0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.8mUnkSSS58 true 0.15/0.36 % Computer : n010.cluster.edu 0.15/0.36 % Model : x86_64 x86_64 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.36 % Memory : 8042.1875MB 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.36 % CPULimit : 1200 0.15/0.36 % WCLimit : 120 0.15/0.36 % DateTime : Tue Jul 13 14:01:21 EDT 2021 0.15/0.37 % CPUTime : 0.15/0.37 % Running portfolio for 120 s 0.15/0.37 % File : /export/starexec/sandbox2/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 0.56/0.70 % Total configuration time : 828 0.56/0.70 % Estimated wc time : 983 0.56/0.70 % Estimated cpu time (8 cpus) : 122.875 0.57/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.57/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.57/0.76 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.57/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.58/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.58/0.82 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.58/0.82 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.58/0.82 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 51.34/7.38 % Solved by lams/40_b.comb.sh. 51.34/7.38 % done 456 iterations in 6.512s 51.34/7.38 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 51.34/7.38 % SZS output start Refutation 51.34/7.38 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 51.34/7.38 thf(n_is_type, type, n_is: $i > $i > $o). 51.34/7.38 thf(l_or_type, type, l_or: $o > $o > $o). 51.34/7.38 thf(moreis_type, type, moreis: $i > $i > $o). 51.34/7.38 thf(binunion_type, type, binunion: $i > $i > $i). 51.34/7.38 thf(in_type, type, in: $i > $i > $o). 51.34/7.38 thf(imp_type, type, imp: $o > $o > $o). 51.34/7.38 thf(lessis_type, type, lessis: $i > $i > $o). 51.34/7.38 thf('#sk1_type', type, '#sk1': $i). 51.34/7.38 thf(nat_type, type, nat: $i). 51.34/7.38 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 51.34/7.38 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 51.34/7.38 thf(d_Sing_type, type, d_Sing: $i > $i). 51.34/7.38 thf(n_some_type, type, n_some: ($i > $o) > $o). 51.34/7.38 thf(ordsucc_type, type, ordsucc: $i > $i). 51.34/7.38 thf(iii_type, type, iii: $i > $i > $o). 51.34/7.38 thf('#sk2_type', type, '#sk2': $i). 51.34/7.38 thf(omega_type, type, omega: $i). 51.34/7.38 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 51.34/7.38 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o). 51.34/7.38 thf(d_not_type, type, d_not: $o > $o). 51.34/7.38 thf(emptyset_type, type, emptyset: $i). 51.34/7.38 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 51.34/7.38 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 51.34/7.38 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 51.34/7.38 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 51.34/7.38 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 51.34/7.38 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 51.34/7.38 thf(suc_p, axiom, 51.34/7.38 (all_of @ 51.34/7.38 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 51.34/7.38 ( ^[X0:$i]: ( is_of @ ( ordsucc @ X0 ) @ ( ^[X1:$i]: ( in @ X1 @ nat ) ) ) ))). 51.34/7.38 thf(zip_derived_cl35, plain, 51.34/7.38 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 51.34/7.38 (^[Y0 : $i]: (is_of @ (ordsucc @ Y0) @ (^[Y1 : $i]: (in @ Y1 @ nat)))))), 51.34/7.38 inference('cnf', [status(esa)], [suc_p])). 51.34/7.38 thf(zip_derived_cl36, plain, 51.34/7.38 ( (all_of @ ((('#C') @ in @ nat)) @ 51.34/7.38 ((('#C') @ ((('#B') @ is_of @ ordsucc)) @ ((('#C') @ in @ nat)))))), 51.34/7.38 inference('lams2combs', [status(thm)], [zip_derived_cl35])). 51.34/7.38 thf(def_nat, axiom,(( nat ) = 51.34/7.38 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))). 51.34/7.38 thf('0', plain, 51.34/7.38 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )), 51.34/7.38 define([status(thm)])). 51.34/7.38 thf(zip_derived_cl326, plain, 51.34/7.38 ( (all_of @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 51.34/7.38 ((('#C') @ ((('#B') @ is_of @ ordsucc)) @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))), 51.34/7.38 inference('rw', [status(thm)], [zip_derived_cl36, '0'])). 51.34/7.38 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 51.34/7.38 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 51.34/7.38 thf('1', plain, 51.34/7.38 (![X0:( $i > $o ),X1:( $i > $o )]: 51.34/7.38 ( ( all_of @ X0 @ X1 ) <=> 51.34/7.38 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 51.34/7.38 inference('rw.lit', [status(esa)], [def_all_of])). 51.34/7.38 thf(zip_derived_cl327, plain, 51.34/7.38 ( (((!!) @ (^[Y0 : $i]: 51.34/7.38 (((is_of @ Y0 @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 51.34/7.38 ((('#C') @ ((('#B') @ is_of @ ordsucc)) @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 51.34/7.38 Y0)))))))), 51.34/7.38 inference('rw_clause', [status(thm)], [zip_derived_cl326, '1'])). 51.34/7.38 thf(zip_derived_cl328, plain, 51.34/7.38 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 51.34/7.38 ((('#C') @ is_of @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @ 51.34/7.38 ((('#C') @ ((('#B') @ is_of @ ordsucc)) @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))))))), 51.34/7.38 inference('comb-normalize', [status(thm)], [zip_derived_cl327])). 51.34/7.38 thf(zip_derived_cl329, plain, 51.34/7.38 (![X2 : $i]: 51.34/7.38 (((is_of @ X2 @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 51.34/7.38 (is_of @ (ordsucc @ X2) @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))), 51.34/7.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl328])). 51.34/7.38 thf(def_is_of, axiom,(( is_of @ (X1)@ (X0)) = ((X0 @ X1)))). 51.34/7.38 thf('2', plain, 51.34/7.38 (![X0:( $i > $o ),X1:$i]: ( ( is_of @ X1 @ X0 ) = ( X0 @ X1 ) )), 51.34/7.38 define([status(thm)])). 51.34/7.38 thf(def_ordsucc, axiom,(( ordsucc @ (X0)) = 51.34/7.38 ((binunion @ X0 @ (d_Sing @ X0))))). 51.34/7.38 thf('3', plain, 51.34/7.38 (![X0:$i]: ( ( ordsucc @ X0 ) = ( binunion @ X0 @ ( d_Sing @ X0 ) ) )), 51.34/7.38 define([status(thm)])). 51.34/7.38 thf(zip_derived_cl330, plain, 51.34/7.38 (![X2 : $i]: 51.34/7.38 (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 51.34/7.38 (in @ (binunion @ X2 @ (d_Sing @ X2)) @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 51.34/7.38 inference('rw', [status(thm)], [zip_derived_cl329, '2', '2', '3'])). 51.34/7.38 thf(zip_derived_cl331, plain, 51.34/7.38 (![X2 : $i]: 51.34/7.38 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | (in @ (binunion @ X2 @ (d_Sing @ X2)) @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl330])). 51.34/7.38 thf(satz25c, conjecture, 51.34/7.38 (all_of @ 51.34/7.38 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 51.34/7.38 ( ^[X0:$i]: 51.34/7.38 ( all_of @ 51.34/7.38 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 51.34/7.38 ( ^[X1:$i]: 51.34/7.38 ( ( iii @ X1 @ X0 ) => ( lessis @ ( ordsucc @ X1 ) @ X0 ) ) ) ) ))). 51.34/7.38 thf(zf_stmt_0, negated_conjecture, 51.34/7.38 (~( all_of @ 51.34/7.38 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 51.34/7.38 ( ^[X0:$i]: 51.34/7.38 ( all_of @ 51.34/7.38 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 51.34/7.38 ( ^[X1:$i]: 51.34/7.38 ( ( iii @ X1 @ X0 ) => ( lessis @ ( ordsucc @ X1 ) @ X0 ) ) ) ) ) )), 51.34/7.38 inference('cnf.neg', [status(esa)], [satz25c])). 51.34/7.38 thf(zip_derived_cl217, plain, 51.34/7.38 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 51.34/7.38 (^[Y0 : $i]: 51.34/7.38 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 51.34/7.38 (^[Y1 : $i]: 51.34/7.38 (((iii @ Y1 @ Y0) => (lessis @ (ordsucc @ Y1) @ Y0)))))))), 51.34/7.38 inference('cnf', [status(esa)], [zf_stmt_0])). 51.34/7.38 thf(zip_derived_cl218, plain, 51.34/7.38 (~ (all_of @ ((('#C') @ in @ nat)) @ 51.34/7.38 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 51.34/7.38 ((('#S') @ ((('#B') @ ('#S') @ 51.34/7.38 ((('#B') @ ((('#B') @ (=>))) @ ((('#C') @ iii)))))) @ 51.34/7.38 ((('#C') @ ((('#B') @ lessis @ ordsucc)))))))))), 51.34/7.38 inference('lams2combs', [status(thm)], [zip_derived_cl217])). 51.34/7.38 thf(zip_derived_cl384, plain, 51.34/7.38 (~ (all_of @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 51.34/7.38 ((('#B') @ (all_of @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ ('#S') @ 51.34/7.38 ((('#B') @ ((('#B') @ (=>))) @ ((('#C') @ iii)))))) @ 51.34/7.38 ((('#C') @ ((('#B') @ lessis @ ordsucc)))))))))), 51.34/7.38 inference('rw', [status(thm)], [zip_derived_cl218, '0'])). 51.34/7.38 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 51.34/7.38 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 51.34/7.38 thf('4', plain, 51.34/7.38 (![X0:( $i > $o ),X1:( $i > $o )]: 51.34/7.38 ( ( ~( all_of @ X0 @ X1 ) ) <=> 51.34/7.38 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 51.34/7.38 inference('rw.lit', [status(esa)], [def_all_of])). 51.34/7.38 thf(zip_derived_cl385, plain, 51.34/7.38 (~ (((!!) @ (^[Y0 : $i]: 51.34/7.38 (((is_of @ Y0 @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 51.34/7.38 ((('#B') @ (all_of @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ 51.34/7.38 ((('#C') @ (!=) @ emptyset)))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ ('#S') @ 51.34/7.38 ((('#B') @ ((('#B') @ (=>))) @ 51.34/7.38 ((('#C') @ iii)))))) @ 51.34/7.38 ((('#C') @ ((('#B') @ lessis @ ordsucc)))))) @ 51.34/7.38 Y0)))))))), 51.34/7.38 inference('rw_clause', [status(thm)], [zip_derived_cl384, '4'])). 51.34/7.38 thf(zip_derived_cl386, plain, 51.34/7.38 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 51.34/7.38 ((('#C') @ is_of @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ 51.34/7.38 ((('#C') @ (!=) @ emptyset))))))))) @ 51.34/7.38 ((('#B') @ (all_of @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ ('#S') @ 51.34/7.38 ((('#B') @ ((('#B') @ (=>))) @ 51.34/7.38 ((('#C') @ iii)))))) @ 51.34/7.38 ((('#C') @ ((('#B') @ lessis @ ordsucc))))))))))))), 51.34/7.38 inference('comb-normalize', [status(thm)], [zip_derived_cl385])). 51.34/7.38 thf(zip_derived_cl387, plain, 51.34/7.38 (~ (((is_of @ '#sk1' @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 51.34/7.38 (all_of @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ iii @ '#sk1')))) @ 51.34/7.38 ((('#C') @ ((('#B') @ lessis @ ordsucc)) @ '#sk1')))))))), 51.34/7.38 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl386])). 51.34/7.38 thf(zip_derived_cl388, plain, 51.34/7.38 (~ (((in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 51.34/7.38 (all_of @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ iii @ '#sk1')))) @ 51.34/7.38 ((('#C') @ ((('#B') @ lessis @ ordsucc)) @ '#sk1')))))))), 51.34/7.38 inference('rw', [status(thm)], [zip_derived_cl387, '2'])). 51.34/7.38 thf(zip_derived_cl390, plain, 51.34/7.38 (~ (all_of @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ iii @ '#sk1')))) @ 51.34/7.38 ((('#C') @ ((('#B') @ lessis @ ordsucc)) @ '#sk1')))))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl388])). 51.34/7.38 thf(zip_derived_cl391, plain, 51.34/7.38 (~ (((!!) @ (^[Y0 : $i]: 51.34/7.38 (((is_of @ Y0 @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 51.34/7.38 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ iii @ '#sk1')))) @ 51.34/7.38 ((('#C') @ ((('#B') @ lessis @ ordsucc)) @ '#sk1')) @ 51.34/7.38 Y0)))))))), 51.34/7.38 inference('rw_clause', [status(thm)], [zip_derived_cl390, '4'])). 51.34/7.38 thf(zip_derived_cl392, plain, 51.34/7.38 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 51.34/7.38 ((('#C') @ is_of @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ 51.34/7.38 ((('#C') @ (!=) @ emptyset))))))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ iii @ '#sk1')))) @ 51.34/7.38 ((('#C') @ ((('#B') @ lessis @ ordsucc)) @ '#sk1'))))))))), 51.34/7.38 inference('comb-normalize', [status(thm)], [zip_derived_cl391])). 51.34/7.38 thf(zip_derived_cl393, plain, 51.34/7.38 (~ (((is_of @ '#sk2' @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 51.34/7.38 (((iii @ '#sk2' @ '#sk1') => (lessis @ (ordsucc @ '#sk2') @ '#sk1')))))), 51.34/7.38 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl392])). 51.34/7.38 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 51.34/7.38 thf('5', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 51.34/7.38 define([status(thm)])). 51.34/7.38 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 51.34/7.38 thf('6', plain, 51.34/7.38 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 51.34/7.38 define([status(thm)])). 51.34/7.38 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))). 51.34/7.38 thf('7', plain, 51.34/7.38 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )), 51.34/7.38 define([status(thm)])). 51.34/7.38 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))). 51.34/7.38 thf('8', plain, 51.34/7.38 (![X1:$i,X0:$i]: 51.34/7.38 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 51.34/7.38 define([status(thm)])). 51.34/7.38 thf(def_lessis, axiom,(( lessis @ (X0)@ (X1)) = 51.34/7.38 ((l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1))))). 51.34/7.38 thf('9', plain, 51.34/7.38 (![X1:$i,X0:$i]: 51.34/7.38 ( ( lessis @ X0 @ X1 ) = 51.34/7.38 ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )), 51.34/7.38 define([status(thm)])). 51.34/7.38 thf(zip_derived_cl394, plain, 51.34/7.38 (~ (((in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 51.34/7.38 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ '#sk1' @ '#sk2')) => (imp @ 51.34/7.38 (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ '#sk1' @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')))) @ 51.34/7.38 ($false)) @ 51.34/7.38 (n_is @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')) @ '#sk1'))))))), 51.34/7.38 inference('rw', [status(thm)], 51.34/7.38 [zip_derived_cl393, '2', '3', '5', '6', '0', '7', '7', '8', 51.34/7.38 '8', '9'])). 51.34/7.38 thf(zip_derived_cl396, plain, 51.34/7.38 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ '#sk1' @ '#sk2')) => (imp @ 51.34/7.38 (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ '#sk1' @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')))) @ 51.34/7.38 ($false)) @ 51.34/7.38 (n_is @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')) @ '#sk1'))))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl394])). 51.34/7.38 thf(zip_derived_cl398, plain, 51.34/7.38 (~ (imp @ 51.34/7.38 (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ '#sk1' @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')))) @ 51.34/7.38 ($false)) @ 51.34/7.38 (n_is @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')) @ '#sk1'))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl396])). 51.34/7.38 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 51.34/7.38 thf('10', plain, 51.34/7.38 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 51.34/7.38 inference('rw.lit', [status(esa)], [def_imp])). 51.34/7.38 thf(zip_derived_cl399, plain, 51.34/7.38 (~ (((imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ '#sk1' @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')))) @ 51.34/7.38 ($false)) => (n_is @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')) @ 51.34/7.38 '#sk1')))), 51.34/7.38 inference('rw_clause', [status(thm)], [zip_derived_cl398, '10'])). 51.34/7.38 thf(zip_derived_cl400, plain, 51.34/7.38 ( (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ '#sk1' @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')))) @ 51.34/7.38 ($false))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl399])). 51.34/7.38 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 51.34/7.38 thf('11', plain, 51.34/7.38 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 51.34/7.38 inference('rw.lit', [status(esa)], [def_imp])). 51.34/7.38 thf(zip_derived_cl402, plain, 51.34/7.38 ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ '#sk1' @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')))) => 51.34/7.38 ($false)))), 51.34/7.38 inference('rw_clause', [status(thm)], [zip_derived_cl400, '11'])). 51.34/7.38 thf(zip_derived_cl403, plain, 51.34/7.38 ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ '#sk1' @ (binunion @ '#sk2' @ (d_Sing @ '#sk2'))))))), 51.34/7.38 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl402])). 51.34/7.38 thf(zip_derived_cl404, plain, 51.34/7.38 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ '#sk1' @ (binunion @ '#sk2' @ (d_Sing @ '#sk2'))))), 51.34/7.38 inference('simplify nested equalities', [status(thm)], 51.34/7.38 [zip_derived_cl403])). 51.34/7.38 thf(satz13, axiom, 51.34/7.38 (all_of @ 51.34/7.38 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 51.34/7.38 ( ^[X0:$i]: 51.34/7.38 ( all_of @ 51.34/7.38 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 51.34/7.38 ( ^[X1:$i]: ( ( moreis @ X0 @ X1 ) => ( lessis @ X1 @ X0 ) ) ) ) ))). 51.34/7.38 thf(zip_derived_cl119, plain, 51.34/7.38 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 51.34/7.38 (^[Y0 : $i]: 51.34/7.38 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 51.34/7.38 (^[Y1 : $i]: (((moreis @ Y0 @ Y1) => (lessis @ Y1 @ Y0)))))))), 51.34/7.38 inference('cnf', [status(esa)], [satz13])). 51.34/7.38 thf(zip_derived_cl120, plain, 51.34/7.38 ( (all_of @ ((('#C') @ in @ nat)) @ 51.34/7.38 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 51.34/7.38 ((('#S') @ ((('#B') @ ('#S') @ 51.34/7.38 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @ 51.34/7.38 ((('#C') @ lessis)))))))), 51.34/7.38 inference('lams2combs', [status(thm)], [zip_derived_cl119])). 51.34/7.38 thf(zip_derived_cl458, plain, 51.34/7.38 ( (all_of @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 51.34/7.38 ((('#B') @ (all_of @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ ('#S') @ 51.34/7.38 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @ 51.34/7.38 ((('#C') @ lessis)))))))), 51.34/7.38 inference('rw', [status(thm)], [zip_derived_cl120, '0'])). 51.34/7.38 thf(zip_derived_cl459, plain, 51.34/7.38 ( (((!!) @ (^[Y0 : $i]: 51.34/7.38 (((is_of @ Y0 @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 51.34/7.38 ((('#B') @ (all_of @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ 51.34/7.38 ((('#C') @ (!=) @ emptyset)))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ ('#S') @ 51.34/7.38 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @ 51.34/7.38 ((('#C') @ lessis)))) @ 51.34/7.38 Y0)))))))), 51.34/7.38 inference('rw_clause', [status(thm)], [zip_derived_cl458, '1'])). 51.34/7.38 thf(zip_derived_cl460, plain, 51.34/7.38 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 51.34/7.38 ((('#C') @ is_of @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @ 51.34/7.38 ((('#B') @ (all_of @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ ('#S') @ 51.34/7.38 ((('#B') @ ((('#B') @ (=>))) @ moreis)))) @ 51.34/7.38 ((('#C') @ lessis))))))))))), 51.34/7.38 inference('comb-normalize', [status(thm)], [zip_derived_cl459])). 51.34/7.38 thf(zip_derived_cl461, plain, 51.34/7.38 (![X2 : $i]: 51.34/7.38 (((is_of @ X2 @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 51.34/7.38 (all_of @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X2))) @ 51.34/7.38 ((('#C') @ lessis @ X2)))))))), 51.34/7.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl460])). 51.34/7.38 thf(zip_derived_cl462, plain, 51.34/7.38 (![X2 : $i]: 51.34/7.38 (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 51.34/7.38 (all_of @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X2))) @ 51.34/7.38 ((('#C') @ lessis @ X2)))))))), 51.34/7.38 inference('rw', [status(thm)], [zip_derived_cl461, '2'])). 51.34/7.38 thf(zip_derived_cl463, plain, 51.34/7.38 (![X2 : $i]: 51.34/7.38 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | (all_of @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X2))) @ 51.34/7.38 ((('#C') @ lessis @ X2))))))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl462])). 51.34/7.38 thf(zip_derived_cl464, plain, 51.34/7.38 (![X0 : $i]: 51.34/7.38 ( (((!!) @ (^[Y0 : $i]: 51.34/7.38 (((is_of @ Y0 @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 51.34/7.38 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X0))) @ 51.34/7.38 ((('#C') @ lessis @ X0)) @ Y0))))))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('rw_clause', [status(thm)], [zip_derived_cl463, '1'])). 51.34/7.38 thf(zip_derived_cl465, plain, 51.34/7.38 (![X0 : $i]: 51.34/7.38 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 51.34/7.38 ((('#C') @ is_of @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ 51.34/7.38 ((('#C') @ (!=) @ emptyset))))))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ (=>) @ (moreis @ X0))) @ 51.34/7.38 ((('#C') @ lessis @ X0)))))))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('comb-normalize', [status(thm)], [zip_derived_cl464])). 51.34/7.38 thf(zip_derived_cl466, plain, 51.34/7.38 (![X0 : $i, X2 : $i]: 51.34/7.38 ( (((is_of @ X2 @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 51.34/7.38 (((moreis @ X0 @ X2) => (lessis @ X2 @ X0))))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl465])). 51.34/7.38 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) = 51.34/7.38 ((n_some @ (diffprop @ X0 @ X1))))). 51.34/7.38 thf('12', plain, 51.34/7.38 (![X1:$i,X0:$i]: 51.34/7.38 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 51.34/7.38 define([status(thm)])). 51.34/7.38 thf(def_moreis, axiom,(( moreis @ (X0)@ (X1)) = 51.34/7.38 ((l_or @ (d_29_ii @ X0 @ X1) @ (n_is @ X0 @ X1))))). 51.34/7.38 thf('13', plain, 51.34/7.38 (![X1:$i,X0:$i]: 51.34/7.38 ( ( moreis @ X0 @ X1 ) = 51.34/7.38 ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )), 51.34/7.38 define([status(thm)])). 51.34/7.38 thf(zip_derived_cl467, plain, 51.34/7.38 (![X0 : $i, X2 : $i]: 51.34/7.38 ( (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 51.34/7.38 (((imp @ 51.34/7.38 (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X2)) @ 51.34/7.38 ($false)) @ 51.34/7.38 (n_is @ X0 @ X2)) => (imp @ 51.34/7.38 (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X2)) @ 51.34/7.38 ($false)) @ 51.34/7.38 (n_is @ X2 @ X0)))))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('rw', [status(thm)], 51.34/7.38 [zip_derived_cl466, '2', '5', '6', '6', '0', '7', '12', '8', 51.34/7.38 '13', '9'])). 51.34/7.38 thf(zip_derived_cl468, plain, 51.34/7.38 (![X0 : $i, X2 : $i]: 51.34/7.38 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | (((imp @ 51.34/7.38 (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X2)) @ 51.34/7.38 ($false)) @ 51.34/7.38 (n_is @ X0 @ X2)) => (imp @ 51.34/7.38 (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X2)) @ 51.34/7.38 ($false)) @ 51.34/7.38 (n_is @ X2 @ X0)))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl467])). 51.34/7.38 thf(zip_derived_cl469, plain, 51.34/7.38 (![X0 : $i, X2 : $i]: 51.34/7.38 (~ (imp @ 51.34/7.38 (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X2)) @ 51.34/7.38 ($false)) @ 51.34/7.38 (n_is @ X0 @ X2)) 51.34/7.38 | (imp @ 51.34/7.38 (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X2)) @ 51.34/7.38 ($false)) @ 51.34/7.38 (n_is @ X2 @ X0)) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl468])). 51.34/7.38 thf(zip_derived_cl470, plain, 51.34/7.38 (![X0 : $i, X1 : $i]: 51.34/7.38 (~ (((imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X1 @ X0)) @ 51.34/7.38 ($false)) => (n_is @ X1 @ X0))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | (imp @ 51.34/7.38 (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X1 @ X0)) @ 51.34/7.38 ($false)) @ 51.34/7.38 (n_is @ X0 @ X1)))), 51.34/7.38 inference('rw_clause', [status(thm)], [zip_derived_cl469, '10'])). 51.34/7.38 thf(zip_derived_cl471, plain, 51.34/7.38 (![X0 : $i, X1 : $i]: 51.34/7.38 ( (((imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X1)) @ 51.34/7.38 ($false)) => (n_is @ X1 @ X0))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (((imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X1)) @ 51.34/7.38 ($false)) => (n_is @ X0 @ X1))))), 51.34/7.38 inference('rw_clause', [status(thm)], [zip_derived_cl470, '11'])). 51.34/7.38 thf(zip_derived_cl472, plain, 51.34/7.38 (![X0 : $i, X1 : $i]: 51.34/7.38 (~ (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X1)) @ 51.34/7.38 ($false)) 51.34/7.38 | (n_is @ X1 @ X0) 51.34/7.38 | ~ (((imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X1)) @ 51.34/7.38 ($false)) => (n_is @ X0 @ X1))) 51.34/7.38 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl471])). 51.34/7.38 thf(zip_derived_cl473, plain, 51.34/7.38 (![X0 : $i, X1 : $i]: 51.34/7.38 (~ (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X1)) @ 51.34/7.38 ($false)) 51.34/7.38 | (n_is @ X1 @ X0) 51.34/7.38 | ~ ((($true) => (n_is @ X0 @ X1))) 51.34/7.38 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('local_rewriting', [status(thm)], [zip_derived_cl472])). 51.34/7.38 thf(zip_derived_cl474, plain, 51.34/7.38 (![X0 : $i, X1 : $i]: 51.34/7.38 (~ (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X1)) @ 51.34/7.38 ($false)) 51.34/7.38 | (n_is @ X1 @ X0) 51.34/7.38 | ~ (n_is @ X0 @ X1) 51.34/7.38 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl473])). 51.34/7.38 thf(zip_derived_cl475, plain, 51.34/7.38 (![X0 : $i, X1 : $i]: 51.34/7.38 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X1)) => ($false))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (n_is @ X0 @ X1) 51.34/7.38 | (n_is @ X1 @ X0))), 51.34/7.38 inference('rw_clause', [status(thm)], [zip_derived_cl474, '10'])). 51.34/7.38 thf(zip_derived_cl476, plain, 51.34/7.38 (![X0 : $i, X1 : $i]: 51.34/7.38 (~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X1)))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (n_is @ X0 @ X1) 51.34/7.38 | (n_is @ X1 @ X0))), 51.34/7.38 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl475])). 51.34/7.38 thf(zip_derived_cl477, plain, 51.34/7.38 (![X0 : $i, X1 : $i]: 51.34/7.38 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X1)) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (n_is @ X0 @ X1) 51.34/7.38 | (n_is @ X1 @ X0))), 51.34/7.38 inference('simplify nested equalities', [status(thm)], 51.34/7.38 [zip_derived_cl476])). 51.34/7.38 thf(zip_derived_cl3148, plain, 51.34/7.38 (( (n_is @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')) @ '#sk1') 51.34/7.38 | ~ (n_is @ '#sk1' @ (binunion @ '#sk2' @ (d_Sing @ '#sk2'))) 51.34/7.38 | ~ (in @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')) @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('sup+', [status(thm)], [zip_derived_cl404, zip_derived_cl477])). 51.34/7.38 thf(zip_derived_cl401, plain, 51.34/7.38 (~ (n_is @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')) @ '#sk1')), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl399])). 51.34/7.38 thf(zip_derived_cl389, plain, 51.34/7.38 ( (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl388])). 51.34/7.38 thf(zip_derived_cl3151, plain, 51.34/7.38 ((~ (n_is @ '#sk1' @ (binunion @ '#sk2' @ (d_Sing @ '#sk2'))) 51.34/7.38 | ~ (in @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')) @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('demod', [status(thm)], 51.34/7.38 [zip_derived_cl3148, zip_derived_cl401, zip_derived_cl389])). 51.34/7.38 thf(zip_derived_cl404, plain, 51.34/7.38 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ '#sk1' @ (binunion @ '#sk2' @ (d_Sing @ '#sk2'))))), 51.34/7.38 inference('simplify nested equalities', [status(thm)], 51.34/7.38 [zip_derived_cl403])). 51.34/7.38 thf(satz25a, axiom, 51.34/7.38 (all_of @ 51.34/7.38 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 51.34/7.38 ( ^[X0:$i]: 51.34/7.38 ( all_of @ 51.34/7.38 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 51.34/7.38 ( ^[X1:$i]: 51.34/7.38 ( ( d_29_ii @ X1 @ X0 ) => ( moreis @ X1 @ ( ordsucc @ X0 ) ) ) ) ) ))). 51.34/7.38 thf(zip_derived_cl139, plain, 51.34/7.38 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 51.34/7.38 (^[Y0 : $i]: 51.34/7.38 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 51.34/7.38 (^[Y1 : $i]: 51.34/7.38 (((d_29_ii @ Y1 @ Y0) => (moreis @ Y1 @ (ordsucc @ Y0))))))))), 51.34/7.38 inference('cnf', [status(esa)], [satz25a])). 51.34/7.38 thf(zip_derived_cl140, plain, 51.34/7.38 ( (all_of @ ((('#C') @ in @ nat)) @ 51.34/7.38 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 51.34/7.38 ((('#S') @ ((('#B') @ ('#S') @ 51.34/7.38 ((('#B') @ ((('#B') @ (=>))) @ ((('#C') @ d_29_ii)))))) @ 51.34/7.38 ((('#B') @ ((('#C') @ moreis)) @ ordsucc)))))))), 51.34/7.38 inference('lams2combs', [status(thm)], [zip_derived_cl139])). 51.34/7.38 thf(zip_derived_cl679, plain, 51.34/7.38 ( (all_of @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 51.34/7.38 ((('#B') @ (all_of @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ ('#S') @ 51.34/7.38 ((('#B') @ ((('#B') @ (=>))) @ ((('#C') @ d_29_ii)))))) @ 51.34/7.38 ((('#B') @ ((('#C') @ moreis)) @ ordsucc)))))))), 51.34/7.38 inference('rw', [status(thm)], [zip_derived_cl140, '0'])). 51.34/7.38 thf(zip_derived_cl680, plain, 51.34/7.38 ( (((!!) @ (^[Y0 : $i]: 51.34/7.38 (((is_of @ Y0 @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 51.34/7.38 ((('#B') @ (all_of @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ 51.34/7.38 ((('#C') @ (!=) @ emptyset)))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ ('#S') @ 51.34/7.38 ((('#B') @ ((('#B') @ (=>))) @ 51.34/7.38 ((('#C') @ d_29_ii)))))) @ 51.34/7.38 ((('#B') @ ((('#C') @ moreis)) @ ordsucc)))) @ 51.34/7.38 Y0)))))))), 51.34/7.38 inference('rw_clause', [status(thm)], [zip_derived_cl679, '1'])). 51.34/7.38 thf(zip_derived_cl681, plain, 51.34/7.38 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 51.34/7.38 ((('#C') @ is_of @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @ 51.34/7.38 ((('#B') @ (all_of @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ ('#S') @ 51.34/7.38 ((('#B') @ ((('#B') @ (=>))) @ 51.34/7.38 ((('#C') @ d_29_ii)))))) @ 51.34/7.38 ((('#B') @ ((('#C') @ moreis)) @ ordsucc))))))))))), 51.34/7.38 inference('comb-normalize', [status(thm)], [zip_derived_cl680])). 51.34/7.38 thf(zip_derived_cl682, plain, 51.34/7.38 (![X2 : $i]: 51.34/7.38 (((is_of @ X2 @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 51.34/7.38 (all_of @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ d_29_ii @ X2)))) @ 51.34/7.38 ((('#C') @ moreis @ (ordsucc @ X2))))))))), 51.34/7.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl681])). 51.34/7.38 thf(zip_derived_cl683, plain, 51.34/7.38 (![X2 : $i]: 51.34/7.38 (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 51.34/7.38 (all_of @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ d_29_ii @ X2)))) @ 51.34/7.38 ((('#C') @ moreis @ (binunion @ X2 @ (d_Sing @ X2)))))))))), 51.34/7.38 inference('rw', [status(thm)], [zip_derived_cl682, '2', '3'])). 51.34/7.38 thf(zip_derived_cl684, plain, 51.34/7.38 (![X2 : $i]: 51.34/7.38 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | (all_of @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ d_29_ii @ X2)))) @ 51.34/7.38 ((('#C') @ moreis @ (binunion @ X2 @ (d_Sing @ X2))))))))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl683])). 51.34/7.38 thf(zip_derived_cl685, plain, 51.34/7.38 (![X0 : $i]: 51.34/7.38 ( (((!!) @ (^[Y0 : $i]: 51.34/7.38 (((is_of @ Y0 @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 51.34/7.38 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ d_29_ii @ X0)))) @ 51.34/7.38 ((('#C') @ moreis @ (binunion @ X0 @ (d_Sing @ X0)))) @ 51.34/7.38 Y0))))))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('rw_clause', [status(thm)], [zip_derived_cl684, '1'])). 51.34/7.38 thf(zip_derived_cl686, plain, 51.34/7.38 (![X0 : $i]: 51.34/7.38 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 51.34/7.38 ((('#C') @ is_of @ 51.34/7.38 ((('#C') @ in @ 51.34/7.38 (d_Sep @ omega @ 51.34/7.38 ((('#C') @ (!=) @ emptyset))))))))) @ 51.34/7.38 ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ d_29_ii @ X0)))) @ 51.34/7.38 ((('#C') @ moreis @ (binunion @ X0 @ (d_Sing @ X0)))))))))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('comb-normalize', [status(thm)], [zip_derived_cl685])). 51.34/7.38 thf(zip_derived_cl687, plain, 51.34/7.38 (![X0 : $i, X2 : $i]: 51.34/7.38 ( (((is_of @ X2 @ 51.34/7.38 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 51.34/7.38 (((d_29_ii @ X2 @ X0) => (moreis @ X2 @ 51.34/7.38 (binunion @ X0 @ (d_Sing @ X0))))))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl686])). 51.34/7.38 thf(zip_derived_cl688, plain, 51.34/7.38 (![X0 : $i, X2 : $i]: 51.34/7.38 ( (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 51.34/7.38 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X2 @ X0)) => (imp @ 51.34/7.38 (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X2 @ (binunion @ X0 @ (d_Sing @ X0)))) @ 51.34/7.38 ($false)) @ 51.34/7.38 (n_is @ X2 @ (binunion @ X0 @ (d_Sing @ X0)))))))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('rw', [status(thm)], 51.34/7.38 [zip_derived_cl687, '2', '5', '6', '0', '7', '7', '12', '12', 51.34/7.38 '13'])). 51.34/7.38 thf(zip_derived_cl689, plain, 51.34/7.38 (![X0 : $i, X2 : $i]: 51.34/7.38 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X2 @ X0)) => (imp @ 51.34/7.38 (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X2 @ (binunion @ X0 @ (d_Sing @ X0)))) @ 51.34/7.38 ($false)) @ 51.34/7.38 (n_is @ X2 @ (binunion @ X0 @ (d_Sing @ X0)))))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl688])). 51.34/7.38 thf(zip_derived_cl690, plain, 51.34/7.38 (![X0 : $i, X2 : $i]: 51.34/7.38 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X2 @ X0)) 51.34/7.38 | (imp @ 51.34/7.38 (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X2 @ (binunion @ X0 @ (d_Sing @ X0)))) @ 51.34/7.38 ($false)) @ 51.34/7.38 (n_is @ X2 @ (binunion @ X0 @ (d_Sing @ X0)))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl689])). 51.34/7.38 thf(zip_derived_cl691, plain, 51.34/7.38 (![X0 : $i, X1 : $i]: 51.34/7.38 ( (((imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ (binunion @ X1 @ (d_Sing @ X1)))) @ 51.34/7.38 ($false)) => (n_is @ X0 @ (binunion @ X1 @ (d_Sing @ X1))))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X1)))), 51.34/7.38 inference('rw_clause', [status(thm)], [zip_derived_cl690, '11'])). 51.34/7.38 thf(zip_derived_cl692, plain, 51.34/7.38 (![X0 : $i, X1 : $i]: 51.34/7.38 (~ (imp @ 51.34/7.38 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ (binunion @ X1 @ (d_Sing @ X1)))) @ 51.34/7.38 ($false)) 51.34/7.38 | (n_is @ X0 @ (binunion @ X1 @ (d_Sing @ X1))) 51.34/7.38 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X1)) 51.34/7.38 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl691])). 51.34/7.38 thf(zip_derived_cl693, plain, 51.34/7.38 (![X0 : $i, X1 : $i]: 51.34/7.38 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ (binunion @ X1 @ (d_Sing @ X1)))) => ($false))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X1)) 51.34/7.38 | (n_is @ X0 @ (binunion @ X1 @ (d_Sing @ X1))))), 51.34/7.38 inference('rw_clause', [status(thm)], [zip_derived_cl692, '10'])). 51.34/7.38 thf(zip_derived_cl694, plain, 51.34/7.38 (![X0 : $i, X1 : $i]: 51.34/7.38 (~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ (binunion @ X1 @ (d_Sing @ X1)))))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X1)) 51.34/7.38 | (n_is @ X0 @ (binunion @ X1 @ (d_Sing @ X1))))), 51.34/7.38 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl693])). 51.34/7.38 thf(zip_derived_cl695, plain, 51.34/7.38 (![X0 : $i, X1 : $i]: 51.34/7.38 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ (binunion @ X1 @ (d_Sing @ X1)))) 51.34/7.38 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ X0 @ X1)) 51.34/7.38 | (n_is @ X0 @ (binunion @ X1 @ (d_Sing @ X1))))), 51.34/7.38 inference('simplify nested equalities', [status(thm)], 51.34/7.38 [zip_derived_cl694])). 51.34/7.38 thf(zip_derived_cl4058, plain, 51.34/7.38 (( (n_is @ '#sk1' @ (binunion @ '#sk2' @ (d_Sing @ '#sk2'))) 51.34/7.38 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ '#sk1' @ '#sk2')) 51.34/7.38 | ~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 51.34/7.38 | ~ (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 51.34/7.38 inference('sup+', [status(thm)], [zip_derived_cl404, zip_derived_cl695])). 51.34/7.38 thf(zip_derived_cl397, plain, 51.34/7.38 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 51.34/7.38 (diffprop @ '#sk1' @ '#sk2'))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl396])). 51.34/7.38 thf(zip_derived_cl395, plain, 51.34/7.38 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl394])). 51.34/7.38 thf(zip_derived_cl389, plain, 51.34/7.38 ( (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl388])). 51.34/7.38 thf(zip_derived_cl4069, plain, 51.34/7.38 ( (n_is @ '#sk1' @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')))), 51.34/7.38 inference('demod', [status(thm)], 51.34/7.38 [zip_derived_cl4058, zip_derived_cl397, zip_derived_cl395, 51.34/7.38 zip_derived_cl389])). 51.34/7.38 thf(zip_derived_cl6622, plain, 51.34/7.38 (~ (in @ (binunion @ '#sk2' @ (d_Sing @ '#sk2')) @ 51.34/7.38 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))), 51.34/7.38 inference('demod', [status(thm)], 51.34/7.38 [zip_derived_cl3151, zip_derived_cl4069])). 51.34/7.38 thf(zip_derived_cl6638, plain, 51.34/7.38 (~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))), 51.34/7.38 inference('sup-', [status(thm)], [zip_derived_cl331, zip_derived_cl6622])). 51.34/7.38 thf(zip_derived_cl395, plain, 51.34/7.38 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))), 51.34/7.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl394])). 51.34/7.38 thf(zip_derived_cl6647, plain, ($false), 51.34/7.38 inference('demod', [status(thm)], [zip_derived_cl6638, zip_derived_cl395])). 51.34/7.38 51.34/7.38 % SZS output end Refutation 51.34/7.38 51.34/7.38 51.34/7.38 % Terminating... 51.73/7.41 % Runner terminated. 51.73/7.42 % Zipperpin 1.5 exiting 51.73/7.43 EOF