/14.39 (n_ts @ (den @ X0) @ (den @ X3)))) @ 108.97/14.39 (n_pf @ X1)))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2591])). 108.97/14.39 thf(zip_derived_cl2593, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X2 : $i]: 108.97/14.39 ( (((!!) @ (^[Y0 : $i]: 108.97/14.39 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.39 ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X1)))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 108.97/14.39 ((('#B') @ (moref @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X2)) @ 108.97/14.39 (n_ts @ (num @ X2) @ (den @ X1))) @ 108.97/14.39 (n_ts @ (den @ X1) @ (den @ X2)))) @ 108.97/14.39 (n_pf @ X0))))) @ 108.97/14.39 Y0))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('rw_clause', [status(thm)], [zip_derived_cl2592, '11'])). 108.97/14.39 thf(zip_derived_cl2594, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X2 : $i]: 108.97/14.39 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 108.97/14.39 ((('#C') @ is_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))))))) @ 108.97/14.39 ((('#B') @ (((=>) @ (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X1)))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 108.97/14.39 ((('#B') @ (moref @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X2)) @ 108.97/14.39 (n_ts @ (num @ X2) @ (den @ X1))) @ 108.97/14.39 (n_ts @ (den @ X1) @ (den @ X2)))) @ 108.97/14.39 (n_pf @ X0))))))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('comb-normalize', [status(thm)], [zip_derived_cl2593])). 108.97/14.39 thf(zip_derived_cl2595, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 108.97/14.39 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.39 (((l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X1)))) => 108.97/14.39 (((moref @ X2 @ X4) => (moref @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 108.97/14.39 (n_ts @ (num @ X2) @ (den @ X1))) @ 108.97/14.39 (n_ts @ (den @ X1) @ (den @ X2))) @ 108.97/14.39 (n_pf @ X0 @ X4)))))))) 108.97/14.39 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2594])). 108.97/14.39 thf(zip_derived_cl2596, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 108.97/14.39 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.39 (((l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X1)))) => 108.97/14.39 (((l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X2)))) => 108.97/14.39 (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 108.97/14.39 (n_ts @ (num @ X2) @ (den @ X1))) @ 108.97/14.39 (n_ts @ (den @ X1) @ (den @ X2)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X0))) @ 108.97/14.39 (n_ts @ (den @ X0) @ (den @ X4))))) @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X0))) @ 108.97/14.39 (n_ts @ (den @ X0) @ (den @ X4)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 108.97/14.39 (n_ts @ (num @ X2) @ (den @ X1))) @ 108.97/14.39 (n_ts @ (den @ X1) @ (den @ X2))))))))))))) 108.97/14.39 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('rw', [status(thm)], 108.97/14.39 [zip_derived_cl2595, '2', '2', '3', '3', '4', '4', '5'])). 108.97/14.39 thf(zip_derived_cl2597, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 108.97/14.39 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | (((l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X1)))) => 108.97/14.39 (((l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X2)))) => 108.97/14.39 (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 108.97/14.39 (n_ts @ (num @ X2) @ (den @ X1))) @ 108.97/14.39 (n_ts @ (den @ X1) @ (den @ X2)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X0))) @ 108.97/14.39 (n_ts @ (den @ X0) @ (den @ X4))))) @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X0))) @ 108.97/14.39 (n_ts @ (den @ X0) @ (den @ X4)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 108.97/14.39 (n_ts @ (num @ X2) @ (den @ X1))) @ 108.97/14.39 (n_ts @ (den @ X1) @ (den @ X2))))))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2596])). 108.97/14.39 thf(zip_derived_cl2598, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 108.97/14.39 (~ (l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X1)))) 108.97/14.39 | (((l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X2)))) => 108.97/14.39 (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 108.97/14.39 (n_ts @ (num @ X2) @ (den @ X1))) @ 108.97/14.39 (n_ts @ (den @ X1) @ (den @ X2)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X0))) @ 108.97/14.39 (n_ts @ (den @ X0) @ (den @ X4))))) @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X0))) @ 108.97/14.39 (n_ts @ (den @ X0) @ (den @ X4)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 108.97/14.39 (n_ts @ (num @ X2) @ (den @ X1))) @ 108.97/14.39 (n_ts @ (den @ X1) @ (den @ X2))))))))) 108.97/14.39 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2597])). 108.97/14.39 thf(zip_derived_cl2599, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 108.97/14.39 (~ (l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X2)))) 108.97/14.39 | (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 108.97/14.39 (n_ts @ (num @ X2) @ (den @ X1))) @ 108.97/14.39 (n_ts @ (den @ X1) @ (den @ X2)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X0))) @ 108.97/14.39 (n_ts @ (den @ X0) @ (den @ X4))))) @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X0))) @ 108.97/14.39 (n_ts @ (den @ X0) @ (den @ X4)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 108.97/14.39 (n_ts @ (num @ X2) @ (den @ X1))) @ 108.97/14.39 (n_ts @ (den @ X1) @ (den @ X2))))))) 108.97/14.39 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X1)))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2598])). 108.97/14.39 thf(zip_derived_cl4063, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 108.97/14.39 (~ (l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X2)))) 108.97/14.39 | (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 108.97/14.39 (n_ts @ (num @ X2) @ (den @ X1))) @ 108.97/14.39 (n_ts @ (den @ X1) @ (den @ X2)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X0))) @ 108.97/14.39 (n_ts @ (den @ X0) @ (den @ X4))))) @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X0))) @ 108.97/14.39 (n_ts @ (den @ X0) @ (den @ X4)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 108.97/14.39 (n_ts @ (num @ X2) @ (den @ X1))) @ 108.97/14.39 (n_ts @ (den @ X1) @ (den @ X2))))))) 108.97/14.39 | ~ (is_of @ X4 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 108.97/14.39 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 108.97/14.39 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 108.97/14.39 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 108.97/14.39 | ~ (l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X1)))))), 108.97/14.39 inference('remove_ty_args', [status(thm)], [zip_derived_cl2599])). 108.97/14.39 thf(zip_derived_cl1539, plain, 108.97/14.39 (~ (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 108.97/14.39 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 108.97/14.39 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 108.97/14.39 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))) @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 108.97/14.39 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 108.97/14.39 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 108.97/14.39 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 108.97/14.39 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1537])). 108.97/14.39 thf(satz62h, axiom, 108.97/14.39 (all_of @ 108.97/14.39 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 108.97/14.39 ( ^[X0:$i]: 108.97/14.39 ( all_of @ 108.97/14.39 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 108.97/14.39 ( ^[X1:$i]: 108.97/14.39 ( all_of @ 108.97/14.39 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 108.97/14.39 ( ^[X2:$i]: 108.97/14.39 ( all_of @ 108.97/14.39 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 108.97/14.39 ( ^[X3:$i]: 108.97/14.39 ( ( n_eq @ X0 @ X1 ) => 108.97/14.39 ( ( moref @ X2 @ X3 ) => 108.97/14.39 ( moref @ ( n_pf @ X2 @ X0 ) @ ( n_pf @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ))). 108.97/14.39 thf(zip_derived_cl10, plain, 108.97/14.39 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 108.97/14.39 (^[Y0 : $i]: 108.97/14.39 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 108.97/14.39 (^[Y1 : $i]: 108.97/14.39 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 108.97/14.39 (^[Y2 : $i]: 108.97/14.39 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 108.97/14.39 (^[Y3 : $i]: 108.97/14.39 (((n_eq @ Y0 @ Y1) => 108.97/14.39 (((moref @ Y2 @ Y3) => (moref @ (n_pf @ Y2 @ Y0) @ 108.97/14.39 (n_pf @ Y3 @ Y1))))))))))))))), 108.97/14.39 inference('cnf', [status(esa)], [satz62h])). 108.97/14.39 thf(zip_derived_cl11, plain, 108.97/14.39 ( (all_of @ ((('#C') @ in @ frac)) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ 108.97/14.39 moref)))))))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ ('#C') @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ moref)) @ 108.97/14.39 ((('#C') @ n_pf)))))))))) @ 108.97/14.39 ((('#C') @ n_pf)))))))))))))))), 108.97/14.39 inference('lams2combs', [status(thm)], [zip_derived_cl10])). 108.97/14.39 thf(zip_derived_cl991, plain, 108.97/14.39 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ 108.97/14.39 (pair1type @ nat)))))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ 108.97/14.39 moref)))))))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ ('#C') @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ moref)) @ 108.97/14.39 ((('#C') @ n_pf)))))))))) @ 108.97/14.39 ((('#C') @ n_pf)))))))))))))))), 108.97/14.39 inference('rw', [status(thm)], [zip_derived_cl11, '0'])). 108.97/14.39 thf(zip_derived_cl992, plain, 108.97/14.39 ( (((!!) @ (^[Y0 : $i]: 108.97/14.39 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ 108.97/14.39 (pair1type @ nat)))))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ 108.97/14.39 (pair1type @ nat)))))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ 108.97/14.39 n_eq)))))))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 108.97/14.39 '#S') @ 108.97/14.39 ((('#B') @ ( 108.97/14.39 (('#B') @ ( 108.97/14.39 =>))) @ 108.97/14.39 moref)))))))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ ('#C') @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ moref)) @ 108.97/14.39 ((('#C') @ n_pf)))))))))) @ 108.97/14.39 ((('#C') @ n_pf)))))))))))) @ 108.97/14.39 Y0)))))))), 108.97/14.39 inference('rw_clause', [status(thm)], [zip_derived_cl991, '11'])). 108.97/14.39 thf(zip_derived_cl993, plain, 108.97/14.39 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 108.97/14.39 ((('#C') @ is_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))))))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat)))))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ 108.97/14.39 (pair1type @ nat)))))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 108.97/14.39 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 108.97/14.39 '#S') @ 108.97/14.39 ((('#B') @ ( 108.97/14.39 (('#B') @ (=>))) @ 108.97/14.39 moref)))))))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ ('#C') @ 108.97/14.39 ((('#B') @ ((('#B') @ ('#B'))) @ 108.97/14.39 ((('#B') @ ((('#B') @ moref)) @ 108.97/14.39 ((('#C') @ n_pf)))))))))) @ 108.97/14.39 ((('#C') @ n_pf))))))))))))))))))), 108.97/14.39 inference('comb-normalize', [status(thm)], [zip_derived_cl992])). 108.97/14.39 thf(zip_derived_cl994, plain, 108.97/14.39 (![X2 : $i]: 108.97/14.39 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat)))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ (=>) @ (n_eq @ X2))))))) @ 108.97/14.39 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 108.97/14.39 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ 108.97/14.39 ((('#C') @ n_pf @ X2)))))))) @ 108.97/14.39 ((('#C') @ n_pf)))))))))))))))), 108.97/14.39 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl993])). 108.97/14.39 thf(zip_derived_cl995, plain, 108.97/14.39 (![X2 : $i]: 108.97/14.39 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat)))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ (=>) @ (n_eq @ X2))))))) @ 108.97/14.39 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ 108.97/14.39 moref)))))) @ 108.97/14.39 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ 108.97/14.39 ((('#C') @ n_pf @ X2)))))))) @ 108.97/14.39 ((('#C') @ n_pf))))))))))))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl994])). 108.97/14.39 thf(zip_derived_cl996, plain, 108.97/14.39 (![X0 : $i]: 108.97/14.39 ( (((!!) @ (^[Y0 : $i]: 108.97/14.39 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.39 ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ 108.97/14.39 (pair1type @ nat)))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ (=>) @ (n_eq @ X0))))))) @ 108.97/14.39 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ ( 108.97/14.39 =>))) @ 108.97/14.39 moref)))))) @ 108.97/14.39 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ 108.97/14.39 ((('#C') @ n_pf @ X0)))))))) @ 108.97/14.39 ((('#C') @ n_pf)))))))))) @ 108.97/14.39 Y0))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('rw_clause', [status(thm)], [zip_derived_cl995, '11'])). 108.97/14.39 thf(zip_derived_cl997, plain, 108.97/14.39 (![X0 : $i]: 108.97/14.39 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 108.97/14.39 ((('#C') @ is_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))))))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ 108.97/14.39 (pair1type @ nat)))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ (=>) @ (n_eq @ X0))))))) @ 108.97/14.39 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ 108.97/14.39 moref)))))) @ 108.97/14.39 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ 108.97/14.39 ((('#C') @ n_pf @ X0)))))))) @ 108.97/14.39 ((('#C') @ n_pf)))))))))))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('comb-normalize', [status(thm)], [zip_derived_cl996])). 108.97/14.39 thf(zip_derived_cl998, plain, 108.97/14.39 (![X0 : $i, X2 : $i]: 108.97/14.39 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ ((('#C') @ n_pf @ X0)))))) @ 108.97/14.39 ((('#C') @ n_pf @ X2))))))))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl997])). 108.97/14.39 thf(zip_derived_cl999, plain, 108.97/14.39 (![X0 : $i, X2 : $i]: 108.97/14.39 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ ((('#C') @ n_pf @ X0)))))) @ 108.97/14.39 ((('#C') @ n_pf @ X2))))))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl998])). 108.97/14.39 thf(zip_derived_cl1000, plain, 108.97/14.39 (![X0 : $i, X1 : $i]: 108.97/14.39 ( (((!!) @ (^[Y0 : $i]: 108.97/14.39 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.39 ((('#B') @ (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ 108.97/14.39 ((('#C') @ n_pf @ X0)))))) @ 108.97/14.39 ((('#C') @ n_pf @ X1)))))))) @ 108.97/14.39 Y0))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('rw_clause', [status(thm)], [zip_derived_cl999, '11'])). 108.97/14.39 thf(zip_derived_cl1001, plain, 108.97/14.39 (![X0 : $i, X1 : $i]: 108.97/14.39 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 108.97/14.39 ((('#C') @ is_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))))))) @ 108.97/14.39 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 108.97/14.39 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))))) @ 108.97/14.39 ((('#S') @ ((('#B') @ ('#S') @ 108.97/14.39 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 108.97/14.39 ((('#C') @ ((('#B') @ ('#B') @ 108.97/14.39 ((('#B') @ moref @ 108.97/14.39 ((('#C') @ n_pf @ X0)))))) @ 108.97/14.39 ((('#C') @ n_pf @ X1)))))))))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('comb-normalize', [status(thm)], [zip_derived_cl1000])). 108.97/14.39 thf(zip_derived_cl1002, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X3 : $i]: 108.97/14.39 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @ 108.97/14.39 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 108.97/14.39 ((('#B') @ (moref @ (n_pf @ X3 @ X0)) @ ((('#C') @ n_pf @ X1))))))))))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1001])). 108.97/14.39 thf(zip_derived_cl1003, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X3 : $i]: 108.97/14.39 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @ 108.97/14.39 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 108.97/14.39 ((('#B') @ (moref @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X3) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X3))) @ 108.97/14.39 (n_ts @ (den @ X3) @ (den @ X0)))) @ 108.97/14.39 ((('#C') @ n_pf @ X1))))))))))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('rw', [status(thm)], [zip_derived_cl1002, '5'])). 108.97/14.39 thf(zip_derived_cl1004, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X3 : $i]: 108.97/14.39 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 108.97/14.39 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @ 108.97/14.39 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 108.97/14.39 ((('#B') @ (moref @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X3) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X3))) @ 108.97/14.39 (n_ts @ (den @ X3) @ (den @ X0)))) @ 108.97/14.39 ((('#C') @ n_pf @ X1))))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1003])). 108.97/14.39 thf(zip_derived_cl1005, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X2 : $i]: 108.97/14.39 ( (((!!) @ (^[Y0 : $i]: 108.97/14.39 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.39 ((('#B') @ (((=>) @ (n_eq @ X1 @ X0))) @ 108.97/14.39 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 108.97/14.39 ((('#B') @ (moref @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ 108.97/14.39 (n_ts @ (num @ X2) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X2))) @ 108.97/14.39 (n_ts @ (den @ X2) @ (den @ X1)))) @ 108.97/14.39 ((('#C') @ n_pf @ X0)))))) @ 108.97/14.39 Y0))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('rw_clause', [status(thm)], [zip_derived_cl1004, '11'])). 108.97/14.39 thf(zip_derived_cl1006, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X2 : $i]: 108.97/14.39 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 108.97/14.39 ((('#C') @ is_of @ 108.97/14.39 ((('#C') @ in @ (pair1type @ nat))))))) @ 108.97/14.39 ((('#B') @ (((=>) @ (n_eq @ X1 @ X0))) @ 108.97/14.39 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 108.97/14.39 ((('#B') @ (moref @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ 108.97/14.39 (n_ts @ (num @ X2) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X2))) @ 108.97/14.39 (n_ts @ (den @ X2) @ (den @ X1)))) @ 108.97/14.39 ((('#C') @ n_pf @ X0)))))))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('comb-normalize', [status(thm)], [zip_derived_cl1005])). 108.97/14.39 thf(zip_derived_cl1007, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 108.97/14.39 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.39 (((n_eq @ X1 @ X0) => 108.97/14.39 (((moref @ X2 @ X4) => (moref @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X2))) @ 108.97/14.39 (n_ts @ (den @ X2) @ (den @ X1))) @ 108.97/14.39 (n_pf @ X4 @ X0)))))))) 108.97/14.39 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1006])). 108.97/14.39 thf(zip_derived_cl1008, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 108.97/14.39 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 108.97/14.39 (((n_eq @ X1 @ X0) => 108.97/14.39 (((l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X2)))) => 108.97/14.39 (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X2))) @ 108.97/14.39 (n_ts @ (den @ X2) @ (den @ X1)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X4))) @ 108.97/14.39 (n_ts @ (den @ X4) @ (den @ X0))))) @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X4))) @ 108.97/14.39 (n_ts @ (den @ X4) @ (den @ X0)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X2))) @ 108.97/14.39 (n_ts @ (den @ X2) @ (den @ X1))))))))))))) 108.97/14.39 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('rw', [status(thm)], 108.97/14.39 [zip_derived_cl1007, '2', '2', '3', '3', '4', '4', '5'])). 108.97/14.39 thf(zip_derived_cl1009, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 108.97/14.39 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | (((n_eq @ X1 @ X0) => 108.97/14.39 (((l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X2)))) => 108.97/14.39 (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X2))) @ 108.97/14.39 (n_ts @ (den @ X2) @ (den @ X1)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X4))) @ 108.97/14.39 (n_ts @ (den @ X4) @ (den @ X0))))) @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X4))) @ 108.97/14.39 (n_ts @ (den @ X4) @ (den @ X0)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X2))) @ 108.97/14.39 (n_ts @ (den @ X2) @ (den @ X1))))))))))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1008])). 108.97/14.39 thf(zip_derived_cl1010, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 108.97/14.39 (~ (n_eq @ X1 @ X0) 108.97/14.39 | (((l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X2)))) => 108.97/14.39 (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X2))) @ 108.97/14.39 (n_ts @ (den @ X2) @ (den @ X1)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X4))) @ 108.97/14.39 (n_ts @ (den @ X4) @ (den @ X0))))) @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X4))) @ 108.97/14.39 (n_ts @ (den @ X4) @ (den @ X0)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X2))) @ 108.97/14.39 (n_ts @ (den @ X2) @ (den @ X1))))))))) 108.97/14.39 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1009])). 108.97/14.39 thf(zip_derived_cl1011, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 108.97/14.39 (~ (l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X2)))) 108.97/14.39 | (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X2))) @ 108.97/14.39 (n_ts @ (den @ X2) @ (den @ X1)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X4))) @ 108.97/14.39 (n_ts @ (den @ X4) @ (den @ X0))))) @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X4))) @ 108.97/14.39 (n_ts @ (den @ X4) @ (den @ X0)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X2))) @ 108.97/14.39 (n_ts @ (den @ X2) @ (den @ X1))))))) 108.97/14.39 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 108.97/14.39 | ~ (n_eq @ X1 @ X0))), 108.97/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1010])). 108.97/14.39 thf(zip_derived_cl3992, plain, 108.97/14.39 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 108.97/14.39 (~ (l_some @ nat @ 108.97/14.39 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 108.97/14.39 (n_ts @ (num @ X4) @ (den @ X2)))) 108.97/14.39 | (l_some @ nat @ 108.97/14.39 (diffprop @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X2))) @ 108.97/14.39 (n_ts @ (den @ X2) @ (den @ X1)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X4))) @ 108.97/14.39 (n_ts @ (den @ X4) @ (den @ X0))))) @ 108.97/14.39 (n_ts @ 108.97/14.39 (num @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X4) @ (den @ X0)) @ 108.97/14.39 (n_ts @ (num @ X0) @ (den @ X4))) @ 108.97/14.39 (n_ts @ (den @ X4) @ (den @ X0)))) @ 108.97/14.39 (den @ 108.97/14.39 (n_fr @ 108.97/14.39 (n_pl @ (n_ts @ (num @ X2) @ (den @ X1)) @ 108.97/14.39 (n_ts @ (num @ X1) @ (den @ X2))) @ 108.97/14.39 (n_ts @ (den @ X2) @ (den @ X1))))))) 108.97/14.39 | ~ (is_of @ X4 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 108.97/14.39 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 108.97/14.39 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 108.97/14.39 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 108.97/14.39 | ~ (n_eq @ X1 @ X0))), 108.97/14.39 inference('remove_ty_args', [status(thm)], [zip_derived_cl1011])). 108.97/14.39 thf(zip_derived_cl4103, plain, ($false), 108.97/14.39 inference('eprover', [status(thm)], 108.97/14.39 [zip_derived_cl1544, zip_derived_cl4021, zip_derived_cl4022, 108.97/14.39 zip_derived_cl4023, zip_derived_cl4024, zip_derived_cl1536, 108.97/14.39 zip_derived_cl4063, zip_derived_cl1539, zip_derived_cl3992])). 108.97/14.39 108.97/14.39 % SZS output end Refutation 108.97/14.39 108.97/14.39 108.97/14.39 % Terminating... 108.97/14.58 % Runner terminated. 108.97/14.61 % Zipperpin 1.5 exiting 108.98/14.61 EOF