0.02/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.17 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.YRAe8SI6Ch true 0.14/0.37 % Computer : n014.cluster.edu 0.14/0.37 % Model : x86_64 x86_64 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.37 % Memory : 8042.1875MB 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.37 % CPULimit : 1440 0.14/0.37 % WCLimit : 180 0.14/0.37 % DateTime : Mon Jul 3 10:48:09 EDT 2023 0.14/0.37 % CPUTime : 0.14/0.37 % Running portfolio for 1440 s 0.14/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.38 % Number of cores: 8 0.14/0.38 % Python version: Python 3.6.8 0.14/0.38 % Running in HO mode 0.53/0.69 % Total configuration time : 828 0.53/0.69 % Estimated wc time : 1656 0.53/0.69 % Estimated cpu time (8 cpus) : 207.0 0.53/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.54/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.54/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.54/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.54/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.54/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 50.94/7.05 % Solved by lams/40_b.comb.sh. 50.94/7.05 % done 504 iterations in 6.216s 50.94/7.05 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 50.94/7.05 % SZS output start Refutation 50.94/7.05 thf(emptyset_type, type, emptyset: $i). 50.94/7.05 thf(lessis_type, type, lessis: $i > $i > $o). 50.94/7.05 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 50.94/7.05 thf(omega_type, type, omega: $i). 50.94/7.05 thf(d_not_type, type, d_not: $o > $o). 50.94/7.05 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 50.94/7.05 thf(in_type, type, in: $i > $i > $o). 50.94/7.05 thf(moreis_type, type, moreis: $i > $i > $o). 50.94/7.05 thf('#sk3_type', type, '#sk3': $i). 50.94/7.05 thf('#sk4_type', type, '#sk4': $i). 50.94/7.05 thf(ap_type, type, ap: $i > $i > $i). 50.94/7.05 thf(nat_type, type, nat: $i). 50.94/7.05 thf(iii_type, type, iii: $i > $i > $o). 50.94/7.05 thf(l_or_type, type, l_or: $o > $o > $o). 50.94/7.05 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 50.94/7.05 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 50.94/7.05 thf(imp_type, type, imp: $o > $o > $o). 50.94/7.05 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 50.94/7.05 thf('#sk5_type', type, '#sk5': $i). 50.94/7.05 thf(plus_type, type, plus: $i > $i). 50.94/7.05 thf(n_is_type, type, n_is: $i > $i > $o). 50.94/7.05 thf(n_some_type, type, n_some: ($i > $o) > $o). 50.94/7.05 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o). 50.94/7.05 thf(n_pl_type, type, n_pl: $i > $i > $i). 50.94/7.05 thf('#sk2_type', type, '#sk2': $i). 50.94/7.05 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 50.94/7.05 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 50.94/7.05 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 50.94/7.05 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 50.94/7.05 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 50.94/7.05 thf(satz22a, conjecture, 50.94/7.05 (all_of @ 50.94/7.05 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 50.94/7.05 ( ^[X0:$i]: 50.94/7.05 ( all_of @ 50.94/7.05 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 50.94/7.05 ( ^[X1:$i]: 50.94/7.05 ( all_of @ 50.94/7.05 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 50.94/7.05 ( ^[X2:$i]: 50.94/7.05 ( all_of @ 50.94/7.05 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @ 50.94/7.05 ( ^[X3:$i]: 50.94/7.05 ( ( moreis @ X0 @ X1 ) => 50.94/7.05 ( ( d_29_ii @ X2 @ X3 ) => 50.94/7.05 ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 50.94/7.05 thf(zf_stmt_0, negated_conjecture, 50.94/7.05 (~( all_of @ 50.94/7.05 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 50.94/7.05 ( ^[X0:$i]: 50.94/7.05 ( all_of @ 50.94/7.05 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 50.94/7.05 ( ^[X1:$i]: 50.94/7.05 ( all_of @ 50.94/7.05 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 50.94/7.05 ( ^[X2:$i]: 50.94/7.05 ( all_of @ 50.94/7.05 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @ 50.94/7.05 ( ^[X3:$i]: 50.94/7.05 ( ( moreis @ X0 @ X1 ) => 50.94/7.05 ( ( d_29_ii @ X2 @ X3 ) => 50.94/7.05 ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) )), 50.94/7.05 inference('cnf.neg', [status(esa)], [satz22a])). 50.94/7.05 thf(zip_derived_cl142, plain, 50.94/7.05 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 50.94/7.05 (^[Y0 : $i]: 50.94/7.05 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 50.94/7.05 (^[Y1 : $i]: 50.94/7.05 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ 50.94/7.05 (^[Y2 : $i]: 50.94/7.05 (all_of @ (^[Y3 : $i]: (in @ Y3 @ nat)) @ 50.94/7.05 (^[Y3 : $i]: 50.94/7.05 (((moreis @ Y0 @ Y1) => 50.94/7.05 (((d_29_ii @ Y2 @ Y3) => (d_29_ii @ 50.94/7.05 (n_pl @ Y0 @ Y2) @ (n_pl @ Y1 @ Y3))))))))))))))), 50.94/7.05 inference('cnf', [status(esa)], [zf_stmt_0])). 50.94/7.05 thf(zip_derived_cl143, plain, 50.94/7.05 (~ (all_of @ ((('#C') @ in @ nat)) @ 50.94/7.05 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ moreis)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ 50.94/7.05 d_29_ii)))))))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#C') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ d_29_ii)) @ n_pl)))))))) @ 50.94/7.05 n_pl)))))))))))))), 50.94/7.05 inference('lams2combs', [status(thm)], [zip_derived_cl142])). 50.94/7.05 thf(def_nat, axiom,(( nat ) = 50.94/7.05 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))). 50.94/7.05 thf('0', plain, 50.94/7.05 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )), 50.94/7.05 define([status(thm)])). 50.94/7.05 thf(zip_derived_cl808, plain, 50.94/7.05 (~ (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ moreis)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ 50.94/7.05 d_29_ii)))))))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#C') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ d_29_ii)) @ n_pl)))))))) @ 50.94/7.05 n_pl)))))))))))))), 50.94/7.05 inference('rw', [status(thm)], [zip_derived_cl143, '0'])). 50.94/7.05 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 50.94/7.05 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 50.94/7.05 thf('1', plain, 50.94/7.05 (![X0:( $i > $o ),X1:( $i > $o )]: 50.94/7.05 ( ( ~( all_of @ X0 @ X1 ) ) <=> 50.94/7.05 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 50.94/7.05 inference('rw.lit', [status(esa)], [def_all_of])). 50.94/7.05 thf(zip_derived_cl809, plain, 50.94/7.05 (~ (((!!) @ (^[Y0 : $i]: 50.94/7.05 (((is_of @ Y0 @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ 50.94/7.05 omega @ 50.94/7.05 ((('#C') @ ( 50.94/7.05 !=) @ 50.94/7.05 emptyset)))))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ 50.94/7.05 moreis)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 50.94/7.05 '#S') @ 50.94/7.05 ((('#B') @ ( 50.94/7.05 (('#B') @ ( 50.94/7.05 =>))) @ 50.94/7.05 d_29_ii)))))))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#C') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ d_29_ii)) @ 50.94/7.05 n_pl)))))))) @ 50.94/7.05 n_pl)))))))))) @ 50.94/7.05 Y0)))))))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl808, '1'])). 50.94/7.05 thf(zip_derived_cl810, plain, 50.94/7.05 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 50.94/7.05 ((('#C') @ is_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))))))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ ( 50.94/7.05 !=) @ emptyset)))))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ 50.94/7.05 moreis)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 50.94/7.05 '#S') @ 50.94/7.05 ((('#B') @ ( 50.94/7.05 (('#B') @ (=>))) @ 50.94/7.05 d_29_ii)))))))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#C') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ d_29_ii)) @ 50.94/7.05 n_pl)))))))) @ 50.94/7.05 n_pl))))))))))))))))), 50.94/7.05 inference('comb-normalize', [status(thm)], [zip_derived_cl809])). 50.94/7.05 thf(zip_derived_cl811, plain, 50.94/7.05 (~ (((is_of @ '#sk2' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ (=>) @ (moreis @ '#sk2'))))))) @ 50.94/7.05 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))) @ 50.94/7.05 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ d_29_ii @ (n_pl @ '#sk2'))))))) @ 50.94/7.05 n_pl)))))))))))))), 50.94/7.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl810])). 50.94/7.05 thf(zip_derived_cl813, plain, 50.94/7.05 (~ (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ (=>) @ (moreis @ '#sk2'))))))) @ 50.94/7.05 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))) @ 50.94/7.05 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ d_29_ii @ (n_pl @ '#sk2'))))))) @ 50.94/7.05 n_pl)))))))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl811])). 50.94/7.05 thf(zip_derived_cl814, plain, 50.94/7.05 (~ (((!!) @ (^[Y0 : $i]: 50.94/7.05 (((is_of @ Y0 @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ (=>) @ (moreis @ '#sk2'))))))) @ 50.94/7.05 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ 50.94/7.05 d_29_ii)))))) @ 50.94/7.05 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ d_29_ii @ 50.94/7.05 (n_pl @ '#sk2'))))))) @ 50.94/7.05 n_pl)))))))) @ 50.94/7.05 Y0)))))))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl813, '1'])). 50.94/7.05 thf(zip_derived_cl815, plain, 50.94/7.05 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 50.94/7.05 ((('#C') @ is_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))))))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ (=>) @ (moreis @ '#sk2'))))))) @ 50.94/7.05 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ 50.94/7.05 d_29_ii)))))) @ 50.94/7.05 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ d_29_ii @ 50.94/7.05 (n_pl @ '#sk2'))))))) @ 50.94/7.05 n_pl))))))))))))))), 50.94/7.05 inference('comb-normalize', [status(thm)], [zip_derived_cl814])). 50.94/7.05 thf(zip_derived_cl816, plain, 50.94/7.05 (~ (((is_of @ '#sk3' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (((=>) @ (moreis @ '#sk2' @ '#sk3'))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ d_29_ii @ (n_pl @ '#sk2'))))) @ 50.94/7.05 (n_pl @ '#sk3'))))))))))))), 50.94/7.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl815])). 50.94/7.05 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 50.94/7.05 thf('2', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 50.94/7.05 define([status(thm)])). 50.94/7.05 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 50.94/7.05 thf('3', plain, 50.94/7.05 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 50.94/7.05 define([status(thm)])). 50.94/7.05 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))). 50.94/7.05 thf('4', plain, 50.94/7.05 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )), 50.94/7.05 define([status(thm)])). 50.94/7.05 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) = 50.94/7.05 ((n_some @ (diffprop @ X0 @ X1))))). 50.94/7.05 thf('5', plain, 50.94/7.05 (![X1:$i,X0:$i]: 50.94/7.05 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 50.94/7.05 define([status(thm)])). 50.94/7.05 thf(def_moreis, axiom,(( moreis @ (X0)@ (X1)) = 50.94/7.05 ((l_or @ (d_29_ii @ X0 @ X1) @ (n_is @ X0 @ X1))))). 50.94/7.05 thf('6', plain, 50.94/7.05 (![X1:$i,X0:$i]: 50.94/7.05 ( ( moreis @ X0 @ X1 ) = 50.94/7.05 ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )), 50.94/7.05 define([status(thm)])). 50.94/7.05 thf(zip_derived_cl817, plain, 50.94/7.05 (~ (((is_of @ '#sk3' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ '#sk2' @ '#sk3')))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ d_29_ii @ (n_pl @ '#sk2'))))) @ 50.94/7.05 (n_pl @ '#sk3'))))))))))))), 50.94/7.05 inference('rw', [status(thm)], 50.94/7.05 [zip_derived_cl816, '2', '3', '0', '4', '5', '6'])). 50.94/7.05 thf(zip_derived_cl819, plain, 50.94/7.05 (~ (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ '#sk2' @ '#sk3')))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ d_29_ii @ (n_pl @ '#sk2'))))) @ 50.94/7.05 (n_pl @ '#sk3'))))))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl817])). 50.94/7.05 thf(zip_derived_cl820, plain, 50.94/7.05 (~ (((!!) @ (^[Y0 : $i]: 50.94/7.05 (((is_of @ Y0 @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ ( 50.94/7.05 !=) @ emptyset))) @ 50.94/7.05 (diffprop @ 50.94/7.05 '#sk2' @ '#sk3')) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ '#sk2' @ 50.94/7.05 '#sk3')))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ d_29_ii @ (n_pl @ '#sk2'))))) @ 50.94/7.05 (n_pl @ '#sk3'))))))) @ 50.94/7.05 Y0)))))))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl819, '1'])). 50.94/7.05 thf(zip_derived_cl821, plain, 50.94/7.05 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 50.94/7.05 ((('#C') @ is_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))))))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ 50.94/7.05 emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ 50.94/7.05 '#sk3')) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ '#sk2' @ '#sk3')))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ d_29_ii @ (n_pl @ '#sk2'))))) @ 50.94/7.05 (n_pl @ '#sk3')))))))))))))), 50.94/7.05 inference('comb-normalize', [status(thm)], [zip_derived_cl820])). 50.94/7.05 thf(zip_derived_cl822, plain, 50.94/7.05 (~ (((is_of @ '#sk4' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (((=>) @ (imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ '#sk2' @ '#sk3')))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk4'))) @ 50.94/7.05 ((('#B') @ (d_29_ii @ (n_pl @ '#sk2' @ '#sk4')) @ 50.94/7.05 (n_pl @ '#sk3'))))))))))), 50.94/7.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl821])). 50.94/7.05 thf(def_n_pl, axiom,(( n_pl @ (X0)@ (X1)) = ((ap @ (plus @ X0) @ X1)))). 50.94/7.05 thf('7', plain, 50.94/7.05 (![X1:$i,X0:$i]: ( ( n_pl @ X0 @ X1 ) = ( ap @ ( plus @ X0 ) @ X1 ) )), 50.94/7.05 define([status(thm)])). 50.94/7.05 thf(zip_derived_cl823, plain, 50.94/7.05 (~ (((is_of @ '#sk4' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (((=>) @ (imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ '#sk2' @ '#sk3')))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk4'))) @ 50.94/7.05 ((('#B') @ (d_29_ii @ (ap @ (plus @ '#sk2') @ '#sk4')) @ 50.94/7.05 (n_pl @ '#sk3'))))))))))), 50.94/7.05 inference('rw', [status(thm)], [zip_derived_cl822, '7'])). 50.94/7.05 thf(zip_derived_cl825, plain, 50.94/7.05 (~ (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (((=>) @ (imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ '#sk2' @ '#sk3')))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk4'))) @ 50.94/7.05 ((('#B') @ (d_29_ii @ (ap @ (plus @ '#sk2') @ '#sk4')) @ 50.94/7.05 (n_pl @ '#sk3'))))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl823])). 50.94/7.05 thf(zip_derived_cl826, plain, 50.94/7.05 (~ (((!!) @ (^[Y0 : $i]: 50.94/7.05 (((is_of @ Y0 @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 ((('#B') @ (((=>) @ (imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ '#sk2' @ '#sk3')))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk4'))) @ 50.94/7.05 ((('#B') @ (d_29_ii @ 50.94/7.05 (ap @ (plus @ '#sk2') @ '#sk4')) @ 50.94/7.05 (n_pl @ '#sk3'))))) @ 50.94/7.05 Y0)))))))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl825, '1'])). 50.94/7.05 thf(zip_derived_cl827, plain, 50.94/7.05 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 50.94/7.05 ((('#C') @ is_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))))))))) @ 50.94/7.05 ((('#B') @ (((=>) @ (imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ '#sk2' @ '#sk3')))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk4'))) @ 50.94/7.05 ((('#B') @ (d_29_ii @ (ap @ (plus @ '#sk2') @ '#sk4')) @ 50.94/7.05 (n_pl @ '#sk3')))))))))))), 50.94/7.05 inference('comb-normalize', [status(thm)], [zip_derived_cl826])). 50.94/7.05 thf(zip_derived_cl828, plain, 50.94/7.05 (~ (((is_of @ '#sk5' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (((imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ '#sk2' @ '#sk3')) => 50.94/7.05 (((d_29_ii @ '#sk4' @ '#sk5') => (d_29_ii @ 50.94/7.05 (ap @ (plus @ '#sk2') @ '#sk4') @ (n_pl @ '#sk3' @ '#sk5'))))))))), 50.94/7.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl827])). 50.94/7.05 thf(zip_derived_cl829, plain, 50.94/7.05 (~ (((is_of @ '#sk5' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (((imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ '#sk2' @ '#sk3')) => 50.94/7.05 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk4' @ '#sk5')) => (l_some @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ (ap @ (plus @ '#sk2') @ '#sk4') @ 50.94/7.05 (ap @ (plus @ '#sk3') @ '#sk5')))))))))), 50.94/7.05 inference('rw', [status(thm)], 50.94/7.05 [zip_derived_cl828, '0', '4', '4', '7', '5', '5'])). 50.94/7.05 thf(zip_derived_cl831, plain, 50.94/7.05 (~ (((imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ '#sk2' @ '#sk3')) => 50.94/7.05 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk4' @ '#sk5')) => (l_some @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ (ap @ (plus @ '#sk2') @ '#sk4') @ 50.94/7.05 (ap @ (plus @ '#sk3') @ '#sk5')))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl829])). 50.94/7.05 thf(zip_derived_cl833, plain, 50.94/7.05 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk4' @ '#sk5')) => (l_some @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ (ap @ (plus @ '#sk2') @ '#sk4') @ 50.94/7.05 (ap @ (plus @ '#sk3') @ '#sk5')))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl831])). 50.94/7.05 thf(zip_derived_cl836, plain, 50.94/7.05 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ (ap @ (plus @ '#sk2') @ '#sk4') @ 50.94/7.05 (ap @ (plus @ '#sk3') @ '#sk5')))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl833])). 50.94/7.05 thf(satz19j, axiom, 50.94/7.05 (all_of @ 50.94/7.05 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 50.94/7.05 ( ^[X0:$i]: 50.94/7.05 ( all_of @ 50.94/7.05 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 50.94/7.05 ( ^[X1:$i]: 50.94/7.05 ( all_of @ 50.94/7.05 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 50.94/7.05 ( ^[X2:$i]: 50.94/7.05 ( all_of @ 50.94/7.05 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @ 50.94/7.05 ( ^[X3:$i]: 50.94/7.05 ( ( n_is @ X0 @ X1 ) => 50.94/7.05 ( ( iii @ X2 @ X3 ) => 50.94/7.05 ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 50.94/7.05 thf(zip_derived_cl68, plain, 50.94/7.05 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 50.94/7.05 (^[Y0 : $i]: 50.94/7.05 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 50.94/7.05 (^[Y1 : $i]: 50.94/7.05 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ 50.94/7.05 (^[Y2 : $i]: 50.94/7.05 (all_of @ (^[Y3 : $i]: (in @ Y3 @ nat)) @ 50.94/7.05 (^[Y3 : $i]: 50.94/7.05 (((n_is @ Y0 @ Y1) => 50.94/7.05 (((iii @ Y2 @ Y3) => (iii @ (n_pl @ Y0 @ Y2) @ 50.94/7.05 (n_pl @ Y1 @ Y3))))))))))))))), 50.94/7.05 inference('cnf', [status(esa)], [satz19j])). 50.94/7.05 thf(zip_derived_cl69, plain, 50.94/7.05 ( (all_of @ ((('#C') @ in @ nat)) @ 50.94/7.05 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ 50.94/7.05 iii)))))))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#C') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))))) @ 50.94/7.05 n_pl)))))))))))))), 50.94/7.05 inference('lams2combs', [status(thm)], [zip_derived_cl68])). 50.94/7.05 thf(zip_derived_cl1277, plain, 50.94/7.05 ( (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ 50.94/7.05 iii)))))))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#C') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))))) @ 50.94/7.05 n_pl)))))))))))))), 50.94/7.05 inference('rw', [status(thm)], [zip_derived_cl69, '0'])). 50.94/7.05 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 50.94/7.05 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 50.94/7.05 thf('8', plain, 50.94/7.05 (![X0:( $i > $o ),X1:( $i > $o )]: 50.94/7.05 ( ( all_of @ X0 @ X1 ) <=> 50.94/7.05 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 50.94/7.05 inference('rw.lit', [status(esa)], [def_all_of])). 50.94/7.05 thf(zip_derived_cl1278, plain, 50.94/7.05 ( (((!!) @ (^[Y0 : $i]: 50.94/7.05 (((is_of @ Y0 @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ ( 50.94/7.05 !=) @ emptyset)))))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ 50.94/7.05 n_is)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 50.94/7.05 '#S') @ 50.94/7.05 ((('#B') @ ( 50.94/7.05 (('#B') @ ( 50.94/7.05 =>))) @ 50.94/7.05 iii)))))))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#C') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ iii)) @ 50.94/7.05 n_pl)))))))) @ 50.94/7.05 n_pl)))))))))) @ 50.94/7.05 Y0)))))))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl1277, '8'])). 50.94/7.05 thf(zip_derived_cl1279, plain, 50.94/7.05 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 50.94/7.05 ((('#C') @ is_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ ( 50.94/7.05 !=) @ emptyset)))))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 50.94/7.05 '#S') @ 50.94/7.05 ((('#B') @ ( 50.94/7.05 (('#B') @ (=>))) @ 50.94/7.05 iii)))))))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#C') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ iii)) @ 50.94/7.05 n_pl)))))))) @ 50.94/7.05 n_pl))))))))))))))))), 50.94/7.05 inference('comb-normalize', [status(thm)], [zip_derived_cl1278])). 50.94/7.05 thf(zip_derived_cl1280, plain, 50.94/7.05 (![X2 : $i]: 50.94/7.05 (((is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ (=>) @ (n_is @ X2))))))) @ 50.94/7.05 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))))) @ 50.94/7.05 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ (n_pl @ X2))))))) @ 50.94/7.05 n_pl)))))))))))))), 50.94/7.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1279])). 50.94/7.05 thf(zip_derived_cl1281, plain, 50.94/7.05 (![X2 : $i]: 50.94/7.05 (~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ (=>) @ (n_is @ X2))))))) @ 50.94/7.05 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))))) @ 50.94/7.05 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ (n_pl @ X2))))))) @ 50.94/7.05 n_pl))))))))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1280])). 50.94/7.05 thf(zip_derived_cl1282, plain, 50.94/7.05 (![X0 : $i]: 50.94/7.05 ( (((!!) @ (^[Y0 : $i]: 50.94/7.05 (((is_of @ Y0 @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ (=>) @ (n_is @ X0))))))) @ 50.94/7.05 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ ( 50.94/7.05 =>))) @ 50.94/7.05 iii)))))) @ 50.94/7.05 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ 50.94/7.05 (n_pl @ X0))))))) @ 50.94/7.05 n_pl)))))))) @ 50.94/7.05 Y0))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl1281, '8'])). 50.94/7.05 thf(zip_derived_cl1283, plain, 50.94/7.05 (![X0 : $i]: 50.94/7.05 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 50.94/7.05 ((('#C') @ is_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))))))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ (=>) @ (n_is @ X0))))))) @ 50.94/7.05 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ 50.94/7.05 iii)))))) @ 50.94/7.05 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ 50.94/7.05 (n_pl @ X0))))))) @ 50.94/7.05 n_pl)))))))))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('comb-normalize', [status(thm)], [zip_derived_cl1282])). 50.94/7.05 thf(zip_derived_cl1284, plain, 50.94/7.05 (![X0 : $i, X2 : $i]: 50.94/7.05 ( (((is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ X0 @ X2))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ (n_pl @ X0))))) @ 50.94/7.05 (n_pl @ X2)))))))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1283])). 50.94/7.05 thf(zip_derived_cl1285, plain, 50.94/7.05 (![X0 : $i, X2 : $i]: 50.94/7.05 (~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ X0 @ X2))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ (n_pl @ X0))))) @ 50.94/7.05 (n_pl @ X2)))))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1284])). 50.94/7.05 thf(zip_derived_cl1286, plain, 50.94/7.05 (![X0 : $i, X1 : $i]: 50.94/7.05 ( (((!!) @ (^[Y0 : $i]: 50.94/7.05 (((is_of @ Y0 @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ X0 @ X1))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ (n_pl @ X0))))) @ 50.94/7.05 (n_pl @ X1))))))) @ 50.94/7.05 Y0))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl1285, '8'])). 50.94/7.05 thf(zip_derived_cl1287, plain, 50.94/7.05 (![X0 : $i, X1 : $i]: 50.94/7.05 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 50.94/7.05 ((('#C') @ is_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))))))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ X0 @ X1))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ (n_pl @ X0))))) @ 50.94/7.05 (n_pl @ X1))))))))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('comb-normalize', [status(thm)], [zip_derived_cl1286])). 50.94/7.05 thf(zip_derived_cl1288, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X3 : $i]: 50.94/7.05 ( (((is_of @ X3 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (((=>) @ (n_is @ X0 @ X1))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (iii @ X3))) @ 50.94/7.05 ((('#B') @ (iii @ (n_pl @ X0 @ X3)) @ (n_pl @ X1)))))))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1287])). 50.94/7.05 thf(zip_derived_cl1289, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X3 : $i]: 50.94/7.05 ( (((is_of @ X3 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (((=>) @ (n_is @ X0 @ X1))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (iii @ X3))) @ 50.94/7.05 ((('#B') @ (iii @ (ap @ (plus @ X0) @ X3)) @ (n_pl @ X1)))))))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('rw', [status(thm)], [zip_derived_cl1288, '7'])). 50.94/7.05 thf(zip_derived_cl1290, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X3 : $i]: 50.94/7.05 (~ (is_of @ X3 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (((=>) @ (n_is @ X0 @ X1))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (iii @ X3))) @ 50.94/7.05 ((('#B') @ (iii @ (ap @ (plus @ X0) @ X3)) @ (n_pl @ X1)))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1289])). 50.94/7.05 thf(zip_derived_cl1291, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X2 : $i]: 50.94/7.05 ( (((!!) @ (^[Y0 : $i]: 50.94/7.05 (((is_of @ Y0 @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 ((('#B') @ (((=>) @ (n_is @ X1 @ X0))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (iii @ X2))) @ 50.94/7.05 ((('#B') @ (iii @ (ap @ (plus @ X1) @ X2)) @ 50.94/7.05 (n_pl @ X0))))) @ 50.94/7.05 Y0))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl1290, '8'])). 50.94/7.05 thf(zip_derived_cl1292, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X2 : $i]: 50.94/7.05 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 50.94/7.05 ((('#C') @ is_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))))))))) @ 50.94/7.05 ((('#B') @ (((=>) @ (n_is @ X1 @ X0))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (iii @ X2))) @ 50.94/7.05 ((('#B') @ (iii @ (ap @ (plus @ X1) @ X2)) @ 50.94/7.05 (n_pl @ X0))))))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('comb-normalize', [status(thm)], [zip_derived_cl1291])). 50.94/7.05 thf(zip_derived_cl1293, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 50.94/7.05 ( (((is_of @ X4 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (((n_is @ X1 @ X0) => 50.94/7.05 (((iii @ X2 @ X4) => (iii @ (ap @ (plus @ X1) @ X2) @ 50.94/7.05 (n_pl @ X0 @ X4)))))))) 50.94/7.05 | ~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1292])). 50.94/7.05 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))). 50.94/7.05 thf('9', plain, 50.94/7.05 (![X1:$i,X0:$i]: 50.94/7.05 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 50.94/7.05 define([status(thm)])). 50.94/7.05 thf(zip_derived_cl1294, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 50.94/7.05 ( (((is_of @ X4 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (((n_is @ X1 @ X0) => 50.94/7.05 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X4 @ X2)) => (l_some @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ (ap @ (plus @ X0) @ X4) @ (ap @ (plus @ X1) @ X2))))))))) 50.94/7.05 | ~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('rw', [status(thm)], 50.94/7.05 [zip_derived_cl1293, '0', '4', '4', '7', '9', '9'])). 50.94/7.05 thf(zip_derived_cl1295, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 50.94/7.05 (~ (is_of @ X4 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | (((n_is @ X1 @ X0) => 50.94/7.05 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X4 @ X2)) => (l_some @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ (ap @ (plus @ X0) @ X4) @ (ap @ (plus @ X1) @ X2))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1294])). 50.94/7.05 thf(zip_derived_cl1296, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 50.94/7.05 (~ (n_is @ X1 @ X0) 50.94/7.05 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X4 @ X2)) => (l_some @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ (ap @ (plus @ X0) @ X4) @ (ap @ (plus @ X1) @ X2))))) 50.94/7.05 | ~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X4 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1295])). 50.94/7.05 thf(zip_derived_cl1297, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 50.94/7.05 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X4 @ X2)) 50.94/7.05 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ (ap @ (plus @ X0) @ X4) @ (ap @ (plus @ X1) @ X2))) 50.94/7.05 | ~ (is_of @ X4 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (n_is @ X1 @ X0))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1296])). 50.94/7.05 thf(zip_derived_cl9081, plain, 50.94/7.05 ((~ (n_is @ '#sk3' @ '#sk2') 50.94/7.05 | ~ (is_of @ '#sk5' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ '#sk3' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ '#sk2' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ '#sk4' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk4' @ '#sk5')))), 50.94/7.05 inference('sup+', [status(thm)], [zip_derived_cl836, zip_derived_cl1297])). 50.94/7.05 thf(satz13, axiom, 50.94/7.05 (all_of @ 50.94/7.05 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 50.94/7.05 ( ^[X0:$i]: 50.94/7.05 ( all_of @ 50.94/7.05 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 50.94/7.05 ( ^[X1:$i]: ( ( moreis @ X0 @ X1 ) => ( lessis @ X1 @ X0 ) ) ) ) ))). 50.94/7.05 thf(zip_derived_cl96, plain, 50.94/7.05 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 50.94/7.05 (^[Y0 : $i]: 50.94/7.05 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 50.94/7.05 (^[Y1 : $i]: (((moreis @ Y0 @ Y1) => (lessis @ Y1 @ Y0)))))))), 50.94/7.05 inference('cnf', [status(esa)], [satz13])). 50.94/7.05 thf(zip_derived_cl97, plain, 50.94/7.05 ( (all_of @ ((('#C') @ in @ nat)) @ 50.94/7.05 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @ 50.94/7.05 ((('#C') @ lessis)))))))), 50.94/7.05 inference('lams2combs', [status(thm)], [zip_derived_cl96])). 50.94/7.05 thf(zip_derived_cl295, plain, 50.94/7.05 ( (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @ 50.94/7.05 ((('#C') @ lessis)))))))), 50.94/7.05 inference('rw', [status(thm)], [zip_derived_cl97, '0'])). 50.94/7.05 thf(zip_derived_cl296, plain, 50.94/7.05 ( (((!!) @ (^[Y0 : $i]: 50.94/7.05 (((is_of @ Y0 @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @ 50.94/7.05 ((('#C') @ lessis)))) @ 50.94/7.05 Y0)))))))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl295, '8'])). 50.94/7.05 thf(zip_derived_cl297, plain, 50.94/7.05 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 50.94/7.05 ((('#C') @ is_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @ 50.94/7.05 ((('#C') @ lessis))))))))))), 50.94/7.05 inference('comb-normalize', [status(thm)], [zip_derived_cl296])). 50.94/7.05 thf(zip_derived_cl298, plain, 50.94/7.05 (![X2 : $i]: 50.94/7.05 (((is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X2))) @ 50.94/7.05 ((('#C') @ lessis @ X2)))))))), 50.94/7.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl297])). 50.94/7.05 thf(zip_derived_cl299, plain, 50.94/7.05 (![X2 : $i]: 50.94/7.05 (~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X2))) @ 50.94/7.05 ((('#C') @ lessis @ X2))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl298])). 50.94/7.05 thf(zip_derived_cl300, plain, 50.94/7.05 (![X0 : $i]: 50.94/7.05 ( (((!!) @ (^[Y0 : $i]: 50.94/7.05 (((is_of @ Y0 @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X0))) @ 50.94/7.05 ((('#C') @ lessis @ X0)) @ Y0))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl299, '8'])). 50.94/7.05 thf(zip_derived_cl301, plain, 50.94/7.05 (![X0 : $i]: 50.94/7.05 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 50.94/7.05 ((('#C') @ is_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X0))) @ 50.94/7.05 ((('#C') @ lessis @ X0)))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('comb-normalize', [status(thm)], [zip_derived_cl300])). 50.94/7.05 thf(zip_derived_cl302, plain, 50.94/7.05 (![X0 : $i, X2 : $i]: 50.94/7.05 ( (((is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (((moreis @ X0 @ X2) => (lessis @ X2 @ X0))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl301])). 50.94/7.05 thf(def_lessis, axiom,(( lessis @ (X0)@ (X1)) = 50.94/7.05 ((l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1))))). 50.94/7.05 thf('10', plain, 50.94/7.05 (![X1:$i,X0:$i]: 50.94/7.05 ( ( lessis @ X0 @ X1 ) = 50.94/7.05 ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )), 50.94/7.05 define([status(thm)])). 50.94/7.05 thf(zip_derived_cl303, plain, 50.94/7.05 (![X0 : $i, X2 : $i]: 50.94/7.05 ( (((is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (((imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X2)) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ X0 @ X2)) => (imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X2)) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ X2 @ X0)))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('rw', [status(thm)], 50.94/7.05 [zip_derived_cl302, '2', '3', '3', '0', '4', '5', '9', '6', 50.94/7.05 '10'])). 50.94/7.05 thf(zip_derived_cl304, plain, 50.94/7.05 (![X0 : $i, X2 : $i]: 50.94/7.05 (~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | (((imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X2)) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ X0 @ X2)) => (imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X2)) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ X2 @ X0)))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl303])). 50.94/7.05 thf(zip_derived_cl305, plain, 50.94/7.05 (![X0 : $i, X2 : $i]: 50.94/7.05 (~ (imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X2)) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ X0 @ X2)) 50.94/7.05 | (imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X2)) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ X2 @ X0)) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl304])). 50.94/7.05 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 50.94/7.05 thf('11', plain, 50.94/7.05 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 50.94/7.05 inference('rw.lit', [status(esa)], [def_imp])). 50.94/7.05 thf(zip_derived_cl306, plain, 50.94/7.05 (![X0 : $i, X1 : $i]: 50.94/7.05 (~ (((imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X1 @ X0)) @ 50.94/7.05 ($false)) => (n_is @ X1 @ X0))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | (imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X1 @ X0)) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ X0 @ X1)))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl305, '11'])). 50.94/7.05 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 50.94/7.05 thf('12', plain, 50.94/7.05 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 50.94/7.05 inference('rw.lit', [status(esa)], [def_imp])). 50.94/7.05 thf(zip_derived_cl307, plain, 50.94/7.05 (![X0 : $i, X1 : $i]: 50.94/7.05 ( (((imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X1)) @ 50.94/7.05 ($false)) => (n_is @ X1 @ X0))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (((imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X1)) @ 50.94/7.05 ($false)) => (n_is @ X0 @ X1))))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl306, '12'])). 50.94/7.05 thf(zip_derived_cl308, plain, 50.94/7.05 (![X0 : $i, X1 : $i]: 50.94/7.05 (~ (imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X1)) @ 50.94/7.05 ($false)) 50.94/7.05 | (n_is @ X1 @ X0) 50.94/7.05 | ~ (((imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X1)) @ 50.94/7.05 ($false)) => (n_is @ X0 @ X1))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl307])). 50.94/7.05 thf(zip_derived_cl309, plain, 50.94/7.05 (![X0 : $i, X1 : $i]: 50.94/7.05 (~ (imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X1)) @ 50.94/7.05 ($false)) 50.94/7.05 | (n_is @ X1 @ X0) 50.94/7.05 | ~ ((($true) => (n_is @ X0 @ X1))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('local_rewriting', [status(thm)], [zip_derived_cl308])). 50.94/7.05 thf(zip_derived_cl310, plain, 50.94/7.05 (![X0 : $i, X1 : $i]: 50.94/7.05 (~ (imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X1)) @ 50.94/7.05 ($false)) 50.94/7.05 | (n_is @ X1 @ X0) 50.94/7.05 | ~ (n_is @ X0 @ X1) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl309])). 50.94/7.05 thf(zip_derived_cl311, plain, 50.94/7.05 (![X0 : $i, X1 : $i]: 50.94/7.05 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X1)) => ($false))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (n_is @ X0 @ X1) 50.94/7.05 | (n_is @ X1 @ X0))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl310, '11'])). 50.94/7.05 thf(zip_derived_cl312, plain, 50.94/7.05 (![X0 : $i, X1 : $i]: 50.94/7.05 (~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X1)))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (n_is @ X0 @ X1) 50.94/7.05 | (n_is @ X1 @ X0))), 50.94/7.05 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl311])). 50.94/7.05 thf(zip_derived_cl313, plain, 50.94/7.05 (![X0 : $i, X1 : $i]: 50.94/7.05 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X1)) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (n_is @ X0 @ X1) 50.94/7.05 | (n_is @ X1 @ X0))), 50.94/7.05 inference('simplify nested equalities', [status(thm)], 50.94/7.05 [zip_derived_cl312])). 50.94/7.05 thf(zip_derived_cl836, plain, 50.94/7.05 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ (ap @ (plus @ '#sk2') @ '#sk4') @ 50.94/7.05 (ap @ (plus @ '#sk3') @ '#sk5')))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl833])). 50.94/7.05 thf(satz21a, axiom, 50.94/7.05 (all_of @ 50.94/7.05 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 50.94/7.05 ( ^[X0:$i]: 50.94/7.05 ( all_of @ 50.94/7.05 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 50.94/7.05 ( ^[X1:$i]: 50.94/7.05 ( all_of @ 50.94/7.05 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 50.94/7.05 ( ^[X2:$i]: 50.94/7.05 ( all_of @ 50.94/7.05 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @ 50.94/7.05 ( ^[X3:$i]: 50.94/7.05 ( ( iii @ X0 @ X1 ) => 50.94/7.05 ( ( iii @ X2 @ X3 ) => 50.94/7.05 ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 50.94/7.05 thf(zip_derived_cl10, plain, 50.94/7.05 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 50.94/7.05 (^[Y0 : $i]: 50.94/7.05 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 50.94/7.05 (^[Y1 : $i]: 50.94/7.05 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ 50.94/7.05 (^[Y2 : $i]: 50.94/7.05 (all_of @ (^[Y3 : $i]: (in @ Y3 @ nat)) @ 50.94/7.05 (^[Y3 : $i]: 50.94/7.05 (((iii @ Y0 @ Y1) => 50.94/7.05 (((iii @ Y2 @ Y3) => (iii @ (n_pl @ Y0 @ Y2) @ 50.94/7.05 (n_pl @ Y1 @ Y3))))))))))))))), 50.94/7.05 inference('cnf', [status(esa)], [satz21a])). 50.94/7.05 thf(zip_derived_cl11, plain, 50.94/7.05 ( (all_of @ ((('#C') @ in @ nat)) @ 50.94/7.05 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ 50.94/7.05 iii)))))))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#C') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))))) @ 50.94/7.05 n_pl)))))))))))))), 50.94/7.05 inference('lams2combs', [status(thm)], [zip_derived_cl10])). 50.94/7.05 thf(zip_derived_cl537, plain, 50.94/7.05 ( (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ 50.94/7.05 iii)))))))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#C') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))))) @ 50.94/7.05 n_pl)))))))))))))), 50.94/7.05 inference('rw', [status(thm)], [zip_derived_cl11, '0'])). 50.94/7.05 thf(zip_derived_cl538, plain, 50.94/7.05 ( (((!!) @ (^[Y0 : $i]: 50.94/7.05 (((is_of @ Y0 @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ ( 50.94/7.05 !=) @ emptyset)))))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 50.94/7.05 '#S') @ 50.94/7.05 ((('#B') @ ( 50.94/7.05 (('#B') @ ( 50.94/7.05 =>))) @ 50.94/7.05 iii)))))))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#C') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ iii)) @ 50.94/7.05 n_pl)))))))) @ 50.94/7.05 n_pl)))))))))) @ 50.94/7.05 Y0)))))))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl537, '8'])). 50.94/7.05 thf(zip_derived_cl539, plain, 50.94/7.05 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 50.94/7.05 ((('#C') @ is_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ ( 50.94/7.05 !=) @ emptyset)))))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 50.94/7.05 '#S') @ 50.94/7.05 ((('#B') @ ( 50.94/7.05 (('#B') @ (=>))) @ 50.94/7.05 iii)))))))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#C') @ 50.94/7.05 ((('#B') @ ((('#B') @ ('#B'))) @ 50.94/7.05 ((('#B') @ ((('#B') @ iii)) @ 50.94/7.05 n_pl)))))))) @ 50.94/7.05 n_pl))))))))))))))))), 50.94/7.05 inference('comb-normalize', [status(thm)], [zip_derived_cl538])). 50.94/7.05 thf(zip_derived_cl540, plain, 50.94/7.05 (![X2 : $i]: 50.94/7.05 (((is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (iii @ X2))))))) @ 50.94/7.05 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))))) @ 50.94/7.05 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ (n_pl @ X2))))))) @ 50.94/7.05 n_pl)))))))))))))), 50.94/7.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl539])). 50.94/7.05 thf(zip_derived_cl541, plain, 50.94/7.05 (![X2 : $i]: 50.94/7.05 (~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ (=>) @ (iii @ X2))))))) @ 50.94/7.05 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))))) @ 50.94/7.05 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ (n_pl @ X2))))))) @ 50.94/7.05 n_pl))))))))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl540])). 50.94/7.05 thf(zip_derived_cl542, plain, 50.94/7.05 (![X0 : $i]: 50.94/7.05 ( (((!!) @ (^[Y0 : $i]: 50.94/7.05 (((is_of @ Y0 @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ (=>) @ (iii @ X0))))))) @ 50.94/7.05 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ ( 50.94/7.05 =>))) @ 50.94/7.05 iii)))))) @ 50.94/7.05 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ 50.94/7.05 (n_pl @ X0))))))) @ 50.94/7.05 n_pl)))))))) @ 50.94/7.05 Y0))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl541, '8'])). 50.94/7.05 thf(zip_derived_cl543, plain, 50.94/7.05 (![X0 : $i]: 50.94/7.05 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 50.94/7.05 ((('#C') @ is_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))))))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ (=>) @ (iii @ X0))))))) @ 50.94/7.05 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ 50.94/7.05 iii)))))) @ 50.94/7.05 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ 50.94/7.05 (n_pl @ X0))))))) @ 50.94/7.05 n_pl)))))))))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('comb-normalize', [status(thm)], [zip_derived_cl542])). 50.94/7.05 thf(zip_derived_cl544, plain, 50.94/7.05 (![X0 : $i, X2 : $i]: 50.94/7.05 ( (((is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (((=>) @ (iii @ X0 @ X2))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ (n_pl @ X0))))) @ 50.94/7.05 (n_pl @ X2)))))))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl543])). 50.94/7.05 thf(zip_derived_cl545, plain, 50.94/7.05 (![X0 : $i, X2 : $i]: 50.94/7.05 ( (((is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X2 @ X0)))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ (n_pl @ X0))))) @ 50.94/7.05 (n_pl @ X2)))))))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('rw', [status(thm)], [zip_derived_cl544, '0', '4', '9'])). 50.94/7.05 thf(zip_derived_cl546, plain, 50.94/7.05 (![X0 : $i, X2 : $i]: 50.94/7.05 (~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X2 @ X0)))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ (n_pl @ X0))))) @ 50.94/7.05 (n_pl @ X2)))))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl545])). 50.94/7.05 thf(zip_derived_cl547, plain, 50.94/7.05 (![X0 : $i, X1 : $i]: 50.94/7.05 ( (((!!) @ (^[Y0 : $i]: 50.94/7.05 (((is_of @ Y0 @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ ( 50.94/7.05 !=) @ emptyset))) @ 50.94/7.05 (diffprop @ X1 @ X0)))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ (n_pl @ X0))))) @ 50.94/7.05 (n_pl @ X1))))))) @ 50.94/7.05 Y0))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl546, '8'])). 50.94/7.05 thf(zip_derived_cl548, plain, 50.94/7.05 (![X0 : $i, X1 : $i]: 50.94/7.05 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 50.94/7.05 ((('#C') @ is_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))))))))) @ 50.94/7.05 ((('#B') @ (all_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset)))))) @ 50.94/7.05 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ 50.94/7.05 emptyset))) @ 50.94/7.05 (diffprop @ X1 @ X0)))))) @ 50.94/7.05 ((('#S') @ ((('#B') @ ('#S') @ 50.94/7.05 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 50.94/7.05 ((('#C') @ ((('#B') @ ('#B') @ 50.94/7.05 ((('#B') @ iii @ (n_pl @ X0))))) @ 50.94/7.05 (n_pl @ X1))))))))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('comb-normalize', [status(thm)], [zip_derived_cl547])). 50.94/7.05 thf(zip_derived_cl549, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X3 : $i]: 50.94/7.05 ( (((is_of @ X3 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (((=>) @ (l_some @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X1 @ X0)))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (iii @ X3))) @ 50.94/7.05 ((('#B') @ (iii @ (n_pl @ X0 @ X3)) @ (n_pl @ X1)))))))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl548])). 50.94/7.05 thf(zip_derived_cl550, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X3 : $i]: 50.94/7.05 ( (((is_of @ X3 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (((=>) @ (l_some @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X1 @ X0)))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (iii @ X3))) @ 50.94/7.05 ((('#B') @ (iii @ (ap @ (plus @ X0) @ X3)) @ (n_pl @ X1)))))))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('rw', [status(thm)], [zip_derived_cl549, '7'])). 50.94/7.05 thf(zip_derived_cl551, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X3 : $i]: 50.94/7.05 (~ (is_of @ X3 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | (all_of @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 50.94/7.05 ((('#B') @ (((=>) @ (l_some @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X1 @ X0)))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (iii @ X3))) @ 50.94/7.05 ((('#B') @ (iii @ (ap @ (plus @ X0) @ X3)) @ (n_pl @ X1)))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl550])). 50.94/7.05 thf(zip_derived_cl552, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X2 : $i]: 50.94/7.05 ( (((!!) @ (^[Y0 : $i]: 50.94/7.05 (((is_of @ Y0 @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 ((('#B') @ (((=>) @ (l_some @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X1)))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (iii @ X2))) @ 50.94/7.05 ((('#B') @ (iii @ (ap @ (plus @ X1) @ X2)) @ 50.94/7.05 (n_pl @ X0))))) @ 50.94/7.05 Y0))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl551, '8'])). 50.94/7.05 thf(zip_derived_cl553, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X2 : $i]: 50.94/7.05 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 50.94/7.05 ((('#C') @ is_of @ 50.94/7.05 ((('#C') @ in @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))))))))) @ 50.94/7.05 ((('#B') @ (((=>) @ (l_some @ 50.94/7.05 (d_Sep @ omega @ 50.94/7.05 ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X1)))) @ 50.94/7.05 ((('#S') @ ((('#B') @ (=>) @ (iii @ X2))) @ 50.94/7.05 ((('#B') @ (iii @ (ap @ (plus @ X1) @ X2)) @ 50.94/7.05 (n_pl @ X0))))))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('comb-normalize', [status(thm)], [zip_derived_cl552])). 50.94/7.05 thf(zip_derived_cl554, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 50.94/7.05 ( (((is_of @ X4 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X1)) => 50.94/7.05 (((iii @ X2 @ X4) => (iii @ (ap @ (plus @ X1) @ X2) @ 50.94/7.05 (n_pl @ X0 @ X4)))))))) 50.94/7.05 | ~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl553])). 50.94/7.05 thf(zip_derived_cl555, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 50.94/7.05 ( (((is_of @ X4 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 50.94/7.05 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X1)) => 50.94/7.05 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X4 @ X2)) => (l_some @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ (ap @ (plus @ X0) @ X4) @ (ap @ (plus @ X1) @ X2))))))))) 50.94/7.05 | ~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('rw', [status(thm)], 50.94/7.05 [zip_derived_cl554, '0', '4', '4', '7', '9', '9'])). 50.94/7.05 thf(zip_derived_cl556, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 50.94/7.05 (~ (is_of @ X4 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X1)) => 50.94/7.05 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X4 @ X2)) => (l_some @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ (ap @ (plus @ X0) @ X4) @ (ap @ (plus @ X1) @ X2))))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl555])). 50.94/7.05 thf(zip_derived_cl557, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 50.94/7.05 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X1)) 50.94/7.05 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X4 @ X2)) => (l_some @ 50.94/7.05 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ (ap @ (plus @ X0) @ X4) @ (ap @ (plus @ X1) @ X2))))) 50.94/7.05 | ~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X4 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl556])). 50.94/7.05 thf(zip_derived_cl558, plain, 50.94/7.05 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 50.94/7.05 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X4 @ X2)) 50.94/7.05 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ (ap @ (plus @ X0) @ X4) @ (ap @ (plus @ X1) @ X2))) 50.94/7.05 | ~ (is_of @ X4 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X0 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X1 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ X2 @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ X0 @ X1)))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl557])). 50.94/7.05 thf(zip_derived_cl4185, plain, 50.94/7.05 ((~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')) 50.94/7.05 | ~ (is_of @ '#sk5' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ '#sk3' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ '#sk2' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ '#sk4' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk4' @ '#sk5')))), 50.94/7.05 inference('sup+', [status(thm)], [zip_derived_cl836, zip_derived_cl558])). 50.94/7.05 thf(zip_derived_cl830, plain, 50.94/7.05 ( (is_of @ '#sk5' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl829])). 50.94/7.05 thf(zip_derived_cl818, plain, 50.94/7.05 ( (is_of @ '#sk3' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl817])). 50.94/7.05 thf(zip_derived_cl812, plain, 50.94/7.05 ( (is_of @ '#sk2' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl811])). 50.94/7.05 thf(zip_derived_cl824, plain, 50.94/7.05 ( (is_of @ '#sk4' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl823])). 50.94/7.05 thf(zip_derived_cl835, plain, 50.94/7.05 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk4' @ '#sk5'))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl833])). 50.94/7.05 thf(zip_derived_cl4197, plain, 50.94/7.05 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3'))), 50.94/7.05 inference('demod', [status(thm)], 50.94/7.05 [zip_derived_cl4185, zip_derived_cl830, zip_derived_cl818, 50.94/7.05 zip_derived_cl812, zip_derived_cl824, zip_derived_cl835])). 50.94/7.05 thf(zip_derived_cl4205, plain, 50.94/7.05 (( (n_is @ '#sk3' @ '#sk2') 50.94/7.05 | ~ (n_is @ '#sk2' @ '#sk3') 50.94/7.05 | ~ (is_of @ '#sk3' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 50.94/7.05 | ~ (is_of @ '#sk2' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 50.94/7.05 inference('sup-', [status(thm)], [zip_derived_cl313, zip_derived_cl4197])). 50.94/7.05 thf(zip_derived_cl818, plain, 50.94/7.05 ( (is_of @ '#sk3' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl817])). 50.94/7.05 thf(zip_derived_cl812, plain, 50.94/7.05 ( (is_of @ '#sk2' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl811])). 50.94/7.05 thf(zip_derived_cl4212, plain, 50.94/7.05 (( (n_is @ '#sk3' @ '#sk2') | ~ (n_is @ '#sk2' @ '#sk3'))), 50.94/7.05 inference('demod', [status(thm)], 50.94/7.05 [zip_derived_cl4205, zip_derived_cl818, zip_derived_cl812])). 50.94/7.05 thf(zip_derived_cl832, plain, 50.94/7.05 ( (imp @ 50.94/7.05 (imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')) @ 50.94/7.05 ($false)) @ 50.94/7.05 (n_is @ '#sk2' @ '#sk3'))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl831])). 50.94/7.05 thf(zip_derived_cl834, plain, 50.94/7.05 ( (((imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')) @ 50.94/7.05 ($false)) => (n_is @ '#sk2' @ '#sk3')))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl832, '12'])). 50.94/7.05 thf(zip_derived_cl837, plain, 50.94/7.05 ((~ (imp @ 50.94/7.05 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')) @ 50.94/7.05 ($false)) 50.94/7.05 | (n_is @ '#sk2' @ '#sk3'))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl834])). 50.94/7.05 thf(zip_derived_cl838, plain, 50.94/7.05 ((~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')) => ($false))) 50.94/7.05 | (n_is @ '#sk2' @ '#sk3'))), 50.94/7.05 inference('rw_clause', [status(thm)], [zip_derived_cl837, '11'])). 50.94/7.05 thf(zip_derived_cl839, plain, 50.94/7.05 ((~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')))) 50.94/7.05 | (n_is @ '#sk2' @ '#sk3'))), 50.94/7.05 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl838])). 50.94/7.05 thf(zip_derived_cl840, plain, 50.94/7.05 (( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3')) 50.94/7.05 | (n_is @ '#sk2' @ '#sk3'))), 50.94/7.05 inference('simplify nested equalities', [status(thm)], 50.94/7.05 [zip_derived_cl839])). 50.94/7.05 thf(zip_derived_cl4197, plain, 50.94/7.05 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk2' @ '#sk3'))), 50.94/7.05 inference('demod', [status(thm)], 50.94/7.05 [zip_derived_cl4185, zip_derived_cl830, zip_derived_cl818, 50.94/7.05 zip_derived_cl812, zip_derived_cl824, zip_derived_cl835])). 50.94/7.05 thf(zip_derived_cl5592, plain, ( (n_is @ '#sk2' @ '#sk3')), 50.94/7.05 inference('clc', [status(thm)], [zip_derived_cl840, zip_derived_cl4197])). 50.94/7.05 thf(zip_derived_cl5593, plain, ( (n_is @ '#sk3' @ '#sk2')), 50.94/7.05 inference('demod', [status(thm)], 50.94/7.05 [zip_derived_cl4212, zip_derived_cl5592])). 50.94/7.05 thf(zip_derived_cl830, plain, 50.94/7.05 ( (is_of @ '#sk5' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl829])). 50.94/7.05 thf(zip_derived_cl818, plain, 50.94/7.05 ( (is_of @ '#sk3' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl817])). 50.94/7.05 thf(zip_derived_cl812, plain, 50.94/7.05 ( (is_of @ '#sk2' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl811])). 50.94/7.05 thf(zip_derived_cl824, plain, 50.94/7.05 ( (is_of @ '#sk4' @ 50.94/7.05 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl823])). 50.94/7.05 thf(zip_derived_cl835, plain, 50.94/7.05 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 50.94/7.05 (diffprop @ '#sk4' @ '#sk5'))), 50.94/7.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl833])). 50.94/7.05 thf(zip_derived_cl9095, plain, ($false), 50.94/7.05 inference('demod', [status(thm)], 50.94/7.05 [zip_derived_cl9081, zip_derived_cl5593, zip_derived_cl830, 50.94/7.05 zip_derived_cl818, zip_derived_cl812, zip_derived_cl824, 50.94/7.05 zip_derived_cl835])). 50.94/7.05 50.94/7.05 % SZS output end Refutation 50.94/7.05 50.94/7.05 50.94/7.05 % Terminating... 51.15/7.11 % Runner terminated. 51.15/7.12 % Zipperpin 1.5 exiting 51.15/7.12 EOF