0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.dhAOf0Immc 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 : 1440 0.15/0.36 % WCLimit : 180 0.15/0.36 % DateTime : Mon Jul 3 09:27:24 EDT 2023 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 0.54/0.69 % Total configuration time : 828 0.54/0.69 % Estimated wc time : 1656 0.54/0.69 % Estimated cpu time (8 cpus) : 207.0 0.59/0.81 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.59/1.07 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.59/1.08 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.59/1.08 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.59/1.08 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 2.12/1.20 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 2.31/1.24 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 2.31/1.26 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 11.06/3.08 % Solved by lams/40_b.comb.sh. 11.06/3.08 % done 137 iterations in 1.758s 11.06/3.08 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 11.06/3.08 % SZS output start Refutation 11.06/3.08 thf(emptyset_type, type, emptyset: $i). 11.06/3.08 thf(lessis_type, type, lessis: $i > $i > $o). 11.06/3.08 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 11.06/3.08 thf('#sk2_type', type, '#sk2': $i). 11.06/3.08 thf(omega_type, type, omega: $i). 11.06/3.08 thf(d_not_type, type, d_not: $o > $o). 11.06/3.08 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 11.06/3.08 thf(in_type, type, in: $i > $i > $o). 11.06/3.08 thf(moreis_type, type, moreis: $i > $i > $o). 11.06/3.08 thf(e_is_type, type, e_is: $i > $i > $i > $o). 11.06/3.08 thf(nat_type, type, nat: $i). 11.06/3.08 thf(iii_type, type, iii: $i > $i > $o). 11.06/3.08 thf(l_or_type, type, l_or: $o > $o > $o). 11.06/3.08 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 11.06/3.08 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 11.06/3.08 thf('#sk1_type', type, '#sk1': $i). 11.06/3.08 thf(imp_type, type, imp: $o > $o > $o). 11.06/3.08 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 11.06/3.08 thf(n_is_type, type, n_is: $i > $i > $o). 11.06/3.08 thf(n_some_type, type, n_some: ($i > $o) > $o). 11.06/3.08 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o). 11.06/3.08 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 11.06/3.08 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 11.06/3.08 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 11.06/3.08 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 11.06/3.08 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 11.06/3.08 thf(satz10k, conjecture, 11.06/3.08 (all_of @ 11.06/3.08 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 11.06/3.08 ( ^[X0:$i]: 11.06/3.08 ( all_of @ 11.06/3.08 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 11.06/3.08 ( ^[X1:$i]: 11.06/3.08 ( ( d_not @ ( lessis @ X0 @ X1 ) ) => ( d_29_ii @ X0 @ X1 ) ) ) ) ))). 11.06/3.08 thf(zf_stmt_0, negated_conjecture, 11.06/3.08 (~( all_of @ 11.06/3.08 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 11.06/3.08 ( ^[X0:$i]: 11.06/3.08 ( all_of @ 11.06/3.08 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 11.06/3.08 ( ^[X1:$i]: 11.06/3.08 ( ( d_not @ ( lessis @ X0 @ X1 ) ) => ( d_29_ii @ X0 @ X1 ) ) ) ) ) )), 11.06/3.08 inference('cnf.neg', [status(esa)], [satz10k])). 11.06/3.08 thf(zip_derived_cl107, plain, 11.06/3.08 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 11.06/3.08 (^[Y0 : $i]: 11.06/3.08 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 11.06/3.08 (^[Y1 : $i]: 11.06/3.08 (((d_not @ (lessis @ Y0 @ Y1)) => (d_29_ii @ Y0 @ Y1)))))))), 11.06/3.08 inference('cnf', [status(esa)], [zf_stmt_0])). 11.06/3.08 thf(zip_derived_cl108, plain, 11.06/3.08 (~ (all_of @ ((('#C') @ in @ nat)) @ 11.06/3.08 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 11.06/3.08 ((('#S') @ ((('#B') @ ('#S') @ 11.06/3.08 ((('#B') @ ((('#B') @ (=>))) @ 11.06/3.08 ((('#B') @ ((('#B') @ d_not)) @ lessis)))))) @ 11.06/3.08 d_29_ii)))))), 11.06/3.08 inference('lams2combs', [status(thm)], [zip_derived_cl107])). 11.06/3.08 thf(def_nat, axiom,(( nat ) = 11.06/3.08 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))). 11.06/3.08 thf('0', plain, 11.06/3.08 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )), 11.06/3.08 define([status(thm)])). 11.06/3.08 thf(zip_derived_cl169, plain, 11.06/3.08 (~ (all_of @ 11.06/3.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 11.06/3.08 ((('#B') @ (all_of @ 11.06/3.08 ((('#C') @ in @ 11.06/3.08 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 11.06/3.08 ((('#S') @ ((('#B') @ ('#S') @ 11.06/3.08 ((('#B') @ ((('#B') @ (=>))) @ 11.06/3.08 ((('#B') @ ((('#B') @ d_not)) @ lessis)))))) @ 11.06/3.08 d_29_ii)))))), 11.06/3.08 inference('rw', [status(thm)], [zip_derived_cl108, '0'])). 11.06/3.08 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 11.06/3.08 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 11.06/3.08 thf('1', plain, 11.06/3.08 (![X0:( $i > $o ),X1:( $i > $o )]: 11.06/3.08 ( ( ~( all_of @ X0 @ X1 ) ) <=> 11.06/3.08 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 11.06/3.08 inference('rw.lit', [status(esa)], [def_all_of])). 11.06/3.08 thf(zip_derived_cl170, plain, 11.06/3.08 (~ (((!!) @ (^[Y0 : $i]: 11.06/3.08 (((is_of @ Y0 @ 11.06/3.08 ((('#C') @ in @ 11.06/3.08 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 11.06/3.08 ((('#B') @ (all_of @ 11.06/3.08 ((('#C') @ in @ 11.06/3.08 (d_Sep @ omega @ 11.06/3.08 ((('#C') @ (!=) @ emptyset)))))) @ 11.06/3.08 ((('#S') @ ((('#B') @ ('#S') @ 11.06/3.08 ((('#B') @ ((('#B') @ (=>))) @ 11.06/3.08 ((('#B') @ ((('#B') @ d_not)) @ lessis)))))) @ 11.06/3.08 d_29_ii)) @ 11.06/3.08 Y0)))))))), 11.06/3.08 inference('rw_clause', [status(thm)], [zip_derived_cl169, '1'])). 11.06/3.08 thf(zip_derived_cl171, plain, 11.06/3.08 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 11.06/3.08 ((('#C') @ is_of @ 11.06/3.08 ((('#C') @ in @ 11.06/3.08 (d_Sep @ omega @ 11.06/3.08 ((('#C') @ (!=) @ emptyset))))))))) @ 11.06/3.08 ((('#B') @ (all_of @ 11.06/3.08 ((('#C') @ in @ 11.06/3.08 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 11.06/3.08 ((('#S') @ ((('#B') @ ('#S') @ 11.06/3.08 ((('#B') @ ((('#B') @ (=>))) @ 11.06/3.08 ((('#B') @ ((('#B') @ d_not)) @ lessis)))))) @ 11.06/3.08 d_29_ii))))))))), 11.06/3.08 inference('comb-normalize', [status(thm)], [zip_derived_cl170])). 11.06/3.08 thf(zip_derived_cl172, plain, 11.06/3.08 (~ (((is_of @ '#sk1' @ 11.06/3.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 11.06/3.08 (all_of @ 11.06/3.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 11.06/3.08 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (lessis @ '#sk1'))))) @ 11.06/3.08 (d_29_ii @ '#sk1'))))))), 11.06/3.08 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl171])). 11.06/3.08 thf(def_is_of, axiom,(( is_of @ (X1)@ (X0)) = ((X0 @ X1)))). 11.06/3.08 thf('2', plain, 11.06/3.08 (![X0:( $i > $o ),X1:$i]: ( ( is_of @ X1 @ X0 ) = ( X0 @ X1 ) )), 11.06/3.08 define([status(thm)])). 11.06/3.08 thf(zip_derived_cl173, plain, 11.06/3.08 (~ (((in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 11.06/3.08 (all_of @ 11.06/3.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 11.06/3.08 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (lessis @ '#sk1'))))) @ 11.06/3.08 (d_29_ii @ '#sk1'))))))), 11.06/3.08 inference('rw', [status(thm)], [zip_derived_cl172, '2'])). 11.06/3.08 thf(zip_derived_cl175, plain, 11.06/3.08 (~ (all_of @ 11.06/3.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 11.06/3.08 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (lessis @ '#sk1'))))) @ 11.06/3.08 (d_29_ii @ '#sk1'))))), 11.06/3.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])). 11.06/3.08 thf(zip_derived_cl176, plain, 11.06/3.08 (~ (((!!) @ (^[Y0 : $i]: 11.06/3.08 (((is_of @ Y0 @ 11.06/3.08 ((('#C') @ in @ 11.06/3.08 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 11.06/3.08 ((('#S') @ ((('#B') @ (=>) @ 11.06/3.08 ((('#B') @ d_not @ (lessis @ '#sk1'))))) @ 11.06/3.08 (d_29_ii @ '#sk1') @ Y0)))))))), 11.06/3.08 inference('rw_clause', [status(thm)], [zip_derived_cl175, '1'])). 11.06/3.08 thf(zip_derived_cl177, plain, 11.06/3.08 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 11.06/3.08 ((('#C') @ is_of @ 11.06/3.08 ((('#C') @ in @ 11.06/3.08 (d_Sep @ omega @ 11.06/3.08 ((('#C') @ (!=) @ emptyset))))))))) @ 11.06/3.08 ((('#S') @ ((('#B') @ (=>) @ 11.06/3.08 ((('#B') @ d_not @ (lessis @ '#sk1'))))) @ 11.06/3.08 (d_29_ii @ '#sk1')))))))), 11.06/3.08 inference('comb-normalize', [status(thm)], [zip_derived_cl176])). 11.06/3.08 thf(zip_derived_cl178, plain, 11.06/3.08 (~ (((is_of @ '#sk2' @ 11.06/3.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 11.06/3.08 (((d_not @ (lessis @ '#sk1' @ '#sk2')) => (d_29_ii @ '#sk1' @ 11.06/3.08 '#sk2')))))), 11.06/3.08 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl177])). 11.06/3.08 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 11.06/3.08 thf('3', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 11.06/3.08 define([status(thm)])). 11.06/3.08 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 11.06/3.08 thf('4', plain, 11.06/3.08 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 11.06/3.08 define([status(thm)])). 11.06/3.08 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))). 11.06/3.08 thf('5', plain, 11.06/3.08 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )), 11.06/3.08 define([status(thm)])). 11.06/3.08 thf(def_n_is, axiom,(( n_is @ (X0)@ (X1)) = ((e_is @ nat @ X0 @ X1)))). 11.06/3.08 thf('6', plain, 11.06/3.08 (![X1:$i,X0:$i]: ( ( n_is @ X0 @ X1 ) = ( e_is @ nat @ X0 @ X1 ) )), 11.06/3.08 define([status(thm)])). 11.06/3.08 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))). 11.06/3.08 thf('7', plain, 11.06/3.08 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )), 11.06/3.08 define([status(thm)])). 11.06/3.08 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) = 11.06/3.08 ((n_some @ (diffprop @ X0 @ X1))))). 11.06/3.08 thf('8', plain, 11.06/3.08 (![X1:$i,X0:$i]: 11.06/3.08 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 11.06/3.08 define([status(thm)])). 11.06/3.08 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))). 11.06/3.08 thf('9', plain, 11.06/3.08 (![X1:$i,X0:$i]: 11.06/3.08 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 11.06/3.08 define([status(thm)])). 11.06/3.08 thf(def_lessis, axiom,(( lessis @ (X0)@ (X1)) = 11.06/3.08 ((l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1))))). 11.06/3.08 thf('10', plain, 11.06/3.08 (![X1:$i,X0:$i]: 11.06/3.08 ( ( lessis @ X0 @ X1 ) = 11.06/3.08 ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )), 11.06/3.08 define([status(thm)])). 11.06/3.08 thf(zip_derived_cl179, plain, 11.06/3.08 (~ (((in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 11.06/3.08 (((imp @ 11.06/3.08 (imp @ 11.06/3.08 (imp @ 11.06/3.08 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk2' @ '#sk1')) @ 11.06/3.08 ($false)) @ 11.06/3.08 ((('#sk1') = ('#sk2')))) @ 11.06/3.08 ($false)) => (l_some @ 11.06/3.08 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk1' @ '#sk2'))))))), 11.06/3.08 inference('rw', [status(thm)], 11.06/3.08 [zip_derived_cl178, '2', '3', '3', '4', '5', '0', '6', '7', 11.06/3.08 '7', '8', '9', '10'])). 11.06/3.08 thf(zip_derived_cl181, plain, 11.06/3.08 (~ (((imp @ 11.06/3.08 (imp @ 11.06/3.08 (imp @ 11.06/3.08 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk2' @ '#sk1')) @ 11.06/3.08 ($false)) @ 11.06/3.08 ((('#sk1') = ('#sk2')))) @ 11.06/3.08 ($false)) => (l_some @ 11.06/3.08 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk1' @ '#sk2'))))), 11.06/3.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])). 11.06/3.08 thf(zip_derived_cl183, plain, 11.06/3.08 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk1' @ '#sk2'))), 11.06/3.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl181])). 11.06/3.08 thf(zip_derived_cl182, plain, 11.06/3.08 ( (imp @ 11.06/3.08 (imp @ 11.06/3.08 (imp @ 11.06/3.08 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk2' @ '#sk1')) @ 11.06/3.08 ($false)) @ 11.06/3.08 ((('#sk1') = ('#sk2')))) @ 11.06/3.08 ($false))), 11.06/3.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl181])). 11.06/3.08 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 11.06/3.08 thf('11', plain, 11.06/3.08 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 11.06/3.08 inference('rw.lit', [status(esa)], [def_imp])). 11.06/3.08 thf(zip_derived_cl184, plain, 11.06/3.08 ( (((imp @ 11.06/3.08 (imp @ 11.06/3.08 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk2' @ '#sk1')) @ 11.06/3.08 ($false)) @ 11.06/3.08 ((('#sk1') = ('#sk2')))) => ($false)))), 11.06/3.08 inference('rw_clause', [status(thm)], [zip_derived_cl182, '11'])). 11.06/3.08 thf(zip_derived_cl185, plain, 11.06/3.08 ( (((~) @ (imp @ 11.06/3.08 (imp @ 11.06/3.08 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk2' @ '#sk1')) @ 11.06/3.08 ($false)) @ 11.06/3.08 ((('#sk1') = ('#sk2'))))))), 11.06/3.08 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl184])). 11.06/3.08 thf(zip_derived_cl186, plain, 11.06/3.08 (~ (imp @ 11.06/3.08 (imp @ 11.06/3.08 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk2' @ '#sk1')) @ 11.06/3.08 ($false)) @ 11.06/3.08 ((('#sk1') = ('#sk2'))))), 11.06/3.08 inference('simplify nested equalities', [status(thm)], 11.06/3.08 [zip_derived_cl185])). 11.06/3.08 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 11.06/3.08 thf('12', plain, 11.06/3.08 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 11.06/3.08 inference('rw.lit', [status(esa)], [def_imp])). 11.06/3.08 thf(zip_derived_cl187, plain, 11.06/3.08 (~ (((imp @ 11.06/3.08 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk2' @ '#sk1')) @ 11.06/3.08 ($false)) => ((('#sk1') = ('#sk2')))))), 11.06/3.08 inference('rw_clause', [status(thm)], [zip_derived_cl186, '12'])). 11.06/3.08 thf(zip_derived_cl188, plain, 11.06/3.08 ( (imp @ 11.06/3.08 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk2' @ '#sk1')) @ 11.06/3.08 ($false))), 11.06/3.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl187])). 11.06/3.08 thf(zip_derived_cl190, plain, 11.06/3.08 ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk2' @ '#sk1')) => ($false)))), 11.06/3.08 inference('rw_clause', [status(thm)], [zip_derived_cl188, '11'])). 11.06/3.08 thf(zip_derived_cl192, plain, 11.06/3.08 ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk2' @ '#sk1'))))), 11.06/3.08 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl190])). 11.06/3.08 thf(zip_derived_cl193, plain, 11.06/3.08 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk2' @ '#sk1'))), 11.06/3.08 inference('simplify nested equalities', [status(thm)], 11.06/3.08 [zip_derived_cl192])). 11.06/3.08 thf(satz10j, axiom, 11.06/3.08 (all_of @ 11.06/3.08 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 11.06/3.08 ( ^[X0:$i]: 11.06/3.08 ( all_of @ 11.06/3.08 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 11.06/3.08 ( ^[X1:$i]: ( ( d_not @ ( moreis @ X0 @ X1 ) ) => ( iii @ X0 @ X1 ) ) ) ) ))). 11.06/3.08 thf(zip_derived_cl47, plain, 11.06/3.08 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 11.06/3.08 (^[Y0 : $i]: 11.06/3.08 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 11.06/3.08 (^[Y1 : $i]: (((d_not @ (moreis @ Y0 @ Y1)) => (iii @ Y0 @ Y1)))))))), 11.06/3.08 inference('cnf', [status(esa)], [satz10j])). 11.06/3.08 thf(zip_derived_cl48, plain, 11.06/3.08 ( (all_of @ ((('#C') @ in @ nat)) @ 11.06/3.08 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 11.06/3.08 ((('#S') @ ((('#B') @ ('#S') @ 11.06/3.08 ((('#B') @ ((('#B') @ (=>))) @ 11.06/3.08 ((('#B') @ ((('#B') @ d_not)) @ moreis)))))) @ 11.06/3.08 iii)))))), 11.06/3.08 inference('lams2combs', [status(thm)], [zip_derived_cl47])). 11.06/3.08 thf(zip_derived_cl309, plain, 11.06/3.08 ( (all_of @ 11.06/3.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 11.06/3.08 ((('#B') @ (all_of @ 11.06/3.08 ((('#C') @ in @ 11.06/3.08 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 11.06/3.08 ((('#S') @ ((('#B') @ ('#S') @ 11.06/3.08 ((('#B') @ ((('#B') @ (=>))) @ 11.06/3.08 ((('#B') @ ((('#B') @ d_not)) @ moreis)))))) @ 11.06/3.08 iii)))))), 11.06/3.08 inference('rw', [status(thm)], [zip_derived_cl48, '0'])). 11.06/3.08 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 11.06/3.08 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 11.06/3.08 thf('13', plain, 11.06/3.08 (![X0:( $i > $o ),X1:( $i > $o )]: 11.06/3.08 ( ( all_of @ X0 @ X1 ) <=> 11.06/3.08 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 11.06/3.08 inference('rw.lit', [status(esa)], [def_all_of])). 11.06/3.08 thf(zip_derived_cl310, plain, 11.06/3.08 ( (((!!) @ (^[Y0 : $i]: 11.06/3.08 (((is_of @ Y0 @ 11.06/3.08 ((('#C') @ in @ 11.06/3.08 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 11.06/3.08 ((('#B') @ (all_of @ 11.06/3.08 ((('#C') @ in @ 11.06/3.08 (d_Sep @ omega @ 11.06/3.08 ((('#C') @ (!=) @ emptyset)))))) @ 11.06/3.08 ((('#S') @ ((('#B') @ ('#S') @ 11.06/3.08 ((('#B') @ ((('#B') @ (=>))) @ 11.06/3.08 ((('#B') @ ((('#B') @ d_not)) @ moreis)))))) @ 11.06/3.08 iii)) @ 11.06/3.08 Y0)))))))), 11.06/3.08 inference('rw_clause', [status(thm)], [zip_derived_cl309, '13'])). 11.06/3.08 thf(zip_derived_cl311, plain, 11.06/3.08 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 11.06/3.08 ((('#C') @ is_of @ 11.06/3.08 ((('#C') @ in @ 11.06/3.08 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @ 11.06/3.08 ((('#B') @ (all_of @ 11.06/3.08 ((('#C') @ in @ 11.06/3.08 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 11.06/3.08 ((('#S') @ ((('#B') @ ('#S') @ 11.06/3.08 ((('#B') @ ((('#B') @ (=>))) @ 11.06/3.08 ((('#B') @ ((('#B') @ d_not)) @ moreis)))))) @ 11.06/3.08 iii))))))))), 11.06/3.08 inference('comb-normalize', [status(thm)], [zip_derived_cl310])). 11.06/3.08 thf(zip_derived_cl312, plain, 11.06/3.08 (![X2 : $i]: 11.06/3.08 (((is_of @ X2 @ 11.06/3.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 11.06/3.08 (all_of @ 11.06/3.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 11.06/3.08 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (moreis @ X2))))) @ 11.06/3.08 (iii @ X2))))))), 11.06/3.08 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl311])). 11.06/3.08 thf(zip_derived_cl313, plain, 11.06/3.08 (![X2 : $i]: 11.06/3.08 (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 11.06/3.08 (all_of @ 11.06/3.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 11.06/3.08 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (moreis @ X2))))) @ 11.06/3.08 (iii @ X2))))))), 11.06/3.08 inference('rw', [status(thm)], [zip_derived_cl312, '2'])). 11.06/3.08 thf(zip_derived_cl314, plain, 11.06/3.08 (![X2 : $i]: 11.06/3.08 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | (all_of @ 11.06/3.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 11.06/3.08 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (moreis @ X2))))) @ 11.06/3.08 (iii @ X2)))))), 11.06/3.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl313])). 11.06/3.08 thf(zip_derived_cl315, plain, 11.06/3.08 (![X0 : $i]: 11.06/3.08 ( (((!!) @ (^[Y0 : $i]: 11.06/3.08 (((is_of @ Y0 @ 11.06/3.08 ((('#C') @ in @ 11.06/3.08 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 11.06/3.08 ((('#S') @ ((('#B') @ (=>) @ 11.06/3.08 ((('#B') @ d_not @ (moreis @ X0))))) @ 11.06/3.08 (iii @ X0) @ Y0))))))) 11.06/3.08 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 11.06/3.08 inference('rw_clause', [status(thm)], [zip_derived_cl314, '13'])). 11.06/3.08 thf(zip_derived_cl316, plain, 11.06/3.08 (![X0 : $i]: 11.06/3.08 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 11.06/3.08 ((('#C') @ is_of @ 11.06/3.08 ((('#C') @ in @ 11.06/3.08 (d_Sep @ omega @ 11.06/3.08 ((('#C') @ (!=) @ emptyset))))))))) @ 11.06/3.08 ((('#S') @ ((('#B') @ (=>) @ 11.06/3.08 ((('#B') @ d_not @ (moreis @ X0))))) @ 11.06/3.08 (iii @ X0))))))) 11.06/3.08 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 11.06/3.08 inference('comb-normalize', [status(thm)], [zip_derived_cl315])). 11.06/3.08 thf(zip_derived_cl317, plain, 11.06/3.08 (![X0 : $i, X2 : $i]: 11.06/3.08 ( (((is_of @ X2 @ 11.06/3.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 11.06/3.08 (((d_not @ (moreis @ X0 @ X2)) => (iii @ X0 @ X2))))) 11.06/3.08 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 11.06/3.08 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl316])). 11.06/3.08 thf(def_moreis, axiom,(( moreis @ (X0)@ (X1)) = 11.06/3.08 ((l_or @ (d_29_ii @ X0 @ X1) @ (n_is @ X0 @ X1))))). 11.06/3.08 thf('14', plain, 11.06/3.08 (![X1:$i,X0:$i]: 11.06/3.08 ( ( moreis @ X0 @ X1 ) = 11.06/3.08 ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )), 11.06/3.08 define([status(thm)])). 11.06/3.08 thf(zip_derived_cl318, plain, 11.06/3.08 (![X0 : $i, X2 : $i]: 11.06/3.08 ( (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 11.06/3.08 (((imp @ 11.06/3.08 (imp @ 11.06/3.08 (imp @ 11.06/3.08 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X0 @ X2)) @ 11.06/3.08 ($false)) @ 11.06/3.08 (((X0) = (X2)))) @ 11.06/3.08 ($false)) => (l_some @ 11.06/3.08 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X2 @ X0)))))) 11.06/3.08 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 11.06/3.08 inference('rw', [status(thm)], 11.06/3.08 [zip_derived_cl317, '2', '3', '3', '4', '5', '0', '6', '7', 11.06/3.08 '7', '8', '9', '14'])). 11.06/3.08 thf(zip_derived_cl319, plain, 11.06/3.08 (![X0 : $i, X2 : $i]: 11.06/3.08 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | (((imp @ 11.06/3.08 (imp @ 11.06/3.08 (imp @ 11.06/3.08 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X0 @ X2)) @ 11.06/3.08 ($false)) @ 11.06/3.08 (((X0) = (X2)))) @ 11.06/3.08 ($false)) => (l_some @ 11.06/3.08 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X2 @ X0)))) 11.06/3.08 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 11.06/3.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl318])). 11.06/3.08 thf(zip_derived_cl320, plain, 11.06/3.08 (![X0 : $i, X2 : $i]: 11.06/3.08 (~ (imp @ 11.06/3.08 (imp @ 11.06/3.08 (imp @ 11.06/3.08 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X0 @ X2)) @ 11.06/3.08 ($false)) @ 11.06/3.08 (((X0) = (X2)))) @ 11.06/3.08 ($false)) 11.06/3.08 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X2 @ X0)) 11.06/3.08 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | ~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 11.06/3.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl319])). 11.06/3.08 thf(zip_derived_cl321, plain, 11.06/3.08 (![X0 : $i, X1 : $i]: 11.06/3.08 (~ (((imp @ 11.06/3.08 (imp @ 11.06/3.08 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X1 @ X0)) @ 11.06/3.08 ($false)) @ 11.06/3.08 (((X1) = (X0)))) => ($false))) 11.06/3.08 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X0 @ X1)))), 11.06/3.08 inference('rw_clause', [status(thm)], [zip_derived_cl320, '12'])). 11.06/3.08 thf(zip_derived_cl322, plain, 11.06/3.08 (![X0 : $i, X1 : $i]: 11.06/3.08 (~ (((~) @ (imp @ 11.06/3.08 (imp @ 11.06/3.08 (l_some @ 11.06/3.08 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X1 @ X0)) @ 11.06/3.08 ($false)) @ 11.06/3.08 (((X1) = (X0)))))) 11.06/3.08 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X0 @ X1)))), 11.06/3.08 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl321])). 11.06/3.08 thf(zip_derived_cl323, plain, 11.06/3.08 (![X0 : $i, X1 : $i]: 11.06/3.08 ( (imp @ 11.06/3.08 (imp @ 11.06/3.08 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X1 @ X0)) @ 11.06/3.08 ($false)) @ 11.06/3.08 (((X1) = (X0)))) 11.06/3.08 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X0 @ X1)))), 11.06/3.08 inference('simplify nested equalities', [status(thm)], 11.06/3.08 [zip_derived_cl322])). 11.06/3.08 thf(zip_derived_cl324, plain, 11.06/3.08 (![X0 : $i, X1 : $i]: 11.06/3.08 ( (((imp @ 11.06/3.08 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X0 @ X1)) @ 11.06/3.08 ($false)) => (((X0) = (X1))))) 11.06/3.08 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X1 @ X0)) 11.06/3.08 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 11.06/3.08 inference('rw_clause', [status(thm)], [zip_derived_cl323, '11'])). 11.06/3.08 thf(zip_derived_cl325, plain, 11.06/3.08 (![X0 : $i, X1 : $i]: 11.06/3.08 (~ (imp @ 11.06/3.08 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X0 @ X1)) @ 11.06/3.08 ($false)) 11.06/3.08 | (((X0) = (X1))) 11.06/3.08 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X1 @ X0)))), 11.06/3.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl324])). 11.06/3.08 thf(zip_derived_cl326, plain, 11.06/3.08 (![X0 : $i, X1 : $i]: 11.06/3.08 (~ (imp @ 11.06/3.08 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X0 @ X1)) @ 11.06/3.08 ($false)) 11.06/3.08 | ((X0) = (X1)) 11.06/3.08 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X1 @ X0)))), 11.06/3.08 inference('simplify nested equalities', [status(thm)], 11.06/3.08 [zip_derived_cl325])). 11.06/3.08 thf(zip_derived_cl327, plain, 11.06/3.08 (![X0 : $i, X1 : $i]: 11.06/3.08 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X0 @ X1)) => ($false))) 11.06/3.08 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X1 @ X0)) 11.06/3.08 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | ((X0) = (X1)))), 11.06/3.08 inference('rw_clause', [status(thm)], [zip_derived_cl326, '12'])). 11.06/3.08 thf(zip_derived_cl328, plain, 11.06/3.08 (![X0 : $i, X1 : $i]: 11.06/3.08 (~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X0 @ X1)))) 11.06/3.08 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X1 @ X0)) 11.06/3.08 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | ((X0) = (X1)))), 11.06/3.08 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl327])). 11.06/3.08 thf(zip_derived_cl329, plain, 11.06/3.08 (![X0 : $i, X1 : $i]: 11.06/3.08 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X0 @ X1)) 11.06/3.08 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ X1 @ X0)) 11.06/3.08 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | ((X0) = (X1)))), 11.06/3.08 inference('simplify nested equalities', [status(thm)], 11.06/3.08 [zip_derived_cl328])). 11.06/3.08 thf(zip_derived_cl1580, plain, 11.06/3.08 (((('#sk2') = ('#sk1')) 11.06/3.08 | ~ (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | ~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 11.06/3.08 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk1' @ '#sk2')))), 11.06/3.08 inference('sup+', [status(thm)], [zip_derived_cl193, zip_derived_cl329])). 11.06/3.08 thf(zip_derived_cl174, plain, 11.06/3.08 ( (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))), 11.06/3.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])). 11.06/3.08 thf(zip_derived_cl180, plain, 11.06/3.08 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))), 11.06/3.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])). 11.06/3.08 thf(zip_derived_cl1594, plain, 11.06/3.08 (((('#sk2') = ('#sk1')) 11.06/3.08 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk1' @ '#sk2')))), 11.06/3.08 inference('demod', [status(thm)], 11.06/3.08 [zip_derived_cl1580, zip_derived_cl174, zip_derived_cl180])). 11.06/3.08 thf(zip_derived_cl189, plain, (~ ((('#sk1') = ('#sk2')))), 11.06/3.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl187])). 11.06/3.08 thf(zip_derived_cl191, plain, ((('#sk1') != ('#sk2'))), 11.06/3.08 inference('simplify nested equalities', [status(thm)], 11.06/3.08 [zip_derived_cl189])). 11.06/3.08 thf(zip_derived_cl1595, plain, 11.06/3.08 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 11.06/3.08 (diffprop @ '#sk1' @ '#sk2'))), 11.06/3.08 inference('simplify_reflect-', [status(thm)], 11.06/3.08 [zip_derived_cl1594, zip_derived_cl191])). 11.06/3.08 thf(zip_derived_cl1714, plain, ($false), 11.06/3.08 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl1595])). 11.06/3.08 11.06/3.08 % SZS output end Refutation 11.06/3.08 11.06/3.08 11.06/3.08 % Terminating... 11.40/3.26 % Runner terminated. 11.40/3.29 % Zipperpin 1.5 exiting 11.40/3.30 EOF