0.00/0.07 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.09 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.8rvcwKD80X true 0.08/0.27 % Computer : n021.cluster.edu 0.08/0.27 % Model : x86_64 x86_64 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.27 % Memory : 8042.1875MB 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64 0.08/0.27 % CPULimit : 960 0.08/0.27 % WCLimit : 120 0.08/0.27 % DateTime : Tue Aug 9 07:55:05 EDT 2022 0.08/0.27 % CPUTime : 0.08/0.27 % Running portfolio for 960 s 0.08/0.27 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.08/0.28 % Number of cores: 8 0.08/0.28 % Python version: Python 3.6.8 0.08/0.28 % Running in HO mode 0.60/0.55 % Total configuration time : 828 0.60/0.55 % Estimated wc time : 1656 0.60/0.55 % Estimated cpu time (8 cpus) : 207.0 0.60/0.57 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.60/0.57 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.60/0.59 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.60/0.62 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.60/0.62 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.60/0.62 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 1.24/0.62 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 1.24/0.62 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 93.24/12.29 % Solved by lams/40_b.comb.sh. 93.24/12.29 % done 660 iterations in 11.599s 93.24/12.29 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 93.24/12.29 % SZS output start Refutation 93.24/12.29 thf(moref_type, type, moref: $i > $i > $o). 93.24/12.29 thf(d_not_type, type, d_not: $o > $o). 93.24/12.29 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 93.24/12.29 thf(in_type, type, in: $i > $i > $o). 93.24/12.29 thf('#sk4_type', type, '#sk4': $i). 93.24/12.29 thf(den_type, type, den: $i > $i). 93.24/12.29 thf(n_fr_type, type, n_fr: $i > $i > $i). 93.24/12.29 thf(nat_type, type, nat: $i). 93.24/12.29 thf(l_or_type, type, l_or: $o > $o > $o). 93.24/12.29 thf(frac_type, type, frac: $i). 93.24/12.29 thf(n_ts_type, type, n_ts: $i > $i > $i). 93.24/12.29 thf(imp_type, type, imp: $o > $o > $o). 93.24/12.29 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 93.24/12.29 thf('#ty_enc6_type', type, '#ty_enc6': ($i > $i > $o) > $i > $i > $o). 93.24/12.29 thf(n_eq_type, type, n_eq: $i > $i > $o). 93.24/12.29 thf('#sk3_type', type, '#sk3': $i). 93.24/12.29 thf('#sk2_type', type, '#sk2': $i). 93.24/12.29 thf('#sk5_type', type, '#sk5': $i). 93.24/12.29 thf(moreq_type, type, moreq: $i > $i > $o). 93.24/12.29 thf(n_pl_type, type, n_pl: $i > $i > $i). 93.24/12.29 thf(n_pf_type, type, n_pf: $i > $i > $i). 93.24/12.29 thf(num_type, type, num: $i > $i). 93.24/12.29 thf(pair1type_type, type, pair1type: $i > $i). 93.24/12.29 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 93.24/12.29 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 93.24/12.29 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 93.24/12.29 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 93.24/12.29 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 93.24/12.29 thf(satz66, conjecture, 93.24/12.29 (all_of @ 93.24/12.29 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 93.24/12.29 ( ^[X0:$i]: 93.24/12.29 ( all_of @ 93.24/12.29 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 93.24/12.29 ( ^[X1:$i]: 93.24/12.29 ( all_of @ 93.24/12.29 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 93.24/12.29 ( ^[X2:$i]: 93.24/12.29 ( all_of @ 93.24/12.29 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 93.24/12.29 ( ^[X3:$i]: 93.24/12.29 ( ( moreq @ X0 @ X1 ) => 93.24/12.29 ( ( moreq @ X2 @ X3 ) => 93.24/12.29 ( moreq @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 93.24/12.29 thf(zf_stmt_0, negated_conjecture, 93.24/12.29 (~( all_of @ 93.24/12.29 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 93.24/12.29 ( ^[X0:$i]: 93.24/12.29 ( all_of @ 93.24/12.29 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 93.24/12.29 ( ^[X1:$i]: 93.24/12.29 ( all_of @ 93.24/12.29 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 93.24/12.29 ( ^[X2:$i]: 93.24/12.29 ( all_of @ 93.24/12.29 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 93.24/12.29 ( ^[X3:$i]: 93.24/12.29 ( ( moreq @ X0 @ X1 ) => 93.24/12.29 ( ( moreq @ X2 @ X3 ) => 93.24/12.29 ( moreq @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) )), 93.24/12.29 inference('cnf.neg', [status(esa)], [satz66])). 93.24/12.29 thf(zip_derived_cl354, plain, 93.24/12.29 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 93.24/12.29 (^[Y0 : $i]: 93.24/12.29 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 93.24/12.29 (^[Y1 : $i]: 93.24/12.29 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 93.24/12.29 (^[Y2 : $i]: 93.24/12.29 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 93.24/12.29 (^[Y3 : $i]: 93.24/12.29 (((moreq @ Y0 @ Y1) => 93.24/12.29 (((moreq @ Y2 @ Y3) => (moreq @ (n_pf @ Y0 @ Y2) @ 93.24/12.29 (n_pf @ Y1 @ Y3))))))))))))))), 93.24/12.29 inference('cnf', [status(esa)], [zf_stmt_0])). 93.24/12.29 thf(zip_derived_cl355, plain, 93.24/12.29 (~ (all_of @ ((('#C') @ in @ frac)) @ 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 93.24/12.29 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ 93.24/12.29 moreq)))))))) @ 93.24/12.29 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ ('#C') @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ moreq)) @ n_pf)))))))) @ 93.24/12.29 n_pf)))))))))))))), 93.24/12.29 inference('lams2combs', [status(thm)], [zip_derived_cl354])). 93.24/12.29 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))). 93.24/12.29 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])). 93.24/12.29 thf(zip_derived_cl1309, plain, 93.24/12.29 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.24/12.29 ((('#C') @ in @ 93.24/12.29 (pair1type @ nat)))))))) @ 93.24/12.29 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ 93.24/12.29 moreq)))))))) @ 93.24/12.29 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ ('#C') @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ moreq)) @ n_pf)))))))) @ 93.24/12.29 n_pf)))))))))))))), 93.24/12.29 inference('rw', [status(thm)], [zip_derived_cl355, '0'])). 93.24/12.29 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 93.24/12.29 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 93.24/12.29 thf('1', plain, 93.24/12.29 (![X0:( $i > $o ),X1:( $i > $o )]: 93.24/12.29 ( ( ~( all_of @ X0 @ X1 ) ) <=> 93.24/12.29 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 93.24/12.29 inference('rw.lit', [status(esa)], [def_all_of])). 93.24/12.29 thf(zip_derived_cl1310, plain, 93.24/12.29 (~ (((!!) @ (^[Y0 : $i]: 93.24/12.29 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.29 ((('#C') @ in @ 93.24/12.29 (pair1type @ nat)))))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.24/12.29 ((('#C') @ in @ 93.24/12.29 (pair1type @ nat)))))))) @ 93.24/12.29 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ 93.24/12.29 moreq)))))))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 93.24/12.29 '#S') @ 93.24/12.29 ((('#B') @ ( 93.24/12.29 (('#B') @ ( 93.24/12.29 =>))) @ 93.24/12.29 moreq)))))))) @ 93.24/12.29 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ ('#C') @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ moreq)) @ 93.24/12.29 n_pf)))))))) @ 93.24/12.29 n_pf)))))))))) @ 93.24/12.29 Y0)))))))), 93.24/12.29 inference('rw_clause', [status(thm)], [zip_derived_cl1309, '1'])). 93.24/12.29 thf(zip_derived_cl1311, plain, 93.24/12.29 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.24/12.29 ((('#C') @ is_of @ 93.24/12.29 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.29 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.24/12.29 ((('#C') @ in @ 93.24/12.29 (pair1type @ nat)))))))) @ 93.24/12.29 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 93.24/12.29 '#S') @ 93.24/12.29 ((('#B') @ ( 93.24/12.29 (('#B') @ (=>))) @ 93.24/12.29 moreq)))))))) @ 93.24/12.29 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ ('#C') @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ moreq)) @ 93.24/12.29 n_pf)))))))) @ 93.24/12.29 n_pf))))))))))))))))), 93.24/12.29 inference('comb-normalize', [status(thm)], [zip_derived_cl1310])). 93.24/12.29 thf(zip_derived_cl1312, plain, 93.24/12.29 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.24/12.29 ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.29 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.24/12.29 ((('#S') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @ 93.24/12.29 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 93.24/12.29 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ moreq @ (n_pf @ '#sk2'))))))) @ 93.24/12.29 n_pf)))))))))))))), 93.24/12.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1311])). 93.24/12.29 thf(zip_derived_cl1314, plain, 93.24/12.29 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 93.24/12.29 ((('#S') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @ 93.24/12.29 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 93.24/12.29 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ moreq @ (n_pf @ '#sk2'))))))) @ 93.24/12.29 n_pf)))))))))))), 93.24/12.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1312])). 93.24/12.29 thf(zip_derived_cl1315, plain, 93.24/12.29 (~ (((!!) @ (^[Y0 : $i]: 93.24/12.29 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.29 ((('#C') @ in @ 93.24/12.29 (pair1type @ nat)))))) @ 93.24/12.29 ((('#S') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @ 93.24/12.29 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ 93.24/12.29 moreq)))))) @ 93.24/12.29 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ moreq @ 93.24/12.29 (n_pf @ '#sk2'))))))) @ 93.24/12.29 n_pf)))))))) @ 93.24/12.29 Y0)))))))), 93.24/12.29 inference('rw_clause', [status(thm)], [zip_derived_cl1314, '1'])). 93.24/12.29 thf(zip_derived_cl1316, plain, 93.24/12.29 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.24/12.29 ((('#C') @ is_of @ 93.24/12.29 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.29 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.24/12.29 ((('#S') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @ 93.24/12.29 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ 93.24/12.29 moreq)))))) @ 93.24/12.29 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ moreq @ 93.24/12.29 (n_pf @ '#sk2'))))))) @ 93.24/12.29 n_pf))))))))))))))), 93.24/12.29 inference('comb-normalize', [status(thm)], [zip_derived_cl1315])). 93.24/12.29 thf(zip_derived_cl1317, plain, 93.24/12.29 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.24/12.29 ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (((=>) @ (moreq @ '#sk2' @ '#sk3'))))) @ 93.24/12.29 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 93.24/12.29 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ moreq @ (n_pf @ '#sk2'))))) @ 93.24/12.29 (n_pf @ '#sk3'))))))))))))), 93.24/12.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1316])). 93.24/12.29 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 93.24/12.29 thf('2', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 93.24/12.29 define([status(thm)])). 93.24/12.29 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 93.24/12.29 thf('3', plain, 93.24/12.29 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 93.24/12.29 define([status(thm)])). 93.24/12.29 thf(def_moreq, axiom,(( moreq @ (X0)@ (X1)) = 93.24/12.29 ((l_or @ (moref @ X0 @ X1) @ (n_eq @ X0 @ X1))))). 93.24/12.29 thf('4', plain, 93.24/12.29 (![X1:$i,X0:$i]: 93.24/12.29 ( ( moreq @ X0 @ X1 ) = 93.24/12.29 ( l_or @ ( moref @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )), 93.24/12.29 define([status(thm)])). 93.24/12.29 thf(zip_derived_cl1318, plain, 93.24/12.29 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.24/12.29 ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 93.24/12.29 (imp @ 93.24/12.29 (moref @ '#sk2' @ '#sk3') @ 93.24/12.29 ($false)) @ 93.24/12.29 (n_eq @ '#sk2' @ '#sk3')))))) @ 93.24/12.29 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 93.24/12.29 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ moreq @ (n_pf @ '#sk2'))))) @ 93.24/12.29 (n_pf @ '#sk3'))))))))))))), 93.24/12.29 inference('rw', [status(thm)], [zip_derived_cl1317, '2', '3', '4'])). 93.24/12.29 thf(zip_derived_cl1320, plain, 93.24/12.29 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 93.24/12.29 (imp @ (moref @ '#sk2' @ '#sk3') @ 93.24/12.29 ($false)) @ 93.24/12.29 (n_eq @ '#sk2' @ '#sk3')))))) @ 93.24/12.29 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 93.24/12.29 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ moreq @ (n_pf @ '#sk2'))))) @ 93.24/12.29 (n_pf @ '#sk3'))))))))))), 93.24/12.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1318])). 93.24/12.29 thf(zip_derived_cl1321, plain, 93.24/12.29 (~ (((!!) @ (^[Y0 : $i]: 93.24/12.29 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 93.24/12.29 (imp @ 93.24/12.29 (moref @ '#sk2' @ 93.24/12.29 '#sk3') @ 93.24/12.29 ($false)) @ 93.24/12.29 (n_eq @ '#sk2' @ 93.24/12.29 '#sk3')))))) @ 93.24/12.29 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 93.24/12.29 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ moreq @ (n_pf @ '#sk2'))))) @ 93.24/12.29 (n_pf @ '#sk3'))))))) @ 93.24/12.29 Y0)))))))), 93.24/12.29 inference('rw_clause', [status(thm)], [zip_derived_cl1320, '1'])). 93.24/12.29 thf(zip_derived_cl1322, plain, 93.24/12.29 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.24/12.29 ((('#C') @ is_of @ 93.24/12.29 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 93.24/12.29 (imp @ 93.24/12.29 (moref @ '#sk2' @ '#sk3') @ 93.24/12.29 ($false)) @ 93.24/12.29 (n_eq @ '#sk2' @ '#sk3')))))) @ 93.24/12.29 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 93.24/12.29 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ moreq @ (n_pf @ '#sk2'))))) @ 93.24/12.29 (n_pf @ '#sk3')))))))))))))), 93.24/12.29 inference('comb-normalize', [status(thm)], [zip_derived_cl1321])). 93.24/12.29 thf(zip_derived_cl1323, plain, 93.24/12.29 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.24/12.29 ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.29 ((('#B') @ (((=>) @ (imp @ 93.24/12.29 (imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) @ 93.24/12.29 (n_eq @ '#sk2' @ '#sk3')))) @ 93.24/12.29 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @ 93.24/12.29 ((('#B') @ (moreq @ (n_pf @ '#sk2' @ '#sk4')) @ (n_pf @ '#sk3'))))))))))), 93.24/12.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1322])). 93.24/12.29 thf(def_n_pf, axiom,(( n_pf @ (X0)@ (X1)) = 93.24/12.29 ((n_fr @ 93.24/12.29 (n_pl @ (n_ts @ (num @ X0) @ (den @ X1)) @ 93.24/12.29 (n_ts @ (num @ X1) @ (den @ X0))) @ 93.24/12.29 (n_ts @ (den @ X0) @ (den @ X1)))))). 93.24/12.29 thf('5', plain, 93.24/12.29 (![X1:$i,X0:$i]: 93.24/12.29 ( ( n_pf @ X0 @ X1 ) = 93.24/12.29 ( n_fr @ 93.24/12.29 ( n_pl @ 93.24/12.29 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 93.24/12.29 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) @ 93.24/12.29 ( n_ts @ ( den @ X0 ) @ ( den @ X1 ) ) ) )), 93.24/12.29 define([status(thm)])). 93.24/12.29 thf(zip_derived_cl1324, plain, 93.24/12.29 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.24/12.29 ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.29 ((('#B') @ (((=>) @ (imp @ 93.24/12.29 (imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) @ 93.24/12.29 (n_eq @ '#sk2' @ '#sk3')))) @ 93.24/12.29 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @ 93.24/12.29 ((('#B') @ (moreq @ 93.24/12.29 (n_fr @ 93.24/12.29 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.24/12.29 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.24/12.29 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 93.24/12.29 (n_pf @ '#sk3'))))))))))), 93.24/12.29 inference('rw', [status(thm)], [zip_derived_cl1323, '5'])). 93.24/12.29 thf(zip_derived_cl1326, plain, 93.24/12.29 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.29 ((('#B') @ (((=>) @ (imp @ 93.24/12.29 (imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) @ 93.24/12.29 (n_eq @ '#sk2' @ '#sk3')))) @ 93.24/12.29 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @ 93.24/12.29 ((('#B') @ (moreq @ 93.24/12.29 (n_fr @ 93.24/12.29 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.24/12.29 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.24/12.29 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 93.24/12.29 (n_pf @ '#sk3'))))))))), 93.24/12.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1324])). 93.24/12.29 thf(zip_derived_cl1327, plain, 93.24/12.29 (~ (((!!) @ (^[Y0 : $i]: 93.24/12.29 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.24/12.29 ((('#B') @ (((=>) @ (imp @ 93.24/12.29 (imp @ (moref @ '#sk2' @ '#sk3') @ 93.24/12.29 ($false)) @ 93.24/12.29 (n_eq @ '#sk2' @ '#sk3')))) @ 93.24/12.29 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @ 93.24/12.29 ((('#B') @ (moreq @ 93.24/12.29 (n_fr @ 93.24/12.29 (n_pl @ 93.24/12.29 (n_ts @ (num @ '#sk2') @ 93.24/12.29 (den @ '#sk4')) @ 93.24/12.29 (n_ts @ (num @ '#sk4') @ 93.24/12.29 (den @ '#sk2'))) @ 93.24/12.29 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 93.24/12.29 (n_pf @ '#sk3'))))) @ 93.24/12.29 Y0)))))))), 93.24/12.29 inference('rw_clause', [status(thm)], [zip_derived_cl1326, '1'])). 93.24/12.29 thf(zip_derived_cl1328, plain, 93.24/12.29 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.24/12.29 ((('#C') @ is_of @ 93.24/12.29 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.24/12.29 ((('#B') @ (((=>) @ (imp @ 93.24/12.29 (imp @ (moref @ '#sk2' @ '#sk3') @ 93.24/12.29 ($false)) @ 93.24/12.29 (n_eq @ '#sk2' @ '#sk3')))) @ 93.24/12.29 ((('#S') @ ((('#B') @ (=>) @ (moreq @ '#sk4'))) @ 93.24/12.29 ((('#B') @ (moreq @ 93.24/12.29 (n_fr @ 93.24/12.29 (n_pl @ 93.24/12.29 (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.24/12.29 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.24/12.29 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 93.24/12.29 (n_pf @ '#sk3')))))))))))), 93.24/12.29 inference('comb-normalize', [status(thm)], [zip_derived_cl1327])). 93.24/12.29 thf(zip_derived_cl1329, plain, 93.24/12.29 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) => 93.24/12.29 (((imp @ (imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) @ 93.24/12.29 (n_eq @ '#sk2' @ '#sk3')) => 93.24/12.29 (((moreq @ '#sk4' @ '#sk5') => (moreq @ 93.24/12.29 (n_fr @ 93.24/12.29 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.24/12.29 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.24/12.29 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.24/12.29 (n_pf @ '#sk3' @ '#sk5'))))))))), 93.24/12.29 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1328])). 93.24/12.29 thf(zip_derived_cl1330, plain, 93.24/12.29 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) => 93.24/12.29 (((imp @ (imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) @ 93.24/12.29 (n_eq @ '#sk2' @ '#sk3')) => 93.24/12.29 (((imp @ (imp @ (moref @ '#sk4' @ '#sk5') @ ($false)) @ 93.24/12.29 (n_eq @ '#sk4' @ '#sk5')) => (imp @ 93.24/12.29 (imp @ 93.24/12.29 (moref @ 93.24/12.29 (n_fr @ 93.24/12.29 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.24/12.29 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.24/12.29 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.24/12.29 (n_fr @ 93.24/12.29 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.24/12.29 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.24/12.29 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @ 93.24/12.29 ($false)) @ 93.24/12.29 (n_eq @ 93.24/12.29 (n_fr @ 93.24/12.29 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.24/12.29 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.24/12.29 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.24/12.29 (n_fr @ 93.24/12.29 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.24/12.29 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.24/12.29 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))))))))))), 93.24/12.29 inference('rw', [status(thm)], 93.24/12.29 [zip_derived_cl1329, '2', '2', '3', '3', '4', '4', '5'])). 93.24/12.29 thf(zip_derived_cl1332, plain, 93.24/12.29 (~ (((imp @ (imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) @ 93.24/12.29 (n_eq @ '#sk2' @ '#sk3')) => 93.24/12.29 (((imp @ (imp @ (moref @ '#sk4' @ '#sk5') @ ($false)) @ 93.24/12.29 (n_eq @ '#sk4' @ '#sk5')) => (imp @ 93.24/12.29 (imp @ 93.24/12.29 (moref @ 93.24/12.29 (n_fr @ 93.24/12.29 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.24/12.29 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.24/12.29 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.24/12.29 (n_fr @ 93.24/12.29 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.24/12.29 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.24/12.29 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @ 93.24/12.29 ($false)) @ 93.24/12.29 (n_eq @ 93.24/12.29 (n_fr @ 93.24/12.29 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.24/12.29 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.24/12.29 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.24/12.29 (n_fr @ 93.24/12.29 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.24/12.29 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.24/12.29 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))))))))), 93.24/12.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1330])). 93.24/12.29 thf(zip_derived_cl1333, plain, 93.24/12.29 ( (imp @ (imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) @ 93.24/12.29 (n_eq @ '#sk2' @ '#sk3'))), 93.24/12.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1332])). 93.24/12.29 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 93.24/12.29 thf('6', plain, 93.24/12.29 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 93.24/12.29 inference('rw.lit', [status(esa)], [def_imp])). 93.24/12.29 thf(zip_derived_cl1335, plain, 93.24/12.29 ( (((imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) => (n_eq @ '#sk2' @ 93.24/12.29 '#sk3')))), 93.24/12.29 inference('rw_clause', [status(thm)], [zip_derived_cl1333, '6'])). 93.24/12.29 thf(zip_derived_cl1338, plain, 93.24/12.29 ((~ (imp @ (moref @ '#sk2' @ '#sk3') @ ($false)) 93.24/12.29 | (n_eq @ '#sk2' @ '#sk3'))), 93.24/12.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1335])). 93.24/12.29 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 93.24/12.29 thf('7', plain, 93.24/12.29 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 93.24/12.29 inference('rw.lit', [status(esa)], [def_imp])). 93.24/12.29 thf(zip_derived_cl1341, plain, 93.24/12.29 ((~ (((moref @ '#sk2' @ '#sk3') => ($false))) | (n_eq @ '#sk2' @ '#sk3'))), 93.24/12.29 inference('rw_clause', [status(thm)], [zip_derived_cl1338, '7'])). 93.24/12.29 thf(zip_derived_cl1345, plain, 93.24/12.29 ((~ (((~) @ (moref @ '#sk2' @ '#sk3'))) | (n_eq @ '#sk2' @ '#sk3'))), 93.24/12.29 inference('simplify boolean subterms', [status(thm)], 93.24/12.29 [zip_derived_cl1341])). 93.24/12.29 thf(zip_derived_cl1346, plain, 93.24/12.29 (( (moref @ '#sk2' @ '#sk3') | (n_eq @ '#sk2' @ '#sk3'))), 93.24/12.29 inference('simplify nested equalities', [status(thm)], 93.24/12.29 [zip_derived_cl1345])). 93.24/12.29 thf(satz65b, axiom, 93.24/12.29 (all_of @ 93.24/12.29 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 93.24/12.29 ( ^[X0:$i]: 93.24/12.29 ( all_of @ 93.24/12.29 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 93.24/12.29 ( ^[X1:$i]: 93.24/12.29 ( all_of @ 93.24/12.29 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 93.24/12.29 ( ^[X2:$i]: 93.24/12.29 ( all_of @ 93.24/12.29 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 93.24/12.29 ( ^[X3:$i]: 93.24/12.29 ( ( moref @ X0 @ X1 ) => 93.24/12.29 ( ( moreq @ X2 @ X3 ) => 93.24/12.29 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 93.24/12.29 thf(zip_derived_cl214, plain, 93.24/12.29 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 93.24/12.29 (^[Y0 : $i]: 93.24/12.29 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 93.24/12.29 (^[Y1 : $i]: 93.24/12.29 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 93.24/12.29 (^[Y2 : $i]: 93.24/12.29 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 93.24/12.29 (^[Y3 : $i]: 93.24/12.29 (((moref @ Y0 @ Y1) => 93.24/12.29 (((moreq @ Y2 @ Y3) => (moref @ (n_pf @ Y0 @ Y2) @ 93.24/12.29 (n_pf @ Y1 @ Y3))))))))))))))), 93.24/12.29 inference('cnf', [status(esa)], [satz65b])). 93.24/12.29 thf(zip_derived_cl215, plain, 93.24/12.29 ( (all_of @ ((('#C') @ in @ frac)) @ 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 93.24/12.29 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ 93.24/12.29 moreq)))))))) @ 93.24/12.29 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ ('#C') @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @ 93.24/12.29 n_pf)))))))))))))), 93.24/12.29 inference('lams2combs', [status(thm)], [zip_derived_cl214])). 93.24/12.29 thf(zip_derived_cl2510, plain, 93.24/12.29 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.24/12.29 ((('#C') @ in @ 93.24/12.29 (pair1type @ nat)))))))) @ 93.24/12.29 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ 93.24/12.29 moreq)))))))) @ 93.24/12.29 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ ('#C') @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @ 93.24/12.29 n_pf)))))))))))))), 93.24/12.29 inference('rw', [status(thm)], [zip_derived_cl215, '0'])). 93.24/12.29 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 93.24/12.29 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 93.24/12.29 thf('8', plain, 93.24/12.29 (![X0:( $i > $o ),X1:( $i > $o )]: 93.24/12.29 ( ( all_of @ X0 @ X1 ) <=> 93.24/12.29 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 93.24/12.29 inference('rw.lit', [status(esa)], [def_all_of])). 93.24/12.29 thf(zip_derived_cl2511, plain, 93.24/12.29 ( (((!!) @ (^[Y0 : $i]: 93.24/12.29 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.29 ((('#C') @ in @ 93.24/12.29 (pair1type @ nat)))))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.24/12.29 ((('#C') @ in @ 93.24/12.29 (pair1type @ nat)))))))) @ 93.24/12.29 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (=>))) @ 93.24/12.29 moref)))))))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 93.24/12.29 '#S') @ 93.24/12.29 ((('#B') @ ( 93.24/12.29 (('#B') @ ( 93.24/12.29 =>))) @ 93.24/12.29 moreq)))))))) @ 93.24/12.29 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.29 ((('#B') @ ('#C') @ 93.24/12.29 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.29 ((('#B') @ ((('#B') @ moref)) @ 93.24/12.29 n_pf)))))))) @ 93.24/12.29 n_pf)))))))))) @ 93.24/12.29 Y0)))))))), 93.24/12.29 inference('rw_clause', [status(thm)], [zip_derived_cl2510, '8'])). 93.24/12.29 thf(zip_derived_cl2512, plain, 93.24/12.29 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.24/12.29 ((('#C') @ is_of @ 93.24/12.29 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.24/12.29 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.29 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.29 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.24/12.29 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.24/12.29 ((('#C') @ in @ 93.24/12.29 (pair1type @ nat)))))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @ 93.24/12.30 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 93.24/12.30 '#S') @ 93.24/12.30 ((('#B') @ ( 93.24/12.30 (('#B') @ (=>))) @ 93.24/12.30 moreq)))))))) @ 93.24/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ ('#C') @ 93.24/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.30 ((('#B') @ ((('#B') @ moref)) @ 93.24/12.30 n_pf)))))))) @ 93.24/12.30 n_pf))))))))))))))))), 93.24/12.30 inference('comb-normalize', [status(thm)], [zip_derived_cl2511])). 93.24/12.30 thf(zip_derived_cl2513, plain, 93.24/12.30 (![X2 : $i]: 93.24/12.30 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ (=>) @ (moref @ X2))))))) @ 93.24/12.30 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 93.24/12.30 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ moref @ (n_pf @ X2))))))) @ 93.24/12.30 n_pf)))))))))))))), 93.24/12.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2512])). 93.24/12.30 thf(zip_derived_cl2514, plain, 93.24/12.30 (![X2 : $i]: 93.24/12.30 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ (=>) @ (moref @ X2))))))) @ 93.24/12.30 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ 93.24/12.30 moreq)))))) @ 93.24/12.30 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ moref @ (n_pf @ X2))))))) @ 93.24/12.30 n_pf))))))))))))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2513])). 93.24/12.30 thf(zip_derived_cl2515, plain, 93.24/12.30 (![X0 : $i]: 93.24/12.30 ( (((!!) @ (^[Y0 : $i]: 93.24/12.30 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.24/12.30 ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ 93.24/12.30 (pair1type @ nat)))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ (=>) @ (moref @ X0))))))) @ 93.24/12.30 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ ( 93.24/12.30 =>))) @ 93.24/12.30 moreq)))))) @ 93.24/12.30 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ moref @ 93.24/12.30 (n_pf @ X0))))))) @ 93.24/12.30 n_pf)))))))) @ 93.24/12.30 Y0))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2514, '8'])). 93.24/12.30 thf(zip_derived_cl2516, plain, 93.24/12.30 (![X0 : $i]: 93.24/12.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.24/12.30 ((('#C') @ is_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.24/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ 93.24/12.30 (pair1type @ nat)))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ (=>) @ (moref @ X0))))))) @ 93.24/12.30 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ 93.24/12.30 moreq)))))) @ 93.24/12.30 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ moref @ 93.24/12.30 (n_pf @ X0))))))) @ 93.24/12.30 n_pf)))))))))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('comb-normalize', [status(thm)], [zip_derived_cl2515])). 93.24/12.30 thf(zip_derived_cl2517, plain, 93.24/12.30 (![X0 : $i, X2 : $i]: 93.24/12.30 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X2))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 93.24/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.24/12.30 (n_pf @ X2)))))))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2516])). 93.24/12.30 thf(zip_derived_cl2518, plain, 93.24/12.30 (![X0 : $i, X2 : $i]: 93.24/12.30 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X2))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 93.24/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.24/12.30 (n_pf @ X2)))))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2517])). 93.24/12.30 thf(zip_derived_cl2519, plain, 93.24/12.30 (![X0 : $i, X1 : $i]: 93.24/12.30 ( (((!!) @ (^[Y0 : $i]: 93.24/12.30 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.24/12.30 ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X1))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 93.24/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.24/12.30 (n_pf @ X1))))))) @ 93.24/12.30 Y0))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2518, '8'])). 93.24/12.30 thf(zip_derived_cl2520, plain, 93.24/12.30 (![X0 : $i, X1 : $i]: 93.24/12.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.24/12.30 ((('#C') @ is_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.24/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X1))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 93.24/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.24/12.30 (n_pf @ X1))))))))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('comb-normalize', [status(thm)], [zip_derived_cl2519])). 93.24/12.30 thf(zip_derived_cl2521, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X3 : $i]: 93.24/12.30 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.30 ((('#B') @ (((=>) @ (moref @ X0 @ X1))) @ 93.24/12.30 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X3))) @ 93.24/12.30 ((('#B') @ (moref @ (n_pf @ X0 @ X3)) @ (n_pf @ X1)))))))))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2520])). 93.24/12.30 thf(zip_derived_cl2522, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X3 : $i]: 93.24/12.30 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.30 ((('#B') @ (((=>) @ (moref @ X0 @ X1))) @ 93.24/12.30 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X3))) @ 93.24/12.30 ((('#B') @ (moref @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 93.24/12.30 (n_ts @ (num @ X3) @ (den @ X0))) @ 93.24/12.30 (n_ts @ (den @ X0) @ (den @ X3)))) @ 93.24/12.30 (n_pf @ X1)))))))))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('rw', [status(thm)], [zip_derived_cl2521, '5'])). 93.24/12.30 thf(zip_derived_cl2523, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X3 : $i]: 93.24/12.30 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.30 ((('#B') @ (((=>) @ (moref @ X0 @ X1))) @ 93.24/12.30 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X3))) @ 93.24/12.30 ((('#B') @ (moref @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 93.24/12.30 (n_ts @ (num @ X3) @ (den @ X0))) @ 93.24/12.30 (n_ts @ (den @ X0) @ (den @ X3)))) @ 93.24/12.30 (n_pf @ X1)))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2522])). 93.24/12.30 thf(zip_derived_cl2524, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X2 : $i]: 93.24/12.30 ( (((!!) @ (^[Y0 : $i]: 93.24/12.30 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.24/12.30 ((('#B') @ (((=>) @ (moref @ X1 @ X0))) @ 93.24/12.30 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X2))) @ 93.24/12.30 ((('#B') @ (moref @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ 93.24/12.30 (n_ts @ (num @ X1) @ (den @ X2)) @ 93.24/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.24/12.30 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.24/12.30 (n_pf @ X0))))) @ 93.24/12.30 Y0))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2523, '8'])). 93.24/12.30 thf(zip_derived_cl2525, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X2 : $i]: 93.24/12.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.24/12.30 ((('#C') @ is_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.24/12.30 ((('#B') @ (((=>) @ (moref @ X1 @ X0))) @ 93.24/12.30 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X2))) @ 93.24/12.30 ((('#B') @ (moref @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ 93.24/12.30 (n_ts @ (num @ X1) @ (den @ X2)) @ 93.24/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.24/12.30 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.24/12.30 (n_pf @ X0))))))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('comb-normalize', [status(thm)], [zip_derived_cl2524])). 93.24/12.30 thf(zip_derived_cl2526, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.24/12.30 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.24/12.30 (((moref @ X1 @ X0) => 93.24/12.30 (((moreq @ X2 @ X4) => (moref @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.24/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.24/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.24/12.30 (n_pf @ X0 @ X4)))))))) 93.24/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2525])). 93.24/12.30 thf(zip_derived_cl2527, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.24/12.30 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.24/12.30 (((moref @ X1 @ X0) => 93.24/12.30 (((imp @ (imp @ (moref @ X2 @ X4) @ ($false)) @ 93.24/12.30 (n_eq @ X2 @ X4)) => (moref @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.24/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.24/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.24/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.24/12.30 (n_ts @ (den @ X0) @ (den @ X4)))))))))) 93.24/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('rw', [status(thm)], [zip_derived_cl2526, '2', '3', '4', '5'])). 93.24/12.30 thf(zip_derived_cl2528, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.24/12.30 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | (((moref @ X1 @ X0) => 93.24/12.30 (((imp @ (imp @ (moref @ X2 @ X4) @ ($false)) @ 93.24/12.30 (n_eq @ X2 @ X4)) => (moref @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.24/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.24/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.24/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.24/12.30 (n_ts @ (den @ X0) @ (den @ X4)))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2527])). 93.24/12.30 thf(zip_derived_cl2529, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.24/12.30 (~ (moref @ X1 @ X0) 93.24/12.30 | (((imp @ (imp @ (moref @ X2 @ X4) @ ($false)) @ 93.24/12.30 (n_eq @ X2 @ X4)) => (moref @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.24/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.24/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.24/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.24/12.30 (n_ts @ (den @ X0) @ (den @ X4)))))) 93.24/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2528])). 93.24/12.30 thf(zip_derived_cl2530, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.24/12.30 (~ (imp @ (imp @ (moref @ X2 @ X4) @ ($false)) @ (n_eq @ X2 @ X4)) 93.24/12.30 | (moref @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.24/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.24/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.24/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.24/12.30 (n_ts @ (den @ X0) @ (den @ X4)))) 93.24/12.30 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (moref @ X1 @ X0))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2529])). 93.24/12.30 thf(zip_derived_cl2531, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 93.24/12.30 (~ (((imp @ (moref @ X2 @ X3) @ ($false)) => (n_eq @ X2 @ X3))) 93.24/12.30 | ~ (moref @ X1 @ X0) 93.24/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | (moref @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.24/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.24/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 93.24/12.30 (n_ts @ (num @ X3) @ (den @ X0))) @ 93.24/12.30 (n_ts @ (den @ X0) @ (den @ X3)))))), 93.24/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2530, '7'])). 93.24/12.30 thf(zip_derived_cl2533, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 93.24/12.30 (~ (n_eq @ X2 @ X3) 93.24/12.30 | (moref @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.24/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.24/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 93.24/12.30 (n_ts @ (num @ X3) @ (den @ X0))) @ 93.24/12.30 (n_ts @ (den @ X0) @ (den @ X3)))) 93.24/12.30 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (moref @ X1 @ X0))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2531])). 93.24/12.30 thf(zip_derived_cl17058, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 93.24/12.30 (~ (n_eq @ X2 @ X3) 93.24/12.30 | (moref @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.24/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.24/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 93.24/12.30 (n_ts @ (num @ X3) @ (den @ X0))) @ 93.24/12.30 (n_ts @ (den @ X0) @ (den @ X3)))) 93.24/12.30 | ~ (is_of @ X3 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.24/12.30 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.24/12.30 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.24/12.30 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.24/12.30 | ~ (moref @ X1 @ X0))), 93.24/12.30 inference('remove_ty_args', [status(thm)], [zip_derived_cl2533])). 93.24/12.30 thf(zip_derived_cl1334, plain, 93.24/12.30 (~ (((imp @ (imp @ (moref @ '#sk4' @ '#sk5') @ ($false)) @ 93.24/12.30 (n_eq @ '#sk4' @ '#sk5')) => (imp @ 93.24/12.30 (imp @ 93.24/12.30 (moref @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.24/12.30 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.24/12.30 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.24/12.30 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.24/12.30 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @ 93.24/12.30 ($false)) @ 93.24/12.30 (n_eq @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.24/12.30 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.24/12.30 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.24/12.30 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.24/12.30 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))))))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1332])). 93.24/12.30 thf(zip_derived_cl1336, plain, 93.24/12.30 ( (imp @ (imp @ (moref @ '#sk4' @ '#sk5') @ ($false)) @ 93.24/12.30 (n_eq @ '#sk4' @ '#sk5'))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1334])). 93.24/12.30 thf(zip_derived_cl1339, plain, 93.24/12.30 ( (((imp @ (moref @ '#sk4' @ '#sk5') @ ($false)) => (n_eq @ '#sk4' @ 93.24/12.30 '#sk5')))), 93.24/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl1336, '6'])). 93.24/12.30 thf(zip_derived_cl1342, plain, 93.24/12.30 ((~ (imp @ (moref @ '#sk4' @ '#sk5') @ ($false)) 93.24/12.30 | (n_eq @ '#sk4' @ '#sk5'))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1339])). 93.24/12.30 thf(zip_derived_cl1347, plain, 93.24/12.30 ((~ (((moref @ '#sk4' @ '#sk5') => ($false))) | (n_eq @ '#sk4' @ '#sk5'))), 93.24/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl1342, '7'])). 93.24/12.30 thf(zip_derived_cl1349, plain, 93.24/12.30 ((~ (((~) @ (moref @ '#sk4' @ '#sk5'))) | (n_eq @ '#sk4' @ '#sk5'))), 93.24/12.30 inference('simplify boolean subterms', [status(thm)], 93.24/12.30 [zip_derived_cl1347])). 93.24/12.30 thf(zip_derived_cl1350, plain, 93.24/12.30 (( (moref @ '#sk4' @ '#sk5') | (n_eq @ '#sk4' @ '#sk5'))), 93.24/12.30 inference('simplify nested equalities', [status(thm)], 93.24/12.30 [zip_derived_cl1349])). 93.24/12.30 thf(zip_derived_cl1325, plain, 93.24/12.30 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1324])). 93.24/12.30 thf(zip_derived_cl17011, plain, 93.24/12.30 ( (is_of @ '#sk4' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 93.24/12.30 inference('remove_ty_args', [status(thm)], [zip_derived_cl1325])). 93.24/12.30 thf(zip_derived_cl1331, plain, 93.24/12.30 ( (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1330])). 93.24/12.30 thf(zip_derived_cl17012, plain, 93.24/12.30 ( (is_of @ '#sk5' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 93.24/12.30 inference('remove_ty_args', [status(thm)], [zip_derived_cl1331])). 93.24/12.30 thf(zip_derived_cl1313, plain, 93.24/12.30 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1312])). 93.24/12.30 thf(zip_derived_cl17009, plain, 93.24/12.30 ( (is_of @ '#sk2' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 93.24/12.30 inference('remove_ty_args', [status(thm)], [zip_derived_cl1313])). 93.24/12.30 thf(zip_derived_cl1319, plain, 93.24/12.30 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1318])). 93.24/12.30 thf(zip_derived_cl17010, plain, 93.24/12.30 ( (is_of @ '#sk3' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 93.24/12.30 inference('remove_ty_args', [status(thm)], [zip_derived_cl1319])). 93.24/12.30 thf(satz64, axiom, 93.24/12.30 (all_of @ 93.24/12.30 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 93.24/12.30 ( ^[X0:$i]: 93.24/12.30 ( all_of @ 93.24/12.30 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 93.24/12.30 ( ^[X1:$i]: 93.24/12.30 ( all_of @ 93.24/12.30 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 93.24/12.30 ( ^[X2:$i]: 93.24/12.30 ( all_of @ 93.24/12.30 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 93.24/12.30 ( ^[X3:$i]: 93.24/12.30 ( ( moref @ X0 @ X1 ) => 93.24/12.30 ( ( moref @ X2 @ X3 ) => 93.24/12.30 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 93.24/12.30 thf(zip_derived_cl80, plain, 93.24/12.30 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 93.24/12.30 (^[Y0 : $i]: 93.24/12.30 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 93.24/12.30 (^[Y1 : $i]: 93.24/12.30 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 93.24/12.30 (^[Y2 : $i]: 93.24/12.30 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 93.24/12.30 (^[Y3 : $i]: 93.24/12.30 (((moref @ Y0 @ Y1) => 93.24/12.30 (((moref @ Y2 @ Y3) => (moref @ (n_pf @ Y0 @ Y2) @ 93.24/12.30 (n_pf @ Y1 @ Y3))))))))))))))), 93.24/12.30 inference('cnf', [status(esa)], [satz64])). 93.24/12.30 thf(zip_derived_cl81, plain, 93.24/12.30 ( (all_of @ ((('#C') @ in @ frac)) @ 93.24/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 93.24/12.30 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @ 93.24/12.30 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ 93.24/12.30 moref)))))))) @ 93.24/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ ('#C') @ 93.24/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.30 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @ 93.24/12.30 n_pf)))))))))))))), 93.24/12.30 inference('lams2combs', [status(thm)], [zip_derived_cl80])). 93.24/12.30 thf(zip_derived_cl2591, plain, 93.24/12.30 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 93.24/12.30 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ 93.24/12.30 (pair1type @ nat)))))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @ 93.24/12.30 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ 93.24/12.30 moref)))))))) @ 93.24/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ ('#C') @ 93.24/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.30 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @ 93.24/12.30 n_pf)))))))))))))), 93.24/12.30 inference('rw', [status(thm)], [zip_derived_cl81, '0'])). 93.24/12.30 thf(zip_derived_cl2592, plain, 93.24/12.30 ( (((!!) @ (^[Y0 : $i]: 93.24/12.30 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.24/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ 93.24/12.30 (pair1type @ nat)))))) @ 93.24/12.30 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ 93.24/12.30 (pair1type @ nat)))))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ 93.24/12.30 moref)))))))) @ 93.24/12.30 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 93.24/12.30 '#S') @ 93.24/12.30 ((('#B') @ ( 93.24/12.30 (('#B') @ ( 93.24/12.30 =>))) @ 93.24/12.30 moref)))))))) @ 93.24/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ ('#C') @ 93.24/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.30 ((('#B') @ ((('#B') @ moref)) @ 93.24/12.30 n_pf)))))))) @ 93.24/12.30 n_pf)))))))))) @ 93.24/12.30 Y0)))))))), 93.24/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2591, '8'])). 93.24/12.30 thf(zip_derived_cl2593, plain, 93.24/12.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.24/12.30 ((('#C') @ is_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.24/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.24/12.30 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ 93.24/12.30 (pair1type @ nat)))))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @ 93.24/12.30 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 93.24/12.30 '#S') @ 93.24/12.30 ((('#B') @ ( 93.24/12.30 (('#B') @ (=>))) @ 93.24/12.30 moref)))))))) @ 93.24/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ ('#C') @ 93.24/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.24/12.30 ((('#B') @ ((('#B') @ moref)) @ 93.24/12.30 n_pf)))))))) @ 93.24/12.30 n_pf))))))))))))))))), 93.24/12.30 inference('comb-normalize', [status(thm)], [zip_derived_cl2592])). 93.24/12.30 thf(zip_derived_cl2594, plain, 93.24/12.30 (![X2 : $i]: 93.24/12.30 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ (=>) @ (moref @ X2))))))) @ 93.24/12.30 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 93.24/12.30 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ moref @ (n_pf @ X2))))))) @ 93.24/12.30 n_pf)))))))))))))), 93.24/12.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2593])). 93.24/12.30 thf(zip_derived_cl2595, plain, 93.24/12.30 (![X2 : $i]: 93.24/12.30 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ (=>) @ (moref @ X2))))))) @ 93.24/12.30 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ 93.24/12.30 moref)))))) @ 93.24/12.30 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ moref @ (n_pf @ X2))))))) @ 93.24/12.30 n_pf))))))))))))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2594])). 93.24/12.30 thf(zip_derived_cl2596, plain, 93.24/12.30 (![X0 : $i]: 93.24/12.30 ( (((!!) @ (^[Y0 : $i]: 93.24/12.30 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.24/12.30 ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ 93.24/12.30 (pair1type @ nat)))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ (=>) @ (moref @ X0))))))) @ 93.24/12.30 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ ( 93.24/12.30 =>))) @ 93.24/12.30 moref)))))) @ 93.24/12.30 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ moref @ 93.24/12.30 (n_pf @ X0))))))) @ 93.24/12.30 n_pf)))))))) @ 93.24/12.30 Y0))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2595, '8'])). 93.24/12.30 thf(zip_derived_cl2597, plain, 93.24/12.30 (![X0 : $i]: 93.24/12.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.24/12.30 ((('#C') @ is_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.24/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ 93.24/12.30 (pair1type @ nat)))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ (=>) @ (moref @ X0))))))) @ 93.24/12.30 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ 93.24/12.30 moref)))))) @ 93.24/12.30 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ moref @ 93.24/12.30 (n_pf @ X0))))))) @ 93.24/12.30 n_pf)))))))))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('comb-normalize', [status(thm)], [zip_derived_cl2596])). 93.24/12.30 thf(zip_derived_cl2598, plain, 93.24/12.30 (![X0 : $i, X2 : $i]: 93.24/12.30 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X2))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.24/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.24/12.30 (n_pf @ X2)))))))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2597])). 93.24/12.30 thf(zip_derived_cl2599, plain, 93.24/12.30 (![X0 : $i, X2 : $i]: 93.24/12.30 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X2))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.24/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.24/12.30 (n_pf @ X2)))))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2598])). 93.24/12.30 thf(zip_derived_cl2600, plain, 93.24/12.30 (![X0 : $i, X1 : $i]: 93.24/12.30 ( (((!!) @ (^[Y0 : $i]: 93.24/12.30 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.24/12.30 ((('#B') @ (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X1))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.24/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.24/12.30 (n_pf @ X1))))))) @ 93.24/12.30 Y0))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2599, '8'])). 93.24/12.30 thf(zip_derived_cl2601, plain, 93.24/12.30 (![X0 : $i, X1 : $i]: 93.24/12.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.24/12.30 ((('#C') @ is_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.24/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.24/12.30 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X1))))) @ 93.24/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.24/12.30 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.24/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.24/12.30 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.24/12.30 (n_pf @ X1))))))))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('comb-normalize', [status(thm)], [zip_derived_cl2600])). 93.24/12.30 thf(zip_derived_cl2602, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X3 : $i]: 93.24/12.30 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.30 ((('#B') @ (((=>) @ (moref @ X0 @ X1))) @ 93.24/12.30 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 93.24/12.30 ((('#B') @ (moref @ (n_pf @ X0 @ X3)) @ (n_pf @ X1)))))))))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2601])). 93.24/12.30 thf(zip_derived_cl2603, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X3 : $i]: 93.24/12.30 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.24/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.30 ((('#B') @ (((=>) @ (moref @ X0 @ X1))) @ 93.24/12.30 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 93.24/12.30 ((('#B') @ (moref @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 93.24/12.30 (n_ts @ (num @ X3) @ (den @ X0))) @ 93.24/12.30 (n_ts @ (den @ X0) @ (den @ X3)))) @ 93.24/12.30 (n_pf @ X1)))))))))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('rw', [status(thm)], [zip_derived_cl2602, '5'])). 93.24/12.30 thf(zip_derived_cl2604, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X3 : $i]: 93.24/12.30 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.24/12.30 ((('#B') @ (((=>) @ (moref @ X0 @ X1))) @ 93.24/12.30 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 93.24/12.30 ((('#B') @ (moref @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 93.24/12.30 (n_ts @ (num @ X3) @ (den @ X0))) @ 93.24/12.30 (n_ts @ (den @ X0) @ (den @ X3)))) @ 93.24/12.30 (n_pf @ X1)))))))) 93.24/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.24/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.24/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2603])). 93.24/12.30 thf(zip_derived_cl2605, plain, 93.24/12.30 (![X0 : $i, X1 : $i, X2 : $i]: 93.24/12.30 ( (((!!) @ (^[Y0 : $i]: 93.24/12.30 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.24/12.30 ((('#B') @ (((=>) @ (moref @ X1 @ X0))) @ 93.24/12.30 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 93.24/12.30 ((('#B') @ (moref @ 93.24/12.30 (n_fr @ 93.24/12.30 (n_pl @ 93.24/12.30 (n_ts @ (num @ X1) @ (den @ X2)) @ 93.24/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.24/12.30 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.24/12.30 (n_pf @ X0))))) @ 93.50/12.30 Y0))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2604, '8'])). 93.50/12.30 thf(zip_derived_cl2606, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i]: 93.50/12.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.50/12.30 ((('#C') @ is_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.50/12.30 ((('#B') @ (((=>) @ (moref @ X1 @ X0))) @ 93.50/12.30 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 93.50/12.30 ((('#B') @ (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ 93.50/12.30 (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.50/12.30 (n_pf @ X0))))))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('comb-normalize', [status(thm)], [zip_derived_cl2605])). 93.50/12.30 thf(zip_derived_cl2607, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.50/12.30 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.50/12.30 (((moref @ X1 @ X0) => 93.50/12.30 (((moref @ X2 @ X4) => (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.50/12.30 (n_pf @ X0 @ X4)))))))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2606])). 93.50/12.30 thf(zip_derived_cl2608, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.50/12.30 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.50/12.30 (((moref @ X1 @ X0) => 93.50/12.30 (((moref @ X2 @ X4) => (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.50/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X4)))))))))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('rw', [status(thm)], [zip_derived_cl2607, '5'])). 93.50/12.30 thf(zip_derived_cl2609, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.50/12.30 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | (((moref @ X1 @ X0) => 93.50/12.30 (((moref @ X2 @ X4) => (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.50/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X4)))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2608])). 93.50/12.30 thf(zip_derived_cl2610, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.50/12.30 (~ (moref @ X1 @ X0) 93.50/12.30 | (((moref @ X2 @ X4) => (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.50/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X4)))))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2609])). 93.50/12.30 thf(zip_derived_cl2611, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.50/12.30 (~ (moref @ X2 @ X4) 93.50/12.30 | (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.50/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X4)))) 93.50/12.30 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (moref @ X1 @ X0))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2610])). 93.50/12.30 thf(zip_derived_cl17062, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.50/12.30 (~ (moref @ X2 @ X4) 93.50/12.30 | (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.50/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X4)))) 93.50/12.30 | ~ (is_of @ X4 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.50/12.30 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.50/12.30 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.50/12.30 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.50/12.30 | ~ (moref @ X1 @ X0))), 93.50/12.30 inference('remove_ty_args', [status(thm)], [zip_derived_cl2611])). 93.50/12.30 thf(zip_derived_cl1337, plain, 93.50/12.30 (~ (imp @ 93.50/12.30 (imp @ 93.50/12.30 (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.50/12.30 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.50/12.30 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.50/12.30 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.50/12.30 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @ 93.50/12.30 ($false)) @ 93.50/12.30 (n_eq @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.50/12.30 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.50/12.30 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.50/12.30 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.50/12.30 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1334])). 93.50/12.30 thf(zip_derived_cl1340, plain, 93.50/12.30 (~ (((imp @ 93.50/12.30 (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.50/12.30 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.50/12.30 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.50/12.30 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.50/12.30 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @ 93.50/12.30 ($false)) => (n_eq @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.50/12.30 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.50/12.30 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.50/12.30 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.50/12.30 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))))), 93.50/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl1337, '7'])). 93.50/12.30 thf(zip_derived_cl1344, plain, 93.50/12.30 (~ (n_eq @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.50/12.30 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.50/12.30 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.50/12.30 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.50/12.30 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1340])). 93.50/12.30 thf(zip_derived_cl1343, plain, 93.50/12.30 ( (imp @ 93.50/12.30 (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.50/12.30 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.50/12.30 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.50/12.30 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.50/12.30 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @ 93.50/12.30 ($false))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1340])). 93.50/12.30 thf(zip_derived_cl1348, plain, 93.50/12.30 ( (((moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.50/12.30 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.50/12.30 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.50/12.30 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.50/12.30 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) => 93.50/12.30 ($false)))), 93.50/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl1343, '6'])). 93.50/12.30 thf(zip_derived_cl1351, plain, 93.50/12.30 ( (((~) @ (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.50/12.30 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.50/12.30 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.50/12.30 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.50/12.30 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))))), 93.50/12.30 inference('simplify boolean subterms', [status(thm)], 93.50/12.30 [zip_derived_cl1348])). 93.50/12.30 thf(zip_derived_cl1352, plain, 93.50/12.30 (~ (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.50/12.30 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.50/12.30 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.50/12.30 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.50/12.30 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))), 93.50/12.30 inference('simplify nested equalities', [status(thm)], 93.50/12.30 [zip_derived_cl1351])). 93.50/12.30 thf(satz56, axiom, 93.50/12.30 (all_of @ 93.50/12.30 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 93.50/12.30 ( ^[X0:$i]: 93.50/12.30 ( all_of @ 93.50/12.30 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 93.50/12.30 ( ^[X1:$i]: 93.50/12.30 ( all_of @ 93.50/12.30 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 93.50/12.30 ( ^[X2:$i]: 93.50/12.30 ( all_of @ 93.50/12.30 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 93.50/12.30 ( ^[X3:$i]: 93.50/12.30 ( ( n_eq @ X0 @ X1 ) => 93.50/12.30 ( ( n_eq @ X2 @ X3 ) => 93.50/12.30 ( n_eq @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 93.50/12.30 thf(zip_derived_cl210, plain, 93.50/12.30 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 93.50/12.30 (^[Y0 : $i]: 93.50/12.30 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 93.50/12.30 (^[Y1 : $i]: 93.50/12.30 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 93.50/12.30 (^[Y2 : $i]: 93.50/12.30 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 93.50/12.30 (^[Y3 : $i]: 93.50/12.30 (((n_eq @ Y0 @ Y1) => 93.50/12.30 (((n_eq @ Y2 @ Y3) => (n_eq @ (n_pf @ Y0 @ Y2) @ 93.50/12.30 (n_pf @ Y1 @ Y3))))))))))))))), 93.50/12.30 inference('cnf', [status(esa)], [satz56])). 93.50/12.30 thf(zip_derived_cl211, plain, 93.50/12.30 ( (all_of @ ((('#C') @ in @ frac)) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ 93.50/12.30 n_eq)))))))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ ('#C') @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ n_eq)) @ n_pf)))))))) @ 93.50/12.30 n_pf)))))))))))))), 93.50/12.30 inference('lams2combs', [status(thm)], [zip_derived_cl210])). 93.50/12.30 thf(zip_derived_cl2957, plain, 93.50/12.30 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ 93.50/12.30 (pair1type @ nat)))))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ 93.50/12.30 n_eq)))))))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ ('#C') @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ n_eq)) @ n_pf)))))))) @ 93.50/12.30 n_pf)))))))))))))), 93.50/12.30 inference('rw', [status(thm)], [zip_derived_cl211, '0'])). 93.50/12.30 thf(zip_derived_cl2958, plain, 93.50/12.30 ( (((!!) @ (^[Y0 : $i]: 93.50/12.30 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ 93.50/12.30 (pair1type @ nat)))))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ 93.50/12.30 (pair1type @ nat)))))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ 93.50/12.30 n_eq)))))))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 93.50/12.30 '#S') @ 93.50/12.30 ((('#B') @ ( 93.50/12.30 (('#B') @ ( 93.50/12.30 =>))) @ 93.50/12.30 n_eq)))))))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ ('#C') @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ n_eq)) @ 93.50/12.30 n_pf)))))))) @ 93.50/12.30 n_pf)))))))))) @ 93.50/12.30 Y0)))))))), 93.50/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2957, '8'])). 93.50/12.30 thf(zip_derived_cl2959, plain, 93.50/12.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.50/12.30 ((('#C') @ is_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ 93.50/12.30 (pair1type @ nat)))))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 93.50/12.30 '#S') @ 93.50/12.30 ((('#B') @ ( 93.50/12.30 (('#B') @ (=>))) @ 93.50/12.30 n_eq)))))))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ ('#C') @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ n_eq)) @ 93.50/12.30 n_pf)))))))) @ 93.50/12.30 n_pf))))))))))))))))), 93.50/12.30 inference('comb-normalize', [status(thm)], [zip_derived_cl2958])). 93.50/12.30 thf(zip_derived_cl2960, plain, 93.50/12.30 (![X2 : $i]: 93.50/12.30 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ (=>) @ (n_eq @ X2))))))) @ 93.50/12.30 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 93.50/12.30 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ n_eq @ (n_pf @ X2))))))) @ 93.50/12.30 n_pf)))))))))))))), 93.50/12.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2959])). 93.50/12.30 thf(zip_derived_cl2961, plain, 93.50/12.30 (![X2 : $i]: 93.50/12.30 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ (=>) @ (n_eq @ X2))))))) @ 93.50/12.30 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 93.50/12.30 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ n_eq @ (n_pf @ X2))))))) @ 93.50/12.30 n_pf))))))))))))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2960])). 93.50/12.30 thf(zip_derived_cl2962, plain, 93.50/12.30 (![X0 : $i]: 93.50/12.30 ( (((!!) @ (^[Y0 : $i]: 93.50/12.30 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.50/12.30 ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ 93.50/12.30 (pair1type @ nat)))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ (=>) @ (n_eq @ X0))))))) @ 93.50/12.30 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ ( 93.50/12.30 =>))) @ 93.50/12.30 n_eq)))))) @ 93.50/12.30 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ n_eq @ 93.50/12.30 (n_pf @ X0))))))) @ 93.50/12.30 n_pf)))))))) @ 93.50/12.30 Y0))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2961, '8'])). 93.50/12.30 thf(zip_derived_cl2963, plain, 93.50/12.30 (![X0 : $i]: 93.50/12.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.50/12.30 ((('#C') @ is_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ 93.50/12.30 (pair1type @ nat)))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ (=>) @ (n_eq @ X0))))))) @ 93.50/12.30 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ 93.50/12.30 n_eq)))))) @ 93.50/12.30 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ n_eq @ 93.50/12.30 (n_pf @ X0))))))) @ 93.50/12.30 n_pf)))))))))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('comb-normalize', [status(thm)], [zip_derived_cl2962])). 93.50/12.30 thf(zip_derived_cl2964, plain, 93.50/12.30 (![X0 : $i, X2 : $i]: 93.50/12.30 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ n_eq @ (n_pf @ X0))))) @ 93.50/12.30 (n_pf @ X2)))))))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2963])). 93.50/12.30 thf(zip_derived_cl2965, plain, 93.50/12.30 (![X0 : $i, X2 : $i]: 93.50/12.30 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ n_eq @ (n_pf @ X0))))) @ 93.50/12.30 (n_pf @ X2)))))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2964])). 93.50/12.30 thf(zip_derived_cl2966, plain, 93.50/12.30 (![X0 : $i, X1 : $i]: 93.50/12.30 ( (((!!) @ (^[Y0 : $i]: 93.50/12.30 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.50/12.30 ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ n_eq @ (n_pf @ X0))))) @ 93.50/12.30 (n_pf @ X1))))))) @ 93.50/12.30 Y0))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2965, '8'])). 93.50/12.30 thf(zip_derived_cl2967, plain, 93.50/12.30 (![X0 : $i, X1 : $i]: 93.50/12.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.50/12.30 ((('#C') @ is_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ n_eq @ (n_pf @ X0))))) @ 93.50/12.30 (n_pf @ X1))))))))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('comb-normalize', [status(thm)], [zip_derived_cl2966])). 93.50/12.30 thf(zip_derived_cl2968, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X3 : $i]: 93.50/12.30 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @ 93.50/12.30 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X3))) @ 93.50/12.30 ((('#B') @ (n_eq @ (n_pf @ X0 @ X3)) @ (n_pf @ X1)))))))))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2967])). 93.50/12.30 thf(zip_derived_cl2969, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X3 : $i]: 93.50/12.30 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @ 93.50/12.30 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X3))) @ 93.50/12.30 ((('#B') @ (n_eq @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 93.50/12.30 (n_ts @ (num @ X3) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X3)))) @ 93.50/12.30 (n_pf @ X1)))))))))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('rw', [status(thm)], [zip_derived_cl2968, '5'])). 93.50/12.30 thf(zip_derived_cl2970, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X3 : $i]: 93.50/12.30 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @ 93.50/12.30 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X3))) @ 93.50/12.30 ((('#B') @ (n_eq @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 93.50/12.30 (n_ts @ (num @ X3) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X3)))) @ 93.50/12.30 (n_pf @ X1)))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2969])). 93.50/12.30 thf(zip_derived_cl2971, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i]: 93.50/12.30 ( (((!!) @ (^[Y0 : $i]: 93.50/12.30 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.50/12.30 ((('#B') @ (((=>) @ (n_eq @ X1 @ X0))) @ 93.50/12.30 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ 93.50/12.30 ((('#B') @ (n_eq @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ 93.50/12.30 (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.50/12.30 (n_pf @ X0))))) @ 93.50/12.30 Y0))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2970, '8'])). 93.50/12.30 thf(zip_derived_cl2972, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i]: 93.50/12.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.50/12.30 ((('#C') @ is_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.50/12.30 ((('#B') @ (((=>) @ (n_eq @ X1 @ X0))) @ 93.50/12.30 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ 93.50/12.30 ((('#B') @ (n_eq @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ 93.50/12.30 (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.50/12.30 (n_pf @ X0))))))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('comb-normalize', [status(thm)], [zip_derived_cl2971])). 93.50/12.30 thf(zip_derived_cl2973, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.50/12.30 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.50/12.30 (((n_eq @ X1 @ X0) => 93.50/12.30 (((n_eq @ X2 @ X4) => (n_eq @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.50/12.30 (n_pf @ X0 @ X4)))))))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2972])). 93.50/12.30 thf(zip_derived_cl2974, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.50/12.30 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.50/12.30 (((n_eq @ X1 @ X0) => 93.50/12.30 (((n_eq @ X2 @ X4) => (n_eq @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.50/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X4)))))))))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('rw', [status(thm)], [zip_derived_cl2973, '5'])). 93.50/12.30 thf(zip_derived_cl2975, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.50/12.30 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | (((n_eq @ X1 @ X0) => 93.50/12.30 (((n_eq @ X2 @ X4) => (n_eq @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.50/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X4)))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2974])). 93.50/12.30 thf(zip_derived_cl2976, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.50/12.30 (~ (n_eq @ X1 @ X0) 93.50/12.30 | (((n_eq @ X2 @ X4) => (n_eq @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.50/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X4)))))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2975])). 93.50/12.30 thf(zip_derived_cl2977, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.50/12.30 (~ (n_eq @ X2 @ X4) 93.50/12.30 | (n_eq @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.50/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X4)))) 93.50/12.30 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (n_eq @ X1 @ X0))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2976])). 93.50/12.30 thf(zip_derived_cl17074, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.50/12.30 (~ (n_eq @ X2 @ X4) 93.50/12.30 | (n_eq @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.50/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X4)))) 93.50/12.30 | ~ (is_of @ X4 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.50/12.30 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.50/12.30 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.50/12.30 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.50/12.30 | ~ (n_eq @ X1 @ X0))), 93.50/12.30 inference('remove_ty_args', [status(thm)], [zip_derived_cl2977])). 93.50/12.30 thf(satz65a, axiom, 93.50/12.30 (all_of @ 93.50/12.30 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 93.50/12.30 ( ^[X0:$i]: 93.50/12.30 ( all_of @ 93.50/12.30 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 93.50/12.30 ( ^[X1:$i]: 93.50/12.30 ( all_of @ 93.50/12.30 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 93.50/12.30 ( ^[X2:$i]: 93.50/12.30 ( all_of @ 93.50/12.30 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 93.50/12.30 ( ^[X3:$i]: 93.50/12.30 ( ( moreq @ X0 @ X1 ) => 93.50/12.30 ( ( moref @ X2 @ X3 ) => 93.50/12.30 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 93.50/12.30 thf(zip_derived_cl234, plain, 93.50/12.30 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 93.50/12.30 (^[Y0 : $i]: 93.50/12.30 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 93.50/12.30 (^[Y1 : $i]: 93.50/12.30 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 93.50/12.30 (^[Y2 : $i]: 93.50/12.30 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 93.50/12.30 (^[Y3 : $i]: 93.50/12.30 (((moreq @ Y0 @ Y1) => 93.50/12.30 (((moref @ Y2 @ Y3) => (moref @ (n_pf @ Y0 @ Y2) @ 93.50/12.30 (n_pf @ Y1 @ Y3))))))))))))))), 93.50/12.30 inference('cnf', [status(esa)], [satz65a])). 93.50/12.30 thf(zip_derived_cl235, plain, 93.50/12.30 ( (all_of @ ((('#C') @ in @ frac)) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ 93.50/12.30 moref)))))))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ ('#C') @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @ 93.50/12.30 n_pf)))))))))))))), 93.50/12.30 inference('lams2combs', [status(thm)], [zip_derived_cl234])). 93.50/12.30 thf(zip_derived_cl2701, plain, 93.50/12.30 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ 93.50/12.30 (pair1type @ nat)))))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ 93.50/12.30 moref)))))))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ ('#C') @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @ 93.50/12.30 n_pf)))))))))))))), 93.50/12.30 inference('rw', [status(thm)], [zip_derived_cl235, '0'])). 93.50/12.30 thf(zip_derived_cl2702, plain, 93.50/12.30 ( (((!!) @ (^[Y0 : $i]: 93.50/12.30 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ 93.50/12.30 (pair1type @ nat)))))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ 93.50/12.30 (pair1type @ nat)))))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ 93.50/12.30 moreq)))))))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 93.50/12.30 '#S') @ 93.50/12.30 ((('#B') @ ( 93.50/12.30 (('#B') @ ( 93.50/12.30 =>))) @ 93.50/12.30 moref)))))))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ ('#C') @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ moref)) @ 93.50/12.30 n_pf)))))))) @ 93.50/12.30 n_pf)))))))))) @ 93.50/12.30 Y0)))))))), 93.50/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2701, '8'])). 93.50/12.30 thf(zip_derived_cl2703, plain, 93.50/12.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.50/12.30 ((('#C') @ is_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ 93.50/12.30 (pair1type @ nat)))))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @ 93.50/12.30 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 93.50/12.30 '#S') @ 93.50/12.30 ((('#B') @ ( 93.50/12.30 (('#B') @ (=>))) @ 93.50/12.30 moref)))))))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ ('#C') @ 93.50/12.30 ((('#B') @ ((('#B') @ ('#B'))) @ 93.50/12.30 ((('#B') @ ((('#B') @ moref)) @ 93.50/12.30 n_pf)))))))) @ 93.50/12.30 n_pf))))))))))))))))), 93.50/12.30 inference('comb-normalize', [status(thm)], [zip_derived_cl2702])). 93.50/12.30 thf(zip_derived_cl2704, plain, 93.50/12.30 (![X2 : $i]: 93.50/12.30 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ (=>) @ (moreq @ X2))))))) @ 93.50/12.30 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 93.50/12.30 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ moref @ (n_pf @ X2))))))) @ 93.50/12.30 n_pf)))))))))))))), 93.50/12.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2703])). 93.50/12.30 thf(zip_derived_cl2705, plain, 93.50/12.30 (![X2 : $i]: 93.50/12.30 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ (=>) @ (moreq @ X2))))))) @ 93.50/12.30 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ 93.50/12.30 moref)))))) @ 93.50/12.30 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ moref @ (n_pf @ X2))))))) @ 93.50/12.30 n_pf))))))))))))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2704])). 93.50/12.30 thf(zip_derived_cl2706, plain, 93.50/12.30 (![X0 : $i]: 93.50/12.30 ( (((!!) @ (^[Y0 : $i]: 93.50/12.30 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.50/12.30 ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ 93.50/12.30 (pair1type @ nat)))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ (=>) @ (moreq @ X0))))))) @ 93.50/12.30 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ ( 93.50/12.30 =>))) @ 93.50/12.30 moref)))))) @ 93.50/12.30 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ moref @ 93.50/12.30 (n_pf @ X0))))))) @ 93.50/12.30 n_pf)))))))) @ 93.50/12.30 Y0))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2705, '8'])). 93.50/12.30 thf(zip_derived_cl2707, plain, 93.50/12.30 (![X0 : $i]: 93.50/12.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.50/12.30 ((('#C') @ is_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ 93.50/12.30 (pair1type @ nat)))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ (=>) @ (moreq @ X0))))))) @ 93.50/12.30 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ 93.50/12.30 moref)))))) @ 93.50/12.30 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ moref @ 93.50/12.30 (n_pf @ X0))))))) @ 93.50/12.30 n_pf)))))))))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('comb-normalize', [status(thm)], [zip_derived_cl2706])). 93.50/12.30 thf(zip_derived_cl2708, plain, 93.50/12.30 (![X0 : $i, X2 : $i]: 93.50/12.30 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (((=>) @ (moreq @ X0 @ X2))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.50/12.30 (n_pf @ X2)))))))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2707])). 93.50/12.30 thf(zip_derived_cl2709, plain, 93.50/12.30 (![X0 : $i, X2 : $i]: 93.50/12.30 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 93.50/12.30 (imp @ (moref @ X0 @ X2) @ 93.50/12.30 ($false)) @ 93.50/12.30 (n_eq @ X0 @ X2)))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.50/12.30 (n_pf @ X2)))))))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('rw', [status(thm)], [zip_derived_cl2708, '2', '3', '4'])). 93.50/12.30 thf(zip_derived_cl2710, plain, 93.50/12.30 (![X0 : $i, X2 : $i]: 93.50/12.30 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 93.50/12.30 (imp @ (moref @ X0 @ X2) @ 93.50/12.30 ($false)) @ 93.50/12.30 (n_eq @ X0 @ X2)))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.50/12.30 (n_pf @ X2)))))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2709])). 93.50/12.30 thf(zip_derived_cl2711, plain, 93.50/12.30 (![X0 : $i, X1 : $i]: 93.50/12.30 ( (((!!) @ (^[Y0 : $i]: 93.50/12.30 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.50/12.30 ((('#B') @ (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 93.50/12.30 (imp @ 93.50/12.30 (moref @ X0 @ X1) @ 93.50/12.30 ($false)) @ 93.50/12.30 (n_eq @ X0 @ X1)))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.50/12.30 (n_pf @ X1))))))) @ 93.50/12.30 Y0))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2710, '8'])). 93.50/12.30 thf(zip_derived_cl2712, plain, 93.50/12.30 (![X0 : $i, X1 : $i]: 93.50/12.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.50/12.30 ((('#C') @ is_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.50/12.30 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.50/12.30 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 93.50/12.30 (imp @ 93.50/12.30 (moref @ X0 @ X1) @ 93.50/12.30 ($false)) @ 93.50/12.30 (n_eq @ X0 @ X1)))))) @ 93.50/12.30 ((('#S') @ ((('#B') @ ('#S') @ 93.50/12.30 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.50/12.30 ((('#C') @ ((('#B') @ ('#B') @ 93.50/12.30 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.50/12.30 (n_pf @ X1))))))))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('comb-normalize', [status(thm)], [zip_derived_cl2711])). 93.50/12.30 thf(zip_derived_cl2713, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X3 : $i]: 93.50/12.30 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (((=>) @ (imp @ (imp @ (moref @ X0 @ X1) @ ($false)) @ 93.50/12.30 (n_eq @ X0 @ X1)))) @ 93.50/12.30 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 93.50/12.30 ((('#B') @ (moref @ (n_pf @ X0 @ X3)) @ (n_pf @ X1)))))))))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2712])). 93.50/12.30 thf(zip_derived_cl2714, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X3 : $i]: 93.50/12.30 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (((=>) @ (imp @ (imp @ (moref @ X0 @ X1) @ ($false)) @ 93.50/12.30 (n_eq @ X0 @ X1)))) @ 93.50/12.30 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 93.50/12.30 ((('#B') @ (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 93.50/12.30 (n_ts @ (num @ X3) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X3)))) @ 93.50/12.30 (n_pf @ X1)))))))))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('rw', [status(thm)], [zip_derived_cl2713, '5'])). 93.50/12.30 thf(zip_derived_cl2715, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X3 : $i]: 93.50/12.30 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.50/12.30 ((('#B') @ (((=>) @ (imp @ 93.50/12.30 (imp @ (moref @ X0 @ X1) @ ($false)) @ 93.50/12.30 (n_eq @ X0 @ X1)))) @ 93.50/12.30 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 93.50/12.30 ((('#B') @ (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 93.50/12.30 (n_ts @ (num @ X3) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X3)))) @ 93.50/12.30 (n_pf @ X1)))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2714])). 93.50/12.30 thf(zip_derived_cl2716, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i]: 93.50/12.30 ( (((!!) @ (^[Y0 : $i]: 93.50/12.30 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.50/12.30 ((('#B') @ (((=>) @ (imp @ 93.50/12.30 (imp @ (moref @ X1 @ X0) @ 93.50/12.30 ($false)) @ 93.50/12.30 (n_eq @ X1 @ X0)))) @ 93.50/12.30 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 93.50/12.30 ((('#B') @ (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ 93.50/12.30 (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.50/12.30 (n_pf @ X0))))) @ 93.50/12.30 Y0))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2715, '8'])). 93.50/12.30 thf(zip_derived_cl2717, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i]: 93.50/12.30 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.50/12.30 ((('#C') @ is_of @ 93.50/12.30 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.50/12.30 ((('#B') @ (((=>) @ (imp @ 93.50/12.30 (imp @ (moref @ X1 @ X0) @ ($false)) @ 93.50/12.30 (n_eq @ X1 @ X0)))) @ 93.50/12.30 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 93.50/12.30 ((('#B') @ (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ 93.50/12.30 (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.50/12.30 (n_pf @ X0))))))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('comb-normalize', [status(thm)], [zip_derived_cl2716])). 93.50/12.30 thf(zip_derived_cl2718, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.50/12.30 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.50/12.30 (((imp @ (imp @ (moref @ X1 @ X0) @ ($false)) @ 93.50/12.30 (n_eq @ X1 @ X0)) => 93.50/12.30 (((moref @ X2 @ X4) => (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.50/12.30 (n_pf @ X0 @ X4)))))))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2717])). 93.50/12.30 thf(zip_derived_cl2719, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.50/12.30 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.50/12.30 (((imp @ (imp @ (moref @ X1 @ X0) @ ($false)) @ 93.50/12.30 (n_eq @ X1 @ X0)) => 93.50/12.30 (((moref @ X2 @ X4) => (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.50/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X4)))))))))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('rw', [status(thm)], [zip_derived_cl2718, '5'])). 93.50/12.30 thf(zip_derived_cl2720, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.50/12.30 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | (((imp @ (imp @ (moref @ X1 @ X0) @ ($false)) @ 93.50/12.30 (n_eq @ X1 @ X0)) => 93.50/12.30 (((moref @ X2 @ X4) => (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.50/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X4)))))))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2719])). 93.50/12.30 thf(zip_derived_cl2721, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.50/12.30 (~ (imp @ (imp @ (moref @ X1 @ X0) @ ($false)) @ (n_eq @ X1 @ X0)) 93.50/12.30 | (((moref @ X2 @ X4) => (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.50/12.30 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.50/12.30 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.50/12.30 (n_ts @ (den @ X0) @ (den @ X4)))))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2720])). 93.50/12.30 thf(zip_derived_cl2722, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 93.50/12.30 (~ (((imp @ (moref @ X2 @ X1) @ ($false)) => (n_eq @ X2 @ X1))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | (((moref @ X3 @ X0) => (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X2) @ (den @ X3)) @ 93.50/12.30 (n_ts @ (num @ X3) @ (den @ X2))) @ 93.50/12.30 (n_ts @ (den @ X2) @ (den @ X3))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X0)) @ 93.50/12.30 (n_ts @ (num @ X0) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X0)))))))), 93.50/12.30 inference('rw_clause', [status(thm)], [zip_derived_cl2721, '7'])). 93.50/12.30 thf(zip_derived_cl2724, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 93.50/12.30 (~ (n_eq @ X2 @ X1) 93.50/12.30 | (((moref @ X3 @ X0) => (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X2) @ (den @ X3)) @ 93.50/12.30 (n_ts @ (num @ X3) @ (den @ X2))) @ 93.50/12.30 (n_ts @ (den @ X2) @ (den @ X3))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X0)) @ 93.50/12.30 (n_ts @ (num @ X0) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X0)))))) 93.50/12.30 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2722])). 93.50/12.30 thf(zip_derived_cl2726, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 93.50/12.30 (~ (moref @ X3 @ X0) 93.50/12.30 | (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X2) @ (den @ X3)) @ 93.50/12.30 (n_ts @ (num @ X3) @ (den @ X2))) @ 93.50/12.30 (n_ts @ (den @ X2) @ (den @ X3))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X0)) @ 93.50/12.30 (n_ts @ (num @ X0) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X0)))) 93.50/12.30 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 93.50/12.30 | ~ (n_eq @ X2 @ X1))), 93.50/12.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2724])). 93.50/12.30 thf(zip_derived_cl17066, plain, 93.50/12.30 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 93.50/12.30 (~ (moref @ X3 @ X0) 93.50/12.30 | (moref @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X2) @ (den @ X3)) @ 93.50/12.30 (n_ts @ (num @ X3) @ (den @ X2))) @ 93.50/12.30 (n_ts @ (den @ X2) @ (den @ X3))) @ 93.50/12.30 (n_fr @ 93.50/12.30 (n_pl @ (n_ts @ (num @ X1) @ (den @ X0)) @ 93.50/12.30 (n_ts @ (num @ X0) @ (den @ X1))) @ 93.50/12.30 (n_ts @ (den @ X1) @ (den @ X0)))) 93.50/12.30 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.50/12.30 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.50/12.30 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.50/12.30 | ~ (is_of @ X3 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.50/12.30 | ~ (n_eq @ X2 @ X1))), 93.50/12.30 inference('remove_ty_args', [status(thm)], [zip_derived_cl2726])). 93.50/12.30 thf(zip_derived_cl17100, plain, ($false), 93.50/12.30 inference('eprover', [status(thm)], 93.50/12.30 [zip_derived_cl1346, zip_derived_cl17058, zip_derived_cl1350, 93.50/12.30 zip_derived_cl17011, zip_derived_cl17012, 93.50/12.30 zip_derived_cl17009, zip_derived_cl17010, 93.50/12.30 zip_derived_cl17062, zip_derived_cl1344, zip_derived_cl1352, 93.50/12.30 zip_derived_cl17074, zip_derived_cl17066])). 93.50/12.30 93.50/12.30 % SZS output end Refutation 93.50/12.30 93.50/12.30 93.50/12.30 % Terminating... 93.74/12.39 % Runner terminated. 93.74/12.39 % Zipperpin 1.5 exiting 93.74/12.39 EOF