0.02/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.vUUp74MyBZ true 0.11/0.33 % Computer : n003.cluster.edu 0.11/0.33 % Model : x86_64 x86_64 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.33 % Memory : 8042.1875MB 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.33 % CPULimit : 1200 0.11/0.33 % WCLimit : 120 0.11/0.33 % DateTime : Tue Jul 13 14:45:09 EDT 2021 0.11/0.33 % CPUTime : 0.11/0.33 % Running portfolio for 120 s 0.11/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.11/0.33 % Number of cores: 8 0.11/0.33 % Python version: Python 3.6.8 0.11/0.33 % Running in HO mode 0.18/0.61 % Total configuration time : 828 0.18/0.61 % Estimated wc time : 983 0.18/0.61 % Estimated cpu time (8 cpus) : 122.875 0.87/0.66 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 1.07/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 1.07/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 1.07/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 1.07/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 1.12/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 1.12/0.81 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 1.12/0.83 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 4.92/1.46 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 53s 10.40/2.44 % Solved by lams/40_b.comb.sh. 10.40/2.44 % done 141 iterations in 1.509s 10.40/2.44 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 10.40/2.44 % SZS output start Refutation 10.40/2.44 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 10.40/2.44 thf(n_is_type, type, n_is: $i > $i > $o). 10.40/2.44 thf(l_or_type, type, l_or: $o > $o > $o). 10.40/2.44 thf(moreis_type, type, moreis: $i > $i > $o). 10.40/2.44 thf(in_type, type, in: $i > $i > $o). 10.40/2.44 thf(imp_type, type, imp: $o > $o > $o). 10.40/2.44 thf(lessis_type, type, lessis: $i > $i > $o). 10.40/2.44 thf(nat_type, type, nat: $i). 10.40/2.44 thf('#sk2_type', type, '#sk2': $i). 10.40/2.44 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 10.40/2.44 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 10.40/2.44 thf('#sk1_type', type, '#sk1': $i). 10.40/2.44 thf(e_is_type, type, e_is: $i > $i > $i > $o). 10.40/2.44 thf(n_some_type, type, n_some: ($i > $o) > $o). 10.40/2.44 thf(iii_type, type, iii: $i > $i > $o). 10.40/2.44 thf(omega_type, type, omega: $i). 10.40/2.44 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 10.40/2.44 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o). 10.40/2.44 thf(d_not_type, type, d_not: $o > $o). 10.40/2.44 thf(emptyset_type, type, emptyset: $i). 10.40/2.44 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 10.40/2.44 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 10.40/2.44 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 10.40/2.44 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 10.40/2.44 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 10.40/2.44 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 10.40/2.44 thf(satz10h, conjecture, 10.40/2.44 (all_of @ 10.40/2.44 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 10.40/2.44 ( ^[X0:$i]: 10.40/2.44 ( all_of @ 10.40/2.44 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 10.40/2.44 ( ^[X1:$i]: ( ( iii @ X0 @ X1 ) => ( d_not @ ( moreis @ X0 @ X1 ) ) ) ) ) ))). 10.40/2.44 thf(zf_stmt_0, negated_conjecture, 10.40/2.44 (~( all_of @ 10.40/2.44 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 10.40/2.44 ( ^[X0:$i]: 10.40/2.44 ( all_of @ 10.40/2.44 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 10.40/2.44 ( ^[X1:$i]: 10.40/2.44 ( ( iii @ X0 @ X1 ) => ( d_not @ ( moreis @ X0 @ X1 ) ) ) ) ) ) )), 10.40/2.44 inference('cnf.neg', [status(esa)], [satz10h])). 10.40/2.44 thf(zip_derived_cl103, plain, 10.40/2.44 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 10.40/2.44 (^[Y0 : $i]: 10.40/2.44 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 10.40/2.44 (^[Y1 : $i]: (((iii @ Y0 @ Y1) => (d_not @ (moreis @ Y0 @ Y1))))))))), 10.40/2.44 inference('cnf', [status(esa)], [zf_stmt_0])). 10.40/2.44 thf(zip_derived_cl104, plain, 10.40/2.44 (~ (all_of @ ((('#C') @ in @ nat)) @ 10.40/2.44 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 10.40/2.44 ((('#S') @ ((('#B') @ ('#S') @ ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 10.40/2.44 ((('#B') @ ((('#B') @ d_not)) @ moreis)))))))), 10.40/2.44 inference('lams2combs', [status(thm)], [zip_derived_cl103])). 10.40/2.44 thf(def_nat, axiom,(( nat ) = 10.40/2.44 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))). 10.40/2.44 thf('0', plain, 10.40/2.44 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )), 10.40/2.44 define([status(thm)])). 10.40/2.44 thf(zip_derived_cl165, plain, 10.40/2.44 (~ (all_of @ 10.40/2.44 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 10.40/2.44 ((('#B') @ (all_of @ 10.40/2.44 ((('#C') @ in @ 10.40/2.44 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 10.40/2.44 ((('#S') @ ((('#B') @ ('#S') @ ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 10.40/2.44 ((('#B') @ ((('#B') @ d_not)) @ moreis)))))))), 10.40/2.44 inference('rw', [status(thm)], [zip_derived_cl104, '0'])). 10.40/2.44 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 10.40/2.44 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 10.40/2.44 thf('1', plain, 10.40/2.44 (![X0:( $i > $o ),X1:( $i > $o )]: 10.40/2.44 ( ( ~( all_of @ X0 @ X1 ) ) <=> 10.40/2.44 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 10.40/2.44 inference('rw.lit', [status(esa)], [def_all_of])). 10.40/2.44 thf(zip_derived_cl166, plain, 10.40/2.44 (~ (((!!) @ (^[Y0 : $i]: 10.40/2.44 (((is_of @ Y0 @ 10.40/2.44 ((('#C') @ in @ 10.40/2.44 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 10.40/2.44 ((('#B') @ (all_of @ 10.40/2.44 ((('#C') @ in @ 10.40/2.44 (d_Sep @ omega @ 10.40/2.44 ((('#C') @ (!=) @ emptyset)))))) @ 10.40/2.44 ((('#S') @ ((('#B') @ ('#S') @ 10.40/2.44 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 10.40/2.44 ((('#B') @ ((('#B') @ d_not)) @ moreis)))) @ 10.40/2.44 Y0)))))))), 10.40/2.44 inference('rw_clause', [status(thm)], [zip_derived_cl165, '1'])). 10.40/2.44 thf(zip_derived_cl167, plain, 10.40/2.44 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 10.40/2.44 ((('#C') @ is_of @ 10.40/2.44 ((('#C') @ in @ 10.40/2.44 (d_Sep @ omega @ 10.40/2.44 ((('#C') @ (!=) @ emptyset))))))))) @ 10.40/2.44 ((('#B') @ (all_of @ 10.40/2.44 ((('#C') @ in @ 10.40/2.44 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 10.40/2.44 ((('#S') @ ((('#B') @ ('#S') @ 10.40/2.44 ((('#B') @ ((('#B') @ (=>))) @ iii)))) @ 10.40/2.44 ((('#B') @ ((('#B') @ d_not)) @ moreis))))))))))), 10.40/2.44 inference('comb-normalize', [status(thm)], [zip_derived_cl166])). 10.40/2.44 thf(zip_derived_cl168, plain, 10.40/2.44 (~ (((is_of @ '#sk1' @ 10.40/2.44 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 10.40/2.44 (all_of @ 10.40/2.44 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 10.40/2.44 ((('#S') @ ((('#B') @ (=>) @ (iii @ '#sk1'))) @ 10.40/2.44 ((('#B') @ d_not @ (moreis @ '#sk1'))))))))), 10.40/2.44 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl167])). 10.40/2.44 thf(def_is_of, axiom,(( is_of @ (X1)@ (X0)) = ((X0 @ X1)))). 10.40/2.44 thf('2', plain, 10.40/2.44 (![X0:( $i > $o ),X1:$i]: ( ( is_of @ X1 @ X0 ) = ( X0 @ X1 ) )), 10.40/2.44 define([status(thm)])). 10.40/2.44 thf(zip_derived_cl169, plain, 10.40/2.44 (~ (((in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 10.40/2.44 (all_of @ 10.40/2.44 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 10.40/2.44 ((('#S') @ ((('#B') @ (=>) @ (iii @ '#sk1'))) @ 10.40/2.44 ((('#B') @ d_not @ (moreis @ '#sk1'))))))))), 10.40/2.44 inference('rw', [status(thm)], [zip_derived_cl168, '2'])). 10.40/2.44 thf(zip_derived_cl171, plain, 10.40/2.44 (~ (all_of @ 10.40/2.44 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 10.40/2.44 ((('#S') @ ((('#B') @ (=>) @ (iii @ '#sk1'))) @ 10.40/2.44 ((('#B') @ d_not @ (moreis @ '#sk1'))))))), 10.40/2.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl169])). 10.40/2.44 thf(zip_derived_cl172, plain, 10.40/2.44 (~ (((!!) @ (^[Y0 : $i]: 10.40/2.44 (((is_of @ Y0 @ 10.40/2.44 ((('#C') @ in @ 10.40/2.44 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 10.40/2.44 ((('#S') @ ((('#B') @ (=>) @ (iii @ '#sk1'))) @ 10.40/2.44 ((('#B') @ d_not @ (moreis @ '#sk1'))) @ Y0)))))))), 10.40/2.44 inference('rw_clause', [status(thm)], [zip_derived_cl171, '1'])). 10.40/2.44 thf(zip_derived_cl173, plain, 10.40/2.44 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 10.40/2.44 ((('#C') @ is_of @ 10.40/2.44 ((('#C') @ in @ 10.40/2.44 (d_Sep @ omega @ 10.40/2.44 ((('#C') @ (!=) @ emptyset))))))))) @ 10.40/2.44 ((('#S') @ ((('#B') @ (=>) @ (iii @ '#sk1'))) @ 10.40/2.44 ((('#B') @ d_not @ (moreis @ '#sk1')))))))))), 10.40/2.44 inference('comb-normalize', [status(thm)], [zip_derived_cl172])). 10.40/2.44 thf(zip_derived_cl174, plain, 10.40/2.44 (~ (((is_of @ '#sk2' @ 10.40/2.44 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 10.40/2.44 (((iii @ '#sk1' @ '#sk2') => (d_not @ (moreis @ '#sk1' @ '#sk2'))))))), 10.40/2.44 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl173])). 10.40/2.44 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 10.40/2.44 thf('3', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 10.40/2.44 define([status(thm)])). 10.40/2.44 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 10.40/2.44 thf('4', plain, 10.40/2.44 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 10.40/2.44 define([status(thm)])). 10.40/2.44 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))). 10.40/2.44 thf('5', plain, 10.40/2.44 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )), 10.40/2.44 define([status(thm)])). 10.40/2.44 thf(def_n_is, axiom,(( n_is @ (X0)@ (X1)) = ((e_is @ nat @ X0 @ X1)))). 10.40/2.44 thf('6', plain, 10.40/2.44 (![X1:$i,X0:$i]: ( ( n_is @ X0 @ X1 ) = ( e_is @ nat @ X0 @ X1 ) )), 10.40/2.44 define([status(thm)])). 10.40/2.44 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))). 10.40/2.44 thf('7', plain, 10.40/2.44 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )), 10.40/2.44 define([status(thm)])). 10.40/2.44 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) = 10.40/2.44 ((n_some @ (diffprop @ X0 @ X1))))). 10.40/2.44 thf('8', plain, 10.40/2.44 (![X1:$i,X0:$i]: 10.40/2.44 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 10.40/2.44 define([status(thm)])). 10.40/2.44 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))). 10.40/2.44 thf('9', plain, 10.40/2.44 (![X1:$i,X0:$i]: 10.40/2.44 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 10.40/2.44 define([status(thm)])). 10.40/2.44 thf(def_moreis, axiom,(( moreis @ (X0)@ (X1)) = 10.40/2.44 ((l_or @ (d_29_ii @ X0 @ X1) @ (n_is @ X0 @ X1))))). 10.40/2.44 thf('10', plain, 10.40/2.44 (![X1:$i,X0:$i]: 10.40/2.44 ( ( moreis @ X0 @ X1 ) = 10.40/2.44 ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )), 10.40/2.44 define([status(thm)])). 10.40/2.44 thf(zip_derived_cl175, plain, 10.40/2.44 (~ (((in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 10.40/2.44 (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk2' @ '#sk1')) => (imp @ 10.40/2.44 (imp @ 10.40/2.44 (imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk1' @ '#sk2')) @ 10.40/2.44 ($false)) @ 10.40/2.44 ((('#sk1') = ('#sk2')))) @ 10.40/2.44 ($false))))))), 10.40/2.44 inference('rw', [status(thm)], 10.40/2.44 [zip_derived_cl174, '2', '3', '3', '4', '5', '0', '6', '7', 10.40/2.44 '7', '8', '9', '10'])). 10.40/2.44 thf(zip_derived_cl177, plain, 10.40/2.44 (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk2' @ '#sk1')) => (imp @ 10.40/2.44 (imp @ 10.40/2.44 (imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk1' @ '#sk2')) @ 10.40/2.44 ($false)) @ 10.40/2.44 ((('#sk1') = ('#sk2')))) @ 10.40/2.44 ($false))))), 10.40/2.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl175])). 10.40/2.44 thf(zip_derived_cl179, plain, 10.40/2.44 (~ (imp @ 10.40/2.44 (imp @ 10.40/2.44 (imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk1' @ '#sk2')) @ 10.40/2.44 ($false)) @ 10.40/2.44 ((('#sk1') = ('#sk2')))) @ 10.40/2.44 ($false))), 10.40/2.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl177])). 10.40/2.44 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 10.40/2.44 thf('11', plain, 10.40/2.44 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 10.40/2.44 inference('rw.lit', [status(esa)], [def_imp])). 10.40/2.44 thf(zip_derived_cl180, plain, 10.40/2.44 (~ (((imp @ 10.40/2.44 (imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk1' @ '#sk2')) @ 10.40/2.44 ($false)) @ 10.40/2.44 ((('#sk1') = ('#sk2')))) => ($false)))), 10.40/2.44 inference('rw_clause', [status(thm)], [zip_derived_cl179, '11'])). 10.40/2.44 thf(zip_derived_cl181, plain, 10.40/2.44 (~ (((~) @ (imp @ 10.40/2.44 (imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk1' @ '#sk2')) @ 10.40/2.44 ($false)) @ 10.40/2.44 ((('#sk1') = ('#sk2'))))))), 10.40/2.44 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl180])). 10.40/2.44 thf(zip_derived_cl182, plain, 10.40/2.44 ( (imp @ 10.40/2.44 (imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk1' @ '#sk2')) @ 10.40/2.44 ($false)) @ 10.40/2.44 ((('#sk1') = ('#sk2'))))), 10.40/2.44 inference('simplify nested equalities', [status(thm)], 10.40/2.44 [zip_derived_cl181])). 10.40/2.44 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 10.40/2.44 thf('12', plain, 10.40/2.44 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 10.40/2.44 inference('rw.lit', [status(esa)], [def_imp])). 10.40/2.44 thf(zip_derived_cl183, plain, 10.40/2.44 ( (((imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk1' @ '#sk2')) @ 10.40/2.44 ($false)) => ((('#sk1') = ('#sk2')))))), 10.40/2.44 inference('rw_clause', [status(thm)], [zip_derived_cl182, '12'])). 10.40/2.44 thf(zip_derived_cl184, plain, 10.40/2.44 ((~ (imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk1' @ '#sk2')) @ 10.40/2.44 ($false)) 10.40/2.44 | ((('#sk1') = ('#sk2'))))), 10.40/2.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl183])). 10.40/2.44 thf(zip_derived_cl185, plain, 10.40/2.44 ((~ (imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk1' @ '#sk2')) @ 10.40/2.44 ($false)) 10.40/2.44 | (('#sk1') = ('#sk2')))), 10.40/2.44 inference('simplify nested equalities', [status(thm)], 10.40/2.44 [zip_derived_cl184])). 10.40/2.44 thf(zip_derived_cl186, plain, 10.40/2.44 ((~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk1' @ '#sk2')) => ($false))) 10.40/2.44 | (('#sk1') = ('#sk2')))), 10.40/2.44 inference('rw_clause', [status(thm)], [zip_derived_cl185, '11'])). 10.40/2.44 thf(zip_derived_cl187, plain, 10.40/2.44 ((~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk1' @ '#sk2')))) 10.40/2.44 | (('#sk1') = ('#sk2')))), 10.40/2.44 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl186])). 10.40/2.44 thf(zip_derived_cl188, plain, 10.40/2.44 (( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk1' @ '#sk2')) 10.40/2.44 | (('#sk1') = ('#sk2')))), 10.40/2.44 inference('simplify nested equalities', [status(thm)], 10.40/2.44 [zip_derived_cl187])). 10.40/2.44 thf(satz10d, axiom, 10.40/2.44 (all_of @ 10.40/2.44 ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 10.40/2.44 ( ^[X0:$i]: 10.40/2.44 ( all_of @ 10.40/2.44 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 10.40/2.44 ( ^[X1:$i]: 10.40/2.44 ( ( lessis @ X0 @ X1 ) => ( d_not @ ( d_29_ii @ X0 @ X1 ) ) ) ) ) ))). 10.40/2.44 thf(zip_derived_cl91, plain, 10.40/2.44 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 10.40/2.44 (^[Y0 : $i]: 10.40/2.44 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 10.40/2.44 (^[Y1 : $i]: 10.40/2.44 (((lessis @ Y0 @ Y1) => (d_not @ (d_29_ii @ Y0 @ Y1))))))))), 10.40/2.44 inference('cnf', [status(esa)], [satz10d])). 10.40/2.44 thf(zip_derived_cl92, plain, 10.40/2.44 ( (all_of @ ((('#C') @ in @ nat)) @ 10.40/2.44 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 10.40/2.44 ((('#S') @ ((('#B') @ ('#S') @ 10.40/2.44 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @ 10.40/2.44 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))))), 10.40/2.44 inference('lams2combs', [status(thm)], [zip_derived_cl91])). 10.40/2.44 thf(zip_derived_cl304, plain, 10.40/2.44 ( (all_of @ 10.40/2.44 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 10.40/2.44 ((('#B') @ (all_of @ 10.40/2.44 ((('#C') @ in @ 10.40/2.44 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 10.40/2.44 ((('#S') @ ((('#B') @ ('#S') @ 10.40/2.44 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @ 10.40/2.44 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))))), 10.40/2.44 inference('rw', [status(thm)], [zip_derived_cl92, '0'])). 10.40/2.44 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 10.40/2.44 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 10.40/2.44 thf('13', plain, 10.40/2.44 (![X0:( $i > $o ),X1:( $i > $o )]: 10.40/2.44 ( ( all_of @ X0 @ X1 ) <=> 10.40/2.44 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 10.40/2.44 inference('rw.lit', [status(esa)], [def_all_of])). 10.40/2.44 thf(zip_derived_cl305, plain, 10.40/2.44 ( (((!!) @ (^[Y0 : $i]: 10.40/2.44 (((is_of @ Y0 @ 10.40/2.44 ((('#C') @ in @ 10.40/2.44 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 10.40/2.44 ((('#B') @ (all_of @ 10.40/2.44 ((('#C') @ in @ 10.40/2.44 (d_Sep @ omega @ 10.40/2.44 ((('#C') @ (!=) @ emptyset)))))) @ 10.40/2.44 ((('#S') @ ((('#B') @ ('#S') @ 10.40/2.44 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @ 10.40/2.44 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))) @ 10.40/2.44 Y0)))))))), 10.40/2.44 inference('rw_clause', [status(thm)], [zip_derived_cl304, '13'])). 10.40/2.44 thf(zip_derived_cl306, plain, 10.40/2.44 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 10.40/2.44 ((('#C') @ is_of @ 10.40/2.44 ((('#C') @ in @ 10.40/2.44 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @ 10.40/2.44 ((('#B') @ (all_of @ 10.40/2.44 ((('#C') @ in @ 10.40/2.44 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 10.40/2.44 ((('#S') @ ((('#B') @ ('#S') @ 10.40/2.44 ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @ 10.40/2.44 ((('#B') @ ((('#B') @ d_not)) @ d_29_ii))))))))))), 10.40/2.44 inference('comb-normalize', [status(thm)], [zip_derived_cl305])). 10.40/2.44 thf(zip_derived_cl307, plain, 10.40/2.44 (![X2 : $i]: 10.40/2.44 (((is_of @ X2 @ 10.40/2.44 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 10.40/2.44 (all_of @ 10.40/2.44 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 10.40/2.44 ((('#S') @ ((('#B') @ (=>) @ (lessis @ X2))) @ 10.40/2.44 ((('#B') @ d_not @ (d_29_ii @ X2))))))))), 10.40/2.44 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl306])). 10.40/2.44 thf(zip_derived_cl308, plain, 10.40/2.44 (![X2 : $i]: 10.40/2.44 (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 10.40/2.44 (all_of @ 10.40/2.44 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 10.40/2.44 ((('#S') @ ((('#B') @ (=>) @ (lessis @ X2))) @ 10.40/2.44 ((('#B') @ d_not @ (d_29_ii @ X2))))))))), 10.40/2.44 inference('rw', [status(thm)], [zip_derived_cl307, '2'])). 10.40/2.44 thf(zip_derived_cl309, plain, 10.40/2.44 (![X2 : $i]: 10.40/2.44 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | (all_of @ 10.40/2.44 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 10.40/2.44 ((('#S') @ ((('#B') @ (=>) @ (lessis @ X2))) @ 10.40/2.44 ((('#B') @ d_not @ (d_29_ii @ X2)))))))), 10.40/2.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl308])). 10.40/2.44 thf(zip_derived_cl310, plain, 10.40/2.44 (![X0 : $i]: 10.40/2.44 ( (((!!) @ (^[Y0 : $i]: 10.40/2.44 (((is_of @ Y0 @ 10.40/2.44 ((('#C') @ in @ 10.40/2.44 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 10.40/2.44 ((('#S') @ ((('#B') @ (=>) @ (lessis @ X0))) @ 10.40/2.44 ((('#B') @ d_not @ (d_29_ii @ X0))) @ Y0))))))) 10.40/2.44 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.40/2.44 inference('rw_clause', [status(thm)], [zip_derived_cl309, '13'])). 10.40/2.44 thf(zip_derived_cl311, plain, 10.40/2.44 (![X0 : $i]: 10.40/2.44 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 10.40/2.44 ((('#C') @ is_of @ 10.40/2.44 ((('#C') @ in @ 10.40/2.44 (d_Sep @ omega @ 10.40/2.44 ((('#C') @ (!=) @ emptyset))))))))) @ 10.40/2.44 ((('#S') @ ((('#B') @ (=>) @ (lessis @ X0))) @ 10.40/2.44 ((('#B') @ d_not @ (d_29_ii @ X0))))))))) 10.40/2.44 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.40/2.44 inference('comb-normalize', [status(thm)], [zip_derived_cl310])). 10.40/2.44 thf(zip_derived_cl312, plain, 10.40/2.44 (![X0 : $i, X2 : $i]: 10.40/2.44 ( (((is_of @ X2 @ 10.40/2.44 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 10.40/2.44 (((lessis @ X0 @ X2) => (d_not @ (d_29_ii @ X0 @ X2)))))) 10.40/2.44 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.40/2.44 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl311])). 10.40/2.44 thf(def_lessis, axiom,(( lessis @ (X0)@ (X1)) = 10.40/2.44 ((l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1))))). 10.40/2.44 thf('14', plain, 10.40/2.44 (![X1:$i,X0:$i]: 10.40/2.44 ( ( lessis @ X0 @ X1 ) = 10.40/2.44 ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )), 10.40/2.44 define([status(thm)])). 10.40/2.44 thf(zip_derived_cl313, plain, 10.40/2.44 (![X0 : $i, X2 : $i]: 10.40/2.44 ( (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) => 10.40/2.44 (((imp @ 10.40/2.44 (imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X2 @ X0)) @ 10.40/2.44 ($false)) @ 10.40/2.44 (((X0) = (X2)))) => (imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X0 @ X2)) @ 10.40/2.44 ($false)))))) 10.40/2.44 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.40/2.44 inference('rw', [status(thm)], 10.40/2.44 [zip_derived_cl312, '2', '3', '3', '4', '5', '0', '6', '7', 10.40/2.44 '7', '8', '9', '14'])). 10.40/2.44 thf(zip_derived_cl314, plain, 10.40/2.44 (![X0 : $i, X2 : $i]: 10.40/2.44 (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | (((imp @ 10.40/2.44 (imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X2 @ X0)) @ 10.40/2.44 ($false)) @ 10.40/2.44 (((X0) = (X2)))) => (imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X0 @ X2)) @ 10.40/2.44 ($false)))) 10.40/2.44 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.40/2.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl313])). 10.40/2.44 thf(zip_derived_cl315, plain, 10.40/2.44 (![X0 : $i, X2 : $i]: 10.40/2.44 (~ (imp @ 10.40/2.44 (imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X2 @ X0)) @ 10.40/2.44 ($false)) @ 10.40/2.44 (((X0) = (X2)))) 10.40/2.44 | (imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X0 @ X2)) @ 10.40/2.44 ($false)) 10.40/2.44 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.40/2.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl314])). 10.40/2.44 thf(zip_derived_cl316, plain, 10.40/2.44 (![X0 : $i, X1 : $i]: 10.40/2.44 (~ (((imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X0 @ X1)) @ 10.40/2.44 ($false)) => (((X1) = (X0))))) 10.40/2.44 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | (imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X1 @ X0)) @ 10.40/2.44 ($false)))), 10.40/2.44 inference('rw_clause', [status(thm)], [zip_derived_cl315, '11'])). 10.40/2.44 thf(zip_derived_cl317, plain, 10.40/2.44 (![X0 : $i, X1 : $i]: 10.40/2.44 ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X0 @ X1)) => ($false))) 10.40/2.44 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (((imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X1 @ X0)) @ 10.40/2.44 ($false)) => (((X0) = (X1))))))), 10.40/2.44 inference('rw_clause', [status(thm)], [zip_derived_cl316, '12'])). 10.40/2.44 thf(zip_derived_cl318, plain, 10.40/2.44 (![X0 : $i, X1 : $i]: 10.40/2.44 ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X0 @ X1)))) 10.40/2.44 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (((imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X1 @ X0)) @ 10.40/2.44 ($false)) => (((X0) = (X1))))))), 10.40/2.44 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl317])). 10.40/2.44 thf(zip_derived_cl319, plain, 10.40/2.44 (![X0 : $i, X1 : $i]: 10.40/2.44 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X0 @ X1)) 10.40/2.44 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (((imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X1 @ X0)) @ 10.40/2.44 ($false)) => (((X0) = (X1))))))), 10.40/2.44 inference('simplify nested equalities', [status(thm)], 10.40/2.44 [zip_derived_cl318])). 10.40/2.44 thf(zip_derived_cl320, plain, 10.40/2.44 (![X0 : $i, X1 : $i]: 10.40/2.44 ( (imp @ 10.40/2.44 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X1 @ X0)) @ 10.40/2.44 ($false)) 10.40/2.44 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X0 @ X1)))), 10.40/2.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl319])). 10.40/2.44 thf(zip_derived_cl322, plain, 10.40/2.44 (![X0 : $i, X1 : $i]: 10.40/2.44 ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X0 @ X1)) => ($false))) 10.40/2.44 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X1 @ X0)) 10.40/2.44 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.40/2.44 inference('rw_clause', [status(thm)], [zip_derived_cl320, '12'])). 10.40/2.44 thf(zip_derived_cl324, plain, 10.40/2.44 (![X0 : $i, X1 : $i]: 10.40/2.44 ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X0 @ X1)))) 10.40/2.44 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X1 @ X0)) 10.40/2.44 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.40/2.44 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl322])). 10.40/2.44 thf(zip_derived_cl325, plain, 10.40/2.44 (![X0 : $i, X1 : $i]: 10.40/2.44 (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X0 @ X1)) 10.40/2.44 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X1 @ X0)) 10.40/2.44 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))), 10.40/2.44 inference('simplify nested equalities', [status(thm)], 10.40/2.44 [zip_derived_cl324])). 10.40/2.44 thf(zip_derived_cl1783, plain, 10.40/2.44 (((('#sk1') = ('#sk2')) 10.40/2.44 | ~ (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk2' @ '#sk1')))), 10.40/2.44 inference('sup-', [status(thm)], [zip_derived_cl188, zip_derived_cl325])). 10.40/2.44 thf(zip_derived_cl170, plain, 10.40/2.44 ( (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))), 10.40/2.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl169])). 10.40/2.44 thf(zip_derived_cl176, plain, 10.40/2.44 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))), 10.40/2.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl175])). 10.40/2.44 thf(zip_derived_cl178, plain, 10.40/2.44 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk2' @ '#sk1'))), 10.40/2.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl177])). 10.40/2.44 thf(zip_derived_cl1796, plain, ((('#sk1') = ('#sk2'))), 10.40/2.44 inference('demod', [status(thm)], 10.40/2.44 [zip_derived_cl1783, zip_derived_cl170, zip_derived_cl176, 10.40/2.44 zip_derived_cl178])). 10.40/2.44 thf(zip_derived_cl178, plain, 10.40/2.44 ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ '#sk2' @ '#sk1'))), 10.40/2.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl177])). 10.40/2.44 thf(zip_derived_cl321, plain, 10.40/2.44 (![X0 : $i, X1 : $i]: 10.40/2.44 (~ (((X0) = (X1))) 10.40/2.44 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X0 @ X1)))), 10.40/2.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl319])). 10.40/2.44 thf(zip_derived_cl323, plain, 10.40/2.44 (![X0 : $i, X1 : $i]: 10.40/2.44 (((X0) != (X1)) 10.40/2.44 | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 10.40/2.44 (diffprop @ X0 @ X1)))), 10.40/2.44 inference('simplify nested equalities', [status(thm)], 10.40/2.44 [zip_derived_cl321])). 10.40/2.44 thf(zip_derived_cl1765, plain, 10.40/2.44 ((~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | ~ (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) 10.40/2.44 | (('#sk2') != ('#sk1')))), 10.40/2.44 inference('sup-', [status(thm)], [zip_derived_cl178, zip_derived_cl323])). 10.40/2.44 thf(zip_derived_cl176, plain, 10.40/2.44 ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))), 10.40/2.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl175])). 10.40/2.44 thf(zip_derived_cl170, plain, 10.40/2.44 ( (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))), 10.40/2.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl169])). 10.40/2.44 thf(zip_derived_cl1769, plain, ((('#sk2') != ('#sk1'))), 10.40/2.44 inference('demod', [status(thm)], 10.40/2.44 [zip_derived_cl1765, zip_derived_cl176, zip_derived_cl170])). 10.40/2.44 thf(zip_derived_cl1797, plain, ($false), 10.40/2.44 inference('simplify_reflect-', [status(thm)], 10.40/2.44 [zip_derived_cl1796, zip_derived_cl1769])). 10.40/2.44 10.40/2.44 % SZS output end Refutation 10.40/2.44 10.40/2.44 10.40/2.44 % Terminating... 11.15/2.58 % Runner terminated. 11.15/2.59 % Zipperpin 1.5 exiting 11.15/2.61 EOF