0.02/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.14/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.riTImcAk19 true 0.15/0.37 % Computer : n027.cluster.edu 0.15/0.37 % Model : x86_64 x86_64 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.37 % Memory : 8042.1875MB 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.37 % CPULimit : 1200 0.15/0.37 % WCLimit : 120 0.15/0.37 % DateTime : Tue Jul 13 15:43:55 EDT 2021 0.15/0.37 % CPUTime : 0.15/0.37 % Running portfolio for 120 s 0.15/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.22/0.37 % Number of cores: 8 0.22/0.37 % Python version: Python 3.6.8 0.22/0.37 % Running in HO mode 0.60/0.67 % Total configuration time : 828 0.60/0.67 % Estimated wc time : 983 0.60/0.67 % Estimated cpu time (8 cpus) : 122.875 0.61/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 47s 0.61/0.77 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 47s 0.61/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 47s 0.61/0.78 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 18s 0.61/0.80 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 41s 0.61/0.80 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 53s 0.61/0.80 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.61/0.81 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 35s 68.72/9.46 % Solved by lams/40_b.comb.sh. 68.72/9.46 % running E: timeout 28 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.riTImcAk19/e_input06acd4 --cpu-limit=26 --auto-schedule -s -p 68.72/9.46 % done 487 iterations in 8.560s 68.72/9.46 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 68.72/9.46 % SZS output start Refutation 68.72/9.46 thf('#sk5_type', type, '#sk5': $i). 68.72/9.46 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 68.72/9.46 thf(n_is_type, type, n_is: $i > $i > $o). 68.72/9.46 thf(ap_type, type, ap: $i > $i > $i). 68.72/9.46 thf('#sk2_type', type, '#sk2': $i). 68.72/9.46 thf(plus_type, type, plus: $i > $i). 68.72/9.46 thf('#sk4_type', type, '#sk4': $i). 68.72/9.46 thf(l_or_type, type, l_or: $o > $o > $o). 68.72/9.46 thf(in_type, type, in: $i > $i > $o). 68.72/9.46 thf(imp_type, type, imp: $o > $o > $o). 68.72/9.46 thf(lessis_type, type, lessis: $i > $i > $o). 68.72/9.46 thf(nat_type, type, nat: $i). 68.72/9.46 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 68.72/9.46 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 68.72/9.46 thf(n_some_type, type, n_some: ($i > $o) > $o). 68.72/9.46 thf(n_pl_type, type, n_pl: $i > $i > $i). 68.72/9.46 thf(iii_type, type, iii: $i > $i > $o). 68.72/9.46 thf(omega_type, type, omega: $i). 68.72/9.46 thf('#sk3_type', type, '#sk3': $i). 68.72/9.46 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 68.72/9.46 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o). 68.72/9.46 thf(d_not_type, type, d_not: $o > $o). 68.72/9.46 thf(emptyset_type, type, emptyset: $i). 68.72/9.46 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 68.72/9.46 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 68.72/9.46 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 68.72/9.46 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 68.72/9.46 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 68.72/9.46 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 68.72/9.46 thf(satz22d, conjecture, 68.72/9.46 (all_of @ 68.72/9.46 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 68.72/9.46 ( ^[X0:$i]: 68.72/9.46 ( all_of @ 68.72/9.46 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 68.72/9.46 ( ^[X1:$i]: 68.72/9.46 ( all_of @ 68.72/9.46 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 68.72/9.46 ( ^[X2:$i]: 68.72/9.46 ( all_of @ 68.72/9.46 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @ 68.72/9.46 ( ^[X3:$i]: 68.72/9.46 ( ( iii @ X0 @ X1 ) => 68.72/9.46 ( ( lessis @ X2 @ X3 ) => 68.72/9.46 ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 68.72/9.46 thf(zf_stmt_0, negated_conjecture, 68.72/9.46 (~( all_of @ 68.72/9.46 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 68.72/9.46 ( ^[X0:$i]: 68.72/9.46 ( all_of @ 68.72/9.46 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 68.72/9.46 ( ^[X1:$i]: 68.72/9.46 ( all_of @ 68.72/9.46 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 68.72/9.46 ( ^[X2:$i]: 68.72/9.46 ( all_of @ 68.72/9.46 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @ 68.72/9.46 ( ^[X3:$i]: 68.72/9.46 ( ( iii @ X0 @ X1 ) => 68.72/9.46 ( ( lessis @ X2 @ X3 ) => 68.72/9.46 ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) )), 68.72/9.46 inference('cnf.neg', [status(esa)], [satz22d])). 68.72/9.46 thf(zip_derived_cl140, plain, 68.72/9.46 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 68.72/9.46 (^[Y0 : $i]: 68.72/9.46 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 68.72/9.46 (^[Y1 : $i]: 68.72/9.46 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ 68.72/9.46 (^[Y2 : $i]: 68.72/9.46 (all_of @ (^[Y3 : $i]: (in @ Y3 @ nat)) @ 68.72/9.46 (^[Y3 : $i]: 68.72/9.46 (((iii @ Y0 @ Y1) => 68.72/9.46 (((lessis @ Y2 @ Y3) => (iii @ (n_pl @ Y0 @ Y2) @ 68.72/9.46 (n_pl @ Y1 @ Y3))))))))))))))), 68.72/9.46 inference('cnf', [status(esa)], [zf_stmt_0])). 68.72/9.46 thf(zip_derived_cl141, plain, 68.72/9.46 (~ (all_of @ ((('#C') @ in @ nat)) @ 68.72/9.46 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ iii)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 lessis)))))))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#C') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))))) @ 68.72/9.46 n_pl)))))))))))))), 68.72/9.46 inference('lams2combs', [status(thm)], [zip_derived_cl140])). 68.72/9.46 thf(def_nat, axiom,(( nat ) = 68.72/9.46 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))). 68.72/9.46 thf('0', plain, 68.72/9.46 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )), 68.72/9.46 define([status(thm)])). 68.72/9.46 thf(zip_derived_cl575, plain, 68.72/9.46 (~ (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ iii)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 lessis)))))))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#C') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ iii)) @ n_pl)))))))) @ 68.72/9.46 n_pl)))))))))))))), 68.72/9.46 inference('rw', [status(thm)], [zip_derived_cl141, '0'])). 68.72/9.46 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 68.72/9.46 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 68.72/9.46 thf('1', plain, 68.72/9.46 (![X0:( $i > $o ),X1:( $i > $o )]: 68.72/9.46 ( ( ~( all_of @ X0 @ X1 ) ) <=> 68.72/9.46 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 68.72/9.46 inference('rw.lit', [status(esa)], [def_all_of])). 68.72/9.46 thf(zip_derived_cl576, plain, 68.72/9.46 (~ (((!!) @ (^[Y0 : $i]: 68.72/9.46 (((is_of @ Y0 @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ 68.72/9.46 omega @ 68.72/9.46 ((('#C') @ ( 68.72/9.46 !=) @ 68.72/9.46 emptyset)))))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 iii)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 68.72/9.46 '#S') @ 68.72/9.46 ((('#B') @ ( 68.72/9.46 (('#B') @ ( 68.72/9.46 =>))) @ 68.72/9.46 lessis)))))))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#C') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ iii)) @ 68.72/9.46 n_pl)))))))) @ 68.72/9.46 n_pl)))))))))) @ 68.72/9.46 Y0)))))))), 68.72/9.46 inference('rw_clause', [status(thm)], [zip_derived_cl575, '1'])). 68.72/9.46 thf(zip_derived_cl577, plain, 68.72/9.46 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.72/9.46 ((('#C') @ is_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))))))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ ( 68.72/9.46 !=) @ emptyset)))))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ iii)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 68.72/9.46 '#S') @ 68.72/9.46 ((('#B') @ ( 68.72/9.46 (('#B') @ (=>))) @ 68.72/9.46 lessis)))))))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#C') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ iii)) @ 68.72/9.46 n_pl)))))))) @ 68.72/9.46 n_pl))))))))))))))))), 68.72/9.46 inference('comb-normalize', [status(thm)], [zip_derived_cl576])). 68.72/9.46 thf(zip_derived_cl578, plain, 68.72/9.46 (~ (((is_of @ '#sk2' @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ (=>) @ (iii @ '#sk2'))))))) @ 68.72/9.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ lessis)))))) @ 68.72/9.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ (n_pl @ '#sk2'))))))) @ 68.72/9.46 n_pl)))))))))))))), 68.72/9.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl577])). 68.72/9.46 thf(zip_derived_cl580, plain, 68.72/9.46 (~ (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ (=>) @ (iii @ '#sk2'))))))) @ 68.72/9.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ lessis)))))) @ 68.72/9.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ (n_pl @ '#sk2'))))))) @ 68.72/9.46 n_pl)))))))))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])). 68.72/9.46 thf(zip_derived_cl581, plain, 68.72/9.46 (~ (((!!) @ (^[Y0 : $i]: 68.72/9.46 (((is_of @ Y0 @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ (=>) @ (iii @ '#sk2'))))))) @ 68.72/9.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 lessis)))))) @ 68.72/9.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ 68.72/9.46 (n_pl @ '#sk2'))))))) @ 68.72/9.46 n_pl)))))))) @ 68.72/9.46 Y0)))))))), 68.72/9.46 inference('rw_clause', [status(thm)], [zip_derived_cl580, '1'])). 68.72/9.46 thf(zip_derived_cl582, plain, 68.72/9.46 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.72/9.46 ((('#C') @ is_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))))))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ (=>) @ (iii @ '#sk2'))))))) @ 68.72/9.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 lessis)))))) @ 68.72/9.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ 68.72/9.46 (n_pl @ '#sk2'))))))) @ 68.72/9.46 n_pl))))))))))))))), 68.72/9.46 inference('comb-normalize', [status(thm)], [zip_derived_cl581])). 68.72/9.46 thf(zip_derived_cl583, plain, 68.72/9.46 (~ (((is_of @ '#sk3' @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (((=>) @ (iii @ '#sk2' @ '#sk3'))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ (n_pl @ '#sk2'))))) @ 68.72/9.46 (n_pl @ '#sk3'))))))))))))), 68.72/9.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl582])). 68.72/9.46 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))). 68.72/9.46 thf('2', plain, 68.72/9.46 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )), 68.72/9.46 define([status(thm)])). 68.72/9.46 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))). 68.72/9.46 thf('3', plain, 68.72/9.46 (![X1:$i,X0:$i]: 68.72/9.46 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 68.72/9.46 define([status(thm)])). 68.72/9.46 thf(zip_derived_cl584, plain, 68.72/9.46 (~ (((is_of @ '#sk3' @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk3' @ '#sk2')))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ (n_pl @ '#sk2'))))) @ 68.72/9.46 (n_pl @ '#sk3'))))))))))))), 68.72/9.46 inference('rw', [status(thm)], [zip_derived_cl583, '0', '2', '3'])). 68.72/9.46 thf(zip_derived_cl586, plain, 68.72/9.46 (~ (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk3' @ '#sk2')))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ (n_pl @ '#sk2'))))) @ 68.72/9.46 (n_pl @ '#sk3'))))))))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl584])). 68.72/9.46 thf(zip_derived_cl587, plain, 68.72/9.46 (~ (((!!) @ (^[Y0 : $i]: 68.72/9.46 (((is_of @ Y0 @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ 68.72/9.46 emptyset))) @ 68.72/9.46 (diffprop @ '#sk3' @ 68.72/9.46 '#sk2')))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ (n_pl @ '#sk2'))))) @ 68.72/9.46 (n_pl @ '#sk3'))))))) @ 68.72/9.46 Y0)))))))), 68.72/9.46 inference('rw_clause', [status(thm)], [zip_derived_cl586, '1'])). 68.72/9.46 thf(zip_derived_cl588, plain, 68.72/9.46 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.72/9.46 ((('#C') @ is_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))))))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ 68.72/9.46 emptyset))) @ 68.72/9.46 (diffprop @ '#sk3' @ 68.72/9.46 '#sk2')))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ (n_pl @ '#sk2'))))) @ 68.72/9.46 (n_pl @ '#sk3')))))))))))))), 68.72/9.46 inference('comb-normalize', [status(thm)], [zip_derived_cl587])). 68.72/9.46 thf(zip_derived_cl589, plain, 68.72/9.46 (~ (((is_of @ '#sk4' @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk3' @ '#sk2')))) @ 68.72/9.46 ((('#S') @ ((('#B') @ (=>) @ (lessis @ '#sk4'))) @ 68.72/9.46 ((('#B') @ (iii @ (n_pl @ '#sk2' @ '#sk4')) @ (n_pl @ '#sk3'))))))))))), 68.72/9.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl588])). 68.72/9.46 thf(def_n_pl, axiom,(( n_pl @ (X0)@ (X1)) = ((ap @ (plus @ X0) @ X1)))). 68.72/9.46 thf('4', plain, 68.72/9.46 (![X1:$i,X0:$i]: ( ( n_pl @ X0 @ X1 ) = ( ap @ ( plus @ X0 ) @ X1 ) )), 68.72/9.46 define([status(thm)])). 68.72/9.46 thf(zip_derived_cl590, plain, 68.72/9.46 (~ (((is_of @ '#sk4' @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk3' @ '#sk2')))) @ 68.72/9.46 ((('#S') @ ((('#B') @ (=>) @ (lessis @ '#sk4'))) @ 68.72/9.46 ((('#B') @ (iii @ (ap @ (plus @ '#sk2') @ '#sk4')) @ 68.72/9.46 (n_pl @ '#sk3'))))))))))), 68.72/9.46 inference('rw', [status(thm)], [zip_derived_cl589, '4'])). 68.72/9.46 thf(zip_derived_cl592, plain, 68.72/9.46 (~ (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk3' @ '#sk2')))) @ 68.72/9.46 ((('#S') @ ((('#B') @ (=>) @ (lessis @ '#sk4'))) @ 68.72/9.46 ((('#B') @ (iii @ (ap @ (plus @ '#sk2') @ '#sk4')) @ 68.72/9.46 (n_pl @ '#sk3'))))))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl590])). 68.72/9.46 thf(zip_derived_cl593, plain, 68.72/9.46 (~ (((!!) @ (^[Y0 : $i]: 68.72/9.46 (((is_of @ Y0 @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk3' @ '#sk2')))) @ 68.72/9.46 ((('#S') @ ((('#B') @ (=>) @ (lessis @ '#sk4'))) @ 68.72/9.46 ((('#B') @ (iii @ (ap @ (plus @ '#sk2') @ '#sk4')) @ 68.72/9.46 (n_pl @ '#sk3'))))) @ 68.72/9.46 Y0)))))))), 68.72/9.46 inference('rw_clause', [status(thm)], [zip_derived_cl592, '1'])). 68.72/9.46 thf(zip_derived_cl594, plain, 68.72/9.46 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.72/9.46 ((('#C') @ is_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))))))))) @ 68.72/9.46 ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk3' @ '#sk2')))) @ 68.72/9.46 ((('#S') @ ((('#B') @ (=>) @ (lessis @ '#sk4'))) @ 68.72/9.46 ((('#B') @ (iii @ (ap @ (plus @ '#sk2') @ '#sk4')) @ 68.72/9.46 (n_pl @ '#sk3')))))))))))), 68.72/9.46 inference('comb-normalize', [status(thm)], [zip_derived_cl593])). 68.72/9.46 thf(zip_derived_cl595, plain, 68.72/9.46 (~ (((is_of @ '#sk5' @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk3' @ '#sk2')) => 68.72/9.46 (((lessis @ '#sk4' @ '#sk5') => (iii @ 68.72/9.46 (ap @ (plus @ '#sk2') @ '#sk4') @ (n_pl @ '#sk3' @ '#sk5'))))))))), 68.72/9.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl594])). 68.72/9.46 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 68.72/9.46 thf('5', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 68.72/9.46 define([status(thm)])). 68.72/9.46 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 68.72/9.46 thf('6', plain, 68.72/9.46 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 68.72/9.46 define([status(thm)])). 68.72/9.46 thf(def_lessis, axiom,(( lessis @ (X0)@ (X1)) = 68.72/9.46 ((l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1))))). 68.72/9.46 thf('7', plain, 68.72/9.46 (![X1:$i,X0:$i]: 68.72/9.46 ( ( lessis @ X0 @ X1 ) = 68.72/9.46 ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )), 68.72/9.46 define([status(thm)])). 68.72/9.46 thf(zip_derived_cl596, plain, 68.72/9.46 (~ (((is_of @ '#sk5' @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk3' @ '#sk2')) => 68.72/9.46 (((imp @ 68.72/9.46 (imp @ 68.72/9.46 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk5' @ '#sk4')) @ 68.72/9.46 ($false)) @ 68.72/9.46 (n_is @ '#sk4' @ '#sk5')) => (l_some @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk5') @ 68.72/9.46 (ap @ (plus @ '#sk2') @ '#sk4')))))))))), 68.72/9.46 inference('rw', [status(thm)], 68.72/9.46 [zip_derived_cl595, '5', '6', '0', '2', '2', '4', '3', '3', '7'])). 68.72/9.46 thf(zip_derived_cl598, plain, 68.72/9.46 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk3' @ '#sk2')) => 68.72/9.46 (((imp @ 68.72/9.46 (imp @ 68.72/9.46 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk5' @ '#sk4')) @ 68.72/9.46 ($false)) @ 68.72/9.46 (n_is @ '#sk4' @ '#sk5')) => (l_some @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk5') @ 68.72/9.46 (ap @ (plus @ '#sk2') @ '#sk4')))))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl596])). 68.72/9.46 thf(zip_derived_cl600, plain, 68.72/9.46 (~ (((imp @ 68.72/9.46 (imp @ 68.72/9.46 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk5' @ '#sk4')) @ 68.72/9.46 ($false)) @ 68.72/9.46 (n_is @ '#sk4' @ '#sk5')) => (l_some @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk5') @ 68.72/9.46 (ap @ (plus @ '#sk2') @ '#sk4')))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl598])). 68.72/9.46 thf(zip_derived_cl602, plain, 68.72/9.46 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk5') @ 68.72/9.46 (ap @ (plus @ '#sk2') @ '#sk4')))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl600])). 68.72/9.46 thf(satz21, axiom, 68.72/9.46 (all_of @ 68.72/9.46 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 68.72/9.46 ( ^[X0:$i]: 68.72/9.46 ( all_of @ 68.72/9.46 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 68.72/9.46 ( ^[X1:$i]: 68.72/9.46 ( all_of @ 68.72/9.46 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 68.72/9.46 ( ^[X2:$i]: 68.72/9.46 ( all_of @ 68.72/9.46 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @ 68.72/9.46 ( ^[X3:$i]: 68.72/9.46 ( ( d_29_ii @ X0 @ X1 ) => 68.72/9.46 ( ( d_29_ii @ X2 @ X3 ) => 68.72/9.46 ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 68.72/9.46 thf(zip_derived_cl26, plain, 68.72/9.46 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 68.72/9.46 (^[Y0 : $i]: 68.72/9.46 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 68.72/9.46 (^[Y1 : $i]: 68.72/9.46 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ 68.72/9.46 (^[Y2 : $i]: 68.72/9.46 (all_of @ (^[Y3 : $i]: (in @ Y3 @ nat)) @ 68.72/9.46 (^[Y3 : $i]: 68.72/9.46 (((d_29_ii @ Y0 @ Y1) => 68.72/9.46 (((d_29_ii @ Y2 @ Y3) => (d_29_ii @ 68.72/9.46 (n_pl @ Y0 @ Y2) @ (n_pl @ Y1 @ Y3))))))))))))))), 68.72/9.46 inference('cnf', [status(esa)], [satz21])). 68.72/9.46 thf(zip_derived_cl27, plain, 68.72/9.46 ( (all_of @ ((('#C') @ in @ nat)) @ 68.72/9.46 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 d_29_ii)))))))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#C') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ d_29_ii)) @ n_pl)))))))) @ 68.72/9.46 n_pl)))))))))))))), 68.72/9.46 inference('lams2combs', [status(thm)], [zip_derived_cl26])). 68.72/9.46 thf(zip_derived_cl1165, plain, 68.72/9.46 ( (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 d_29_ii)))))))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#C') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ d_29_ii)) @ n_pl)))))))) @ 68.72/9.46 n_pl)))))))))))))), 68.72/9.46 inference('rw', [status(thm)], [zip_derived_cl27, '0'])). 68.72/9.46 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 68.72/9.46 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 68.72/9.46 thf('8', plain, 68.72/9.46 (![X0:( $i > $o ),X1:( $i > $o )]: 68.72/9.46 ( ( all_of @ X0 @ X1 ) <=> 68.72/9.46 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 68.72/9.46 inference('rw.lit', [status(esa)], [def_all_of])). 68.72/9.46 thf(zip_derived_cl1166, plain, 68.72/9.46 ( (((!!) @ (^[Y0 : $i]: 68.72/9.46 (((is_of @ Y0 @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ ( 68.72/9.46 !=) @ emptyset)))))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 d_29_ii)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 68.72/9.46 '#S') @ 68.72/9.46 ((('#B') @ ( 68.72/9.46 (('#B') @ ( 68.72/9.46 =>))) @ 68.72/9.46 d_29_ii)))))))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#C') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ d_29_ii)) @ 68.72/9.46 n_pl)))))))) @ 68.72/9.46 n_pl)))))))))) @ 68.72/9.46 Y0)))))))), 68.72/9.46 inference('rw_clause', [status(thm)], [zip_derived_cl1165, '8'])). 68.72/9.46 thf(zip_derived_cl1167, plain, 68.72/9.46 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.72/9.46 ((('#C') @ is_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ ( 68.72/9.46 !=) @ emptyset)))))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 d_29_ii)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 68.72/9.46 '#S') @ 68.72/9.46 ((('#B') @ ( 68.72/9.46 (('#B') @ (=>))) @ 68.72/9.46 d_29_ii)))))))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#C') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ d_29_ii)) @ 68.72/9.46 n_pl)))))))) @ 68.72/9.46 n_pl))))))))))))))))), 68.72/9.46 inference('comb-normalize', [status(thm)], [zip_derived_cl1166])). 68.72/9.46 thf(zip_derived_cl1168, plain, 68.72/9.46 (![X2 : $i]: 68.72/9.46 (((is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ (=>) @ (d_29_ii @ X2))))))) @ 68.72/9.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 d_29_ii)))))) @ 68.72/9.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ d_29_ii @ (n_pl @ X2))))))) @ 68.72/9.46 n_pl)))))))))))))), 68.72/9.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1167])). 68.72/9.46 thf(zip_derived_cl1169, plain, 68.72/9.46 (![X2 : $i]: 68.72/9.46 (~ (is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ (=>) @ (d_29_ii @ X2))))))) @ 68.72/9.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 d_29_ii)))))) @ 68.72/9.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ d_29_ii @ (n_pl @ X2))))))) @ 68.72/9.46 n_pl))))))))))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1168])). 68.72/9.46 thf(zip_derived_cl1170, plain, 68.72/9.46 (![X0 : $i]: 68.72/9.46 ( (((!!) @ (^[Y0 : $i]: 68.72/9.46 (((is_of @ Y0 @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ (=>) @ (d_29_ii @ X0))))))) @ 68.72/9.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ ( 68.72/9.46 =>))) @ 68.72/9.46 d_29_ii)))))) @ 68.72/9.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ d_29_ii @ 68.72/9.46 (n_pl @ X0))))))) @ 68.72/9.46 n_pl)))))))) @ 68.72/9.46 Y0))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('rw_clause', [status(thm)], [zip_derived_cl1169, '8'])). 68.72/9.46 thf(zip_derived_cl1171, plain, 68.72/9.46 (![X0 : $i]: 68.72/9.46 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.72/9.46 ((('#C') @ is_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))))))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ (=>) @ (d_29_ii @ X0))))))) @ 68.72/9.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 d_29_ii)))))) @ 68.72/9.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ d_29_ii @ 68.72/9.46 (n_pl @ X0))))))) @ 68.72/9.46 n_pl)))))))))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('comb-normalize', [status(thm)], [zip_derived_cl1170])). 68.72/9.46 thf(zip_derived_cl1172, plain, 68.72/9.46 (![X0 : $i, X2 : $i]: 68.72/9.46 ( (((is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (((=>) @ (d_29_ii @ X0 @ X2))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ d_29_ii @ (n_pl @ X0))))) @ 68.72/9.46 (n_pl @ X2)))))))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1171])). 68.72/9.46 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) = 68.72/9.46 ((n_some @ (diffprop @ X0 @ X1))))). 68.72/9.46 thf('9', plain, 68.72/9.46 (![X1:$i,X0:$i]: 68.72/9.46 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 68.72/9.46 define([status(thm)])). 68.72/9.46 thf(zip_derived_cl1173, plain, 68.72/9.46 (![X0 : $i, X2 : $i]: 68.72/9.46 ( (((is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ X0 @ X2)))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ d_29_ii @ (n_pl @ X0))))) @ 68.72/9.46 (n_pl @ X2)))))))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('rw', [status(thm)], [zip_derived_cl1172, '0', '2', '9'])). 68.72/9.46 thf(zip_derived_cl1174, plain, 68.72/9.46 (![X0 : $i, X2 : $i]: 68.72/9.46 (~ (is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ X0 @ X2)))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ d_29_ii @ (n_pl @ X0))))) @ 68.72/9.46 (n_pl @ X2)))))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1173])). 68.72/9.46 thf(zip_derived_cl1175, plain, 68.72/9.46 (![X0 : $i, X1 : $i]: 68.72/9.46 ( (((!!) @ (^[Y0 : $i]: 68.72/9.46 (((is_of @ Y0 @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ ( 68.72/9.46 !=) @ emptyset))) @ 68.72/9.46 (diffprop @ X0 @ X1)))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 d_29_ii)))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ d_29_ii @ (n_pl @ X0))))) @ 68.72/9.46 (n_pl @ X1))))))) @ 68.72/9.46 Y0))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('rw_clause', [status(thm)], [zip_derived_cl1174, '8'])). 68.72/9.46 thf(zip_derived_cl1176, plain, 68.72/9.46 (![X0 : $i, X1 : $i]: 68.72/9.46 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.72/9.46 ((('#C') @ is_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))))))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ 68.72/9.46 emptyset))) @ 68.72/9.46 (diffprop @ X0 @ X1)))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ d_29_ii @ (n_pl @ X0))))) @ 68.72/9.46 (n_pl @ X1))))))))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('comb-normalize', [status(thm)], [zip_derived_cl1175])). 68.72/9.46 thf(zip_derived_cl1177, plain, 68.72/9.46 (![X0 : $i, X1 : $i, X3 : $i]: 68.72/9.46 ( (((is_of @ X3 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ X0 @ X1)))) @ 68.72/9.46 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X3))) @ 68.72/9.46 ((('#B') @ (d_29_ii @ (n_pl @ X0 @ X3)) @ (n_pl @ X1)))))))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1176])). 68.72/9.46 thf(zip_derived_cl1178, plain, 68.72/9.46 (![X0 : $i, X1 : $i, X3 : $i]: 68.72/9.46 ( (((is_of @ X3 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ X0 @ X1)))) @ 68.72/9.46 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X3))) @ 68.72/9.46 ((('#B') @ (d_29_ii @ (ap @ (plus @ X0) @ X3)) @ (n_pl @ X1)))))))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('rw', [status(thm)], [zip_derived_cl1177, '4'])). 68.72/9.46 thf(zip_derived_cl1179, plain, 68.72/9.46 (![X0 : $i, X1 : $i, X3 : $i]: 68.72/9.46 (~ (is_of @ X3 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ X0 @ X1)))) @ 68.72/9.46 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X3))) @ 68.72/9.46 ((('#B') @ (d_29_ii @ (ap @ (plus @ X0) @ X3)) @ (n_pl @ X1)))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1178])). 68.72/9.46 thf(zip_derived_cl1180, plain, 68.72/9.46 (![X0 : $i, X1 : $i, X2 : $i]: 68.72/9.46 ( (((!!) @ (^[Y0 : $i]: 68.72/9.46 (((is_of @ Y0 @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ X1 @ X0)))) @ 68.72/9.46 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X2))) @ 68.72/9.46 ((('#B') @ (d_29_ii @ (ap @ (plus @ X1) @ X2)) @ 68.72/9.46 (n_pl @ X0))))) @ 68.72/9.46 Y0))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('rw_clause', [status(thm)], [zip_derived_cl1179, '8'])). 68.72/9.46 thf(zip_derived_cl1181, plain, 68.72/9.46 (![X0 : $i, X1 : $i, X2 : $i]: 68.72/9.46 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.72/9.46 ((('#C') @ is_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))))))))) @ 68.72/9.46 ((('#B') @ (((=>) @ (l_some @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ X1 @ X0)))) @ 68.72/9.46 ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ X2))) @ 68.72/9.46 ((('#B') @ (d_29_ii @ (ap @ (plus @ X1) @ X2)) @ 68.72/9.46 (n_pl @ X0))))))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('comb-normalize', [status(thm)], [zip_derived_cl1180])). 68.72/9.46 thf(zip_derived_cl1182, plain, 68.72/9.46 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 68.72/9.46 ( (((is_of @ X4 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ X1 @ X0)) => 68.72/9.46 (((d_29_ii @ X2 @ X4) => (d_29_ii @ (ap @ (plus @ X1) @ X2) @ 68.72/9.46 (n_pl @ X0 @ X4)))))))) 68.72/9.46 | ~ (is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1181])). 68.72/9.46 thf(zip_derived_cl1183, plain, 68.72/9.46 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 68.72/9.46 ( (((is_of @ X4 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ X1 @ X0)) => 68.72/9.46 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ X2 @ X4)) => (l_some @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ (ap @ (plus @ X1) @ X2) @ (ap @ (plus @ X0) @ X4))))))))) 68.72/9.46 | ~ (is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('rw', [status(thm)], 68.72/9.46 [zip_derived_cl1182, '0', '2', '2', '4', '9', '9'])). 68.72/9.46 thf(zip_derived_cl1184, plain, 68.72/9.46 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 68.72/9.46 (~ (is_of @ X4 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ X1 @ X0)) => 68.72/9.46 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ X2 @ X4)) => (l_some @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ (ap @ (plus @ X1) @ X2) @ (ap @ (plus @ X0) @ X4))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1183])). 68.72/9.46 thf(zip_derived_cl1185, plain, 68.72/9.46 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 68.72/9.46 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ X1 @ X0)) 68.72/9.46 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ X2 @ X4)) => (l_some @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ (ap @ (plus @ X1) @ X2) @ (ap @ (plus @ X0) @ X4))))) 68.72/9.46 | ~ (is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X4 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1184])). 68.72/9.46 thf(zip_derived_cl1186, plain, 68.72/9.46 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 68.72/9.46 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ X2 @ X4)) 68.72/9.46 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ (ap @ (plus @ X1) @ X2) @ (ap @ (plus @ X0) @ X4))) 68.72/9.46 | ~ (is_of @ X4 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ X1 @ X0)))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1185])). 68.72/9.46 thf(zip_derived_cl8619, plain, 68.72/9.46 ((~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk3' @ '#sk2')) 68.72/9.46 | ~ (is_of @ '#sk5' @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ '#sk3' @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ '#sk2' @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ '#sk4' @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk5' @ '#sk4')))), 68.72/9.46 inference('sup+', [status(thm)], [zip_derived_cl602, zip_derived_cl1186])). 68.72/9.46 thf(zip_derived_cl599, plain, 68.72/9.46 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk3' @ '#sk2'))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl598])). 68.72/9.46 thf(zip_derived_cl597, plain, 68.72/9.46 ( (is_of @ '#sk5' @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl596])). 68.72/9.46 thf(zip_derived_cl585, plain, 68.72/9.46 ( (is_of @ '#sk3' @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl584])). 68.72/9.46 thf(zip_derived_cl579, plain, 68.72/9.46 ( (is_of @ '#sk2' @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])). 68.72/9.46 thf(zip_derived_cl591, plain, 68.72/9.46 ( (is_of @ '#sk4' @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl590])). 68.72/9.46 thf(zip_derived_cl601, plain, 68.72/9.46 ( (imp @ 68.72/9.46 (imp @ 68.72/9.46 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk5' @ '#sk4')) @ 68.72/9.46 ($false)) @ 68.72/9.46 (n_is @ '#sk4' @ '#sk5'))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl600])). 68.72/9.46 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 68.72/9.46 thf('10', plain, 68.72/9.46 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 68.72/9.46 inference('rw.lit', [status(esa)], [def_imp])). 68.72/9.46 thf(zip_derived_cl603, plain, 68.72/9.46 ( (((imp @ 68.72/9.46 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk5' @ '#sk4')) @ 68.72/9.46 ($false)) => (n_is @ '#sk4' @ '#sk5')))), 68.72/9.46 inference('rw_clause', [status(thm)], [zip_derived_cl601, '10'])). 68.72/9.46 thf(zip_derived_cl604, plain, 68.72/9.46 ((~ (imp @ 68.72/9.46 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk5' @ '#sk4')) @ 68.72/9.46 ($false)) 68.72/9.46 | (n_is @ '#sk4' @ '#sk5'))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl603])). 68.72/9.46 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 68.72/9.46 thf('11', plain, 68.72/9.46 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 68.72/9.46 inference('rw.lit', [status(esa)], [def_imp])). 68.72/9.46 thf(zip_derived_cl605, plain, 68.72/9.46 ((~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk5' @ '#sk4')) => ($false))) 68.72/9.46 | (n_is @ '#sk4' @ '#sk5'))), 68.72/9.46 inference('rw_clause', [status(thm)], [zip_derived_cl604, '11'])). 68.72/9.46 thf(zip_derived_cl606, plain, 68.72/9.46 ((~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk5' @ '#sk4')))) 68.72/9.46 | (n_is @ '#sk4' @ '#sk5'))), 68.72/9.46 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl605])). 68.72/9.46 thf(zip_derived_cl607, plain, 68.72/9.46 (( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ '#sk5' @ '#sk4')) 68.72/9.46 | (n_is @ '#sk4' @ '#sk5'))), 68.72/9.46 inference('simplify nested equalities', [status(thm)], 68.72/9.46 [zip_derived_cl606])). 68.72/9.46 thf(zip_derived_cl602, plain, 68.72/9.46 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 68.72/9.46 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk5') @ 68.72/9.46 (ap @ (plus @ '#sk2') @ '#sk4')))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl600])). 68.72/9.46 thf(satz19k, axiom, 68.72/9.46 (all_of @ 68.72/9.46 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 68.72/9.46 ( ^[X0:$i]: 68.72/9.46 ( all_of @ 68.72/9.46 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 68.72/9.46 ( ^[X1:$i]: 68.72/9.46 ( all_of @ 68.72/9.46 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 68.72/9.46 ( ^[X2:$i]: 68.72/9.46 ( all_of @ 68.72/9.46 ( ^[X3:$i]: ( in @ X3 @ nat ) ) @ 68.72/9.46 ( ^[X3:$i]: 68.72/9.46 ( ( n_is @ X0 @ X1 ) => 68.72/9.46 ( ( iii @ X2 @ X3 ) => 68.72/9.46 ( iii @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ))). 68.72/9.46 thf(zip_derived_cl20, plain, 68.72/9.46 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 68.72/9.46 (^[Y0 : $i]: 68.72/9.46 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 68.72/9.46 (^[Y1 : $i]: 68.72/9.46 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ 68.72/9.46 (^[Y2 : $i]: 68.72/9.46 (all_of @ (^[Y3 : $i]: (in @ Y3 @ nat)) @ 68.72/9.46 (^[Y3 : $i]: 68.72/9.46 (((n_is @ Y0 @ Y1) => 68.72/9.46 (((iii @ Y2 @ Y3) => (iii @ (n_pl @ Y2 @ Y0) @ 68.72/9.46 (n_pl @ Y3 @ Y1))))))))))))))), 68.72/9.46 inference('cnf', [status(esa)], [satz19k])). 68.72/9.46 thf(zip_derived_cl21, plain, 68.72/9.46 ( (all_of @ ((('#C') @ in @ nat)) @ 68.72/9.46 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 iii)))))))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#C') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ iii)) @ 68.72/9.46 ((('#C') @ n_pl)))))))))) @ 68.72/9.46 ((('#C') @ n_pl)))))))))))))))), 68.72/9.46 inference('lams2combs', [status(thm)], [zip_derived_cl20])). 68.72/9.46 thf(zip_derived_cl1032, plain, 68.72/9.46 ( (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 iii)))))))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#C') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ iii)) @ 68.72/9.46 ((('#C') @ n_pl)))))))))) @ 68.72/9.46 ((('#C') @ n_pl)))))))))))))))), 68.72/9.46 inference('rw', [status(thm)], [zip_derived_cl21, '0'])). 68.72/9.46 thf(zip_derived_cl1033, plain, 68.72/9.46 ( (((!!) @ (^[Y0 : $i]: 68.72/9.46 (((is_of @ Y0 @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ ( 68.72/9.46 !=) @ emptyset)))))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 n_is)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 68.72/9.46 '#S') @ 68.72/9.46 ((('#B') @ ( 68.72/9.46 (('#B') @ ( 68.72/9.46 =>))) @ 68.72/9.46 iii)))))))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#C') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ iii)) @ 68.72/9.46 ((('#C') @ n_pl)))))))))) @ 68.72/9.46 ((('#C') @ n_pl)))))))))))) @ 68.72/9.46 Y0)))))))), 68.72/9.46 inference('rw_clause', [status(thm)], [zip_derived_cl1032, '8'])). 68.72/9.46 thf(zip_derived_cl1034, plain, 68.72/9.46 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.72/9.46 ((('#C') @ is_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ ( 68.72/9.46 !=) @ emptyset)))))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ n_is)))))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 68.72/9.46 '#S') @ 68.72/9.46 ((('#B') @ ( 68.72/9.46 (('#B') @ (=>))) @ 68.72/9.46 iii)))))))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#C') @ 68.72/9.46 ((('#B') @ ((('#B') @ ('#B'))) @ 68.72/9.46 ((('#B') @ ((('#B') @ iii)) @ 68.72/9.46 ((('#C') @ n_pl)))))))))) @ 68.72/9.46 ((('#C') @ n_pl))))))))))))))))))), 68.72/9.46 inference('comb-normalize', [status(thm)], [zip_derived_cl1033])). 68.72/9.46 thf(zip_derived_cl1035, plain, 68.72/9.46 (![X2 : $i]: 68.72/9.46 (((is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ (=>) @ (n_is @ X2))))))) @ 68.72/9.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ iii)))))) @ 68.72/9.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ 68.72/9.46 ((('#C') @ n_pl @ X2)))))))) @ 68.72/9.46 ((('#C') @ n_pl)))))))))))))))), 68.72/9.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1034])). 68.72/9.46 thf(zip_derived_cl1036, plain, 68.72/9.46 (![X2 : $i]: 68.72/9.46 (~ (is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ (=>) @ (n_is @ X2))))))) @ 68.72/9.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ iii)))))) @ 68.72/9.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ 68.72/9.46 ((('#C') @ n_pl @ X2)))))))) @ 68.72/9.46 ((('#C') @ n_pl))))))))))))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1035])). 68.72/9.46 thf(zip_derived_cl1037, plain, 68.72/9.46 (![X0 : $i]: 68.72/9.46 ( (((!!) @ (^[Y0 : $i]: 68.72/9.46 (((is_of @ Y0 @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ (=>) @ (n_is @ X0))))))) @ 68.72/9.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ ( 68.72/9.46 =>))) @ 68.72/9.46 iii)))))) @ 68.72/9.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ 68.72/9.46 ((('#C') @ n_pl @ X0)))))))) @ 68.72/9.46 ((('#C') @ n_pl)))))))))) @ 68.72/9.46 Y0))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('rw_clause', [status(thm)], [zip_derived_cl1036, '8'])). 68.72/9.46 thf(zip_derived_cl1038, plain, 68.72/9.46 (![X0 : $i]: 68.72/9.46 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.72/9.46 ((('#C') @ is_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))))))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ (=>) @ (n_is @ X0))))))) @ 68.72/9.46 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ 68.72/9.46 iii)))))) @ 68.72/9.46 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ 68.72/9.46 ((('#C') @ n_pl @ X0)))))))) @ 68.72/9.46 ((('#C') @ n_pl)))))))))))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('comb-normalize', [status(thm)], [zip_derived_cl1037])). 68.72/9.46 thf(zip_derived_cl1039, plain, 68.72/9.46 (![X0 : $i, X2 : $i]: 68.72/9.46 ( (((is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ X0 @ X2))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ ((('#C') @ n_pl @ X0)))))) @ 68.72/9.46 ((('#C') @ n_pl @ X2))))))))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1038])). 68.72/9.46 thf(zip_derived_cl1040, plain, 68.72/9.46 (![X0 : $i, X2 : $i]: 68.72/9.46 (~ (is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ X0 @ X2))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ ((('#C') @ n_pl @ X0)))))) @ 68.72/9.46 ((('#C') @ n_pl @ X2))))))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1039])). 68.72/9.46 thf(zip_derived_cl1041, plain, 68.72/9.46 (![X0 : $i, X1 : $i]: 68.72/9.46 ( (((!!) @ (^[Y0 : $i]: 68.72/9.46 (((is_of @ Y0 @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ X0 @ X1))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ 68.72/9.46 ((('#C') @ n_pl @ X0)))))) @ 68.72/9.46 ((('#C') @ n_pl @ X1)))))))) @ 68.72/9.46 Y0))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('rw_clause', [status(thm)], [zip_derived_cl1040, '8'])). 68.72/9.46 thf(zip_derived_cl1042, plain, 68.72/9.46 (![X0 : $i, X1 : $i]: 68.72/9.46 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.72/9.46 ((('#C') @ is_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))))))))) @ 68.72/9.46 ((('#B') @ (all_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset)))))) @ 68.72/9.46 ((('#B') @ ((('#B') @ (((=>) @ (n_is @ X0 @ X1))))) @ 68.72/9.46 ((('#S') @ ((('#B') @ ('#S') @ 68.72/9.46 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 68.72/9.46 ((('#C') @ ((('#B') @ ('#B') @ 68.72/9.46 ((('#B') @ iii @ 68.72/9.46 ((('#C') @ n_pl @ X0)))))) @ 68.72/9.46 ((('#C') @ n_pl @ X1)))))))))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('comb-normalize', [status(thm)], [zip_derived_cl1041])). 68.72/9.46 thf(zip_derived_cl1043, plain, 68.72/9.46 (![X0 : $i, X1 : $i, X3 : $i]: 68.72/9.46 ( (((is_of @ X3 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (((=>) @ (n_is @ X0 @ X1))) @ 68.72/9.46 ((('#S') @ ((('#B') @ (=>) @ (iii @ X3))) @ 68.72/9.46 ((('#B') @ (iii @ (n_pl @ X3 @ X0)) @ ((('#C') @ n_pl @ X1))))))))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1042])). 68.72/9.46 thf(zip_derived_cl1044, plain, 68.72/9.46 (![X0 : $i, X1 : $i, X3 : $i]: 68.72/9.46 ( (((is_of @ X3 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (((=>) @ (n_is @ X0 @ X1))) @ 68.72/9.46 ((('#S') @ ((('#B') @ (=>) @ (iii @ X3))) @ 68.72/9.46 ((('#B') @ (iii @ (ap @ (plus @ X3) @ X0)) @ 68.72/9.46 ((('#C') @ n_pl @ X1))))))))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('rw', [status(thm)], [zip_derived_cl1043, '4'])). 68.72/9.46 thf(zip_derived_cl1045, plain, 68.72/9.46 (![X0 : $i, X1 : $i, X3 : $i]: 68.72/9.46 (~ (is_of @ X3 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | (all_of @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 68.72/9.46 ((('#B') @ (((=>) @ (n_is @ X0 @ X1))) @ 68.72/9.46 ((('#S') @ ((('#B') @ (=>) @ (iii @ X3))) @ 68.72/9.46 ((('#B') @ (iii @ (ap @ (plus @ X3) @ X0)) @ 68.72/9.46 ((('#C') @ n_pl @ X1))))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1044])). 68.72/9.46 thf(zip_derived_cl1046, plain, 68.72/9.46 (![X0 : $i, X1 : $i, X2 : $i]: 68.72/9.46 ( (((!!) @ (^[Y0 : $i]: 68.72/9.46 (((is_of @ Y0 @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 ((('#B') @ (((=>) @ (n_is @ X1 @ X0))) @ 68.72/9.46 ((('#S') @ ((('#B') @ (=>) @ (iii @ X2))) @ 68.72/9.46 ((('#B') @ (iii @ (ap @ (plus @ X2) @ X1)) @ 68.72/9.46 ((('#C') @ n_pl @ X0)))))) @ 68.72/9.46 Y0))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('rw_clause', [status(thm)], [zip_derived_cl1045, '8'])). 68.72/9.46 thf(zip_derived_cl1047, plain, 68.72/9.46 (![X0 : $i, X1 : $i, X2 : $i]: 68.72/9.46 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 68.72/9.46 ((('#C') @ is_of @ 68.72/9.46 ((('#C') @ in @ 68.72/9.46 (d_Sep @ omega @ 68.72/9.46 ((('#C') @ (!=) @ emptyset))))))))) @ 68.72/9.46 ((('#B') @ (((=>) @ (n_is @ X1 @ X0))) @ 68.72/9.46 ((('#S') @ ((('#B') @ (=>) @ (iii @ X2))) @ 68.72/9.46 ((('#B') @ (iii @ (ap @ (plus @ X2) @ X1)) @ 68.72/9.46 ((('#C') @ n_pl @ X0)))))))))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('comb-normalize', [status(thm)], [zip_derived_cl1046])). 68.72/9.46 thf(zip_derived_cl1048, plain, 68.72/9.46 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 68.72/9.46 ( (((is_of @ X4 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 68.72/9.46 (((n_is @ X1 @ X0) => 68.72/9.46 (((iii @ X2 @ X4) => (iii @ (ap @ (plus @ X2) @ X1) @ 68.72/9.46 (n_pl @ X4 @ X0)))))))) 68.72/9.46 | ~ (is_of @ X2 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X1 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 68.72/9.46 | ~ (is_of @ X0 @ 68.72/9.46 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 68.72/9.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1047])). 68.72/9.46 thf(zip_derived_cl1049, plain, 69.12/9.47 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 69.12/9.47 ( (((is_of @ X4 @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 69.12/9.47 (((n_is @ X1 @ X0) => 69.12/9.47 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 69.12/9.47 (diffprop @ X4 @ X2)) => (l_some @ 69.12/9.47 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 69.12/9.47 (diffprop @ (ap @ (plus @ X4) @ X0) @ (ap @ (plus @ X2) @ X1))))))))) 69.12/9.47 | ~ (is_of @ X2 @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 69.12/9.47 | ~ (is_of @ X1 @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 69.12/9.47 | ~ (is_of @ X0 @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 69.12/9.47 inference('rw', [status(thm)], 69.12/9.47 [zip_derived_cl1048, '0', '2', '2', '4', '3', '3'])). 69.12/9.47 thf(zip_derived_cl1050, plain, 69.12/9.47 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 69.12/9.47 (~ (is_of @ X4 @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 69.12/9.47 | (((n_is @ X1 @ X0) => 69.12/9.47 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 69.12/9.47 (diffprop @ X4 @ X2)) => (l_some @ 69.12/9.47 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 69.12/9.47 (diffprop @ (ap @ (plus @ X4) @ X0) @ (ap @ (plus @ X2) @ X1))))))) 69.12/9.47 | ~ (is_of @ X0 @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 69.12/9.47 | ~ (is_of @ X1 @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 69.12/9.47 | ~ (is_of @ X2 @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 69.12/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1049])). 69.12/9.47 thf(zip_derived_cl1051, plain, 69.12/9.47 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 69.12/9.47 (~ (n_is @ X1 @ X0) 69.12/9.47 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 69.12/9.47 (diffprop @ X4 @ X2)) => (l_some @ 69.12/9.47 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 69.12/9.47 (diffprop @ (ap @ (plus @ X4) @ X0) @ (ap @ (plus @ X2) @ X1))))) 69.12/9.47 | ~ (is_of @ X2 @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 69.12/9.47 | ~ (is_of @ X1 @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 69.12/9.47 | ~ (is_of @ X0 @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 69.12/9.47 | ~ (is_of @ X4 @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 69.12/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1050])). 69.12/9.47 thf(zip_derived_cl1052, plain, 69.12/9.47 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 69.12/9.47 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 69.12/9.47 (diffprop @ X4 @ X2)) 69.12/9.47 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 69.12/9.47 (diffprop @ (ap @ (plus @ X4) @ X0) @ (ap @ (plus @ X2) @ X1))) 69.12/9.47 | ~ (is_of @ X4 @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 69.12/9.47 | ~ (is_of @ X0 @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 69.12/9.47 | ~ (is_of @ X1 @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 69.12/9.47 | ~ (is_of @ X2 @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 69.12/9.47 | ~ (n_is @ X1 @ X0))), 69.12/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1051])). 69.12/9.47 thf(zip_derived_cl8037, plain, 69.12/9.47 ((~ (n_is @ '#sk4' @ '#sk5') 69.12/9.47 | ~ (is_of @ '#sk2' @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 69.12/9.47 | ~ (is_of @ '#sk4' @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 69.12/9.47 | ~ (is_of @ '#sk5' @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 69.12/9.47 | ~ (is_of @ '#sk3' @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 69.12/9.47 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 69.12/9.47 (diffprop @ '#sk3' @ '#sk2')))), 69.12/9.47 inference('sup+', [status(thm)], [zip_derived_cl602, zip_derived_cl1052])). 69.12/9.47 thf(zip_derived_cl579, plain, 69.12/9.47 ( (is_of @ '#sk2' @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 69.12/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])). 69.12/9.47 thf(zip_derived_cl591, plain, 69.12/9.47 ( (is_of @ '#sk4' @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 69.12/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl590])). 69.12/9.47 thf(zip_derived_cl597, plain, 69.12/9.47 ( (is_of @ '#sk5' @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 69.12/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl596])). 69.12/9.47 thf(zip_derived_cl585, plain, 69.12/9.47 ( (is_of @ '#sk3' @ 69.12/9.47 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 69.12/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl584])). 69.12/9.47 thf(zip_derived_cl599, plain, 69.12/9.47 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 69.12/9.47 (diffprop @ '#sk3' @ '#sk2'))), 69.12/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl598])). 69.12/9.47 thf(zip_derived_cl8050, plain, (~ (n_is @ '#sk4' @ '#sk5')), 69.12/9.47 inference('demod', [status(thm)], 69.12/9.47 [zip_derived_cl8037, zip_derived_cl579, zip_derived_cl591, 69.12/9.47 zip_derived_cl597, zip_derived_cl585, zip_derived_cl599])). 69.12/9.47 thf(zip_derived_cl8054, plain, 69.12/9.47 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 69.12/9.47 (diffprop @ '#sk5' @ '#sk4'))), 69.12/9.47 inference('demod', [status(thm)], [zip_derived_cl607, zip_derived_cl8050])). 69.12/9.47 thf(zip_derived_cl8633, plain, ($false), 69.12/9.47 inference('demod', [status(thm)], 69.12/9.47 [zip_derived_cl8619, zip_derived_cl599, zip_derived_cl597, 69.12/9.47 zip_derived_cl585, zip_derived_cl579, zip_derived_cl591, 69.12/9.47 zip_derived_cl8054])). 69.12/9.47 69.12/9.47 % SZS output end Refutation 69.12/9.47 69.12/9.47 69.12/9.47 % Terminating... 69.55/9.55 % Runner terminated. 69.55/9.55 % Zipperpin 1.5 exiting 69.55/9.56 EOF