0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.16 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.gfACchcycE true 0.15/0.37 % Computer : n008.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 : 1440 0.15/0.37 % WCLimit : 180 0.15/0.37 % DateTime : Thu Jul 4 09:33:24 EDT 2024 0.15/0.37 % CPUTime : 0.15/0.37 % Running portfolio for 1440 s 0.15/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.15/0.37 % Number of cores: 8 0.15/0.37 % Python version: Python 3.6.8 0.15/0.37 % Running in HO mode 0.54/0.71 % Total configuration time : 828 0.54/0.71 % Estimated wc time : 1656 0.54/0.71 % Estimated cpu time (8 cpus) : 207.0 0.59/0.81 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.59/0.81 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.59/0.81 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.59/0.82 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.59/0.82 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.59/0.83 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.59/0.83 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.59/0.83 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 42.34/6.03 % Solved by lams/40_b.comb.sh. 42.34/6.03 % done 425 iterations in 5.179s 42.34/6.03 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 42.34/6.03 % SZS output start Refutation 42.34/6.03 thf(emptyset_type, type, emptyset: $i). 42.34/6.03 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 42.34/6.03 thf(omega_type, type, omega: $i). 42.34/6.03 thf('#sk3_type', type, '#sk3': $i). 42.34/6.03 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 42.34/6.03 thf(in_type, type, in: $i > $i > $o). 42.34/6.03 thf(ap_type, type, ap: $i > $i > $i). 42.34/6.03 thf(nat_type, type, nat: $i). 42.34/6.03 thf(iii_type, type, iii: $i > $i > $o). 42.34/6.03 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 42.34/6.03 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 42.34/6.03 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 42.34/6.03 thf(plus_type, type, plus: $i > $i). 42.34/6.03 thf('#sk2_type', type, '#sk2': $i). 42.34/6.03 thf('#sk4_type', type, '#sk4': $i). 42.34/6.03 thf(n_some_type, type, n_some: ($i > $o) > $o). 42.34/6.03 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o). 42.34/6.03 thf(n_pl_type, type, n_pl: $i > $i > $i). 42.34/6.03 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 42.34/6.03 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 42.34/6.03 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 42.34/6.03 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 42.34/6.03 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 42.34/6.03 thf(satz20c, conjecture, 42.34/6.03 (all_of @ 42.34/6.03 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 42.34/6.03 ( ^[X0:$i]: 42.34/6.03 ( all_of @ 42.34/6.03 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 42.34/6.03 ( ^[X1:$i]: 42.34/6.03 ( all_of @ 42.34/6.03 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 42.34/6.03 ( ^[X2:$i]: 42.34/6.03 ( ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) => 42.34/6.03 ( iii @ X0 @ X1 ) ) ) ) ) ) ))). 42.34/6.03 thf(zf_stmt_0, negated_conjecture, 42.34/6.03 (~( all_of @ 42.34/6.03 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 42.34/6.03 ( ^[X0:$i]: 42.34/6.03 ( all_of @ 42.34/6.03 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 42.34/6.03 ( ^[X1:$i]: 42.34/6.03 ( all_of @ 42.34/6.03 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 42.34/6.03 ( ^[X2:$i]: 42.34/6.03 ( ( iii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) => 42.34/6.03 ( iii @ X0 @ X1 ) ) ) ) ) ) ) )), 42.34/6.03 inference('cnf.neg', [status(esa)], [satz20c])). 42.34/6.03 thf(zip_derived_cl124, plain, 42.34/6.03 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 42.34/6.03 (^[Y0 : $i]: 42.34/6.03 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 42.34/6.03 (^[Y1 : $i]: 42.34/6.03 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ 42.34/6.03 (^[Y2 : $i]: 42.34/6.03 (((iii @ (n_pl @ Y0 @ Y2) @ (n_pl @ Y1 @ Y2)) => (iii @ 42.34/6.03 Y0 @ Y1)))))))))), 42.34/6.03 inference('cnf', [status(esa)], [zf_stmt_0])). 42.34/6.03 thf(zip_derived_cl125, plain, 42.34/6.03 (~ (all_of @ ((('#C') @ in @ nat)) @ 42.34/6.03 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 42.34/6.03 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @ 42.34/6.03 ((('#S') @ ((('#B') @ ('#S') @ 42.34/6.03 ((('#B') @ ((('#B') @ ('#C'))) @ 42.34/6.03 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 42.34/6.03 ((('#C') @ ((('#B') @ ('#B') @ 42.34/6.03 ((('#B') @ ('#S') @ 42.34/6.03 ((('#B') @ ((('#B') @ iii)) @ 42.34/6.03 n_pl)))))) @ 42.34/6.03 n_pl)))))))) @ 42.34/6.03 iii)))))))), 42.34/6.03 inference('lams2combs', [status(thm)], [zip_derived_cl124])). 42.34/6.03 thf(def_nat, axiom,(( nat ) = 42.34/6.03 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))). 42.34/6.03 thf('0', plain, 42.34/6.03 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )), 42.34/6.03 define([status(thm)])). 42.34/6.03 thf(zip_derived_cl375, plain, 42.34/6.03 (~ (all_of @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 42.34/6.03 ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 42.34/6.03 ((('#B') @ ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ 42.34/6.03 ((('#C') @ (!=) @ emptyset)))))))) @ 42.34/6.03 ((('#S') @ ((('#B') @ ('#S') @ 42.34/6.03 ((('#B') @ ((('#B') @ ('#C'))) @ 42.34/6.03 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 42.34/6.03 ((('#C') @ ((('#B') @ ('#B') @ 42.34/6.03 ((('#B') @ ('#S') @ 42.34/6.03 ((('#B') @ ((('#B') @ iii)) @ 42.34/6.03 n_pl)))))) @ 42.34/6.03 n_pl)))))))) @ 42.34/6.03 iii)))))))), 42.34/6.03 inference('rw', [status(thm)], [zip_derived_cl125, '0'])). 42.34/6.03 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 42.34/6.03 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 42.34/6.03 thf('1', plain, 42.34/6.03 (![X0:( $i > $o ),X1:( $i > $o )]: 42.34/6.03 ( ( ~( all_of @ X0 @ X1 ) ) <=> 42.34/6.03 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 42.34/6.03 inference('rw.lit', [status(esa)], [def_all_of])). 42.34/6.03 thf(zip_derived_cl376, plain, 42.34/6.03 (~ (((!!) @ (^[Y0 : $i]: 42.34/6.03 (((is_of @ Y0 @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 42.34/6.03 ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ 42.34/6.03 ((('#C') @ (!=) @ emptyset)))))) @ 42.34/6.03 ((('#B') @ ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ 42.34/6.03 ((('#C') @ (!=) @ emptyset)))))))) @ 42.34/6.03 ((('#S') @ ((('#B') @ ('#S') @ 42.34/6.03 ((('#B') @ ((('#B') @ ('#C'))) @ 42.34/6.03 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 42.34/6.03 ((('#C') @ ((('#B') @ ('#B') @ 42.34/6.03 ((('#B') @ ('#S') @ 42.34/6.03 ((('#B') @ ( 42.34/6.03 (('#B') @ iii)) @ 42.34/6.03 n_pl)))))) @ 42.34/6.03 n_pl)))))))) @ 42.34/6.03 iii)))) @ 42.34/6.03 Y0)))))))), 42.34/6.03 inference('rw_clause', [status(thm)], [zip_derived_cl375, '1'])). 42.34/6.03 thf(zip_derived_cl377, plain, 42.34/6.03 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 42.34/6.03 ((('#C') @ is_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ 42.34/6.03 ((('#C') @ (!=) @ emptyset))))))))) @ 42.34/6.03 ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 42.34/6.03 ((('#B') @ ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ 42.34/6.03 ((('#C') @ (!=) @ emptyset)))))))) @ 42.34/6.03 ((('#S') @ ((('#B') @ ('#S') @ 42.34/6.03 ((('#B') @ ((('#B') @ ('#C'))) @ 42.34/6.03 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 42.34/6.03 ((('#C') @ ((('#B') @ ('#B') @ 42.34/6.03 ((('#B') @ ('#S') @ 42.34/6.03 ((('#B') @ ((('#B') @ iii)) @ 42.34/6.03 n_pl)))))) @ 42.34/6.03 n_pl)))))))) @ 42.34/6.03 iii))))))))))), 42.34/6.03 inference('comb-normalize', [status(thm)], [zip_derived_cl376])). 42.34/6.03 thf(zip_derived_cl378, plain, 42.34/6.03 (~ (((is_of @ '#sk2' @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 42.34/6.03 (all_of @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 42.34/6.03 ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 42.34/6.03 ((('#S') @ ((('#B') @ ('#C') @ 42.34/6.03 ((('#B') @ ((('#B') @ (=>))) @ 42.34/6.03 ((('#B') @ ((('#S') @ ((('#B') @ iii @ 42.34/6.03 (n_pl @ '#sk2'))))) @ 42.34/6.03 n_pl)))))) @ 42.34/6.03 (iii @ '#sk2'))))))))), 42.34/6.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl377])). 42.34/6.03 thf(zip_derived_cl380, plain, 42.34/6.03 (~ (all_of @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 42.34/6.03 ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 42.34/6.03 ((('#S') @ ((('#B') @ ('#C') @ 42.34/6.03 ((('#B') @ ((('#B') @ (=>))) @ 42.34/6.03 ((('#B') @ ((('#S') @ ((('#B') @ iii @ 42.34/6.03 (n_pl @ '#sk2'))))) @ 42.34/6.03 n_pl)))))) @ 42.34/6.03 (iii @ '#sk2'))))))), 42.34/6.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl378])). 42.34/6.03 thf(zip_derived_cl381, plain, 42.34/6.03 (~ (((!!) @ (^[Y0 : $i]: 42.34/6.03 (((is_of @ Y0 @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 42.34/6.03 ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ 42.34/6.03 ((('#C') @ (!=) @ emptyset)))))) @ 42.34/6.03 ((('#S') @ ((('#B') @ ('#C') @ 42.34/6.03 ((('#B') @ ((('#B') @ (=>))) @ 42.34/6.03 ((('#B') @ ((('#S') @ ((('#B') @ iii @ 42.34/6.03 (n_pl @ '#sk2'))))) @ 42.34/6.03 n_pl)))))) @ 42.34/6.03 (iii @ '#sk2'))) @ 42.34/6.03 Y0)))))))), 42.34/6.03 inference('rw_clause', [status(thm)], [zip_derived_cl380, '1'])). 42.34/6.03 thf(zip_derived_cl382, plain, 42.34/6.03 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 42.34/6.03 ((('#C') @ is_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ 42.34/6.03 ((('#C') @ (!=) @ emptyset))))))))) @ 42.34/6.03 ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 42.34/6.03 ((('#S') @ ((('#B') @ ('#C') @ 42.34/6.03 ((('#B') @ ((('#B') @ (=>))) @ 42.34/6.03 ((('#B') @ ((('#S') @ ((('#B') @ iii @ 42.34/6.03 (n_pl @ '#sk2'))))) @ 42.34/6.03 n_pl)))))) @ 42.34/6.03 (iii @ '#sk2')))))))))), 42.34/6.03 inference('comb-normalize', [status(thm)], [zip_derived_cl381])). 42.34/6.03 thf(zip_derived_cl383, plain, 42.34/6.03 (~ (((is_of @ '#sk3' @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 42.34/6.03 (all_of @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 42.34/6.03 ((('#C') @ ((('#B') @ (=>) @ 42.34/6.03 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @ 42.34/6.03 (n_pl @ '#sk3'))))) @ 42.34/6.03 (iii @ '#sk2' @ '#sk3'))))))), 42.34/6.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl382])). 42.34/6.03 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))). 42.34/6.03 thf('2', plain, 42.34/6.03 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )), 42.34/6.03 define([status(thm)])). 42.34/6.03 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))). 42.34/6.03 thf('3', plain, 42.34/6.03 (![X1:$i,X0:$i]: 42.34/6.03 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 42.34/6.03 define([status(thm)])). 42.34/6.03 thf(zip_derived_cl384, plain, 42.34/6.03 (~ (((is_of @ '#sk3' @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 42.34/6.03 (all_of @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 42.34/6.03 ((('#C') @ ((('#B') @ (=>) @ 42.34/6.03 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @ 42.34/6.03 (n_pl @ '#sk3'))))) @ 42.34/6.03 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ '#sk3' @ '#sk2')))))))), 42.34/6.03 inference('rw', [status(thm)], [zip_derived_cl383, '0', '2', '3'])). 42.34/6.03 thf(zip_derived_cl386, plain, 42.34/6.03 (~ (all_of @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 42.34/6.03 ((('#C') @ ((('#B') @ (=>) @ 42.34/6.03 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @ 42.34/6.03 (n_pl @ '#sk3'))))) @ 42.34/6.03 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ '#sk3' @ '#sk2')))))), 42.34/6.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl384])). 42.34/6.03 thf(zip_derived_cl387, plain, 42.34/6.03 (~ (((!!) @ (^[Y0 : $i]: 42.34/6.03 (((is_of @ Y0 @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 42.34/6.03 ((('#C') @ ((('#B') @ (=>) @ 42.34/6.03 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @ 42.34/6.03 (n_pl @ '#sk3'))))) @ 42.34/6.03 (l_some @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ '#sk3' @ '#sk2')) @ 42.34/6.03 Y0)))))))), 42.34/6.03 inference('rw_clause', [status(thm)], [zip_derived_cl386, '1'])). 42.34/6.03 thf(zip_derived_cl388, plain, 42.34/6.03 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 42.34/6.03 ((('#C') @ is_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ 42.34/6.03 ((('#C') @ (!=) @ emptyset))))))))) @ 42.34/6.03 ((('#C') @ ((('#B') @ (=>) @ 42.34/6.03 ((('#S') @ ((('#B') @ iii @ (n_pl @ '#sk2'))) @ 42.34/6.03 (n_pl @ '#sk3'))))) @ 42.34/6.03 (l_some @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ '#sk3' @ '#sk2'))))))))), 42.34/6.03 inference('comb-normalize', [status(thm)], [zip_derived_cl387])). 42.34/6.03 thf(zip_derived_cl389, plain, 42.34/6.03 (~ (((is_of @ '#sk4' @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 42.34/6.03 (((iii @ (n_pl @ '#sk2' @ '#sk4') @ (n_pl @ '#sk3' @ '#sk4')) => 42.34/6.03 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ '#sk3' @ '#sk2'))))))), 42.34/6.03 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl388])). 42.34/6.03 thf(def_n_pl, axiom,(( n_pl @ (X0)@ (X1)) = ((ap @ (plus @ X0) @ X1)))). 42.34/6.03 thf('4', plain, 42.34/6.03 (![X1:$i,X0:$i]: ( ( n_pl @ X0 @ X1 ) = ( ap @ ( plus @ X0 ) @ X1 ) )), 42.34/6.03 define([status(thm)])). 42.34/6.03 thf(zip_derived_cl390, plain, 42.34/6.03 (~ (((is_of @ '#sk4' @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 42.34/6.03 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk4') @ 42.34/6.03 (ap @ (plus @ '#sk2') @ '#sk4'))) => 42.34/6.03 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ '#sk3' @ '#sk2'))))))), 42.34/6.03 inference('rw', [status(thm)], 42.34/6.03 [zip_derived_cl389, '0', '2', '4', '4', '3'])). 42.34/6.03 thf(zip_derived_cl392, plain, 42.34/6.03 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk4') @ 42.34/6.03 (ap @ (plus @ '#sk2') @ '#sk4'))) => 42.34/6.03 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ '#sk3' @ '#sk2'))))), 42.34/6.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl390])). 42.34/6.03 thf(zip_derived_cl394, plain, 42.34/6.03 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ '#sk3' @ '#sk2'))), 42.34/6.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl392])). 42.34/6.03 thf(zip_derived_cl393, plain, 42.34/6.03 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ (ap @ (plus @ '#sk3') @ '#sk4') @ 42.34/6.03 (ap @ (plus @ '#sk2') @ '#sk4')))), 42.34/6.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl392])). 42.34/6.03 thf(satz20a, axiom, 42.34/6.03 (all_of @ 42.34/6.03 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 42.34/6.03 ( ^[X0:$i]: 42.34/6.03 ( all_of @ 42.34/6.03 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 42.34/6.03 ( ^[X1:$i]: 42.34/6.03 ( all_of @ 42.34/6.03 ( ^[X2:$i]: ( in @ X2 @ nat ) ) @ 42.34/6.03 ( ^[X2:$i]: 42.34/6.03 ( ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) => 42.34/6.03 ( d_29_ii @ X0 @ X1 ) ) ) ) ) ) ))). 42.34/6.03 thf(zip_derived_cl114, plain, 42.34/6.03 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 42.34/6.03 (^[Y0 : $i]: 42.34/6.03 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 42.34/6.03 (^[Y1 : $i]: 42.34/6.03 (all_of @ (^[Y2 : $i]: (in @ Y2 @ nat)) @ 42.34/6.03 (^[Y2 : $i]: 42.34/6.03 (((d_29_ii @ (n_pl @ Y0 @ Y2) @ (n_pl @ Y1 @ Y2)) => 42.34/6.03 (d_29_ii @ Y0 @ Y1)))))))))), 42.34/6.03 inference('cnf', [status(esa)], [satz20a])). 42.34/6.03 thf(zip_derived_cl115, plain, 42.34/6.03 ( (all_of @ ((('#C') @ in @ nat)) @ 42.34/6.03 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 42.34/6.03 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ nat))))) @ 42.34/6.03 ((('#S') @ ((('#B') @ ('#S') @ 42.34/6.03 ((('#B') @ ((('#B') @ ('#C'))) @ 42.34/6.03 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 42.34/6.03 ((('#C') @ ((('#B') @ ('#B') @ 42.34/6.03 ((('#B') @ ('#S') @ 42.34/6.03 ((('#B') @ ((('#B') @ d_29_ii)) @ 42.34/6.03 n_pl)))))) @ 42.34/6.03 n_pl)))))))) @ 42.34/6.03 d_29_ii)))))))), 42.34/6.03 inference('lams2combs', [status(thm)], [zip_derived_cl114])). 42.34/6.03 thf(zip_derived_cl946, plain, 42.34/6.03 ( (all_of @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 42.34/6.03 ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 42.34/6.03 ((('#B') @ ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ 42.34/6.03 ((('#C') @ (!=) @ emptyset)))))))) @ 42.34/6.03 ((('#S') @ ((('#B') @ ('#S') @ 42.34/6.03 ((('#B') @ ((('#B') @ ('#C'))) @ 42.34/6.03 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 42.34/6.03 ((('#C') @ ((('#B') @ ('#B') @ 42.34/6.03 ((('#B') @ ('#S') @ 42.34/6.03 ((('#B') @ ((('#B') @ d_29_ii)) @ 42.34/6.03 n_pl)))))) @ 42.34/6.03 n_pl)))))))) @ 42.34/6.03 d_29_ii)))))))), 42.34/6.03 inference('rw', [status(thm)], [zip_derived_cl115, '0'])). 42.34/6.03 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 42.34/6.03 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 42.34/6.03 thf('5', plain, 42.34/6.03 (![X0:( $i > $o ),X1:( $i > $o )]: 42.34/6.03 ( ( all_of @ X0 @ X1 ) <=> 42.34/6.03 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 42.34/6.03 inference('rw.lit', [status(esa)], [def_all_of])). 42.34/6.03 thf(zip_derived_cl947, plain, 42.34/6.03 ( (((!!) @ (^[Y0 : $i]: 42.34/6.03 (((is_of @ Y0 @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 42.34/6.03 ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ 42.34/6.03 ((('#C') @ (!=) @ emptyset)))))) @ 42.34/6.03 ((('#B') @ ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ 42.34/6.03 ((('#C') @ (!=) @ emptyset)))))))) @ 42.34/6.03 ((('#S') @ ((('#B') @ ('#S') @ 42.34/6.03 ((('#B') @ ((('#B') @ ('#C'))) @ 42.34/6.03 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 42.34/6.03 ((('#C') @ ((('#B') @ ('#B') @ 42.34/6.03 ((('#B') @ ('#S') @ 42.34/6.03 ((('#B') @ (( 42.34/6.03 ('#B') @ d_29_ii)) @ 42.34/6.03 n_pl)))))) @ 42.34/6.03 n_pl)))))))) @ 42.34/6.03 d_29_ii)))) @ 42.34/6.03 Y0)))))))), 42.34/6.03 inference('rw_clause', [status(thm)], [zip_derived_cl946, '5'])). 42.34/6.03 thf(zip_derived_cl948, plain, 42.34/6.03 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 42.34/6.03 ((('#C') @ is_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @ 42.34/6.03 ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 42.34/6.03 ((('#B') @ ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ 42.34/6.03 ((('#C') @ (!=) @ emptyset)))))))) @ 42.34/6.03 ((('#S') @ ((('#B') @ ('#S') @ 42.34/6.03 ((('#B') @ ((('#B') @ ('#C'))) @ 42.34/6.03 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 42.34/6.03 ((('#C') @ ((('#B') @ ('#B') @ 42.34/6.03 ((('#B') @ ('#S') @ 42.34/6.03 ((('#B') @ ((('#B') @ d_29_ii)) @ 42.34/6.03 n_pl)))))) @ 42.34/6.03 n_pl)))))))) @ 42.34/6.03 d_29_ii))))))))))), 42.34/6.03 inference('comb-normalize', [status(thm)], [zip_derived_cl947])). 42.34/6.03 thf(zip_derived_cl949, plain, 42.34/6.03 (![X2 : $i]: 42.34/6.03 (((is_of @ X2 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 42.34/6.03 (all_of @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 42.34/6.03 ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 42.34/6.03 ((('#S') @ ((('#B') @ ('#C') @ 42.34/6.03 ((('#B') @ ((('#B') @ (=>))) @ 42.34/6.03 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @ 42.34/6.03 (n_pl @ X2))))) @ 42.34/6.03 n_pl)))))) @ 42.34/6.03 (d_29_ii @ X2))))))))), 42.34/6.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl948])). 42.34/6.03 thf(zip_derived_cl950, plain, 42.34/6.03 (![X2 : $i]: 42.34/6.03 (~ (is_of @ X2 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 42.34/6.03 | (all_of @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 42.34/6.03 ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 42.34/6.03 ((('#S') @ ((('#B') @ ('#C') @ 42.34/6.03 ((('#B') @ ((('#B') @ (=>))) @ 42.34/6.03 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @ 42.34/6.03 (n_pl @ X2))))) @ 42.34/6.03 n_pl)))))) @ 42.34/6.03 (d_29_ii @ X2)))))))), 42.34/6.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl949])). 42.34/6.03 thf(zip_derived_cl951, plain, 42.34/6.03 (![X0 : $i]: 42.34/6.03 ( (((!!) @ (^[Y0 : $i]: 42.34/6.03 (((is_of @ Y0 @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 42.34/6.03 ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ 42.34/6.03 ((('#C') @ (!=) @ emptyset)))))) @ 42.34/6.03 ((('#S') @ ((('#B') @ ('#C') @ 42.34/6.03 ((('#B') @ ((('#B') @ (=>))) @ 42.34/6.03 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @ 42.34/6.03 (n_pl @ X0))))) @ 42.34/6.03 n_pl)))))) @ 42.34/6.03 (d_29_ii @ X0))) @ 42.34/6.03 Y0))))))) 42.34/6.03 | ~ (is_of @ X0 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 42.34/6.03 inference('rw_clause', [status(thm)], [zip_derived_cl950, '5'])). 42.34/6.03 thf(zip_derived_cl952, plain, 42.34/6.03 (![X0 : $i]: 42.34/6.03 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 42.34/6.03 ((('#C') @ is_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ 42.34/6.03 ((('#C') @ (!=) @ emptyset))))))))) @ 42.34/6.03 ((('#B') @ (all_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ 42.34/6.03 ((('#C') @ (!=) @ emptyset)))))) @ 42.34/6.03 ((('#S') @ ((('#B') @ ('#C') @ 42.34/6.03 ((('#B') @ ((('#B') @ (=>))) @ 42.34/6.03 ((('#B') @ ((('#S') @ ((('#B') @ d_29_ii @ 42.34/6.03 (n_pl @ X0))))) @ 42.34/6.03 n_pl)))))) @ 42.34/6.03 (d_29_ii @ X0))))))))) 42.34/6.03 | ~ (is_of @ X0 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 42.34/6.03 inference('comb-normalize', [status(thm)], [zip_derived_cl951])). 42.34/6.03 thf(zip_derived_cl953, plain, 42.34/6.03 (![X0 : $i, X2 : $i]: 42.34/6.03 ( (((is_of @ X2 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 42.34/6.03 (all_of @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 42.34/6.03 ((('#C') @ ((('#B') @ (=>) @ 42.34/6.03 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @ 42.34/6.03 (n_pl @ X2))))) @ 42.34/6.03 (d_29_ii @ X0 @ X2)))))) 42.34/6.03 | ~ (is_of @ X0 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 42.34/6.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl952])). 42.34/6.03 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) = 42.34/6.03 ((n_some @ (diffprop @ X0 @ X1))))). 42.34/6.03 thf('6', plain, 42.34/6.03 (![X1:$i,X0:$i]: 42.34/6.03 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 42.34/6.03 define([status(thm)])). 42.34/6.03 thf(zip_derived_cl954, plain, 42.34/6.03 (![X0 : $i, X2 : $i]: 42.34/6.03 ( (((is_of @ X2 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 42.34/6.03 (all_of @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 42.34/6.03 ((('#C') @ ((('#B') @ (=>) @ 42.34/6.03 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @ 42.34/6.03 (n_pl @ X2))))) @ 42.34/6.03 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ X0 @ X2))))))) 42.34/6.03 | ~ (is_of @ X0 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 42.34/6.03 inference('rw', [status(thm)], [zip_derived_cl953, '0', '2', '6'])). 42.34/6.03 thf(zip_derived_cl955, plain, 42.34/6.03 (![X0 : $i, X2 : $i]: 42.34/6.03 (~ (is_of @ X2 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 42.34/6.03 | (all_of @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 42.34/6.03 ((('#C') @ ((('#B') @ (=>) @ 42.34/6.03 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @ 42.34/6.03 (n_pl @ X2))))) @ 42.34/6.03 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ X0 @ X2))))) 42.34/6.03 | ~ (is_of @ X0 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 42.34/6.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl954])). 42.34/6.03 thf(zip_derived_cl956, plain, 42.34/6.03 (![X0 : $i, X1 : $i]: 42.34/6.03 ( (((!!) @ (^[Y0 : $i]: 42.34/6.03 (((is_of @ Y0 @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 42.34/6.03 ((('#C') @ ((('#B') @ (=>) @ 42.34/6.03 ((('#S') @ ((('#B') @ d_29_ii @ 42.34/6.03 (n_pl @ X0))) @ 42.34/6.03 (n_pl @ X1))))) @ 42.34/6.03 (l_some @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ X0 @ X1)) @ 42.34/6.03 Y0))))))) 42.34/6.03 | ~ (is_of @ X0 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 42.34/6.03 | ~ (is_of @ X1 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 42.34/6.03 inference('rw_clause', [status(thm)], [zip_derived_cl955, '5'])). 42.34/6.03 thf(zip_derived_cl957, plain, 42.34/6.03 (![X0 : $i, X1 : $i]: 42.34/6.03 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 42.34/6.03 ((('#C') @ is_of @ 42.34/6.03 ((('#C') @ in @ 42.34/6.03 (d_Sep @ omega @ 42.34/6.03 ((('#C') @ (!=) @ emptyset))))))))) @ 42.34/6.03 ((('#C') @ ((('#B') @ (=>) @ 42.34/6.03 ((('#S') @ ((('#B') @ d_29_ii @ (n_pl @ X0))) @ 42.34/6.03 (n_pl @ X1))))) @ 42.34/6.03 (l_some @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ X0 @ X1)))))))) 42.34/6.03 | ~ (is_of @ X0 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 42.34/6.03 | ~ (is_of @ X1 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 42.34/6.03 inference('comb-normalize', [status(thm)], [zip_derived_cl956])). 42.34/6.03 thf(zip_derived_cl958, plain, 42.34/6.03 (![X0 : $i, X1 : $i, X3 : $i]: 42.34/6.03 ( (((is_of @ X3 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 42.34/6.03 (((d_29_ii @ (n_pl @ X0 @ X3) @ (n_pl @ X1 @ X3)) => (l_some @ 42.34/6.03 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ X0 @ X1)))))) 42.34/6.03 | ~ (is_of @ X1 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 42.34/6.03 | ~ (is_of @ X0 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 42.34/6.03 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl957])). 42.34/6.03 thf(zip_derived_cl959, plain, 42.34/6.03 (![X0 : $i, X1 : $i, X3 : $i]: 42.34/6.03 ( (((is_of @ X3 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 42.34/6.03 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ (ap @ (plus @ X0) @ X3) @ (ap @ (plus @ X1) @ X3))) => 42.34/6.03 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ X0 @ X1)))))) 42.34/6.03 | ~ (is_of @ X1 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 42.34/6.03 | ~ (is_of @ X0 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 42.34/6.03 inference('rw', [status(thm)], 42.34/6.03 [zip_derived_cl958, '0', '2', '4', '4', '6'])). 42.34/6.03 thf(zip_derived_cl960, plain, 42.34/6.03 (![X0 : $i, X1 : $i, X3 : $i]: 42.34/6.03 (~ (is_of @ X3 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 42.34/6.03 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ (ap @ (plus @ X0) @ X3) @ (ap @ (plus @ X1) @ X3))) => 42.34/6.03 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ X0 @ X1)))) 42.34/6.03 | ~ (is_of @ X0 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 42.34/6.03 | ~ (is_of @ X1 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 42.34/6.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl959])). 42.34/6.03 thf(zip_derived_cl961, plain, 42.34/6.03 (![X0 : $i, X1 : $i, X3 : $i]: 42.34/6.03 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ (ap @ (plus @ X0) @ X3) @ (ap @ (plus @ X1) @ X3))) 42.34/6.03 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ X0 @ X1)) 42.34/6.03 | ~ (is_of @ X1 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 42.34/6.03 | ~ (is_of @ X0 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 42.34/6.03 | ~ (is_of @ X3 @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 42.34/6.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl960])). 42.34/6.03 thf(zip_derived_cl7618, plain, 42.34/6.03 ((~ (is_of @ '#sk4' @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 42.34/6.03 | ~ (is_of @ '#sk3' @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 42.34/6.03 | ~ (is_of @ '#sk2' @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 42.34/6.03 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ '#sk3' @ '#sk2')))), 42.34/6.03 inference('sup-', [status(thm)], [zip_derived_cl393, zip_derived_cl961])). 42.34/6.03 thf(zip_derived_cl391, plain, 42.34/6.03 ( (is_of @ '#sk4' @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 42.34/6.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl390])). 42.34/6.03 thf(zip_derived_cl385, plain, 42.34/6.03 ( (is_of @ '#sk3' @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 42.34/6.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl384])). 42.34/6.03 thf(zip_derived_cl379, plain, 42.34/6.03 ( (is_of @ '#sk2' @ 42.34/6.03 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 42.34/6.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl378])). 42.34/6.03 thf(zip_derived_cl7644, plain, 42.34/6.03 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 42.34/6.03 (diffprop @ '#sk3' @ '#sk2'))), 42.34/6.03 inference('demod', [status(thm)], 42.34/6.03 [zip_derived_cl7618, zip_derived_cl391, zip_derived_cl385, 42.34/6.03 zip_derived_cl379])). 42.34/6.03 thf(zip_derived_cl7700, plain, ($false), 42.34/6.03 inference('demod', [status(thm)], [zip_derived_cl394, zip_derived_cl7644])). 42.34/6.03 42.34/6.03 % SZS output end Refutation 42.34/6.03 42.34/6.03 42.34/6.03 % Terminating... 43.06/6.14 % Runner terminated. 43.08/6.15 % Zipperpin 1.5 exiting 43.08/6.15 EOF