0.12/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.16 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Gl7ft9juGA true 0.16/0.36 % Computer : n023.cluster.edu 0.16/0.36 % Model : x86_64 x86_64 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.36 % Memory : 8042.1875MB 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.36 % CPULimit : 960 0.16/0.36 % WCLimit : 120 0.16/0.36 % DateTime : Tue Aug 9 08:13:58 EDT 2022 0.16/0.36 % CPUTime : 0.16/0.36 % Running portfolio for 960 s 0.16/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.16/0.36 % Number of cores: 8 0.16/0.37 % Python version: Python 3.6.8 0.16/0.37 % Running in HO mode 0.21/0.61 % Total configuration time : 828 0.21/0.61 % Estimated wc time : 1656 0.21/0.61 % Estimated cpu time (8 cpus) : 207.0 0.21/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.21/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.21/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.21/0.71 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.21/0.71 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.21/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.21/0.71 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.21/0.72 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 93.76/13.06 % Solved by lams/40_b.comb.sh. 93.76/13.06 % running E: timeout 28 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.Gl7ft9juGA/e_input930724 --cpu-limit=26 --auto-schedule -s -p 93.76/13.06 % done 315 iterations in 12.288s 93.76/13.06 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 93.76/13.06 % SZS output start Refutation 93.76/13.06 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 93.76/13.06 thf('#ty_enc6_type', type, '#ty_enc6': ($i > $i > $o) > $i > $i > $o). 93.76/13.06 thf(moreq_type, type, moreq: $i > $i > $o). 93.76/13.06 thf(num_type, type, num: $i > $i). 93.76/13.06 thf(n_eq_type, type, n_eq: $i > $i > $o). 93.76/13.06 thf(l_or_type, type, l_or: $o > $o > $o). 93.76/13.06 thf(n_ts_type, type, n_ts: $i > $i > $i). 93.76/13.06 thf('#sk2_type', type, '#sk2': $i). 93.76/13.06 thf(frac_type, type, frac: $i). 93.76/13.06 thf(in_type, type, in: $i > $i > $o). 93.76/13.06 thf(imp_type, type, imp: $o > $o > $o). 93.76/13.06 thf(n_pf_type, type, n_pf: $i > $i > $i). 93.76/13.06 thf(moref_type, type, moref: $i > $i > $o). 93.76/13.06 thf('#sk4_type', type, '#sk4': $i). 93.76/13.06 thf('#sk5_type', type, '#sk5': $i). 93.76/13.06 thf(nat_type, type, nat: $i). 93.76/13.06 thf('#sk3_type', type, '#sk3': $i). 93.76/13.06 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 93.76/13.06 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 93.76/13.06 thf(den_type, type, den: $i > $i). 93.76/13.06 thf(n_some_type, type, n_some: ($i > $o) > $o). 93.76/13.06 thf(n_pl_type, type, n_pl: $i > $i > $i). 93.76/13.06 thf(pair1type_type, type, pair1type: $i > $i). 93.76/13.06 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o). 93.76/13.06 thf(d_not_type, type, d_not: $o > $o). 93.76/13.06 thf(n_fr_type, type, n_fr: $i > $i > $i). 93.76/13.06 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 93.76/13.06 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 93.76/13.06 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 93.76/13.06 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 93.76/13.06 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 93.76/13.06 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 93.76/13.06 thf(satz65a, conjecture, 93.76/13.06 (all_of @ 93.76/13.06 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 93.76/13.06 ( ^[X0:$i]: 93.76/13.06 ( all_of @ 93.76/13.06 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 93.76/13.06 ( ^[X1:$i]: 93.76/13.06 ( all_of @ 93.76/13.06 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 93.76/13.06 ( ^[X2:$i]: 93.76/13.06 ( all_of @ 93.76/13.06 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 93.76/13.06 ( ^[X3:$i]: 93.76/13.06 ( ( moreq @ X0 @ X1 ) => 93.76/13.06 ( ( moref @ X2 @ X3 ) => 93.76/13.06 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 93.76/13.06 thf(zf_stmt_0, negated_conjecture, 93.76/13.06 (~( all_of @ 93.76/13.06 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 93.76/13.06 ( ^[X0:$i]: 93.76/13.06 ( all_of @ 93.76/13.06 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 93.76/13.06 ( ^[X1:$i]: 93.76/13.06 ( all_of @ 93.76/13.06 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 93.76/13.06 ( ^[X2:$i]: 93.76/13.06 ( all_of @ 93.76/13.06 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 93.76/13.06 ( ^[X3:$i]: 93.76/13.06 ( ( moreq @ X0 @ X1 ) => 93.76/13.06 ( ( moref @ X2 @ X3 ) => 93.76/13.06 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) )), 93.76/13.06 inference('cnf.neg', [status(esa)], [satz65a])). 93.76/13.06 thf(zip_derived_cl356, plain, 93.76/13.06 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 93.76/13.06 (^[Y0 : $i]: 93.76/13.06 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 93.76/13.06 (^[Y1 : $i]: 93.76/13.06 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 93.76/13.06 (^[Y2 : $i]: 93.76/13.06 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 93.76/13.06 (^[Y3 : $i]: 93.76/13.06 (((moreq @ Y0 @ Y1) => 93.76/13.06 (((moref @ Y2 @ Y3) => (moref @ (n_pf @ Y0 @ Y2) @ 93.76/13.06 (n_pf @ Y1 @ Y3))))))))))))))), 93.76/13.06 inference('cnf', [status(esa)], [zf_stmt_0])). 93.76/13.06 thf(zip_derived_cl357, plain, 93.76/13.06 (~ (all_of @ ((('#C') @ in @ frac)) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ 93.76/13.06 moref)))))))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#C') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @ 93.76/13.06 n_pf)))))))))))))), 93.76/13.06 inference('lams2combs', [status(thm)], [zip_derived_cl356])). 93.76/13.06 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))). 93.76/13.06 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])). 93.76/13.06 thf(zip_derived_cl1522, plain, 93.76/13.06 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ 93.76/13.06 moref)))))))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#C') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @ 93.76/13.06 n_pf)))))))))))))), 93.76/13.06 inference('rw', [status(thm)], [zip_derived_cl357, '0'])). 93.76/13.06 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 93.76/13.06 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 93.76/13.06 thf('1', plain, 93.76/13.06 (![X0:( $i > $o ),X1:( $i > $o )]: 93.76/13.06 ( ( ~( all_of @ X0 @ X1 ) ) <=> 93.76/13.06 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 93.76/13.06 inference('rw.lit', [status(esa)], [def_all_of])). 93.76/13.06 thf(zip_derived_cl1523, plain, 93.76/13.06 (~ (((!!) @ (^[Y0 : $i]: 93.76/13.06 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ 93.76/13.06 moreq)))))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 93.76/13.06 '#S') @ 93.76/13.06 ((('#B') @ ( 93.76/13.06 (('#B') @ ( 93.76/13.06 =>))) @ 93.76/13.06 moref)))))))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#C') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ moref)) @ 93.76/13.06 n_pf)))))))) @ 93.76/13.06 n_pf)))))))))) @ 93.76/13.06 Y0)))))))), 93.76/13.06 inference('rw_clause', [status(thm)], [zip_derived_cl1522, '1'])). 93.76/13.06 thf(zip_derived_cl1524, plain, 93.76/13.06 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.76/13.06 ((('#C') @ is_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 93.76/13.06 '#S') @ 93.76/13.06 ((('#B') @ ( 93.76/13.06 (('#B') @ (=>))) @ 93.76/13.06 moref)))))))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#C') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ moref)) @ 93.76/13.06 n_pf)))))))) @ 93.76/13.06 n_pf))))))))))))))))), 93.76/13.06 inference('comb-normalize', [status(thm)], [zip_derived_cl1523])). 93.76/13.06 thf(zip_derived_cl1525, plain, 93.76/13.06 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @ 93.76/13.06 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 93.76/13.06 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ '#sk2'))))))) @ 93.76/13.06 n_pf)))))))))))))), 93.76/13.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1524])). 93.76/13.06 thf(zip_derived_cl1527, plain, 93.76/13.06 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @ 93.76/13.06 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 93.76/13.06 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ '#sk2'))))))) @ 93.76/13.06 n_pf)))))))))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1525])). 93.76/13.06 thf(zip_derived_cl1528, plain, 93.76/13.06 (~ (((!!) @ (^[Y0 : $i]: 93.76/13.06 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @ 93.76/13.06 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ 93.76/13.06 moref)))))) @ 93.76/13.06 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ 93.76/13.06 (n_pf @ '#sk2'))))))) @ 93.76/13.06 n_pf)))))))) @ 93.76/13.06 Y0)))))))), 93.76/13.06 inference('rw_clause', [status(thm)], [zip_derived_cl1527, '1'])). 93.76/13.06 thf(zip_derived_cl1529, plain, 93.76/13.06 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.76/13.06 ((('#C') @ is_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @ 93.76/13.06 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ 93.76/13.06 moref)))))) @ 93.76/13.06 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ 93.76/13.06 (n_pf @ '#sk2'))))))) @ 93.76/13.06 n_pf))))))))))))))), 93.76/13.06 inference('comb-normalize', [status(thm)], [zip_derived_cl1528])). 93.76/13.06 thf(zip_derived_cl1530, plain, 93.76/13.06 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (((=>) @ (moreq @ '#sk2' @ '#sk3'))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @ 93.76/13.06 (n_pf @ '#sk3'))))))))))))), 93.76/13.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1529])). 93.76/13.06 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 93.76/13.06 thf('2', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 93.76/13.06 define([status(thm)])). 93.76/13.06 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 93.76/13.06 thf('3', plain, 93.76/13.06 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 93.76/13.06 define([status(thm)])). 93.76/13.06 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))). 93.76/13.06 thf('4', plain, 93.76/13.06 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )), 93.76/13.06 define([status(thm)])). 93.76/13.06 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) = 93.76/13.06 ((n_some @ (diffprop @ X0 @ X1))))). 93.76/13.06 thf('5', plain, 93.76/13.06 (![X1:$i,X0:$i]: 93.76/13.06 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 93.76/13.06 define([status(thm)])). 93.76/13.06 thf(def_moref, axiom,(( moref @ (X0)@ (X1)) = 93.76/13.06 ((d_29_ii @ (n_ts @ (num @ X0) @ (den @ X1)) @ 93.76/13.06 (n_ts @ (num @ X1) @ (den @ X0)))))). 93.76/13.06 thf('6', plain, 93.76/13.06 (![X1:$i,X0:$i]: 93.76/13.06 ( ( moref @ X0 @ X1 ) = 93.76/13.06 ( d_29_ii @ 93.76/13.06 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 93.76/13.06 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )), 93.76/13.06 define([status(thm)])). 93.76/13.06 thf(def_moreq, axiom,(( moreq @ (X0)@ (X1)) = 93.76/13.06 ((l_or @ (moref @ X0 @ X1) @ (n_eq @ X0 @ X1))))). 93.76/13.06 thf('7', plain, 93.76/13.06 (![X1:$i,X0:$i]: 93.76/13.06 ( ( moreq @ X0 @ X1 ) = 93.76/13.06 ( l_or @ ( moref @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )), 93.76/13.06 define([status(thm)])). 93.76/13.06 thf(zip_derived_cl1531, plain, 93.76/13.06 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 93.76/13.06 (imp @ 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ (num @ '#sk2') @ 93.76/13.06 (den @ '#sk3')) @ 93.76/13.06 (n_ts @ (num @ '#sk3') @ 93.76/13.06 (den @ '#sk2')))) @ 93.76/13.06 ($false)) @ 93.76/13.06 (n_eq @ '#sk2' @ '#sk3')))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @ 93.76/13.06 (n_pf @ '#sk3'))))))))))))), 93.76/13.06 inference('rw', [status(thm)], 93.76/13.06 [zip_derived_cl1530, '2', '3', '4', '5', '6', '7'])). 93.76/13.06 thf(zip_derived_cl1533, plain, 93.76/13.06 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 93.76/13.06 (imp @ 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ (num @ '#sk2') @ 93.76/13.06 (den @ '#sk3')) @ 93.76/13.06 (n_ts @ (num @ '#sk3') @ 93.76/13.06 (den @ '#sk2')))) @ 93.76/13.06 ($false)) @ 93.76/13.06 (n_eq @ '#sk2' @ '#sk3')))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @ 93.76/13.06 (n_pf @ '#sk3'))))))))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1531])). 93.76/13.06 thf(zip_derived_cl1534, plain, 93.76/13.06 (~ (((!!) @ (^[Y0 : $i]: 93.76/13.06 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 93.76/13.06 (imp @ 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ '#sk2') @ 93.76/13.06 (den @ '#sk3')) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ '#sk3') @ 93.76/13.06 (den @ '#sk2')))) @ 93.76/13.06 ($false)) @ 93.76/13.06 (n_eq @ '#sk2' @ 93.76/13.06 '#sk3')))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @ 93.76/13.06 (n_pf @ '#sk3'))))))) @ 93.76/13.06 Y0)))))))), 93.76/13.06 inference('rw_clause', [status(thm)], [zip_derived_cl1533, '1'])). 93.76/13.06 thf(zip_derived_cl1535, plain, 93.76/13.06 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.76/13.06 ((('#C') @ is_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 93.76/13.06 (imp @ 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ '#sk2') @ 93.76/13.06 (den @ '#sk3')) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ '#sk3') @ 93.76/13.06 (den @ '#sk2')))) @ 93.76/13.06 ($false)) @ 93.76/13.06 (n_eq @ '#sk2' @ '#sk3')))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ '#sk2'))))) @ 93.76/13.06 (n_pf @ '#sk3')))))))))))))), 93.76/13.06 inference('comb-normalize', [status(thm)], [zip_derived_cl1534])). 93.76/13.06 thf(zip_derived_cl1536, plain, 93.76/13.06 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (((=>) @ (imp @ 93.76/13.06 (imp @ 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 93.76/13.06 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @ 93.76/13.06 ($false)) @ 93.76/13.06 (n_eq @ '#sk2' @ '#sk3')))) @ 93.76/13.06 ((('#S') @ ((('#B') @ (=>) @ (moref @ '#sk4'))) @ 93.76/13.06 ((('#B') @ (moref @ (n_pf @ '#sk2' @ '#sk4')) @ (n_pf @ '#sk3'))))))))))), 93.76/13.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1535])). 93.76/13.06 thf(def_n_pf, axiom,(( n_pf @ (X0)@ (X1)) = 93.76/13.06 ((n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X1)) @ 93.76/13.06 (n_ts @ (num @ X1) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X1)))))). 93.76/13.06 thf('8', plain, 93.76/13.06 (![X1:$i,X0:$i]: 93.76/13.06 ( ( n_pf @ X0 @ X1 ) = 93.76/13.06 ( n_fr @ 93.76/13.06 ( n_pl @ 93.76/13.06 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 93.76/13.06 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) @ 93.76/13.06 ( n_ts @ ( den @ X0 ) @ ( den @ X1 ) ) ) )), 93.76/13.06 define([status(thm)])). 93.76/13.06 thf(zip_derived_cl1537, plain, 93.76/13.06 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (((=>) @ (imp @ 93.76/13.06 (imp @ 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 93.76/13.06 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @ 93.76/13.06 ($false)) @ 93.76/13.06 (n_eq @ '#sk2' @ '#sk3')))) @ 93.76/13.06 ((('#S') @ ((('#B') @ (=>) @ (moref @ '#sk4'))) @ 93.76/13.06 ((('#B') @ (moref @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.76/13.06 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.76/13.06 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 93.76/13.06 (n_pf @ '#sk3'))))))))))), 93.76/13.06 inference('rw', [status(thm)], [zip_derived_cl1536, '8'])). 93.76/13.06 thf(zip_derived_cl1539, plain, 93.76/13.06 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (((=>) @ (imp @ 93.76/13.06 (imp @ 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 93.76/13.06 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @ 93.76/13.06 ($false)) @ 93.76/13.06 (n_eq @ '#sk2' @ '#sk3')))) @ 93.76/13.06 ((('#S') @ ((('#B') @ (=>) @ (moref @ '#sk4'))) @ 93.76/13.06 ((('#B') @ (moref @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.76/13.06 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.76/13.06 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 93.76/13.06 (n_pf @ '#sk3'))))))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1537])). 93.76/13.06 thf(zip_derived_cl1540, plain, 93.76/13.06 (~ (((!!) @ (^[Y0 : $i]: 93.76/13.06 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 ((('#B') @ (((=>) @ (imp @ 93.76/13.06 (imp @ 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ (num @ '#sk2') @ 93.76/13.06 (den @ '#sk3')) @ 93.76/13.06 (n_ts @ (num @ '#sk3') @ 93.76/13.06 (den @ '#sk2')))) @ 93.76/13.06 ($false)) @ 93.76/13.06 (n_eq @ '#sk2' @ '#sk3')))) @ 93.76/13.06 ((('#S') @ ((('#B') @ (=>) @ (moref @ '#sk4'))) @ 93.76/13.06 ((('#B') @ (moref @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ 93.76/13.06 (n_ts @ (num @ '#sk2') @ 93.76/13.06 (den @ '#sk4')) @ 93.76/13.06 (n_ts @ (num @ '#sk4') @ 93.76/13.06 (den @ '#sk2'))) @ 93.76/13.06 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 93.76/13.06 (n_pf @ '#sk3'))))) @ 93.76/13.06 Y0)))))))), 93.76/13.06 inference('rw_clause', [status(thm)], [zip_derived_cl1539, '1'])). 93.76/13.06 thf(zip_derived_cl1541, plain, 93.76/13.06 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.76/13.06 ((('#C') @ is_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.76/13.06 ((('#B') @ (((=>) @ (imp @ 93.76/13.06 (imp @ 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ (num @ '#sk2') @ 93.76/13.06 (den @ '#sk3')) @ 93.76/13.06 (n_ts @ (num @ '#sk3') @ 93.76/13.06 (den @ '#sk2')))) @ 93.76/13.06 ($false)) @ 93.76/13.06 (n_eq @ '#sk2' @ '#sk3')))) @ 93.76/13.06 ((('#S') @ ((('#B') @ (=>) @ (moref @ '#sk4'))) @ 93.76/13.06 ((('#B') @ (moref @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ 93.76/13.06 (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.76/13.06 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.76/13.06 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 93.76/13.06 (n_pf @ '#sk3')))))))))))), 93.76/13.06 inference('comb-normalize', [status(thm)], [zip_derived_cl1540])). 93.76/13.06 thf(zip_derived_cl1542, plain, 93.76/13.06 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 (((imp @ 93.76/13.06 (imp @ 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 93.76/13.06 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @ 93.76/13.06 ($false)) @ 93.76/13.06 (n_eq @ '#sk2' @ '#sk3')) => 93.76/13.06 (((moref @ '#sk4' @ '#sk5') => (moref @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.76/13.06 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.76/13.06 (n_ts @ (den @ '#sk2') @ (den @ '#sk4'))) @ 93.76/13.06 (n_pf @ '#sk3' @ '#sk5'))))))))), 93.76/13.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1541])). 93.76/13.06 thf(zip_derived_cl1543, plain, 93.76/13.06 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 (((imp @ 93.76/13.06 (imp @ 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 93.76/13.06 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @ 93.76/13.06 ($false)) @ 93.76/13.06 (n_eq @ '#sk2' @ '#sk3')) => 93.76/13.06 (((l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @ 93.76/13.06 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) => 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.76/13.06 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.76/13.06 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.76/13.06 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.76/13.06 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.76/13.06 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.76/13.06 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.76/13.06 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.76/13.06 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))))))))))))), 93.76/13.06 inference('rw', [status(thm)], 93.76/13.06 [zip_derived_cl1542, '4', '4', '5', '5', '6', '6', '8'])). 93.76/13.06 thf(zip_derived_cl1545, plain, 93.76/13.06 (~ (((imp @ 93.76/13.06 (imp @ 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 93.76/13.06 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @ 93.76/13.06 ($false)) @ 93.76/13.06 (n_eq @ '#sk2' @ '#sk3')) => 93.76/13.06 (((l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @ 93.76/13.06 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) => 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.76/13.06 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.76/13.06 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.76/13.06 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.76/13.06 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.76/13.06 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.76/13.06 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.76/13.06 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.76/13.06 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))))))))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1543])). 93.76/13.06 thf(zip_derived_cl1546, plain, 93.76/13.06 ( (imp @ 93.76/13.06 (imp @ 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 93.76/13.06 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @ 93.76/13.06 ($false)) @ 93.76/13.06 (n_eq @ '#sk2' @ '#sk3'))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1545])). 93.76/13.06 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 93.76/13.06 thf('9', plain, 93.76/13.06 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 93.76/13.06 inference('rw.lit', [status(esa)], [def_imp])). 93.76/13.06 thf(zip_derived_cl1548, plain, 93.76/13.06 ( (((imp @ 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 93.76/13.06 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @ 93.76/13.06 ($false)) => (n_eq @ '#sk2' @ '#sk3')))), 93.76/13.06 inference('rw_clause', [status(thm)], [zip_derived_cl1546, '9'])). 93.76/13.06 thf(zip_derived_cl1551, plain, 93.76/13.06 ((~ (imp @ 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 93.76/13.06 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) @ 93.76/13.06 ($false)) 93.76/13.06 | (n_eq @ '#sk2' @ '#sk3'))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1548])). 93.76/13.06 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 93.76/13.06 thf('10', plain, 93.76/13.06 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 93.76/13.06 inference('rw.lit', [status(esa)], [def_imp])). 93.76/13.06 thf(zip_derived_cl1552, plain, 93.76/13.06 ((~ (((l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 93.76/13.06 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) => 93.76/13.06 ($false))) 93.76/13.06 | (n_eq @ '#sk2' @ '#sk3'))), 93.76/13.06 inference('rw_clause', [status(thm)], [zip_derived_cl1551, '10'])). 93.76/13.06 thf(zip_derived_cl1553, plain, 93.76/13.06 ((~ (((~) @ (l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 93.76/13.06 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))))) 93.76/13.06 | (n_eq @ '#sk2' @ '#sk3'))), 93.76/13.06 inference('simplify boolean subterms', [status(thm)], 93.76/13.06 [zip_derived_cl1552])). 93.76/13.06 thf(zip_derived_cl1554, plain, 93.76/13.06 (( (l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ '#sk2') @ (den @ '#sk3')) @ 93.76/13.06 (n_ts @ (num @ '#sk3') @ (den @ '#sk2')))) 93.76/13.06 | (n_eq @ '#sk2' @ '#sk3'))), 93.76/13.06 inference('simplify nested equalities', [status(thm)], 93.76/13.06 [zip_derived_cl1553])). 93.76/13.06 thf(zip_derived_cl1538, plain, 93.76/13.06 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1537])). 93.76/13.06 thf(zip_derived_cl7551, plain, 93.76/13.06 ( (is_of @ '#sk4' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 93.76/13.06 inference('remove_ty_args', [status(thm)], [zip_derived_cl1538])). 93.76/13.06 thf(zip_derived_cl1544, plain, 93.76/13.06 ( (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1543])). 93.76/13.06 thf(zip_derived_cl7552, plain, 93.76/13.06 ( (is_of @ '#sk5' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 93.76/13.06 inference('remove_ty_args', [status(thm)], [zip_derived_cl1544])). 93.76/13.06 thf(zip_derived_cl1526, plain, 93.76/13.06 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1525])). 93.76/13.06 thf(zip_derived_cl7549, plain, 93.76/13.06 ( (is_of @ '#sk2' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 93.76/13.06 inference('remove_ty_args', [status(thm)], [zip_derived_cl1526])). 93.76/13.06 thf(zip_derived_cl1532, plain, 93.76/13.06 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1531])). 93.76/13.06 thf(zip_derived_cl7550, plain, 93.76/13.06 ( (is_of @ '#sk3' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 93.76/13.06 inference('remove_ty_args', [status(thm)], [zip_derived_cl1532])). 93.76/13.06 thf(zip_derived_cl1547, plain, 93.76/13.06 (~ (((l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @ 93.76/13.06 (n_ts @ (num @ '#sk5') @ (den @ '#sk4')))) => 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.76/13.06 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.76/13.06 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.76/13.06 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.76/13.06 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.76/13.06 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.76/13.06 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.76/13.06 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.76/13.06 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))))))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1545])). 93.76/13.06 thf(zip_derived_cl1549, plain, 93.76/13.06 ( (l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ '#sk4') @ (den @ '#sk5')) @ 93.76/13.06 (n_ts @ (num @ '#sk5') @ (den @ '#sk4'))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1547])). 93.76/13.06 thf(satz64, axiom, 93.76/13.06 (all_of @ 93.76/13.06 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 93.76/13.06 ( ^[X0:$i]: 93.76/13.06 ( all_of @ 93.76/13.06 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 93.76/13.06 ( ^[X1:$i]: 93.76/13.06 ( all_of @ 93.76/13.06 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 93.76/13.06 ( ^[X2:$i]: 93.76/13.06 ( all_of @ 93.76/13.06 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 93.76/13.06 ( ^[X3:$i]: 93.76/13.06 ( ( moref @ X0 @ X1 ) => 93.76/13.06 ( ( moref @ X2 @ X3 ) => 93.76/13.06 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 93.76/13.06 thf(zip_derived_cl230, plain, 93.76/13.06 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 93.76/13.06 (^[Y0 : $i]: 93.76/13.06 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 93.76/13.06 (^[Y1 : $i]: 93.76/13.06 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 93.76/13.06 (^[Y2 : $i]: 93.76/13.06 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 93.76/13.06 (^[Y3 : $i]: 93.76/13.06 (((moref @ Y0 @ Y1) => 93.76/13.06 (((moref @ Y2 @ Y3) => (moref @ (n_pf @ Y0 @ Y2) @ 93.76/13.06 (n_pf @ Y1 @ Y3))))))))))))))), 93.76/13.06 inference('cnf', [status(esa)], [satz64])). 93.76/13.06 thf(zip_derived_cl231, plain, 93.76/13.06 ( (all_of @ ((('#C') @ in @ frac)) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ 93.76/13.06 moref)))))))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#C') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @ 93.76/13.06 n_pf)))))))))))))), 93.76/13.06 inference('lams2combs', [status(thm)], [zip_derived_cl230])). 93.76/13.06 thf(zip_derived_cl2715, plain, 93.76/13.06 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ 93.76/13.06 moref)))))))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#C') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @ 93.76/13.06 n_pf)))))))))))))), 93.76/13.06 inference('rw', [status(thm)], [zip_derived_cl231, '0'])). 93.76/13.06 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 93.76/13.06 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 93.76/13.06 thf('11', plain, 93.76/13.06 (![X0:( $i > $o ),X1:( $i > $o )]: 93.76/13.06 ( ( all_of @ X0 @ X1 ) <=> 93.76/13.06 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 93.76/13.06 inference('rw.lit', [status(esa)], [def_all_of])). 93.76/13.06 thf(zip_derived_cl2716, plain, 93.76/13.06 ( (((!!) @ (^[Y0 : $i]: 93.76/13.06 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ 93.76/13.06 moref)))))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 93.76/13.06 '#S') @ 93.76/13.06 ((('#B') @ ( 93.76/13.06 (('#B') @ ( 93.76/13.06 =>))) @ 93.76/13.06 moref)))))))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#C') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ moref)) @ 93.76/13.06 n_pf)))))))) @ 93.76/13.06 n_pf)))))))))) @ 93.76/13.06 Y0)))))))), 93.76/13.06 inference('rw_clause', [status(thm)], [zip_derived_cl2715, '11'])). 93.76/13.06 thf(zip_derived_cl2717, plain, 93.76/13.06 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.76/13.06 ((('#C') @ is_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 93.76/13.06 '#S') @ 93.76/13.06 ((('#B') @ ( 93.76/13.06 (('#B') @ (=>))) @ 93.76/13.06 moref)))))))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#C') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ moref)) @ 93.76/13.06 n_pf)))))))) @ 93.76/13.06 n_pf))))))))))))))))), 93.76/13.06 inference('comb-normalize', [status(thm)], [zip_derived_cl2716])). 93.76/13.06 thf(zip_derived_cl2718, plain, 93.76/13.06 (![X2 : $i]: 93.76/13.06 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ (=>) @ (moref @ X2))))))) @ 93.76/13.06 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 93.76/13.06 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ X2))))))) @ 93.76/13.06 n_pf)))))))))))))), 93.76/13.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2717])). 93.76/13.06 thf(zip_derived_cl2719, plain, 93.76/13.06 (![X2 : $i]: 93.76/13.06 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ (=>) @ (moref @ X2))))))) @ 93.76/13.06 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ 93.76/13.06 moref)))))) @ 93.76/13.06 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ X2))))))) @ 93.76/13.06 n_pf))))))))))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2718])). 93.76/13.06 thf(zip_derived_cl2720, plain, 93.76/13.06 (![X0 : $i]: 93.76/13.06 ( (((!!) @ (^[Y0 : $i]: 93.76/13.06 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ (=>) @ (moref @ X0))))))) @ 93.76/13.06 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ ( 93.76/13.06 =>))) @ 93.76/13.06 moref)))))) @ 93.76/13.06 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ 93.76/13.06 (n_pf @ X0))))))) @ 93.76/13.06 n_pf)))))))) @ 93.76/13.06 Y0))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('rw_clause', [status(thm)], [zip_derived_cl2719, '11'])). 93.76/13.06 thf(zip_derived_cl2721, plain, 93.76/13.06 (![X0 : $i]: 93.76/13.06 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.76/13.06 ((('#C') @ is_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ (=>) @ (moref @ X0))))))) @ 93.76/13.06 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ 93.76/13.06 moref)))))) @ 93.76/13.06 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ 93.76/13.06 (n_pf @ X0))))))) @ 93.76/13.06 n_pf)))))))))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('comb-normalize', [status(thm)], [zip_derived_cl2720])). 93.76/13.06 thf(zip_derived_cl2722, plain, 93.76/13.06 (![X0 : $i, X2 : $i]: 93.76/13.06 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (((=>) @ (moref @ X0 @ X2))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.76/13.06 (n_pf @ X2)))))))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2721])). 93.76/13.06 thf(zip_derived_cl2723, plain, 93.76/13.06 (![X0 : $i, X2 : $i]: 93.76/13.06 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ (num @ X0) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X0)))))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.76/13.06 (n_pf @ X2)))))))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('rw', [status(thm)], [zip_derived_cl2722, '4', '5', '6'])). 93.76/13.06 thf(zip_derived_cl2724, plain, 93.76/13.06 (![X0 : $i, X2 : $i]: 93.76/13.06 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ (num @ X0) @ 93.76/13.06 (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ 93.76/13.06 (den @ X0)))))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.76/13.06 (n_pf @ X2)))))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2723])). 93.76/13.06 thf(zip_derived_cl2725, plain, 93.76/13.06 (![X0 : $i, X1 : $i]: 93.76/13.06 ( (((!!) @ (^[Y0 : $i]: 93.76/13.06 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ X0) @ 93.76/13.06 (den @ X1)) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ X1) @ 93.76/13.06 (den @ X0)))))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.76/13.06 (n_pf @ X1))))))) @ 93.76/13.06 Y0))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('rw_clause', [status(thm)], [zip_derived_cl2724, '11'])). 93.76/13.06 thf(zip_derived_cl2726, plain, 93.76/13.06 (![X0 : $i, X1 : $i]: 93.76/13.06 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.76/13.06 ((('#C') @ is_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ (num @ X0) @ 93.76/13.06 (den @ X1)) @ 93.76/13.06 (n_ts @ (num @ X1) @ 93.76/13.06 (den @ X0)))))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.76/13.06 (n_pf @ X1))))))))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('comb-normalize', [status(thm)], [zip_derived_cl2725])). 93.76/13.06 thf(zip_derived_cl2727, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X3 : $i]: 93.76/13.06 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (((=>) @ (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ (num @ X0) @ (den @ X1)) @ 93.76/13.06 (n_ts @ (num @ X1) @ (den @ X0)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 93.76/13.06 ((('#B') @ (moref @ (n_pf @ X0 @ X3)) @ (n_pf @ X1)))))))))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2726])). 93.76/13.06 thf(zip_derived_cl2728, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X3 : $i]: 93.76/13.06 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (((=>) @ (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ (num @ X0) @ (den @ X1)) @ 93.76/13.06 (n_ts @ (num @ X1) @ (den @ X0)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 93.76/13.06 ((('#B') @ (moref @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 93.76/13.06 (n_ts @ (num @ X3) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X3)))) @ 93.76/13.06 (n_pf @ X1)))))))))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('rw', [status(thm)], [zip_derived_cl2727, '8'])). 93.76/13.06 thf(zip_derived_cl2729, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X3 : $i]: 93.76/13.06 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (((=>) @ (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ (num @ X0) @ (den @ X1)) @ 93.76/13.06 (n_ts @ (num @ X1) @ (den @ X0)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 93.76/13.06 ((('#B') @ (moref @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 93.76/13.06 (n_ts @ (num @ X3) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X3)))) @ 93.76/13.06 (n_pf @ X1)))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2728])). 93.76/13.06 thf(zip_derived_cl2730, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X2 : $i]: 93.76/13.06 ( (((!!) @ (^[Y0 : $i]: 93.76/13.06 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 ((('#B') @ (((=>) @ (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ (num @ X1) @ (den @ X0)) @ 93.76/13.06 (n_ts @ (num @ X0) @ (den @ X1)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 93.76/13.06 ((('#B') @ (moref @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ 93.76/13.06 (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.76/13.06 (n_pf @ X0))))) @ 93.76/13.06 Y0))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('rw_clause', [status(thm)], [zip_derived_cl2729, '11'])). 93.76/13.06 thf(zip_derived_cl2731, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X2 : $i]: 93.76/13.06 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.76/13.06 ((('#C') @ is_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.76/13.06 ((('#B') @ (((=>) @ (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ (num @ X1) @ (den @ X0)) @ 93.76/13.06 (n_ts @ (num @ X0) @ (den @ X1)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 93.76/13.06 ((('#B') @ (moref @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ 93.76/13.06 (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.76/13.06 (n_pf @ X0))))))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('comb-normalize', [status(thm)], [zip_derived_cl2730])). 93.76/13.06 thf(zip_derived_cl2732, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.76/13.06 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 (((l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @ 93.76/13.06 (n_ts @ (num @ X0) @ (den @ X1)))) => 93.76/13.06 (((moref @ X2 @ X4) => (moref @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.76/13.06 (n_pf @ X0 @ X4)))))))) 93.76/13.06 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2731])). 93.76/13.06 thf(zip_derived_cl2733, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.76/13.06 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 (((l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @ 93.76/13.06 (n_ts @ (num @ X0) @ (den @ X1)))) => 93.76/13.06 (((l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X2)))) => 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4))))) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2))))))))))))) 93.76/13.06 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('rw', [status(thm)], 93.76/13.06 [zip_derived_cl2732, '4', '4', '5', '5', '6', '6', '8'])). 93.76/13.06 thf(zip_derived_cl2734, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.76/13.06 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | (((l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @ 93.76/13.06 (n_ts @ (num @ X0) @ (den @ X1)))) => 93.76/13.06 (((l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X2)))) => 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4))))) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2))))))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2733])). 93.76/13.06 thf(zip_derived_cl2735, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.76/13.06 (~ (l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @ 93.76/13.06 (n_ts @ (num @ X0) @ (den @ X1)))) 93.76/13.06 | (((l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X2)))) => 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4))))) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2))))))))) 93.76/13.06 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2734])). 93.76/13.06 thf(zip_derived_cl2736, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.76/13.06 (~ (l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X2)))) 93.76/13.06 | (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4))))) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2))))))) 93.76/13.06 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @ 93.76/13.06 (n_ts @ (num @ X0) @ (den @ X1)))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2735])). 93.76/13.06 thf(zip_derived_cl7594, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.76/13.06 (~ (l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X2)))) 93.76/13.06 | (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4))))) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2))))))) 93.76/13.06 | ~ (is_of @ X4 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.76/13.06 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.76/13.06 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.76/13.06 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.76/13.06 | ~ (l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ X1) @ (den @ X0)) @ 93.76/13.06 (n_ts @ (num @ X0) @ (den @ X1)))))), 93.76/13.06 inference('remove_ty_args', [status(thm)], [zip_derived_cl2736])). 93.76/13.06 thf(zip_derived_cl1550, plain, 93.76/13.06 (~ (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.76/13.06 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.76/13.06 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.76/13.06 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.76/13.06 (n_ts @ (den @ '#sk3') @ (den @ '#sk5'))))) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk3') @ (den @ '#sk5')) @ 93.76/13.06 (n_ts @ (num @ '#sk5') @ (den @ '#sk3'))) @ 93.76/13.06 (n_ts @ (den @ '#sk3') @ (den @ '#sk5')))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ '#sk2') @ (den @ '#sk4')) @ 93.76/13.06 (n_ts @ (num @ '#sk4') @ (den @ '#sk2'))) @ 93.76/13.06 (n_ts @ (den @ '#sk2') @ (den @ '#sk4')))))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1547])). 93.76/13.06 thf(satz62g, axiom, 93.76/13.06 (all_of @ 93.76/13.06 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 93.76/13.06 ( ^[X0:$i]: 93.76/13.06 ( all_of @ 93.76/13.06 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 93.76/13.06 ( ^[X1:$i]: 93.76/13.06 ( all_of @ 93.76/13.06 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 93.76/13.06 ( ^[X2:$i]: 93.76/13.06 ( all_of @ 93.76/13.06 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 93.76/13.06 ( ^[X3:$i]: 93.76/13.06 ( ( n_eq @ X0 @ X1 ) => 93.76/13.06 ( ( moref @ X2 @ X3 ) => 93.76/13.06 ( moref @ ( n_pf @ X0 @ X2 ) @ ( n_pf @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 93.76/13.06 thf(zip_derived_cl84, plain, 93.76/13.06 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 93.76/13.06 (^[Y0 : $i]: 93.76/13.06 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 93.76/13.06 (^[Y1 : $i]: 93.76/13.06 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 93.76/13.06 (^[Y2 : $i]: 93.76/13.06 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 93.76/13.06 (^[Y3 : $i]: 93.76/13.06 (((n_eq @ Y0 @ Y1) => 93.76/13.06 (((moref @ Y2 @ Y3) => (moref @ (n_pf @ Y0 @ Y2) @ 93.76/13.06 (n_pf @ Y1 @ Y3))))))))))))))), 93.76/13.06 inference('cnf', [status(esa)], [satz62g])). 93.76/13.06 thf(zip_derived_cl85, plain, 93.76/13.06 ( (all_of @ ((('#C') @ in @ frac)) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ 93.76/13.06 moref)))))))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#C') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @ 93.76/13.06 n_pf)))))))))))))), 93.76/13.06 inference('lams2combs', [status(thm)], [zip_derived_cl84])). 93.76/13.06 thf(zip_derived_cl2666, plain, 93.76/13.06 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ 93.76/13.06 moref)))))))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#C') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ moref)) @ n_pf)))))))) @ 93.76/13.06 n_pf)))))))))))))), 93.76/13.06 inference('rw', [status(thm)], [zip_derived_cl85, '0'])). 93.76/13.06 thf(zip_derived_cl2667, plain, 93.76/13.06 ( (((!!) @ (^[Y0 : $i]: 93.76/13.06 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ 93.76/13.06 n_eq)))))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 93.76/13.06 '#S') @ 93.76/13.06 ((('#B') @ ( 93.76/13.06 (('#B') @ ( 93.76/13.06 =>))) @ 93.76/13.06 moref)))))))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#C') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ moref)) @ 93.76/13.06 n_pf)))))))) @ 93.76/13.06 n_pf)))))))))) @ 93.76/13.06 Y0)))))))), 93.76/13.06 inference('rw_clause', [status(thm)], [zip_derived_cl2666, '11'])). 93.76/13.06 thf(zip_derived_cl2668, plain, 93.76/13.06 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.76/13.06 ((('#C') @ is_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 93.76/13.06 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 93.76/13.06 '#S') @ 93.76/13.06 ((('#B') @ ( 93.76/13.06 (('#B') @ (=>))) @ 93.76/13.06 moref)))))))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#C') @ 93.76/13.06 ((('#B') @ ((('#B') @ ('#B'))) @ 93.76/13.06 ((('#B') @ ((('#B') @ moref)) @ 93.76/13.06 n_pf)))))))) @ 93.76/13.06 n_pf))))))))))))))))), 93.76/13.06 inference('comb-normalize', [status(thm)], [zip_derived_cl2667])). 93.76/13.06 thf(zip_derived_cl2669, plain, 93.76/13.06 (![X2 : $i]: 93.76/13.06 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ (=>) @ (n_eq @ X2))))))) @ 93.76/13.06 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 93.76/13.06 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ X2))))))) @ 93.76/13.06 n_pf)))))))))))))), 93.76/13.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2668])). 93.76/13.06 thf(zip_derived_cl2670, plain, 93.76/13.06 (![X2 : $i]: 93.76/13.06 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ (=>) @ (n_eq @ X2))))))) @ 93.76/13.06 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ 93.76/13.06 moref)))))) @ 93.76/13.06 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ X2))))))) @ 93.76/13.06 n_pf))))))))))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2669])). 93.76/13.06 thf(zip_derived_cl2671, plain, 93.76/13.06 (![X0 : $i]: 93.76/13.06 ( (((!!) @ (^[Y0 : $i]: 93.76/13.06 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ (=>) @ (n_eq @ X0))))))) @ 93.76/13.06 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ ( 93.76/13.06 =>))) @ 93.76/13.06 moref)))))) @ 93.76/13.06 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ 93.76/13.06 (n_pf @ X0))))))) @ 93.76/13.06 n_pf)))))))) @ 93.76/13.06 Y0))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('rw_clause', [status(thm)], [zip_derived_cl2670, '11'])). 93.76/13.06 thf(zip_derived_cl2672, plain, 93.76/13.06 (![X0 : $i]: 93.76/13.06 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.76/13.06 ((('#C') @ is_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ 93.76/13.06 (pair1type @ nat)))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ (=>) @ (n_eq @ X0))))))) @ 93.76/13.06 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ 93.76/13.06 moref)))))) @ 93.76/13.06 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ 93.76/13.06 (n_pf @ X0))))))) @ 93.76/13.06 n_pf)))))))))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('comb-normalize', [status(thm)], [zip_derived_cl2671])). 93.76/13.06 thf(zip_derived_cl2673, plain, 93.76/13.06 (![X0 : $i, X2 : $i]: 93.76/13.06 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.76/13.06 (n_pf @ X2)))))))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2672])). 93.76/13.06 thf(zip_derived_cl2674, plain, 93.76/13.06 (![X0 : $i, X2 : $i]: 93.76/13.06 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.76/13.06 (n_pf @ X2)))))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2673])). 93.76/13.06 thf(zip_derived_cl2675, plain, 93.76/13.06 (![X0 : $i, X1 : $i]: 93.76/13.06 ( (((!!) @ (^[Y0 : $i]: 93.76/13.06 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 ((('#B') @ (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.76/13.06 (n_pf @ X1))))))) @ 93.76/13.06 Y0))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('rw_clause', [status(thm)], [zip_derived_cl2674, '11'])). 93.76/13.06 thf(zip_derived_cl2676, plain, 93.76/13.06 (![X0 : $i, X1 : $i]: 93.76/13.06 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.76/13.06 ((('#C') @ is_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.76/13.06 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 93.76/13.06 ((('#B') @ ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))))) @ 93.76/13.06 ((('#S') @ ((('#B') @ ('#S') @ 93.76/13.06 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 93.76/13.06 ((('#C') @ ((('#B') @ ('#B') @ 93.76/13.06 ((('#B') @ moref @ (n_pf @ X0))))) @ 93.76/13.06 (n_pf @ X1))))))))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('comb-normalize', [status(thm)], [zip_derived_cl2675])). 93.76/13.06 thf(zip_derived_cl2677, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X3 : $i]: 93.76/13.06 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @ 93.76/13.06 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 93.76/13.06 ((('#B') @ (moref @ (n_pf @ X0 @ X3)) @ (n_pf @ X1)))))))))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2676])). 93.76/13.06 thf(zip_derived_cl2678, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X3 : $i]: 93.76/13.06 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @ 93.76/13.06 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 93.76/13.06 ((('#B') @ (moref @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 93.76/13.06 (n_ts @ (num @ X3) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X3)))) @ 93.76/13.06 (n_pf @ X1)))))))))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('rw', [status(thm)], [zip_derived_cl2677, '8'])). 93.76/13.06 thf(zip_derived_cl2679, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X3 : $i]: 93.76/13.06 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 93.76/13.06 ((('#B') @ (((=>) @ (n_eq @ X0 @ X1))) @ 93.76/13.06 ((('#S') @ ((('#B') @ (=>) @ (moref @ X3))) @ 93.76/13.06 ((('#B') @ (moref @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X3)) @ 93.76/13.06 (n_ts @ (num @ X3) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X3)))) @ 93.76/13.06 (n_pf @ X1)))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2678])). 93.76/13.06 thf(zip_derived_cl2680, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X2 : $i]: 93.76/13.06 ( (((!!) @ (^[Y0 : $i]: 93.76/13.06 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 ((('#B') @ (((=>) @ (n_eq @ X1 @ X0))) @ 93.76/13.06 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 93.76/13.06 ((('#B') @ (moref @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ 93.76/13.06 (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.76/13.06 (n_pf @ X0))))) @ 93.76/13.06 Y0))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('rw_clause', [status(thm)], [zip_derived_cl2679, '11'])). 93.76/13.06 thf(zip_derived_cl2681, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X2 : $i]: 93.76/13.06 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 93.76/13.06 ((('#C') @ is_of @ 93.76/13.06 ((('#C') @ in @ (pair1type @ nat))))))) @ 93.76/13.06 ((('#B') @ (((=>) @ (n_eq @ X1 @ X0))) @ 93.76/13.06 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 93.76/13.06 ((('#B') @ (moref @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ 93.76/13.06 (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.76/13.06 (n_pf @ X0))))))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('comb-normalize', [status(thm)], [zip_derived_cl2680])). 93.76/13.06 thf(zip_derived_cl2682, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.76/13.06 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 (((n_eq @ X1 @ X0) => 93.76/13.06 (((moref @ X2 @ X4) => (moref @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2))) @ 93.76/13.06 (n_pf @ X0 @ X4)))))))) 93.76/13.06 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2681])). 93.76/13.06 thf(zip_derived_cl2683, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.76/13.06 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 93.76/13.06 (((n_eq @ X1 @ X0) => 93.76/13.06 (((l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X2)))) => 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4))))) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2))))))))))))) 93.76/13.06 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('rw', [status(thm)], 93.76/13.06 [zip_derived_cl2682, '4', '4', '5', '5', '6', '6', '8'])). 93.76/13.06 thf(zip_derived_cl2684, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.76/13.06 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | (((n_eq @ X1 @ X0) => 93.76/13.06 (((l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X2)))) => 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4))))) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2))))))))))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2683])). 93.76/13.06 thf(zip_derived_cl2685, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.76/13.06 (~ (n_eq @ X1 @ X0) 93.76/13.06 | (((l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X2)))) => 93.76/13.06 (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4))))) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2))))))))) 93.76/13.06 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2684])). 93.76/13.06 thf(zip_derived_cl2686, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.76/13.06 (~ (l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X2)))) 93.76/13.06 | (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4))))) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2))))))) 93.76/13.06 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 93.76/13.06 | ~ (n_eq @ X1 @ X0))), 93.76/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2685])). 93.76/13.06 thf(zip_derived_cl7591, plain, 93.76/13.06 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 93.76/13.06 (~ (l_some @ nat @ 93.76/13.06 (diffprop @ (n_ts @ (num @ X2) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X2)))) 93.76/13.06 | (l_some @ nat @ 93.76/13.06 (diffprop @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4))))) @ 93.76/13.06 (n_ts @ 93.76/13.06 (num @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X0) @ (den @ X4)) @ 93.76/13.06 (n_ts @ (num @ X4) @ (den @ X0))) @ 93.76/13.06 (n_ts @ (den @ X0) @ (den @ X4)))) @ 93.76/13.06 (den @ 93.76/13.06 (n_fr @ 93.76/13.06 (n_pl @ (n_ts @ (num @ X1) @ (den @ X2)) @ 93.76/13.06 (n_ts @ (num @ X2) @ (den @ X1))) @ 93.76/13.06 (n_ts @ (den @ X1) @ (den @ X2))))))) 93.76/13.06 | ~ (is_of @ X4 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.76/13.06 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.76/13.06 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.76/13.06 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 93.76/13.06 | ~ (n_eq @ X1 @ X0))), 93.76/13.06 inference('remove_ty_args', [status(thm)], [zip_derived_cl2686])). 93.76/13.06 thf(zip_derived_cl7627, plain, ($false), 93.76/13.06 inference('eprover', [status(thm)], 93.76/13.06 [zip_derived_cl1554, zip_derived_cl7551, zip_derived_cl7552, 93.76/13.06 zip_derived_cl7549, zip_derived_cl7550, zip_derived_cl1549, 93.76/13.06 zip_derived_cl7594, zip_derived_cl1550, zip_derived_cl7591])). 93.76/13.06 93.76/13.06 % SZS output end Refutation 93.76/13.06 93.76/13.06 93.76/13.06 % Terminating... 94.40/13.15 % Runner terminated. 94.40/13.15 % Zipperpin 1.5 exiting 94.40/13.15 EOF