0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.16 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.v7ryNYDzlg true 0.16/0.38 % Computer : n018.cluster.edu 0.16/0.38 % Model : x86_64 x86_64 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.38 % Memory : 8042.1875MB 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.38 % CPULimit : 960 0.16/0.38 % WCLimit : 120 0.16/0.38 % DateTime : Tue Aug 9 06:57:46 EDT 2022 0.16/0.38 % CPUTime : 0.16/0.38 % Running portfolio for 960 s 0.16/0.38 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.16/0.38 % Number of cores: 8 0.16/0.38 % Python version: Python 3.6.8 0.16/0.38 % Running in HO mode 0.56/0.70 % Total configuration time : 828 0.56/0.70 % Estimated wc time : 1656 0.56/0.70 % Estimated cpu time (8 cpus) : 207.0 0.59/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.59/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.59/0.78 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.59/0.78 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.59/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.59/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.59/0.80 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.59/0.82 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 43.62/6.19 % Solved by lams/40_b.comb.sh. 43.62/6.19 % done 429 iterations in 5.370s 43.62/6.19 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 43.62/6.19 % SZS output start Refutation 43.62/6.19 thf(emptyset_type, type, emptyset: $i). 43.62/6.19 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 43.62/6.19 thf(omega_type, type, omega: $i). 43.62/6.19 thf('#sk3_type', type, '#sk3': $i). 43.62/6.19 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 43.62/6.19 thf(in_type, type, in: $i > $i > $o). 43.62/6.19 thf(ap_type, type, ap: $i > $i > $i). 43.62/6.19 thf(nat_type, type, nat: $i). 43.62/6.19 thf(iii_type, type, iii: $i > $i > $o). 43.62/6.19 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 43.62/6.19 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 43.62/6.19 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 43.62/6.19 thf(plus_type, type, plus: $i > $i). 43.62/6.19 thf('#sk2_type', type, '#sk2': $i). 43.62/6.19 thf('#sk4_type', type, '#sk4': $i). 43.62/6.19 thf(n_some_type, type, n_some: ($i > $o) > $o). 43.62/6.19 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o). 43.62/6.19 thf(n_pl_type, type, n_pl: $i > $i > $i). 43.62/6.19 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 43.62/6.19 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 43.62/6.19 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 43.62/6.19 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 43.62/6.19 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 43.62/6.19 thf(satz20c, conjecture, 43.62/6.19 (all_of @ 43.62/6.19 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 43.62/6.19 ( ^[X0:$i]: 43.62/6.19 ( all_of @ 43.62/6.19 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 43.62/6.19 ( ^[X1:$i]: 43.62/6.19 ( all_of @ 43.62/6.19 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 43.62/6.19 ( ^[X2:$i]: 43.62/6.19 ( ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) => 43.62/6.19 ( iii @ X0 @ X1 ) ) ) ) ) ) ))). 43.62/6.19 thf(zf_stmt_0, negated_conjecture, 43.62/6.19 (~( all_of @ 43.62/6.19 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 43.62/6.19 ( ^[X0:$i]: 43.62/6.19 ( all_of @ 43.62/6.19 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 43.62/6.19 ( ^[X1:$i]: 43.62/6.19 ( all_of @ 43.62/6.19 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 43.62/6.19 ( ^[X2:$i]: 43.62/6.19 ( ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) => 43.62/6.19 ( iii @ X0 @ X1 ) ) ) ) ) ) ) )), 43.62/6.19 inference('cnf.neg', [status(esa)], [satz20c])). 43.62/6.19 thf(zip_derived_cl124, plain, 43.62/6.19 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 43.62/6.19 (^[Y0 : $i]: 43.62/6.19 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 43.62/6.19 (^[Y1 : $i]: 43.62/6.19 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ 43.62/6.19 (^[Y2 : $i]: 43.62/6.19 (((iii @ (n_pl @ Y0 @ Y2) @ (n_pl @ Y1 @ Y2)) => (iii @ 43.62/6.19 Y0 @ Y1)))))))))), 43.62/6.19 inference('cnf', [status(esa)], [zf_stmt_0])). 43.62/6.19 thf(zip_derived_cl125, plain, 43.62/6.19 (~ (all_of @ ((('#C') @ in @ nat)) @ 43.62/6.19 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 43.62/6.19 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @ 43.62/6.19 ((('#S') @ ((('#B') @ ('#S') @ 43.62/6.19 ((('#B') @ ((('#B') @ ('#C'))) @ 43.62/6.19 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 43.62/6.19 ((('#C') @ ((('#B') @ ('#B') @ 43.62/6.19 ((('#B') @ ('#S') @ 43.62/6.19 ((('#B') @ ((('#B') @ iii)) @ 43.62/6.19 n_pl)))))) @ 43.62/6.19 n_pl)))))))) @ 43.62/6.19 iii)))))))), 43.62/6.19 inference('lams2combs', [status(thm)], [zip_derived_cl124])). 43.62/6.19 thf(def_nat, axiom,(( nat ) = 43.62/6.19 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))). 43.62/6.19 thf('0', plain, 43.62/6.19 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )), 43.62/6.19 define([status(thm)])). 43.62/6.19 thf(zip_derived_cl384, plain, 43.62/6.19 (~ (all_of @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 43.62/6.19 ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 43.62/6.19 ((('#B') @ ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ 43.62/6.19 ((('#C') @ (!=) @ emptyset)))))))) @ 43.62/6.19 ((('#S') @ ((('#B') @ ('#S') @ 43.62/6.19 ((('#B') @ ((('#B') @ ('#C'))) @ 43.62/6.19 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 43.62/6.19 ((('#C') @ ((('#B') @ ('#B') @ 43.62/6.19 ((('#B') @ ('#S') @ 43.62/6.19 ((('#B') @ ((('#B') @ iii)) @ 43.62/6.19 n_pl)))))) @ 43.62/6.19 n_pl)))))))) @ 43.62/6.19 iii)))))))), 43.62/6.19 inference('rw', [status(thm)], [zip_derived_cl125, '0'])). 43.62/6.19 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 43.62/6.19 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 43.62/6.19 thf('1', plain, 43.62/6.19 (![X0:( $i > $o ),X1:( $i > $o )]: 43.62/6.19 ( ( ~( all_of @ X0 @ X1 ) ) <=> 43.62/6.19 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 43.62/6.19 inference('rw.lit', [status(esa)], [def_all_of])). 43.62/6.19 thf(zip_derived_cl385, plain, 43.62/6.19 (~ (((!!) @ (^[Y0 : $i]: 43.62/6.19 (((is_of @ Y0 @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 43.62/6.19 ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ 43.62/6.19 ((('#C') @ (!=) @ emptyset)))))) @ 43.62/6.19 ((('#B') @ ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ 43.62/6.19 ((('#C') @ (!=) @ emptyset)))))))) @ 43.62/6.19 ((('#S') @ ((('#B') @ ('#S') @ 43.62/6.19 ((('#B') @ ((('#B') @ ('#C'))) @ 43.62/6.19 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 43.62/6.19 ((('#C') @ ((('#B') @ ('#B') @ 43.62/6.19 ((('#B') @ ('#S') @ 43.62/6.19 ((('#B') @ ( 43.62/6.19 (('#B') @ iii)) @ 43.62/6.19 n_pl)))))) @ 43.62/6.19 n_pl)))))))) @ 43.62/6.19 iii)))) @ 43.62/6.19 Y0)))))))), 43.62/6.19 inference('rw_clause', [status(thm)], [zip_derived_cl384, '1'])). 43.62/6.19 thf(zip_derived_cl386, plain, 43.62/6.19 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 43.62/6.19 ((('#C') @ is_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ 43.62/6.19 ((('#C') @ (!=) @ emptyset))))))))) @ 43.62/6.19 ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 43.62/6.19 ((('#B') @ ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ 43.62/6.19 ((('#C') @ (!=) @ emptyset)))))))) @ 43.62/6.19 ((('#S') @ ((('#B') @ ('#S') @ 43.62/6.19 ((('#B') @ ((('#B') @ ('#C'))) @ 43.62/6.19 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 43.62/6.19 ((('#C') @ ((('#B') @ ('#B') @ 43.62/6.19 ((('#B') @ ('#S') @ 43.62/6.19 ((('#B') @ ((('#B') @ iii)) @ 43.62/6.19 n_pl)))))) @ 43.62/6.19 n_pl)))))))) @ 43.62/6.19 iii))))))))))), 43.62/6.19 inference('comb-normalize', [status(thm)], [zip_derived_cl385])). 43.62/6.19 thf(zip_derived_cl387, plain, 43.62/6.19 (~ (((is_of @ '#sk2' @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 43.62/6.19 (all_of @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 43.62/6.19 ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 43.62/6.19 ((('#S') @ ((('#B') @ ('#C') @ 43.62/6.19 ((('#B') @ ((('#B') @ (=>))) @ 43.62/6.19 ((('#B') @ ((('#S') @ ((('#B') @ iii @ 43.62/6.19 (n_pl @ '#sk2'))))) @ 43.62/6.19 n_pl)))))) @ 43.62/6.19 (iii @ '#sk2'))))))))), 43.62/6.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl386])). 43.62/6.19 thf(zip_derived_cl389, plain, 43.62/6.19 (~ (all_of @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 43.62/6.19 ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 43.62/6.19 ((('#S') @ ((('#B') @ ('#C') @ 43.62/6.19 ((('#B') @ ((('#B') @ (=>))) @ 43.62/6.19 ((('#B') @ ((('#S') @ ((('#B') @ iii @ 43.62/6.19 (n_pl @ '#sk2'))))) @ 43.62/6.19 n_pl)))))) @ 43.62/6.19 (iii @ '#sk2'))))))), 43.62/6.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl387])). 43.62/6.19 thf(zip_derived_cl390, plain, 43.62/6.19 (~ (((!!) @ (^[Y0 : $i]: 43.62/6.19 (((is_of @ Y0 @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 43.62/6.19 ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ 43.62/6.19 ((('#C') @ (!=) @ emptyset)))))) @ 43.62/6.19 ((('#S') @ ((('#B') @ ('#C') @ 43.62/6.19 ((('#B') @ ((('#B') @ (=>))) @ 43.62/6.19 ((('#B') @ ((('#S') @ ((('#B') @ iii @ 43.62/6.19 (n_pl @ '#sk2'))))) @ 43.62/6.19 n_pl)))))) @ 43.62/6.19 (iii @ '#sk2'))) @ 43.62/6.19 Y0)))))))), 43.62/6.19 inference('rw_clause', [status(thm)], [zip_derived_cl389, '1'])). 43.62/6.19 thf(zip_derived_cl391, plain, 43.62/6.19 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 43.62/6.19 ((('#C') @ is_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ 43.62/6.19 ((('#C') @ (!=) @ emptyset))))))))) @ 43.62/6.19 ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 43.62/6.19 ((('#S') @ ((('#B') @ ('#C') @ 43.62/6.19 ((('#B') @ ((('#B') @ (=>))) @ 43.62/6.19 ((('#B') @ ((('#S') @ ((('#B') @ iii @ 43.62/6.19 (n_pl @ '#sk2'))))) @ 43.62/6.19 n_pl)))))) @ 43.62/6.19 (iii @ '#sk2')))))))))), 43.62/6.19 inference('comb-normalize', [status(thm)], [zip_derived_cl390])). 43.62/6.19 thf(zip_derived_cl392, plain, 43.62/6.19 (~ (((is_of @ '#sk3' @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 43.62/6.19 (all_of @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 43.62/6.19 ((('#C') @ ((('#B') @ (=>) @ 43.62/6.19 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @ 43.62/6.19 (n_pl @ '#sk3'))))) @ 43.62/6.19 (iii @ '#sk2' @ '#sk3'))))))), 43.62/6.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl391])). 43.62/6.19 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))). 43.62/6.19 thf('2', plain, 43.62/6.19 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )), 43.62/6.19 define([status(thm)])). 43.62/6.19 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))). 43.62/6.19 thf('3', plain, 43.62/6.19 (![X1:$i,X0:$i]: 43.62/6.19 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 43.62/6.19 define([status(thm)])). 43.62/6.19 thf(zip_derived_cl393, plain, 43.62/6.19 (~ (((is_of @ '#sk3' @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 43.62/6.19 (all_of @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 43.62/6.19 ((('#C') @ ((('#B') @ (=>) @ 43.62/6.19 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @ 43.62/6.19 (n_pl @ '#sk3'))))) @ 43.62/6.19 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ '#sk3' @ '#sk2')))))))), 43.62/6.19 inference('rw', [status(thm)], [zip_derived_cl392, '0', '2', '3'])). 43.62/6.19 thf(zip_derived_cl395, plain, 43.62/6.19 (~ (all_of @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 43.62/6.19 ((('#C') @ ((('#B') @ (=>) @ 43.62/6.19 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @ 43.62/6.19 (n_pl @ '#sk3'))))) @ 43.62/6.19 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ '#sk3' @ '#sk2')))))), 43.62/6.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl393])). 43.62/6.19 thf(zip_derived_cl396, plain, 43.62/6.19 (~ (((!!) @ (^[Y0 : $i]: 43.62/6.19 (((is_of @ Y0 @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 43.62/6.19 ((('#C') @ ((('#B') @ (=>) @ 43.62/6.19 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @ 43.62/6.19 (n_pl @ '#sk3'))))) @ 43.62/6.19 (l_some @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ '#sk3' @ '#sk2')) @ 43.62/6.19 Y0)))))))), 43.62/6.19 inference('rw_clause', [status(thm)], [zip_derived_cl395, '1'])). 43.62/6.19 thf(zip_derived_cl397, plain, 43.62/6.19 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 43.62/6.19 ((('#C') @ is_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ 43.62/6.19 ((('#C') @ (!=) @ emptyset))))))))) @ 43.62/6.19 ((('#C') @ ((('#B') @ (=>) @ 43.62/6.19 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @ 43.62/6.19 (n_pl @ '#sk3'))))) @ 43.62/6.19 (l_some @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ '#sk3' @ '#sk2'))))))))), 43.62/6.19 inference('comb-normalize', [status(thm)], [zip_derived_cl396])). 43.62/6.19 thf(zip_derived_cl398, plain, 43.62/6.19 (~ (((is_of @ '#sk4' @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 43.62/6.19 (((iii @ (n_pl @ '#sk2' @ '#sk4') @ (n_pl @ '#sk3' @ '#sk4')) => 43.62/6.19 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ '#sk3' @ '#sk2'))))))), 43.62/6.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl397])). 43.62/6.19 thf(def_n_pl, axiom,(( n_pl @ (X0)@ (X1)) = ((ap @ (plus @ X0) @ X1)))). 43.62/6.19 thf('4', plain, 43.62/6.19 (![X1:$i,X0:$i]: ( ( n_pl @ X0 @ X1 ) = ( ap @ ( plus @ X0 ) @ X1 ) )), 43.62/6.19 define([status(thm)])). 43.62/6.19 thf(zip_derived_cl399, plain, 43.62/6.19 (~ (((is_of @ '#sk4' @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 43.62/6.19 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk4') @ 43.62/6.19 (ap @ (plus @ '#sk2') @ '#sk4'))) => 43.62/6.19 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ '#sk3' @ '#sk2'))))))), 43.62/6.19 inference('rw', [status(thm)], 43.62/6.19 [zip_derived_cl398, '0', '2', '4', '4', '3'])). 43.62/6.19 thf(zip_derived_cl401, plain, 43.62/6.19 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk4') @ 43.62/6.19 (ap @ (plus @ '#sk2') @ '#sk4'))) => 43.62/6.19 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ '#sk3' @ '#sk2'))))), 43.62/6.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl399])). 43.62/6.19 thf(zip_derived_cl403, plain, 43.62/6.19 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ '#sk3' @ '#sk2'))), 43.62/6.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl401])). 43.62/6.19 thf(zip_derived_cl402, plain, 43.62/6.19 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk4') @ 43.62/6.19 (ap @ (plus @ '#sk2') @ '#sk4')))), 43.62/6.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl401])). 43.62/6.19 thf(satz20a, axiom, 43.62/6.19 (all_of @ 43.62/6.19 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 43.62/6.19 ( ^[X0:$i]: 43.62/6.19 ( all_of @ 43.62/6.19 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 43.62/6.19 ( ^[X1:$i]: 43.62/6.19 ( all_of @ 43.62/6.19 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 43.62/6.19 ( ^[X2:$i]: 43.62/6.19 ( ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) => 43.62/6.19 ( d_29_ii @ X0 @ X1 ) ) ) ) ) ) ))). 43.62/6.19 thf(zip_derived_cl122, plain, 43.62/6.19 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 43.62/6.19 (^[Y0 : $i]: 43.62/6.19 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 43.62/6.19 (^[Y1 : $i]: 43.62/6.19 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ 43.62/6.19 (^[Y2 : $i]: 43.62/6.19 (((d_29_ii @ (n_pl @ Y0 @ Y2) @ (n_pl @ Y1 @ Y2)) => 43.62/6.19 (d_29_ii @ Y0 @ Y1)))))))))), 43.62/6.19 inference('cnf', [status(esa)], [satz20a])). 43.62/6.19 thf(zip_derived_cl123, plain, 43.62/6.19 ( (all_of @ ((('#C') @ in @ nat)) @ 43.62/6.19 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 43.62/6.19 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @ 43.62/6.19 ((('#S') @ ((('#B') @ ('#S') @ 43.62/6.19 ((('#B') @ ((('#B') @ ('#C'))) @ 43.62/6.19 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 43.62/6.19 ((('#C') @ ((('#B') @ ('#B') @ 43.62/6.19 ((('#B') @ ('#S') @ 43.62/6.19 ((('#B') @ ((('#B') @ d_29_ii)) @ 43.62/6.19 n_pl)))))) @ 43.62/6.19 n_pl)))))))) @ 43.62/6.19 d_29_ii)))))))), 43.62/6.19 inference('lams2combs', [status(thm)], [zip_derived_cl122])). 43.62/6.19 thf(zip_derived_cl950, plain, 43.62/6.19 ( (all_of @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 43.62/6.19 ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 43.62/6.19 ((('#B') @ ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ 43.62/6.19 ((('#C') @ (!=) @ emptyset)))))))) @ 43.62/6.19 ((('#S') @ ((('#B') @ ('#S') @ 43.62/6.19 ((('#B') @ ((('#B') @ ('#C'))) @ 43.62/6.19 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 43.62/6.19 ((('#C') @ ((('#B') @ ('#B') @ 43.62/6.19 ((('#B') @ ('#S') @ 43.62/6.19 ((('#B') @ ((('#B') @ d_29_ii)) @ 43.62/6.19 n_pl)))))) @ 43.62/6.19 n_pl)))))))) @ 43.62/6.19 d_29_ii)))))))), 43.62/6.19 inference('rw', [status(thm)], [zip_derived_cl123, '0'])). 43.62/6.19 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 43.62/6.19 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 43.62/6.19 thf('5', plain, 43.62/6.19 (![X0:( $i > $o ),X1:( $i > $o )]: 43.62/6.19 ( ( all_of @ X0 @ X1 ) <=> 43.62/6.19 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 43.62/6.19 inference('rw.lit', [status(esa)], [def_all_of])). 43.62/6.19 thf(zip_derived_cl951, plain, 43.62/6.19 ( (((!!) @ (^[Y0 : $i]: 43.62/6.19 (((is_of @ Y0 @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 43.62/6.19 ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ 43.62/6.19 ((('#C') @ (!=) @ emptyset)))))) @ 43.62/6.19 ((('#B') @ ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ 43.62/6.19 ((('#C') @ (!=) @ emptyset)))))))) @ 43.62/6.19 ((('#S') @ ((('#B') @ ('#S') @ 43.62/6.19 ((('#B') @ ((('#B') @ ('#C'))) @ 43.62/6.19 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 43.62/6.19 ((('#C') @ ((('#B') @ ('#B') @ 43.62/6.19 ((('#B') @ ('#S') @ 43.62/6.19 ((('#B') @ (( 43.62/6.19 ('#B') @ d_29_ii)) @ 43.62/6.19 n_pl)))))) @ 43.62/6.19 n_pl)))))))) @ 43.62/6.19 d_29_ii)))) @ 43.62/6.19 Y0)))))))), 43.62/6.19 inference('rw_clause', [status(thm)], [zip_derived_cl950, '5'])). 43.62/6.19 thf(zip_derived_cl952, plain, 43.62/6.19 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 43.62/6.19 ((('#C') @ is_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @ 43.62/6.19 ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 43.62/6.19 ((('#B') @ ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ 43.62/6.19 ((('#C') @ (!=) @ emptyset)))))))) @ 43.62/6.19 ((('#S') @ ((('#B') @ ('#S') @ 43.62/6.19 ((('#B') @ ((('#B') @ ('#C'))) @ 43.62/6.19 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 43.62/6.19 ((('#C') @ ((('#B') @ ('#B') @ 43.62/6.19 ((('#B') @ ('#S') @ 43.62/6.19 ((('#B') @ ((('#B') @ d_29_ii)) @ 43.62/6.19 n_pl)))))) @ 43.62/6.19 n_pl)))))))) @ 43.62/6.19 d_29_ii))))))))))), 43.62/6.19 inference('comb-normalize', [status(thm)], [zip_derived_cl951])). 43.62/6.19 thf(zip_derived_cl953, plain, 43.62/6.19 (![X2 : $i]: 43.62/6.19 (((is_of @ X2 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 43.62/6.19 (all_of @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 43.62/6.19 ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 43.62/6.19 ((('#S') @ ((('#B') @ ('#C') @ 43.62/6.19 ((('#B') @ ((('#B') @ (=>))) @ 43.62/6.19 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @ 43.62/6.19 (n_pl @ X2))))) @ 43.62/6.19 n_pl)))))) @ 43.62/6.19 (d_29_ii @ X2))))))))), 43.62/6.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl952])). 43.62/6.19 thf(zip_derived_cl954, plain, 43.62/6.19 (![X2 : $i]: 43.62/6.19 (~ (is_of @ X2 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 43.62/6.19 | (all_of @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 43.62/6.19 ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 43.62/6.19 ((('#S') @ ((('#B') @ ('#C') @ 43.62/6.19 ((('#B') @ ((('#B') @ (=>))) @ 43.62/6.19 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @ 43.62/6.19 (n_pl @ X2))))) @ 43.62/6.19 n_pl)))))) @ 43.62/6.19 (d_29_ii @ X2)))))))), 43.62/6.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl953])). 43.62/6.19 thf(zip_derived_cl955, plain, 43.62/6.19 (![X0 : $i]: 43.62/6.19 ( (((!!) @ (^[Y0 : $i]: 43.62/6.19 (((is_of @ Y0 @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 43.62/6.19 ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ 43.62/6.19 ((('#C') @ (!=) @ emptyset)))))) @ 43.62/6.19 ((('#S') @ ((('#B') @ ('#C') @ 43.62/6.19 ((('#B') @ ((('#B') @ (=>))) @ 43.62/6.19 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @ 43.62/6.19 (n_pl @ X0))))) @ 43.62/6.19 n_pl)))))) @ 43.62/6.19 (d_29_ii @ X0))) @ 43.62/6.19 Y0))))))) 43.62/6.19 | ~ (is_of @ X0 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 43.62/6.19 inference('rw_clause', [status(thm)], [zip_derived_cl954, '5'])). 43.62/6.19 thf(zip_derived_cl956, plain, 43.62/6.19 (![X0 : $i]: 43.62/6.19 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 43.62/6.19 ((('#C') @ is_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ 43.62/6.19 ((('#C') @ (!=) @ emptyset))))))))) @ 43.62/6.19 ((('#B') @ (all_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ 43.62/6.19 ((('#C') @ (!=) @ emptyset)))))) @ 43.62/6.19 ((('#S') @ ((('#B') @ ('#C') @ 43.62/6.19 ((('#B') @ ((('#B') @ (=>))) @ 43.62/6.19 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @ 43.62/6.19 (n_pl @ X0))))) @ 43.62/6.19 n_pl)))))) @ 43.62/6.19 (d_29_ii @ X0))))))))) 43.62/6.19 | ~ (is_of @ X0 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 43.62/6.19 inference('comb-normalize', [status(thm)], [zip_derived_cl955])). 43.62/6.19 thf(zip_derived_cl957, plain, 43.62/6.19 (![X0 : $i, X2 : $i]: 43.62/6.19 ( (((is_of @ X2 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 43.62/6.19 (all_of @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 43.62/6.19 ((('#C') @ ((('#B') @ (=>) @ 43.62/6.19 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @ 43.62/6.19 (n_pl @ X2))))) @ 43.62/6.19 (d_29_ii @ X0 @ X2)))))) 43.62/6.19 | ~ (is_of @ X0 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 43.62/6.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl956])). 43.62/6.19 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) = 43.62/6.19 ((n_some @ (diffprop @ X0 @ X1))))). 43.62/6.19 thf('6', plain, 43.62/6.19 (![X1:$i,X0:$i]: 43.62/6.19 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 43.62/6.19 define([status(thm)])). 43.62/6.19 thf(zip_derived_cl958, plain, 43.62/6.19 (![X0 : $i, X2 : $i]: 43.62/6.19 ( (((is_of @ X2 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 43.62/6.19 (all_of @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 43.62/6.19 ((('#C') @ ((('#B') @ (=>) @ 43.62/6.19 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @ 43.62/6.19 (n_pl @ X2))))) @ 43.62/6.19 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ X0 @ X2))))))) 43.62/6.19 | ~ (is_of @ X0 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 43.62/6.19 inference('rw', [status(thm)], [zip_derived_cl957, '0', '2', '6'])). 43.62/6.19 thf(zip_derived_cl959, plain, 43.62/6.19 (![X0 : $i, X2 : $i]: 43.62/6.19 (~ (is_of @ X2 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 43.62/6.19 | (all_of @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 43.62/6.19 ((('#C') @ ((('#B') @ (=>) @ 43.62/6.19 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @ 43.62/6.19 (n_pl @ X2))))) @ 43.62/6.19 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ X0 @ X2))))) 43.62/6.19 | ~ (is_of @ X0 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 43.62/6.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl958])). 43.62/6.19 thf(zip_derived_cl960, plain, 43.62/6.19 (![X0 : $i, X1 : $i]: 43.62/6.19 ( (((!!) @ (^[Y0 : $i]: 43.62/6.19 (((is_of @ Y0 @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 43.62/6.19 ((('#C') @ ((('#B') @ (=>) @ 43.62/6.19 ((('#S') @ ((('#B') @ d_29_ii @ 43.62/6.19 (n_pl @ X0))) @ 43.62/6.19 (n_pl @ X1))))) @ 43.62/6.19 (l_some @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ X0 @ X1)) @ 43.62/6.19 Y0))))))) 43.62/6.19 | ~ (is_of @ X0 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 43.62/6.19 | ~ (is_of @ X1 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 43.62/6.19 inference('rw_clause', [status(thm)], [zip_derived_cl959, '5'])). 43.62/6.19 thf(zip_derived_cl961, plain, 43.62/6.19 (![X0 : $i, X1 : $i]: 43.62/6.19 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 43.62/6.19 ((('#C') @ is_of @ 43.62/6.19 ((('#C') @ in @ 43.62/6.19 (d_Sep @ omega @ 43.62/6.19 ((('#C') @ (!=) @ emptyset))))))))) @ 43.62/6.19 ((('#C') @ ((('#B') @ (=>) @ 43.62/6.19 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @ 43.62/6.19 (n_pl @ X1))))) @ 43.62/6.19 (l_some @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ X0 @ X1)))))))) 43.62/6.19 | ~ (is_of @ X0 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 43.62/6.19 | ~ (is_of @ X1 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 43.62/6.19 inference('comb-normalize', [status(thm)], [zip_derived_cl960])). 43.62/6.19 thf(zip_derived_cl962, plain, 43.62/6.19 (![X0 : $i, X1 : $i, X3 : $i]: 43.62/6.19 ( (((is_of @ X3 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 43.62/6.19 (((d_29_ii @ (n_pl @ X0 @ X3) @ (n_pl @ X1 @ X3)) => (l_some @ 43.62/6.19 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ X0 @ X1)))))) 43.62/6.19 | ~ (is_of @ X1 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 43.62/6.19 | ~ (is_of @ X0 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 43.62/6.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl961])). 43.62/6.19 thf(zip_derived_cl963, plain, 43.62/6.19 (![X0 : $i, X1 : $i, X3 : $i]: 43.62/6.19 ( (((is_of @ X3 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 43.62/6.19 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ (ap @ (plus @ X0) @ X3) @ (ap @ (plus @ X1) @ X3))) => 43.62/6.19 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ X0 @ X1)))))) 43.62/6.19 | ~ (is_of @ X1 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 43.62/6.19 | ~ (is_of @ X0 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 43.62/6.19 inference('rw', [status(thm)], 43.62/6.19 [zip_derived_cl962, '0', '2', '4', '4', '6'])). 43.62/6.19 thf(zip_derived_cl964, plain, 43.62/6.19 (![X0 : $i, X1 : $i, X3 : $i]: 43.62/6.19 (~ (is_of @ X3 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 43.62/6.19 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ (ap @ (plus @ X0) @ X3) @ (ap @ (plus @ X1) @ X3))) => 43.62/6.19 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ X0 @ X1)))) 43.62/6.19 | ~ (is_of @ X0 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 43.62/6.19 | ~ (is_of @ X1 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 43.62/6.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl963])). 43.62/6.19 thf(zip_derived_cl965, plain, 43.62/6.19 (![X0 : $i, X1 : $i, X3 : $i]: 43.62/6.19 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ (ap @ (plus @ X0) @ X3) @ (ap @ (plus @ X1) @ X3))) 43.62/6.19 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ X0 @ X1)) 43.62/6.19 | ~ (is_of @ X1 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 43.62/6.19 | ~ (is_of @ X0 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 43.62/6.19 | ~ (is_of @ X3 @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 43.62/6.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl964])). 43.62/6.19 thf(zip_derived_cl7186, plain, 43.62/6.19 ((~ (is_of @ '#sk4' @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 43.62/6.19 | ~ (is_of @ '#sk3' @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 43.62/6.19 | ~ (is_of @ '#sk2' @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 43.62/6.19 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ '#sk3' @ '#sk2')))), 43.62/6.19 inference('sup-', [status(thm)], [zip_derived_cl402, zip_derived_cl965])). 43.62/6.19 thf(zip_derived_cl400, plain, 43.62/6.19 ( (is_of @ '#sk4' @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 43.62/6.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl399])). 43.62/6.19 thf(zip_derived_cl394, plain, 43.62/6.19 ( (is_of @ '#sk3' @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 43.62/6.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl393])). 43.62/6.19 thf(zip_derived_cl388, plain, 43.62/6.19 ( (is_of @ '#sk2' @ 43.62/6.19 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 43.62/6.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl387])). 43.62/6.19 thf(zip_derived_cl7204, plain, 43.62/6.19 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 43.62/6.19 (diffprop @ '#sk3' @ '#sk2'))), 43.62/6.19 inference('demod', [status(thm)], 43.62/6.19 [zip_derived_cl7186, zip_derived_cl400, zip_derived_cl394, 43.62/6.19 zip_derived_cl388])). 43.62/6.19 thf(zip_derived_cl7262, plain, ($false), 43.62/6.19 inference('demod', [status(thm)], [zip_derived_cl403, zip_derived_cl7204])). 43.62/6.19 43.62/6.19 % SZS output end Refutation 43.62/6.19 43.62/6.19 43.62/6.19 % Terminating... 44.31/6.31 % Runner terminated. 44.31/6.32 % Zipperpin 1.5 exiting 44.31/6.33 EOF