0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.zXZtme87zJ true 0.15/0.36 % Computer : n021.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 12:50:11 EDT 2021 0.15/0.36 % CPUTime : 0.15/0.36 % Running portfolio for 120 s 0.15/0.36 % 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 0.58/0.69 % Total configuration time : 828 0.58/0.69 % Estimated wc time : 983 0.58/0.69 % Estimated cpu time (8 cpus) : 122.875 0.58/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.58/0.75 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.58/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.58/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.58/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.58/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.58/0.80 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.58/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 5.92/1.40 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 53s 10.31/1.93 % Solved by lams/40_b.comb.sh. 10.31/1.93 % done 173 iterations in 1.095s 10.31/1.93 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 10.31/1.93 % SZS output start Refutation 10.31/1.93 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 10.31/1.93 thf('#sk1_type', type, '#sk1': $i). 10.31/1.93 thf(n_is_type, type, n_is: $i > $i > $o). 10.31/1.93 thf('#sk2_type', type, '#sk2': $i). 10.31/1.93 thf(l_or_type, type, l_or: $o > $o > $o). 10.31/1.93 thf(in_type, type, in: $i > $i > $o). 10.31/1.93 thf(imp_type, type, imp: $o > $o > $o). 10.31/1.93 thf(lessis_type, type, lessis: $i > $i > $o). 10.31/1.93 thf(nat_type, type, nat: $i). 10.31/1.93 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 10.31/1.93 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 10.31/1.93 thf(e_is_type, type, e_is: $i > $i > $i > $o). 10.31/1.93 thf(n_some_type, type, n_some: ($i > $o) > $o). 10.31/1.93 thf(iii_type, type, iii: $i > $i > $o). 10.31/1.93 thf(omega_type, type, omega: $i). 10.31/1.93 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 10.31/1.93 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o). 10.31/1.93 thf(d_not_type, type, d_not: $o > $o). 10.31/1.93 thf(emptyset_type, type, emptyset: $i). 10.31/1.93 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 10.31/1.93 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 10.31/1.93 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 10.31/1.93 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 10.31/1.93 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 10.31/1.93 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 10.31/1.93 thf(satz10k, conjecture, 10.31/1.93 (all_of @ 10.31/1.93 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 10.31/1.93 ( ^[X0:$i]: 10.31/1.93 ( all_of @ 10.31/1.93 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 10.31/1.93 ( ^[X1:$i]: 10.31/1.93 ( ( d_not @ ( lessis @ X0 @ X1 ) ) => ( d_29_ii @ X0 @ X1 ) ) ) ) ))). 10.31/1.93 thf(zf_stmt_0, negated_conjecture, 10.31/1.93 (~( all_of @ 10.31/1.93 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 10.31/1.93 ( ^[X0:$i]: 10.31/1.93 ( all_of @ 10.31/1.93 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 10.31/1.93 ( ^[X1:$i]: 10.31/1.93 ( ( d_not @ ( lessis @ X0 @ X1 ) ) => ( d_29_ii @ X0 @ X1 ) ) ) ) ) )), 10.31/1.93 inference('cnf.neg', [status(esa)], [satz10k])). 10.31/1.93 thf(zip_derived_cl107, plain, 10.31/1.93 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 10.31/1.93 (^[Y0 : $i]: 10.31/1.93 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 10.31/1.93 (^[Y1 : $i]: 10.31/1.93 (((d_not @ (lessis @ Y0 @ Y1)) => (d_29_ii @ Y0 @ Y1)))))))), 10.31/1.93 inference('cnf', [status(esa)], [zf_stmt_0])). 10.31/1.93 thf(zip_derived_cl108, plain, 10.31/1.93 (~ (all_of @ ((('#C') @ in @ nat)) @ 10.31/1.93 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 10.31/1.93 ((('#S') @ ((('#B') @ ('#S') @ 10.31/1.93 ((('#B') @ ((('#B') @ (=>))) @ 10.31/1.93 ((('#B') @ ((('#B') @ d_not)) @ lessis)))))) @ 10.31/1.93 d_29_ii)))))), 10.31/1.93 inference('lams2combs', [status(thm)], [zip_derived_cl107])). 10.31/1.93 thf(def_nat, axiom,(( nat ) = 10.31/1.93 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))). 10.31/1.93 thf('0', plain, 10.31/1.93 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )), 10.31/1.93 define([status(thm)])). 10.31/1.93 thf(zip_derived_cl169, plain, 10.31/1.93 (~ (all_of @ 10.31/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 10.31/1.93 ((('#B') @ (all_of @ 10.31/1.93 ((('#C') @ in @ 10.31/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 10.31/1.93 ((('#S') @ ((('#B') @ ('#S') @ 10.31/1.93 ((('#B') @ ((('#B') @ (=>))) @ 10.31/1.93 ((('#B') @ ((('#B') @ d_not)) @ lessis)))))) @ 10.31/1.93 d_29_ii)))))), 10.31/1.93 inference('rw', [status(thm)], [zip_derived_cl108, '0'])). 10.31/1.93 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 10.31/1.93 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 10.31/1.93 thf('1', plain, 10.31/1.93 (![X0:( $i > $o ),X1:( $i > $o )]: 10.31/1.93 ( ( ~( all_of @ X0 @ X1 ) ) <=> 10.31/1.93 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 10.31/1.93 inference('rw.lit', [status(esa)], [def_all_of])). 10.31/1.93 thf(zip_derived_cl170, plain, 10.31/1.93 (~ (((!!) @ (^[Y0 : $i]: 10.31/1.93 (((is_of @ Y0 @ 10.31/1.93 ((('#C') @ in @ 10.31/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 10.31/1.93 ((('#B') @ (all_of @ 10.31/1.93 ((('#C') @ in @ 10.31/1.93 (d_Sep @ omega @ 10.31/1.93 ((('#C') @ (!=) @ emptyset)))))) @ 10.31/1.93 ((('#S') @ ((('#B') @ ('#S') @ 10.31/1.93 ((('#B') @ ((('#B') @ (=>))) @ 10.31/1.93 ((('#B') @ ((('#B') @ d_not)) @ lessis)))))) @ 10.31/1.93 d_29_ii)) @ 10.31/1.93 Y0)))))))), 10.31/1.93 inference('rw_clause', [status(thm)], [zip_derived_cl169, '1'])). 10.31/1.93 thf(zip_derived_cl171, plain, 10.31/1.93 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 10.31/1.93 ((('#C') @ is_of @ 10.31/1.93 ((('#C') @ in @ 10.31/1.93 (d_Sep @ omega @ 10.31/1.93 ((('#C') @ (!=) @ emptyset))))))))) @ 10.31/1.93 ((('#B') @ (all_of @ 10.31/1.93 ((('#C') @ in @ 10.31/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 10.31/1.93 ((('#S') @ ((('#B') @ ('#S') @ 10.31/1.93 ((('#B') @ ((('#B') @ (=>))) @ 10.31/1.93 ((('#B') @ ((('#B') @ d_not)) @ lessis)))))) @ 10.31/1.93 d_29_ii))))))))), 10.31/1.93 inference('comb-normalize', [status(thm)], [zip_derived_cl170])). 10.31/1.93 thf(zip_derived_cl172, plain, 10.31/1.93 (~ (((is_of @ '#sk1' @ 10.31/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 10.31/1.93 (all_of @ 10.31/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 10.31/1.93 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (lessis @ '#sk1'))))) @ 10.31/1.93 (d_29_ii @ '#sk1'))))))), 10.31/1.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl171])). 10.31/1.93 thf(def_is_of, axiom,(( is_of @ (X1)@ (X0)) = ((X0 @ X1)))). 10.31/1.93 thf('2', plain, 10.31/1.93 (![X0:( $i > $o ),X1:$i]: ( ( is_of @ X1 @ X0 ) = ( X0 @ X1 ) )), 10.31/1.93 define([status(thm)])). 10.31/1.93 thf(zip_derived_cl173, plain, 10.31/1.93 (~ (((in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 10.31/1.93 (all_of @ 10.31/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 10.31/1.93 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (lessis @ '#sk1'))))) @ 10.31/1.93 (d_29_ii @ '#sk1'))))))), 10.31/1.93 inference('rw', [status(thm)], [zip_derived_cl172, '2'])). 10.31/1.93 thf(zip_derived_cl175, plain, 10.31/1.93 (~ (all_of @ 10.31/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 10.31/1.93 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (lessis @ '#sk1'))))) @ 10.31/1.93 (d_29_ii @ '#sk1'))))), 10.31/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])). 10.31/1.93 thf(zip_derived_cl176, plain, 10.31/1.93 (~ (((!!) @ (^[Y0 : $i]: 10.31/1.93 (((is_of @ Y0 @ 10.31/1.93 ((('#C') @ in @ 10.31/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 10.31/1.93 ((('#S') @ ((('#B') @ (=>) @ 10.31/1.93 ((('#B') @ d_not @ (lessis @ '#sk1'))))) @ 10.31/1.93 (d_29_ii @ '#sk1') @ Y0)))))))), 10.31/1.93 inference('rw_clause', [status(thm)], [zip_derived_cl175, '1'])). 10.31/1.93 thf(zip_derived_cl177, plain, 10.31/1.93 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 10.31/1.93 ((('#C') @ is_of @ 10.31/1.93 ((('#C') @ in @ 10.31/1.93 (d_Sep @ omega @ 10.31/1.93 ((('#C') @ (!=) @ emptyset))))))))) @ 10.31/1.93 ((('#S') @ ((('#B') @ (=>) @ 10.31/1.93 ((('#B') @ d_not @ (lessis @ '#sk1'))))) @ 10.31/1.93 (d_29_ii @ '#sk1')))))))), 10.31/1.93 inference('comb-normalize', [status(thm)], [zip_derived_cl176])). 10.31/1.93 thf(zip_derived_cl178, plain, 10.31/1.93 (~ (((is_of @ '#sk2' @ 10.31/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 10.31/1.93 (((d_not @ (lessis @ '#sk1' @ '#sk2')) => (d_29_ii @ '#sk1' @ 10.31/1.93 '#sk2')))))), 10.31/1.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl177])). 10.31/1.93 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 10.31/1.93 thf('3', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 10.31/1.93 define([status(thm)])). 10.31/1.93 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 10.31/1.93 thf('4', plain, 10.31/1.93 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 10.31/1.93 define([status(thm)])). 10.31/1.93 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))). 10.31/1.93 thf('5', plain, 10.31/1.93 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )), 10.31/1.93 define([status(thm)])). 10.31/1.93 thf(def_n_is, axiom,(( n_is @ (X0)@ (X1)) = ((e_is @ nat @ X0 @ X1)))). 10.31/1.93 thf('6', plain, 10.31/1.93 (![X1:$i,X0:$i]: ( ( n_is @ X0 @ X1 ) = ( e_is @ nat @ X0 @ X1 ) )), 10.31/1.93 define([status(thm)])). 10.31/1.93 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))). 10.31/1.93 thf('7', plain, 10.31/1.93 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )), 10.31/1.93 define([status(thm)])). 10.31/1.93 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) = 10.31/1.93 ((n_some @ (diffprop @ X0 @ X1))))). 10.31/1.93 thf('8', plain, 10.31/1.93 (![X1:$i,X0:$i]: 10.31/1.93 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 10.31/1.93 define([status(thm)])). 10.31/1.93 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))). 10.31/1.93 thf('9', plain, 10.31/1.93 (![X1:$i,X0:$i]: 10.31/1.93 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 10.31/1.93 define([status(thm)])). 10.31/1.93 thf(def_lessis, axiom,(( lessis @ (X0)@ (X1)) = 10.31/1.93 ((l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1))))). 10.31/1.93 thf('10', plain, 10.31/1.93 (![X1:$i,X0:$i]: 10.31/1.93 ( ( lessis @ X0 @ X1 ) = 10.31/1.93 ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )), 10.31/1.93 define([status(thm)])). 10.31/1.93 thf(zip_derived_cl179, plain, 10.31/1.93 (~ (((in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 10.31/1.93 (((imp @ 10.31/1.93 (imp @ 10.31/1.93 (imp @ 10.31/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.93 (diffprop @ '#sk2' @ '#sk1')) @ 10.31/1.93 ($false)) @ 10.31/1.93 ((('#sk1') = ('#sk2')))) @ 10.31/1.93 ($false)) => (l_some @ 10.31/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.93 (diffprop @ '#sk1' @ '#sk2'))))))), 10.31/1.93 inference('rw', [status(thm)], 10.31/1.93 [zip_derived_cl178, '2', '3', '3', '4', '5', '0', '6', '7', 10.31/1.93 '7', '8', '9', '10'])). 10.31/1.93 thf(zip_derived_cl181, plain, 10.31/1.93 (~ (((imp @ 10.31/1.93 (imp @ 10.31/1.93 (imp @ 10.31/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.93 (diffprop @ '#sk2' @ '#sk1')) @ 10.31/1.93 ($false)) @ 10.31/1.93 ((('#sk1') = ('#sk2')))) @ 10.31/1.93 ($false)) => (l_some @ 10.31/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.93 (diffprop @ '#sk1' @ '#sk2'))))), 10.31/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])). 10.31/1.93 thf(zip_derived_cl183, plain, 10.31/1.93 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.93 (diffprop @ '#sk1' @ '#sk2'))), 10.31/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl181])). 10.31/1.93 thf(zip_derived_cl182, plain, 10.31/1.93 ( (imp @ 10.31/1.93 (imp @ 10.31/1.93 (imp @ 10.31/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.93 (diffprop @ '#sk2' @ '#sk1')) @ 10.31/1.93 ($false)) @ 10.31/1.93 ((('#sk1') = ('#sk2')))) @ 10.31/1.93 ($false))), 10.31/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl181])). 10.31/1.93 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 10.31/1.93 thf('11', plain, 10.31/1.93 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 10.31/1.93 inference('rw.lit', [status(esa)], [def_imp])). 10.31/1.93 thf(zip_derived_cl184, plain, 10.31/1.93 ( (((imp @ 10.31/1.93 (imp @ 10.31/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.93 (diffprop @ '#sk2' @ '#sk1')) @ 10.31/1.93 ($false)) @ 10.31/1.93 ((('#sk1') = ('#sk2')))) => ($false)))), 10.31/1.93 inference('rw_clause', [status(thm)], [zip_derived_cl182, '11'])). 10.31/1.93 thf(zip_derived_cl185, plain, 10.31/1.93 ( (((~) @ (imp @ 10.31/1.93 (imp @ 10.31/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.93 (diffprop @ '#sk2' @ '#sk1')) @ 10.31/1.93 ($false)) @ 10.31/1.93 ((('#sk1') = ('#sk2'))))))), 10.31/1.93 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl184])). 10.31/1.93 thf(zip_derived_cl186, plain, 10.31/1.93 (~ (imp @ 10.31/1.93 (imp @ 10.31/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.93 (diffprop @ '#sk2' @ '#sk1')) @ 10.31/1.93 ($false)) @ 10.31/1.93 ((('#sk1') = ('#sk2'))))), 10.31/1.93 inference('simplify nested equalities', [status(thm)], 10.31/1.93 [zip_derived_cl185])). 10.31/1.93 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 10.31/1.93 thf('12', plain, 10.31/1.93 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 10.31/1.93 inference('rw.lit', [status(esa)], [def_imp])). 10.31/1.93 thf(zip_derived_cl187, plain, 10.31/1.93 (~ (((imp @ 10.31/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.93 (diffprop @ '#sk2' @ '#sk1')) @ 10.31/1.93 ($false)) => ((('#sk1') = ('#sk2')))))), 10.31/1.93 inference('rw_clause', [status(thm)], [zip_derived_cl186, '12'])). 10.31/1.93 thf(zip_derived_cl188, plain, 10.31/1.93 ( (imp @ 10.31/1.93 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.93 (diffprop @ '#sk2' @ '#sk1')) @ 10.31/1.93 ($false))), 10.31/1.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl187])). 10.31/1.93 thf(zip_derived_cl190, plain, 10.31/1.93 ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.93 (diffprop @ '#sk2' @ '#sk1')) => ($false)))), 10.31/1.93 inference('rw_clause', [status(thm)], [zip_derived_cl188, '11'])). 10.31/1.93 thf(zip_derived_cl192, plain, 10.31/1.93 ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.93 (diffprop @ '#sk2' @ '#sk1'))))), 10.31/1.93 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl190])). 10.31/1.93 thf(zip_derived_cl193, plain, 10.31/1.93 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.93 (diffprop @ '#sk2' @ '#sk1'))), 10.31/1.93 inference('simplify nested equalities', [status(thm)], 10.31/1.93 [zip_derived_cl192])). 10.31/1.93 thf(satz10e, axiom, 10.31/1.93 (all_of @ 10.31/1.93 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 10.31/1.93 ( ^[X0:$i]: 10.31/1.93 ( all_of @ 10.31/1.93 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 10.31/1.93 ( ^[X1:$i]: 10.31/1.93 ( ( d_not @ ( d_29_ii @ X0 @ X1 ) ) => ( lessis @ X0 @ X1 ) ) ) ) ))). 10.31/1.93 thf(zip_derived_cl67, plain, 10.31/1.93 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 10.31/1.93 (^[Y0 : $i]: 10.31/1.93 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 10.31/1.93 (^[Y1 : $i]: 10.31/1.93 (((d_not @ (d_29_ii @ Y0 @ Y1)) => (lessis @ Y0 @ Y1)))))))), 10.31/1.93 inference('cnf', [status(esa)], [satz10e])). 10.31/1.93 thf(zip_derived_cl68, plain, 10.31/1.93 ( (all_of @ ((('#C') @ in @ nat)) @ 10.31/1.93 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 10.31/1.93 ((('#S') @ ((('#B') @ ('#S') @ 10.31/1.93 ((('#B') @ ((('#B') @ (=>))) @ 10.31/1.93 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))) @ 10.31/1.93 lessis)))))), 10.31/1.93 inference('lams2combs', [status(thm)], [zip_derived_cl67])). 10.31/1.93 thf(zip_derived_cl353, plain, 10.31/1.93 ( (all_of @ 10.31/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 10.31/1.93 ((('#B') @ (all_of @ 10.31/1.93 ((('#C') @ in @ 10.31/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 10.31/1.93 ((('#S') @ ((('#B') @ ('#S') @ 10.31/1.93 ((('#B') @ ((('#B') @ (=>))) @ 10.31/1.93 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))) @ 10.31/1.93 lessis)))))), 10.31/1.93 inference('rw', [status(thm)], [zip_derived_cl68, '0'])). 10.31/1.93 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 10.31/1.93 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 10.31/1.93 thf('13', plain, 10.31/1.93 (![X0:( $i > $o ),X1:( $i > $o )]: 10.31/1.93 ( ( all_of @ X0 @ X1 ) <=> 10.31/1.93 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 10.31/1.93 inference('rw.lit', [status(esa)], [def_all_of])). 10.31/1.93 thf(zip_derived_cl354, plain, 10.31/1.93 ( (((!!) @ (^[Y0 : $i]: 10.31/1.93 (((is_of @ Y0 @ 10.31/1.93 ((('#C') @ in @ 10.31/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 10.31/1.93 ((('#B') @ (all_of @ 10.31/1.93 ((('#C') @ in @ 10.31/1.93 (d_Sep @ omega @ 10.31/1.93 ((('#C') @ (!=) @ emptyset)))))) @ 10.31/1.93 ((('#S') @ ((('#B') @ ('#S') @ 10.31/1.93 ((('#B') @ ((('#B') @ (=>))) @ 10.31/1.93 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))) @ 10.31/1.93 lessis)) @ 10.31/1.93 Y0)))))))), 10.31/1.93 inference('rw_clause', [status(thm)], [zip_derived_cl353, '13'])). 10.31/1.93 thf(zip_derived_cl355, plain, 10.31/1.93 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 10.31/1.93 ((('#C') @ is_of @ 10.31/1.93 ((('#C') @ in @ 10.31/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @ 10.31/1.93 ((('#B') @ (all_of @ 10.31/1.93 ((('#C') @ in @ 10.31/1.93 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 10.31/1.93 ((('#S') @ ((('#B') @ ('#S') @ 10.31/1.93 ((('#B') @ ((('#B') @ (=>))) @ 10.31/1.93 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))) @ 10.31/1.93 lessis))))))))), 10.31/1.93 inference('comb-normalize', [status(thm)], [zip_derived_cl354])). 10.31/1.93 thf(zip_derived_cl356, plain, 10.31/1.93 (![X2 : $i]: 10.31/1.93 (((is_of @ X2 @ 10.31/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 10.31/1.93 (all_of @ 10.31/1.93 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 10.31/1.93 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (d_29_ii @ X2))))) @ 10.31/1.94 (lessis @ X2))))))), 10.31/1.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl355])). 10.31/1.94 thf(zip_derived_cl357, plain, 10.31/1.94 (![X2 : $i]: 10.31/1.94 (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 10.31/1.94 (all_of @ 10.31/1.94 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 10.31/1.94 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (d_29_ii @ X2))))) @ 10.31/1.94 (lessis @ X2))))))), 10.31/1.94 inference('rw', [status(thm)], [zip_derived_cl356, '2'])). 10.31/1.94 thf(zip_derived_cl358, plain, 10.31/1.94 (![X2 : $i]: 10.31/1.94 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | (all_of @ 10.31/1.94 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 10.31/1.94 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (d_29_ii @ X2))))) @ 10.31/1.94 (lessis @ X2)))))), 10.31/1.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl357])). 10.31/1.94 thf(zip_derived_cl359, plain, 10.31/1.94 (![X0 : $i]: 10.31/1.94 ( (((!!) @ (^[Y0 : $i]: 10.31/1.94 (((is_of @ Y0 @ 10.31/1.94 ((('#C') @ in @ 10.31/1.94 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 10.31/1.94 ((('#S') @ ((('#B') @ (=>) @ 10.31/1.94 ((('#B') @ d_not @ (d_29_ii @ X0))))) @ 10.31/1.94 (lessis @ X0) @ Y0))))))) 10.31/1.94 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.31/1.94 inference('rw_clause', [status(thm)], [zip_derived_cl358, '13'])). 10.31/1.94 thf(zip_derived_cl360, plain, 10.31/1.94 (![X0 : $i]: 10.31/1.94 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 10.31/1.94 ((('#C') @ is_of @ 10.31/1.94 ((('#C') @ in @ 10.31/1.94 (d_Sep @ omega @ 10.31/1.94 ((('#C') @ (!=) @ emptyset))))))))) @ 10.31/1.94 ((('#S') @ ((('#B') @ (=>) @ 10.31/1.94 ((('#B') @ d_not @ (d_29_ii @ X0))))) @ 10.31/1.94 (lessis @ X0))))))) 10.31/1.94 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.31/1.94 inference('comb-normalize', [status(thm)], [zip_derived_cl359])). 10.31/1.94 thf(zip_derived_cl361, plain, 10.31/1.94 (![X0 : $i, X2 : $i]: 10.31/1.94 ( (((is_of @ X2 @ 10.31/1.94 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 10.31/1.94 (((d_not @ (d_29_ii @ X0 @ X2)) => (lessis @ X0 @ X2))))) 10.31/1.94 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.31/1.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl360])). 10.31/1.94 thf(zip_derived_cl362, plain, 10.31/1.94 (![X0 : $i, X2 : $i]: 10.31/1.94 ( (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 10.31/1.94 (((imp @ 10.31/1.94 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X0 @ X2)) @ 10.31/1.94 ($false)) => (imp @ 10.31/1.94 (imp @ 10.31/1.94 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X2 @ X0)) @ 10.31/1.94 ($false)) @ 10.31/1.94 (((X0) = (X2)))))))) 10.31/1.94 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.31/1.94 inference('rw', [status(thm)], 10.31/1.94 [zip_derived_cl361, '2', '3', '3', '4', '5', '0', '6', '7', 10.31/1.94 '7', '8', '9', '10'])). 10.31/1.94 thf(zip_derived_cl363, plain, 10.31/1.94 (![X0 : $i, X2 : $i]: 10.31/1.94 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | (((imp @ 10.31/1.94 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X0 @ X2)) @ 10.31/1.94 ($false)) => (imp @ 10.31/1.94 (imp @ 10.31/1.94 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X2 @ X0)) @ 10.31/1.94 ($false)) @ 10.31/1.94 (((X0) = (X2)))))) 10.31/1.94 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.31/1.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl362])). 10.31/1.94 thf(zip_derived_cl364, plain, 10.31/1.94 (![X0 : $i, X2 : $i]: 10.31/1.94 (~ (imp @ 10.31/1.94 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X0 @ X2)) @ 10.31/1.94 ($false)) 10.31/1.94 | (imp @ 10.31/1.94 (imp @ 10.31/1.94 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X2 @ X0)) @ 10.31/1.94 ($false)) @ 10.31/1.94 (((X0) = (X2)))) 10.31/1.94 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | ~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.31/1.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl363])). 10.31/1.94 thf(zip_derived_cl365, plain, 10.31/1.94 (![X0 : $i, X1 : $i]: 10.31/1.94 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X1 @ X0)) => ($false))) 10.31/1.94 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | (imp @ 10.31/1.94 (imp @ 10.31/1.94 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X0 @ X1)) @ 10.31/1.94 ($false)) @ 10.31/1.94 (((X1) = (X0)))))), 10.31/1.94 inference('rw_clause', [status(thm)], [zip_derived_cl364, '12'])). 10.31/1.94 thf(zip_derived_cl366, plain, 10.31/1.94 (![X0 : $i, X1 : $i]: 10.31/1.94 (~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X1 @ X0)))) 10.31/1.94 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | (imp @ 10.31/1.94 (imp @ 10.31/1.94 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X0 @ X1)) @ 10.31/1.94 ($false)) @ 10.31/1.94 (((X1) = (X0)))))), 10.31/1.94 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl365])). 10.31/1.94 thf(zip_derived_cl367, plain, 10.31/1.94 (![X0 : $i, X1 : $i]: 10.31/1.94 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X1 @ X0)) 10.31/1.94 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | (imp @ 10.31/1.94 (imp @ 10.31/1.94 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X0 @ X1)) @ 10.31/1.94 ($false)) @ 10.31/1.94 (((X1) = (X0)))))), 10.31/1.94 inference('simplify nested equalities', [status(thm)], 10.31/1.94 [zip_derived_cl366])). 10.31/1.94 thf(zip_derived_cl368, plain, 10.31/1.94 (![X0 : $i, X1 : $i]: 10.31/1.94 ( (((imp @ 10.31/1.94 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X1 @ X0)) @ 10.31/1.94 ($false)) => (((X0) = (X1))))) 10.31/1.94 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X0 @ X1)))), 10.31/1.94 inference('rw_clause', [status(thm)], [zip_derived_cl367, '11'])). 10.31/1.94 thf(zip_derived_cl369, plain, 10.31/1.94 (![X0 : $i, X1 : $i]: 10.31/1.94 (~ (imp @ 10.31/1.94 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X1 @ X0)) @ 10.31/1.94 ($false)) 10.31/1.94 | (((X0) = (X1))) 10.31/1.94 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X0 @ X1)) 10.31/1.94 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.31/1.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl368])). 10.31/1.94 thf(zip_derived_cl370, plain, 10.31/1.94 (![X0 : $i, X1 : $i]: 10.31/1.94 (~ (imp @ 10.31/1.94 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X1 @ X0)) @ 10.31/1.94 ($false)) 10.31/1.94 | ((X0) = (X1)) 10.31/1.94 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X0 @ X1)) 10.31/1.94 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.31/1.94 inference('simplify nested equalities', [status(thm)], 10.31/1.94 [zip_derived_cl369])). 10.31/1.94 thf(zip_derived_cl371, plain, 10.31/1.94 (![X0 : $i, X1 : $i]: 10.31/1.94 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X1 @ X0)) => ($false))) 10.31/1.94 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X0 @ X1)) 10.31/1.94 | ((X0) = (X1)))), 10.31/1.94 inference('rw_clause', [status(thm)], [zip_derived_cl370, '12'])). 10.31/1.94 thf(zip_derived_cl372, plain, 10.31/1.94 (![X0 : $i, X1 : $i]: 10.31/1.94 (~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X1 @ X0)))) 10.31/1.94 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X0 @ X1)) 10.31/1.94 | ((X0) = (X1)))), 10.31/1.94 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl371])). 10.31/1.94 thf(zip_derived_cl373, plain, 10.31/1.94 (![X0 : $i, X1 : $i]: 10.31/1.94 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X1 @ X0)) 10.31/1.94 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ X0 @ X1)) 10.31/1.94 | ((X0) = (X1)))), 10.31/1.94 inference('simplify nested equalities', [status(thm)], 10.31/1.94 [zip_derived_cl372])). 10.31/1.94 thf(zip_derived_cl1822, plain, 10.31/1.94 (((('#sk1') = ('#sk2')) 10.31/1.94 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ '#sk1' @ '#sk2')) 10.31/1.94 | ~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.31/1.94 | ~ (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.31/1.94 inference('sup+', [status(thm)], [zip_derived_cl193, zip_derived_cl373])). 10.31/1.94 thf(zip_derived_cl180, plain, 10.31/1.94 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))), 10.31/1.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])). 10.31/1.94 thf(zip_derived_cl174, plain, 10.31/1.94 ( (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))), 10.31/1.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])). 10.31/1.94 thf(zip_derived_cl1842, plain, 10.31/1.94 (((('#sk1') = ('#sk2')) 10.31/1.94 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ '#sk1' @ '#sk2')))), 10.31/1.94 inference('demod', [status(thm)], 10.31/1.94 [zip_derived_cl1822, zip_derived_cl180, zip_derived_cl174])). 10.31/1.94 thf(zip_derived_cl189, plain, (~ ((('#sk1') = ('#sk2')))), 10.31/1.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl187])). 10.31/1.94 thf(zip_derived_cl191, plain, ((('#sk1') != ('#sk2'))), 10.31/1.94 inference('simplify nested equalities', [status(thm)], 10.31/1.94 [zip_derived_cl189])). 10.31/1.94 thf(zip_derived_cl1843, plain, 10.31/1.94 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.31/1.94 (diffprop @ '#sk1' @ '#sk2'))), 10.31/1.94 inference('simplify_reflect-', [status(thm)], 10.31/1.94 [zip_derived_cl1842, zip_derived_cl191])). 10.31/1.94 thf(zip_derived_cl2059, plain, ($false), 10.31/1.94 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl1843])). 10.31/1.94 10.31/1.94 % SZS output end Refutation 10.31/1.94 10.31/1.94 10.31/1.94 % Terminating... 10.64/2.07 % Runner terminated. 10.66/2.08 % Zipperpin 1.5 exiting 10.66/2.09 EOF