0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Bd1i5cW3Q0 true 0.15/0.36 % Computer : n013.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 : Thu Jul 4 09:53:54 EDT 2024 0.15/0.36 % CPUTime : 0.15/0.36 % Running portfolio for 1440 s 0.15/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.15/0.36 % Number of cores: 8 0.15/0.36 % Python version: Python 3.6.8 0.15/0.36 % Running in HO mode 0.50/0.62 % Total configuration time : 828 0.50/0.62 % Estimated wc time : 1656 0.50/0.62 % Estimated cpu time (8 cpus) : 207.0 0.51/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.51/0.71 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.51/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.51/0.71 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.51/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.51/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.51/0.72 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.52/0.73 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 7.26/1.53 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 16.65/2.71 % Solved by lams/40_b.comb.sh. 16.65/2.71 % done 152 iterations in 1.962s 16.65/2.71 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 16.65/2.71 % SZS output start Refutation 16.65/2.71 thf(emptyset_type, type, emptyset: $i). 16.65/2.71 thf(lessis_type, type, lessis: $i > $i > $o). 16.65/2.71 thf(orec3_type, type, orec3: $o > $o > $o > $o). 16.65/2.71 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 16.65/2.71 thf(ec3_type, type, ec3: $o > $o > $o > $o). 16.65/2.71 thf(l_ec_type, type, l_ec: $o > $o > $o). 16.65/2.71 thf(omega_type, type, omega: $i). 16.65/2.71 thf(d_not_type, type, d_not: $o > $o). 16.65/2.71 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 16.65/2.71 thf(in_type, type, in: $i > $i > $o). 16.65/2.71 thf(and3_type, type, and3: $o > $o > $o > $o). 16.65/2.71 thf('#sk1_type', type, '#sk1': $i). 16.65/2.71 thf(e_is_type, type, e_is: $i > $i > $i > $o). 16.65/2.71 thf(nat_type, type, nat: $i). 16.65/2.71 thf(iii_type, type, iii: $i > $i > $o). 16.65/2.71 thf(l_or_type, type, l_or: $o > $o > $o). 16.65/2.71 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 16.65/2.71 thf('#sk2_type', type, '#sk2': $i). 16.65/2.71 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 16.65/2.71 thf(d_and_type, type, d_and: $o > $o > $o). 16.65/2.71 thf(imp_type, type, imp: $o > $o > $o). 16.65/2.71 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 16.65/2.71 thf(n_is_type, type, n_is: $i > $i > $o). 16.65/2.71 thf(or3_type, type, or3: $o > $o > $o > $o). 16.65/2.71 thf(n_some_type, type, n_some: ($i > $o) > $o). 16.65/2.71 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o). 16.65/2.71 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 16.65/2.71 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 16.65/2.71 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 16.65/2.71 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 16.65/2.71 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 16.65/2.71 thf(satz10e, conjecture, 16.65/2.71 (all_of @ 16.65/2.71 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 16.65/2.71 ( ^[X0:$i]: 16.65/2.71 ( all_of @ 16.65/2.71 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 16.65/2.71 ( ^[X1:$i]: 16.65/2.71 ( ( d_not @ ( d_29_ii @ X0 @ X1 ) ) => ( lessis @ X0 @ X1 ) ) ) ) ))). 16.65/2.71 thf(zf_stmt_0, negated_conjecture, 16.65/2.71 (~( all_of @ 16.65/2.71 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 16.65/2.71 ( ^[X0:$i]: 16.65/2.71 ( all_of @ 16.65/2.71 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 16.65/2.71 ( ^[X1:$i]: 16.65/2.71 ( ( d_not @ ( d_29_ii @ X0 @ X1 ) ) => ( lessis @ X0 @ X1 ) ) ) ) ) )), 16.65/2.71 inference('cnf.neg', [status(esa)], [satz10e])). 16.65/2.71 thf(zip_derived_cl97, plain, 16.65/2.71 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 16.65/2.71 (^[Y0 : $i]: 16.65/2.71 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 16.65/2.71 (^[Y1 : $i]: 16.65/2.71 (((d_not @ (d_29_ii @ Y0 @ Y1)) => (lessis @ Y0 @ Y1)))))))), 16.65/2.71 inference('cnf', [status(esa)], [zf_stmt_0])). 16.65/2.71 thf(zip_derived_cl98, plain, 16.65/2.71 (~ (all_of @ ((('#C') @ in @ nat)) @ 16.65/2.71 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 16.65/2.71 ((('#S') @ ((('#B') @ ('#S') @ 16.65/2.71 ((('#B') @ ((('#B') @ (=>))) @ 16.65/2.71 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))) @ 16.65/2.71 lessis)))))), 16.65/2.71 inference('lams2combs', [status(thm)], [zip_derived_cl97])). 16.65/2.71 thf(def_nat, axiom,(( nat ) = 16.65/2.71 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))). 16.65/2.71 thf('0', plain, 16.65/2.71 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )), 16.65/2.71 define([status(thm)])). 16.65/2.71 thf(zip_derived_cl160, plain, 16.65/2.71 (~ (all_of @ 16.65/2.71 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 16.65/2.71 ((('#B') @ (all_of @ 16.65/2.71 ((('#C') @ in @ 16.65/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 16.65/2.71 ((('#S') @ ((('#B') @ ('#S') @ 16.65/2.71 ((('#B') @ ((('#B') @ (=>))) @ 16.65/2.71 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))) @ 16.65/2.71 lessis)))))), 16.65/2.71 inference('rw', [status(thm)], [zip_derived_cl98, '0'])). 16.65/2.71 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 16.65/2.71 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 16.65/2.71 thf('1', plain, 16.65/2.71 (![X0:( $i > $o ),X1:( $i > $o )]: 16.65/2.71 ( ( ~( all_of @ X0 @ X1 ) ) <=> 16.65/2.71 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 16.65/2.71 inference('rw.lit', [status(esa)], [def_all_of])). 16.65/2.71 thf(zip_derived_cl161, plain, 16.68/2.71 (~ (((!!) @ (^[Y0 : $i]: 16.68/2.71 (((is_of @ Y0 @ 16.68/2.71 ((('#C') @ in @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 16.68/2.71 ((('#B') @ (all_of @ 16.68/2.71 ((('#C') @ in @ 16.68/2.71 (d_Sep @ omega @ 16.68/2.71 ((('#C') @ (!=) @ emptyset)))))) @ 16.68/2.71 ((('#S') @ ((('#B') @ ('#S') @ 16.68/2.71 ((('#B') @ ((('#B') @ (=>))) @ 16.68/2.71 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))) @ 16.68/2.71 lessis)) @ 16.68/2.71 Y0)))))))), 16.68/2.71 inference('rw_clause', [status(thm)], [zip_derived_cl160, '1'])). 16.68/2.71 thf(zip_derived_cl162, plain, 16.68/2.71 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 16.68/2.71 ((('#C') @ is_of @ 16.68/2.71 ((('#C') @ in @ 16.68/2.71 (d_Sep @ omega @ 16.68/2.71 ((('#C') @ (!=) @ emptyset))))))))) @ 16.68/2.71 ((('#B') @ (all_of @ 16.68/2.71 ((('#C') @ in @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 16.68/2.71 ((('#S') @ ((('#B') @ ('#S') @ 16.68/2.71 ((('#B') @ ((('#B') @ (=>))) @ 16.68/2.71 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))) @ 16.68/2.71 lessis))))))))), 16.68/2.71 inference('comb-normalize', [status(thm)], [zip_derived_cl161])). 16.68/2.71 thf(zip_derived_cl163, plain, 16.68/2.71 (~ (((is_of @ '#sk1' @ 16.68/2.71 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 16.68/2.71 (all_of @ 16.68/2.71 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 16.68/2.71 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (d_29_ii @ '#sk1'))))) @ 16.68/2.71 (lessis @ '#sk1'))))))), 16.68/2.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl162])). 16.68/2.71 thf(def_is_of, axiom,(( is_of @ (X1)@ (X0)) = ((X0 @ X1)))). 16.68/2.71 thf('2', plain, 16.68/2.71 (![X0:( $i > $o ),X1:$i]: ( ( is_of @ X1 @ X0 ) = ( X0 @ X1 ) )), 16.68/2.71 define([status(thm)])). 16.68/2.71 thf(zip_derived_cl164, plain, 16.68/2.71 (~ (((in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 16.68/2.71 (all_of @ 16.68/2.71 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 16.68/2.71 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (d_29_ii @ '#sk1'))))) @ 16.68/2.71 (lessis @ '#sk1'))))))), 16.68/2.71 inference('rw', [status(thm)], [zip_derived_cl163, '2'])). 16.68/2.71 thf(zip_derived_cl166, plain, 16.68/2.71 (~ (all_of @ 16.68/2.71 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 16.68/2.71 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (d_29_ii @ '#sk1'))))) @ 16.68/2.71 (lessis @ '#sk1'))))), 16.68/2.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])). 16.68/2.71 thf(zip_derived_cl167, plain, 16.68/2.71 (~ (((!!) @ (^[Y0 : $i]: 16.68/2.71 (((is_of @ Y0 @ 16.68/2.71 ((('#C') @ in @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 16.68/2.71 ((('#S') @ ((('#B') @ (=>) @ 16.68/2.71 ((('#B') @ d_not @ (d_29_ii @ '#sk1'))))) @ 16.68/2.71 (lessis @ '#sk1') @ Y0)))))))), 16.68/2.71 inference('rw_clause', [status(thm)], [zip_derived_cl166, '1'])). 16.68/2.71 thf(zip_derived_cl168, plain, 16.68/2.71 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 16.68/2.71 ((('#C') @ is_of @ 16.68/2.71 ((('#C') @ in @ 16.68/2.71 (d_Sep @ omega @ 16.68/2.71 ((('#C') @ (!=) @ emptyset))))))))) @ 16.68/2.71 ((('#S') @ ((('#B') @ (=>) @ 16.68/2.71 ((('#B') @ d_not @ (d_29_ii @ '#sk1'))))) @ 16.68/2.71 (lessis @ '#sk1')))))))), 16.68/2.71 inference('comb-normalize', [status(thm)], [zip_derived_cl167])). 16.68/2.71 thf(zip_derived_cl169, plain, 16.68/2.71 (~ (((is_of @ '#sk2' @ 16.68/2.71 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 16.68/2.71 (((d_not @ (d_29_ii @ '#sk1' @ '#sk2')) => (lessis @ '#sk1' @ 16.68/2.71 '#sk2')))))), 16.68/2.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl168])). 16.68/2.71 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 16.68/2.71 thf('3', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 16.68/2.71 define([status(thm)])). 16.68/2.71 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 16.68/2.71 thf('4', plain, 16.68/2.71 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 16.68/2.71 define([status(thm)])). 16.68/2.71 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))). 16.68/2.71 thf('5', plain, 16.68/2.71 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )), 16.68/2.71 define([status(thm)])). 16.68/2.71 thf(def_n_is, axiom,(( n_is @ (X0)@ (X1)) = ((e_is @ nat @ X0 @ X1)))). 16.68/2.71 thf('6', plain, 16.68/2.71 (![X1:$i,X0:$i]: ( ( n_is @ X0 @ X1 ) = ( e_is @ nat @ X0 @ X1 ) )), 16.68/2.71 define([status(thm)])). 16.68/2.71 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))). 16.68/2.71 thf('7', plain, 16.68/2.71 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )), 16.68/2.71 define([status(thm)])). 16.68/2.71 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) = 16.68/2.71 ((n_some @ (diffprop @ X0 @ X1))))). 16.68/2.71 thf('8', plain, 16.68/2.71 (![X1:$i,X0:$i]: 16.68/2.71 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 16.68/2.71 define([status(thm)])). 16.68/2.71 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))). 16.68/2.71 thf('9', plain, 16.68/2.71 (![X1:$i,X0:$i]: 16.68/2.71 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 16.68/2.71 define([status(thm)])). 16.68/2.71 thf(def_lessis, axiom,(( lessis @ (X0)@ (X1)) = 16.68/2.71 ((l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1))))). 16.68/2.71 thf('10', plain, 16.68/2.71 (![X1:$i,X0:$i]: 16.68/2.71 ( ( lessis @ X0 @ X1 ) = 16.68/2.71 ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )), 16.68/2.71 define([status(thm)])). 16.68/2.71 thf(zip_derived_cl170, plain, 16.68/2.71 (~ (((in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 16.68/2.71 (((imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk1' @ '#sk2')) @ 16.68/2.71 ($false)) => (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk2' @ '#sk1')) @ 16.68/2.71 ($false)) @ 16.68/2.71 ((('#sk1') = ('#sk2'))))))))), 16.68/2.71 inference('rw', [status(thm)], 16.68/2.71 [zip_derived_cl169, '2', '3', '3', '4', '5', '0', '6', '7', 16.68/2.71 '7', '8', '9', '10'])). 16.68/2.71 thf(zip_derived_cl172, plain, 16.68/2.71 (~ (((imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk1' @ '#sk2')) @ 16.68/2.71 ($false)) => (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk2' @ '#sk1')) @ 16.68/2.71 ($false)) @ 16.68/2.71 ((('#sk1') = ('#sk2'))))))), 16.68/2.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl170])). 16.68/2.71 thf(zip_derived_cl174, plain, 16.68/2.71 (~ (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk2' @ '#sk1')) @ 16.68/2.71 ($false)) @ 16.68/2.71 ((('#sk1') = ('#sk2'))))), 16.68/2.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl172])). 16.68/2.71 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 16.68/2.71 thf('11', plain, 16.68/2.71 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 16.68/2.71 inference('rw.lit', [status(esa)], [def_imp])). 16.68/2.71 thf(zip_derived_cl176, plain, 16.68/2.71 (~ (((imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk2' @ '#sk1')) @ 16.68/2.71 ($false)) => ((('#sk1') = ('#sk2')))))), 16.68/2.71 inference('rw_clause', [status(thm)], [zip_derived_cl174, '11'])). 16.68/2.71 thf(zip_derived_cl179, plain, 16.68/2.71 ( (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk2' @ '#sk1')) @ 16.68/2.71 ($false))), 16.68/2.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl176])). 16.68/2.71 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 16.68/2.71 thf('12', plain, 16.68/2.71 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 16.68/2.71 inference('rw.lit', [status(esa)], [def_imp])). 16.68/2.71 thf(zip_derived_cl181, plain, 16.68/2.71 ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk2' @ '#sk1')) => ($false)))), 16.68/2.71 inference('rw_clause', [status(thm)], [zip_derived_cl179, '12'])). 16.68/2.71 thf(zip_derived_cl183, plain, 16.68/2.71 ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk2' @ '#sk1'))))), 16.68/2.71 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl181])). 16.68/2.71 thf(zip_derived_cl184, plain, 16.68/2.71 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk2' @ '#sk1'))), 16.68/2.71 inference('simplify nested equalities', [status(thm)], 16.68/2.71 [zip_derived_cl183])). 16.68/2.71 thf(zip_derived_cl173, plain, 16.68/2.71 ( (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk1' @ '#sk2')) @ 16.68/2.71 ($false))), 16.68/2.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl172])). 16.68/2.71 thf(zip_derived_cl175, plain, 16.68/2.71 ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk1' @ '#sk2')) => ($false)))), 16.68/2.71 inference('rw_clause', [status(thm)], [zip_derived_cl173, '12'])). 16.68/2.71 thf(zip_derived_cl177, plain, 16.68/2.71 ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk1' @ '#sk2'))))), 16.68/2.71 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl175])). 16.68/2.71 thf(zip_derived_cl178, plain, 16.68/2.71 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk1' @ '#sk2'))), 16.68/2.71 inference('simplify nested equalities', [status(thm)], 16.68/2.71 [zip_derived_cl177])). 16.68/2.71 thf(satz10, axiom, 16.68/2.71 (all_of @ 16.68/2.71 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 16.68/2.71 ( ^[X0:$i]: 16.68/2.71 ( all_of @ 16.68/2.71 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 16.68/2.71 ( ^[X1:$i]: 16.68/2.71 ( orec3 @ 16.68/2.71 ( n_is @ X0 @ X1 ) @ ( d_29_ii @ X0 @ X1 ) @ ( iii @ X0 @ X1 ) ) ) ) ))). 16.68/2.71 thf(zip_derived_cl55, plain, 16.68/2.71 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 16.68/2.71 (^[Y0 : $i]: 16.68/2.71 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 16.68/2.71 (^[Y1 : $i]: 16.68/2.71 (orec3 @ (n_is @ Y0 @ Y1) @ (d_29_ii @ Y0 @ Y1) @ 16.68/2.71 (iii @ Y0 @ Y1))))))), 16.68/2.71 inference('cnf', [status(esa)], [satz10])). 16.68/2.71 thf(zip_derived_cl56, plain, 16.68/2.71 ( (all_of @ ((('#C') @ in @ nat)) @ 16.68/2.71 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 16.68/2.71 ((('#S') @ ((('#B') @ ('#S') @ 16.68/2.71 ((('#S') @ ((('#B') @ ('#S') @ 16.68/2.71 ((('#B') @ ((('#B') @ orec3)) @ n_is)))) @ 16.68/2.71 d_29_ii)))) @ 16.68/2.71 iii)))))), 16.68/2.71 inference('lams2combs', [status(thm)], [zip_derived_cl55])). 16.68/2.71 thf(zip_derived_cl401, plain, 16.68/2.71 ( (all_of @ 16.68/2.71 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 16.68/2.71 ((('#B') @ (all_of @ 16.68/2.71 ((('#C') @ in @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 16.68/2.71 ((('#S') @ ((('#B') @ ('#S') @ 16.68/2.71 ((('#S') @ ((('#B') @ ('#S') @ 16.68/2.71 ((('#B') @ ((('#B') @ orec3)) @ n_is)))) @ 16.68/2.71 d_29_ii)))) @ 16.68/2.71 iii)))))), 16.68/2.71 inference('rw', [status(thm)], [zip_derived_cl56, '0'])). 16.68/2.71 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 16.68/2.71 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 16.68/2.71 thf('13', plain, 16.68/2.71 (![X0:( $i > $o ),X1:( $i > $o )]: 16.68/2.71 ( ( all_of @ X0 @ X1 ) <=> 16.68/2.71 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 16.68/2.71 inference('rw.lit', [status(esa)], [def_all_of])). 16.68/2.71 thf(zip_derived_cl402, plain, 16.68/2.71 ( (((!!) @ (^[Y0 : $i]: 16.68/2.71 (((is_of @ Y0 @ 16.68/2.71 ((('#C') @ in @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 16.68/2.71 ((('#B') @ (all_of @ 16.68/2.71 ((('#C') @ in @ 16.68/2.71 (d_Sep @ omega @ 16.68/2.71 ((('#C') @ (!=) @ emptyset)))))) @ 16.68/2.71 ((('#S') @ ((('#B') @ ('#S') @ 16.68/2.71 ((('#S') @ ((('#B') @ ('#S') @ 16.68/2.71 ((('#B') @ ((('#B') @ orec3)) @ 16.68/2.71 n_is)))) @ 16.68/2.71 d_29_ii)))) @ 16.68/2.71 iii)) @ 16.68/2.71 Y0)))))))), 16.68/2.71 inference('rw_clause', [status(thm)], [zip_derived_cl401, '13'])). 16.68/2.71 thf(zip_derived_cl403, plain, 16.68/2.71 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 16.68/2.71 ((('#C') @ is_of @ 16.68/2.71 ((('#C') @ in @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @ 16.68/2.71 ((('#B') @ (all_of @ 16.68/2.71 ((('#C') @ in @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 16.68/2.71 ((('#S') @ ((('#B') @ ('#S') @ 16.68/2.71 ((('#S') @ ((('#B') @ ('#S') @ 16.68/2.71 ((('#B') @ ((('#B') @ orec3)) @ 16.68/2.71 n_is)))) @ 16.68/2.71 d_29_ii)))) @ 16.68/2.71 iii))))))))), 16.68/2.71 inference('comb-normalize', [status(thm)], [zip_derived_cl402])). 16.68/2.71 thf(zip_derived_cl404, plain, 16.68/2.71 (![X2 : $i]: 16.68/2.71 (((is_of @ X2 @ 16.68/2.71 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 16.68/2.71 (all_of @ 16.68/2.71 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 16.68/2.71 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (n_is @ X2))) @ 16.68/2.71 (d_29_ii @ X2))) @ 16.68/2.71 (iii @ X2))))))), 16.68/2.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl403])). 16.68/2.71 thf(zip_derived_cl405, plain, 16.68/2.71 (![X2 : $i]: 16.68/2.71 (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 16.68/2.71 (all_of @ 16.68/2.71 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 16.68/2.71 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (n_is @ X2))) @ 16.68/2.71 (d_29_ii @ X2))) @ 16.68/2.71 (iii @ X2))))))), 16.68/2.71 inference('rw', [status(thm)], [zip_derived_cl404, '2'])). 16.68/2.71 thf(zip_derived_cl406, plain, 16.68/2.71 (![X2 : $i]: 16.68/2.71 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | (all_of @ 16.68/2.71 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 16.68/2.71 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (n_is @ X2))) @ 16.68/2.71 (d_29_ii @ X2))) @ 16.68/2.71 (iii @ X2)))))), 16.68/2.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl405])). 16.68/2.71 thf(zip_derived_cl407, plain, 16.68/2.71 (![X0 : $i]: 16.68/2.71 ( (((!!) @ (^[Y0 : $i]: 16.68/2.71 (((is_of @ Y0 @ 16.68/2.71 ((('#C') @ in @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 16.68/2.71 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (n_is @ X0))) @ 16.68/2.71 (d_29_ii @ X0))) @ 16.68/2.71 (iii @ X0) @ Y0))))))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 16.68/2.71 inference('rw_clause', [status(thm)], [zip_derived_cl406, '13'])). 16.68/2.71 thf(zip_derived_cl408, plain, 16.68/2.71 (![X0 : $i]: 16.68/2.71 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 16.68/2.71 ((('#C') @ is_of @ 16.68/2.71 ((('#C') @ in @ 16.68/2.71 (d_Sep @ omega @ 16.68/2.71 ((('#C') @ (!=) @ emptyset))))))))) @ 16.68/2.71 ((('#S') @ ((('#S') @ ((('#B') @ orec3 @ (n_is @ X0))) @ 16.68/2.71 (d_29_ii @ X0))) @ 16.68/2.71 (iii @ X0))))))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 16.68/2.71 inference('comb-normalize', [status(thm)], [zip_derived_cl407])). 16.68/2.71 thf(zip_derived_cl409, plain, 16.68/2.71 (![X0 : $i, X2 : $i]: 16.68/2.71 ( (((is_of @ X2 @ 16.68/2.71 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 16.68/2.71 (orec3 @ (n_is @ X0 @ X2) @ (d_29_ii @ X0 @ X2) @ (iii @ X0 @ X2)))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 16.68/2.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl408])). 16.68/2.71 thf(def_l_ec, axiom,(( l_ec @ (X0)@ (X1)) = ((imp @ X0 @ (d_not @ X1))))). 16.68/2.71 thf('14', plain, 16.68/2.71 (![X1:$o,X0:$o]: ( ( l_ec @ X0 @ X1 ) = ( imp @ X0 @ ( d_not @ X1 ) ) )), 16.68/2.71 define([status(thm)])). 16.68/2.71 thf(def_d_and, axiom,(( d_and @ (X0)@ (X1)) = ((d_not @ (l_ec @ X0 @ X1))))). 16.68/2.71 thf('15', plain, 16.68/2.71 (![X1:$o,X0:$o]: ( ( d_and @ X0 @ X1 ) = ( d_not @ ( l_ec @ X0 @ X1 ) ) )), 16.68/2.71 define([status(thm)])). 16.68/2.71 thf(def_or3, axiom,(( or3 @ (X0)@ (X1)@ (X2)) = 16.68/2.71 ((l_or @ X0 @ (l_or @ X1 @ X2))))). 16.68/2.71 thf('16', plain, 16.68/2.71 (![X2:$o,X1:$o,X0:$o]: 16.68/2.71 ( ( or3 @ X0 @ X1 @ X2 ) = ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) )), 16.68/2.71 define([status(thm)])). 16.68/2.71 thf(def_and3, axiom,(( and3 @ (X0)@ (X1)@ (X2)) = 16.68/2.71 ((d_and @ X0 @ (d_and @ X1 @ X2))))). 16.68/2.71 thf('17', plain, 16.68/2.71 (![X2:$o,X1:$o,X0:$o]: 16.68/2.71 ( ( and3 @ X0 @ X1 @ X2 ) = ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) )), 16.68/2.71 define([status(thm)])). 16.68/2.71 thf(def_ec3, axiom,(( ec3 @ (X0)@ (X1)@ (X2)) = 16.68/2.71 ((and3 @ (l_ec @ X0 @ X1) @ (l_ec @ X1 @ X2) @ (l_ec @ X2 @ X0))))). 16.68/2.71 thf('18', plain, 16.68/2.71 (![X2:$o,X1:$o,X0:$o]: 16.68/2.71 ( ( ec3 @ X0 @ X1 @ X2 ) = 16.68/2.71 ( and3 @ ( l_ec @ X0 @ X1 ) @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X0 ) ) )), 16.68/2.71 define([status(thm)])). 16.68/2.71 thf(def_orec3, axiom,(( orec3 @ (X0)@ (X1)@ (X2)) = 16.68/2.71 ((d_and @ (or3 @ X0 @ X1 @ X2) @ (ec3 @ X0 @ X1 @ X2))))). 16.68/2.71 thf('19', plain, 16.68/2.71 (![X2:$o,X1:$o,X0:$o]: 16.68/2.71 ( ( orec3 @ X0 @ X1 @ X2 ) = 16.68/2.71 ( d_and @ ( or3 @ X0 @ X1 @ X2 ) @ ( ec3 @ X0 @ X1 @ X2 ) ) )), 16.68/2.71 define([status(thm)])). 16.68/2.71 thf(zip_derived_cl410, plain, 16.68/2.71 (![X0 : $i, X2 : $i]: 16.68/2.71 ( (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ (imp @ (((X0) = (X2))) @ ($false)) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X2)) @ 16.68/2.71 ($false)) @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X2 @ X0)))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ (((X0) = (X2))) @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X2)) @ 16.68/2.71 ($false))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X2)) @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X2 @ X0)) @ 16.68/2.71 ($false))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X2 @ X0)) @ 16.68/2.71 (imp @ (((X0) = (X2))) @ ($false))) @ 16.68/2.71 ($false))) @ 16.68/2.71 ($false)) @ 16.68/2.71 ($false))) @ 16.68/2.71 ($false)) @ 16.68/2.71 ($false))) @ 16.68/2.71 ($false)))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 16.68/2.71 inference('rw', [status(thm)], 16.68/2.71 [zip_derived_cl409, '2', '3', '3', '3', '3', '3', '3', '3', 16.68/2.71 '3', '3', '14', '14', '14', '14', '14', '14', '15', '15', 16.68/2.71 '15', '4', '4', '16', '17', '18', '19', '5', '0', '6', '7', 16.68/2.71 '7', '8', '9'])). 16.68/2.71 thf(zip_derived_cl411, plain, 16.68/2.71 (![X0 : $i, X2 : $i]: 16.68/2.71 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ (imp @ (((X0) = (X2))) @ ($false)) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X2)) @ 16.68/2.71 ($false)) @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X2 @ X0)))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ (((X0) = (X2))) @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X2)) @ 16.68/2.71 ($false))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X2)) @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X2 @ X0)) @ 16.68/2.71 ($false))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X2 @ X0)) @ 16.68/2.71 (imp @ (((X0) = (X2))) @ ($false))) @ 16.68/2.71 ($false))) @ 16.68/2.71 ($false)) @ 16.68/2.71 ($false))) @ 16.68/2.71 ($false)) @ 16.68/2.71 ($false))) @ 16.68/2.71 ($false)) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 16.68/2.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl410])). 16.68/2.71 thf(zip_derived_cl412, plain, 16.68/2.71 (![X0 : $i, X1 : $i]: 16.68/2.71 ( (((imp @ 16.68/2.71 (imp @ (imp @ (((X0) = (X1))) @ ($false)) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)) @ 16.68/2.71 ($false)) @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ (((X0) = (X1))) @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)) @ 16.68/2.71 ($false))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)) @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)) @ 16.68/2.71 ($false))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)) @ 16.68/2.71 (imp @ (((X0) = (X1))) @ ($false))) @ 16.68/2.71 ($false))) @ 16.68/2.71 ($false)) @ 16.68/2.71 ($false))) @ 16.68/2.71 ($false)) @ 16.68/2.71 ($false))) => 16.68/2.71 ($false))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 16.68/2.71 inference('rw_clause', [status(thm)], [zip_derived_cl411, '12'])). 16.68/2.71 thf(zip_derived_cl413, plain, 16.68/2.71 (![X0 : $i, X1 : $i]: 16.68/2.71 ( (((~) @ (imp @ 16.68/2.71 (imp @ (imp @ (((X0) = (X1))) @ ($false)) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)) @ 16.68/2.71 ($false)) @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ (((X0) = (X1))) @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)) @ 16.68/2.71 ($false))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)) @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)) @ 16.68/2.71 ($false))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)) @ 16.68/2.71 (imp @ (((X0) = (X1))) @ ($false))) @ 16.68/2.71 ($false))) @ 16.68/2.71 ($false)) @ 16.68/2.71 ($false))) @ 16.68/2.71 ($false)) @ 16.68/2.71 ($false))))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 16.68/2.71 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl412])). 16.68/2.71 thf(zip_derived_cl414, plain, 16.68/2.71 (![X0 : $i, X1 : $i]: 16.68/2.71 (~ (imp @ 16.68/2.71 (imp @ (imp @ (((X0) = (X1))) @ ($false)) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)) @ 16.68/2.71 ($false)) @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ (((X0) = (X1))) @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)) @ 16.68/2.71 ($false))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)) @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)) @ 16.68/2.71 ($false))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)) @ 16.68/2.71 (imp @ (((X0) = (X1))) @ ($false))) @ 16.68/2.71 ($false))) @ 16.68/2.71 ($false)) @ 16.68/2.71 ($false))) @ 16.68/2.71 ($false)) @ 16.68/2.71 ($false))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 16.68/2.71 inference('simplify nested equalities', [status(thm)], 16.68/2.71 [zip_derived_cl413])). 16.68/2.71 thf(zip_derived_cl415, plain, 16.68/2.71 (![X0 : $i, X1 : $i]: 16.68/2.71 (~ (((imp @ (imp @ (((X1) = (X0))) @ ($false)) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)) @ 16.68/2.71 ($false)) @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)))) => 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ (((X1) = (X0))) @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)) @ 16.68/2.71 ($false))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)) @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)) @ 16.68/2.71 ($false))) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)) @ 16.68/2.71 (imp @ (((X1) = (X0))) @ ($false))) @ 16.68/2.71 ($false))) @ 16.68/2.71 ($false)) @ 16.68/2.71 ($false))) @ 16.68/2.71 ($false)) @ 16.68/2.71 ($false)))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 16.68/2.71 inference('rw_clause', [status(thm)], [zip_derived_cl414, '11'])). 16.68/2.71 thf(zip_derived_cl416, plain, 16.68/2.71 (![X0 : $i, X1 : $i]: 16.68/2.71 ( (imp @ (imp @ (((X1) = (X0))) @ ($false)) @ 16.68/2.71 (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)) @ 16.68/2.71 ($false)) @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)))) 16.68/2.71 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 16.68/2.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl415])). 16.68/2.71 thf(zip_derived_cl418, plain, 16.68/2.71 (![X0 : $i, X1 : $i]: 16.68/2.71 ( (((imp @ (((X1) = (X0))) @ ($false)) => (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)) @ 16.68/2.71 ($false)) @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1))))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 16.68/2.71 inference('rw_clause', [status(thm)], [zip_derived_cl416, '12'])). 16.68/2.71 thf(zip_derived_cl420, plain, 16.68/2.71 (![X0 : $i, X1 : $i]: 16.68/2.71 (~ (imp @ (((X1) = (X0))) @ ($false)) 16.68/2.71 | (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)) @ 16.68/2.71 ($false)) @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1))) 16.68/2.71 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 16.68/2.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl418])). 16.68/2.71 thf(zip_derived_cl424, plain, 16.68/2.71 (![X0 : $i, X1 : $i]: 16.68/2.71 (~ (((((X1) = (X0))) => ($false))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)) @ 16.68/2.71 ($false)) @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1))))), 16.68/2.71 inference('rw_clause', [status(thm)], [zip_derived_cl420, '11'])). 16.68/2.71 thf(zip_derived_cl428, plain, 16.68/2.71 (![X0 : $i, X1 : $i]: 16.68/2.71 (~ (((~) @ (((X1) = (X0))))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)) @ 16.68/2.71 ($false)) @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1))))), 16.68/2.71 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl424])). 16.68/2.71 thf(zip_derived_cl429, plain, 16.68/2.71 (![X0 : $i, X1 : $i]: 16.68/2.71 (((X1) = (X0)) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | (imp @ 16.68/2.71 (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)) @ 16.68/2.71 ($false)) @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1))))), 16.68/2.71 inference('simplify nested equalities', [status(thm)], 16.68/2.71 [zip_derived_cl428])). 16.68/2.71 thf(zip_derived_cl430, plain, 16.68/2.71 (![X0 : $i, X1 : $i]: 16.68/2.71 ( (((imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)) @ 16.68/2.71 ($false)) => (l_some @ 16.68/2.71 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ((X0) = (X1)))), 16.68/2.71 inference('rw_clause', [status(thm)], [zip_derived_cl429, '12'])). 16.68/2.71 thf(zip_derived_cl433, plain, 16.68/2.71 (![X0 : $i, X1 : $i]: 16.68/2.71 (~ (imp @ 16.68/2.71 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)) @ 16.68/2.71 ($false)) 16.68/2.71 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)) 16.68/2.71 | ((X0) = (X1)) 16.68/2.71 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 16.68/2.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl430])). 16.68/2.71 thf(zip_derived_cl436, plain, 16.68/2.71 (![X0 : $i, X1 : $i]: 16.68/2.71 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)) => ($false))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ((X0) = (X1)) 16.68/2.71 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)))), 16.68/2.71 inference('rw_clause', [status(thm)], [zip_derived_cl433, '11'])). 16.68/2.71 thf(zip_derived_cl441, plain, 16.68/2.71 (![X0 : $i, X1 : $i]: 16.68/2.71 (~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)))) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ((X0) = (X1)) 16.68/2.71 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)))), 16.68/2.71 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl436])). 16.68/2.71 thf(zip_derived_cl442, plain, 16.68/2.71 (![X0 : $i, X1 : $i]: 16.68/2.71 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X0 @ X1)) 16.68/2.71 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ((X0) = (X1)) 16.68/2.71 | (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ X1 @ X0)))), 16.68/2.71 inference('simplify nested equalities', [status(thm)], 16.68/2.71 [zip_derived_cl441])). 16.68/2.71 thf(zip_derived_cl1941, plain, 16.68/2.71 (( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk2' @ '#sk1')) 16.68/2.71 | (('#sk1') = ('#sk2')) 16.68/2.71 | ~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 16.68/2.71 | ~ (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 16.68/2.71 inference('sup+', [status(thm)], [zip_derived_cl178, zip_derived_cl442])). 16.68/2.71 thf(zip_derived_cl171, plain, 16.68/2.71 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))), 16.68/2.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl170])). 16.68/2.71 thf(zip_derived_cl165, plain, 16.68/2.71 ( (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))), 16.68/2.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])). 16.68/2.71 thf(zip_derived_cl1963, plain, 16.68/2.71 (( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk2' @ '#sk1')) 16.68/2.71 | (('#sk1') = ('#sk2')))), 16.68/2.71 inference('demod', [status(thm)], 16.68/2.71 [zip_derived_cl1941, zip_derived_cl171, zip_derived_cl165])). 16.68/2.71 thf(zip_derived_cl180, plain, (~ ((('#sk1') = ('#sk2')))), 16.68/2.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl176])). 16.68/2.71 thf(zip_derived_cl182, plain, ((('#sk1') != ('#sk2'))), 16.68/2.71 inference('simplify nested equalities', [status(thm)], 16.68/2.71 [zip_derived_cl180])). 16.68/2.71 thf(zip_derived_cl1964, plain, 16.68/2.71 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 16.68/2.71 (diffprop @ '#sk2' @ '#sk1'))), 16.68/2.71 inference('simplify_reflect-', [status(thm)], 16.68/2.71 [zip_derived_cl1963, zip_derived_cl182])). 16.68/2.71 thf(zip_derived_cl1997, plain, ($false), 16.68/2.71 inference('demod', [status(thm)], [zip_derived_cl184, zip_derived_cl1964])). 16.68/2.71 16.68/2.71 % SZS output end Refutation 16.68/2.71 16.68/2.71 16.68/2.72 % Terminating... 17.28/2.84 % Runner terminated. 17.28/2.86 % Zipperpin 1.5 exiting 17.28/2.87 EOF