0.00/0.03	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.06	% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.C7xUIa48hZ true
0.11/0.37	% Computer : n012.cluster.edu
0.11/0.37	% Model    : x86_64 x86_64
0.11/0.37	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.37	% Memory   : 8046.5625MB
0.11/0.37	% OS       : Linux 6.8.0-71-generic
0.11/0.37	% CPULimit : 1440
0.11/0.37	% WCLimit  : 180
0.11/0.37	% DateTime : Mon Jul 27 13:43:33 UTC 2026
0.11/0.38	% CPUTime  : 
0.11/0.38	% Running portfolio for 1440 s
0.11/0.38	% File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.11/0.38	% Number of cores: 8
0.11/0.38	% Python version: Python 3.12.3
0.11/0.38	% Running in HO mode
0.41/0.64	% Total configuration time : 828
0.41/0.64	% Estimated wc time : 1656
0.41/0.64	% Estimated cpu time (8 cpus) : 207.0
0.42/0.73	% /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
0.42/0.74	% /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
0.42/0.75	% /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
0.42/0.75	% /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
0.42/0.75	% /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
0.42/0.75	% /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
0.42/0.75	% /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
0.42/0.76	% /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
10.35/1.91	% /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
21.43/3.36	% Solved by lams/40_b.comb.sh.
21.43/3.36	% done 166 iterations in 2.560s
21.43/3.36	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
21.43/3.36	% SZS output start Refutation
21.43/3.36	thf(emptyset_type, type, emptyset: $i).
21.43/3.36	thf(lessis_type, type, lessis: $i > $i > $o).
21.43/3.36	thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
21.43/3.36	thf('#sk2_type', type, '#sk2': $i).
21.43/3.36	thf(omega_type, type, omega: $i).
21.43/3.36	thf(d_not_type, type, d_not: $o > $o).
21.43/3.36	thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
21.43/3.36	thf(in_type, type, in: $i > $i > $o).
21.43/3.36	thf(e_is_type, type, e_is: $i > $i > $i > $o).
21.43/3.36	thf(nat_type, type, nat: $i).
21.43/3.36	thf(iii_type, type, iii: $i > $i > $o).
21.43/3.36	thf(l_or_type, type, l_or: $o > $o > $o).
21.43/3.36	thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
21.43/3.36	thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
21.43/3.36	thf(imp_type, type, imp: $o > $o > $o).
21.43/3.36	thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
21.43/3.36	thf('#sk1_type', type, '#sk1': $i).
21.43/3.36	thf(n_is_type, type, n_is: $i > $i > $o).
21.43/3.36	thf(n_some_type, type, n_some: ($i > $o) > $o).
21.43/3.36	thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
21.43/3.36	thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
21.43/3.36	thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
21.43/3.36	thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
21.43/3.36	thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
21.43/3.36	thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
21.43/3.36	thf(satz10g, conjecture,
21.43/3.36	  (all_of @
21.43/3.36	   ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 
21.43/3.36	   ( ^[X0:$i]:
21.43/3.36	     ( all_of @
21.43/3.36	       ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 
21.43/3.36	       ( ^[X1:$i]:
21.43/3.36	         ( ( d_29_ii @ X0 @ X1 ) => ( d_not @ ( lessis @ X0 @ X1 ) ) ) ) ) ))).
21.43/3.36	thf(zf_stmt_0, negated_conjecture,
21.43/3.36	  (~( all_of @
21.43/3.36	      ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 
21.43/3.36	      ( ^[X0:$i]:
21.43/3.36	        ( all_of @
21.43/3.36	          ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 
21.43/3.36	          ( ^[X1:$i]:
21.43/3.36	            ( ( d_29_ii @ X0 @ X1 ) => ( d_not @ ( lessis @ X0 @ X1 ) ) ) ) ) ) )),
21.43/3.36	  inference('cnf.neg', [status(esa)], [satz10g])).
21.43/3.36	thf(zip_derived_cl101, plain,
21.43/3.36	    (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 
21.43/3.36	        (^[Y0 : $i]:
21.43/3.36	           (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 
21.43/3.36	            (^[Y1 : $i]:
21.43/3.36	               (((d_29_ii @ Y0 @ Y1) => (d_not @ (lessis @ Y0 @ Y1))))))))),
21.43/3.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
21.43/3.36	thf(zip_derived_cl102, plain,
21.43/3.36	    (~ (all_of @ ((('#C') @ in @ nat)) @ 
21.43/3.36	        ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 
21.43/3.36	          ((('#S') @ ((('#B') @ ('#S') @ 
21.43/3.36	                       ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @ 
21.43/3.36	            ((('#B') @ ((('#B') @ d_not)) @ lessis)))))))),
21.43/3.36	    inference('lams2combs', [status(thm)], [zip_derived_cl101])).
21.43/3.36	thf(def_nat, axiom,(( nat  ) =
21.43/3.36	  ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))).
21.43/3.36	thf('0', plain,
21.43/3.36	    (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )),
21.43/3.36	    define([status(thm)])).
21.43/3.36	thf(zip_derived_cl171, plain,
21.43/3.36	    (~ (all_of @ 
21.43/3.36	        ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 
21.43/3.36	        ((('#B') @ (all_of @ 
21.43/3.36	                    ((('#C') @ in @ 
21.43/3.36	                      (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 
21.43/3.36	          ((('#S') @ ((('#B') @ ('#S') @ 
21.43/3.36	                       ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @ 
21.43/3.36	            ((('#B') @ ((('#B') @ d_not)) @ lessis)))))))),
21.43/3.36	    inference('rw', [status(thm)], [zip_derived_cl102, '0'])).
21.43/3.36	thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
21.43/3.36	  ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
21.43/3.36	thf('1', plain,
21.43/3.36	    (![X0:( $i > $o ),X1:( $i > $o )]:
21.43/3.36	     ( ( ~( all_of @ X0 @ X1 ) ) <=>
21.43/3.36	       ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
21.43/3.36	    inference('rw.lit', [status(esa)], [def_all_of])).
21.43/3.36	thf(zip_derived_cl172, plain,
21.43/3.36	    (~ (((!!) @ (^[Y0 : $i]:
21.43/3.36	                   (((is_of @ Y0 @ 
21.43/3.36	                     ((('#C') @ in @ 
21.43/3.36	                       (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
21.43/3.36	                     ((('#B') @ (all_of @ 
21.43/3.36	                                 ((('#C') @ in @ 
21.43/3.36	                                   (d_Sep @ omega @ 
21.43/3.36	                                    ((('#C') @ (!=) @ emptyset)))))) @ 
21.43/3.36	                       ((('#S') @ ((('#B') @ ('#S') @ 
21.43/3.36	                                    ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @ 
21.43/3.36	                         ((('#B') @ ((('#B') @ d_not)) @ lessis)))) @ 
21.43/3.36	                       Y0)))))))),
21.43/3.36	    inference('rw_clause', [status(thm)], [zip_derived_cl171, '1'])).
21.43/3.36	thf(zip_derived_cl173, plain,
21.43/3.36	    (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 
21.43/3.36	                             ((('#C') @ is_of @ 
21.43/3.36	                               ((('#C') @ in @ 
21.43/3.36	                                 (d_Sep @ omega @ 
21.43/3.36	                                  ((('#C') @ (!=) @ emptyset))))))))) @ 
21.43/3.36	                  ((('#B') @ (all_of @ 
21.43/3.36	                              ((('#C') @ in @ 
21.43/3.36	                                (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 
21.43/3.36	                    ((('#S') @ ((('#B') @ ('#S') @ 
21.43/3.36	                                 ((('#B') @ ((('#B') @ (=>))) @ d_29_ii)))) @ 
21.43/3.36	                      ((('#B') @ ((('#B') @ d_not)) @ lessis))))))))))),
21.43/3.36	    inference('comb-normalize', [status(thm)], [zip_derived_cl172])).
21.43/3.36	thf(zip_derived_cl174, plain,
21.43/3.36	    (~ (((is_of @ '#sk1' @ 
21.43/3.36	         ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
21.43/3.36	         (all_of @ 
21.43/3.36	         ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 
21.43/3.36	         ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk1'))) @ 
21.43/3.36	           ((('#B') @ d_not @ (lessis @ '#sk1'))))))))),
21.43/3.36	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl173])).
21.43/3.36	thf(def_is_of, axiom,(( is_of @ (X1)@ (X0)) = ((X0 @ X1)))).
21.43/3.36	thf('2', plain,
21.43/3.36	    (![X0:( $i > $o ),X1:$i]: ( ( is_of @ X1 @ X0 ) = ( X0 @ X1 ) )),
21.43/3.36	    define([status(thm)])).
21.43/3.36	thf(zip_derived_cl175, plain,
21.43/3.36	    (~ (((in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
21.43/3.36	         (all_of @ 
21.43/3.36	         ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 
21.43/3.36	         ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk1'))) @ 
21.43/3.36	           ((('#B') @ d_not @ (lessis @ '#sk1'))))))))),
21.43/3.36	    inference('rw', [status(thm)], [zip_derived_cl174, '2'])).
21.43/3.36	thf(zip_derived_cl177, plain,
21.43/3.36	    (~ (all_of @ 
21.43/3.36	        ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 
21.43/3.36	        ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk1'))) @ 
21.43/3.36	          ((('#B') @ d_not @ (lessis @ '#sk1'))))))),
21.43/3.36	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl175])).
21.43/3.36	thf(zip_derived_cl178, plain,
21.43/3.36	    (~ (((!!) @ (^[Y0 : $i]:
21.43/3.36	                   (((is_of @ Y0 @ 
21.43/3.36	                     ((('#C') @ in @ 
21.43/3.36	                       (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
21.43/3.36	                     ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk1'))) @ 
21.43/3.36	                       ((('#B') @ d_not @ (lessis @ '#sk1'))) @ Y0)))))))),
21.43/3.36	    inference('rw_clause', [status(thm)], [zip_derived_cl177, '1'])).
21.43/3.36	thf(zip_derived_cl179, plain,
21.43/3.36	    (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 
21.43/3.36	                             ((('#C') @ is_of @ 
21.43/3.36	                               ((('#C') @ in @ 
21.43/3.36	                                 (d_Sep @ omega @ 
21.43/3.36	                                  ((('#C') @ (!=) @ emptyset))))))))) @ 
21.43/3.36	                  ((('#S') @ ((('#B') @ (=>) @ (d_29_ii @ '#sk1'))) @ 
21.43/3.36	                    ((('#B') @ d_not @ (lessis @ '#sk1')))))))))),
21.43/3.36	    inference('comb-normalize', [status(thm)], [zip_derived_cl178])).
21.43/3.36	thf(zip_derived_cl180, plain,
21.43/3.36	    (~ (((is_of @ '#sk2' @ 
21.43/3.36	         ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
21.43/3.36	         (((d_29_ii @ '#sk1' @ '#sk2') => (d_not @ 
21.43/3.36	           (lessis @ '#sk1' @ '#sk2'))))))),
21.43/3.36	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl179])).
21.43/3.36	thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))).
21.43/3.36	thf('3', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )),
21.43/3.36	    define([status(thm)])).
21.43/3.36	thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))).
21.43/3.36	thf('4', plain,
21.43/3.36	    (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )),
21.43/3.36	    define([status(thm)])).
21.43/3.36	thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))).
21.43/3.36	thf('5', plain,
21.43/3.36	    (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )),
21.43/3.36	    define([status(thm)])).
21.43/3.36	thf(def_n_is, axiom,(( n_is @ (X0)@ (X1)) = ((e_is @ nat @ X0 @ X1)))).
21.43/3.36	thf('6', plain,
21.43/3.36	    (![X1:$i,X0:$i]: ( ( n_is @ X0 @ X1 ) = ( e_is @ nat @ X0 @ X1 ) )),
21.43/3.36	    define([status(thm)])).
21.43/3.36	thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))).
21.43/3.36	thf('7', plain,
21.43/3.36	    (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )),
21.43/3.36	    define([status(thm)])).
21.43/3.36	thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) =
21.43/3.36	  ((n_some @ (diffprop @ X0 @ X1))))).
21.43/3.36	thf('8', plain,
21.43/3.36	    (![X1:$i,X0:$i]:
21.43/3.36	     ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
21.43/3.36	    define([status(thm)])).
21.43/3.36	thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))).
21.43/3.36	thf('9', plain,
21.43/3.36	    (![X1:$i,X0:$i]:
21.43/3.36	     ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
21.43/3.36	    define([status(thm)])).
21.43/3.36	thf(def_lessis, axiom,(( lessis @ (X0)@ (X1)) =
21.43/3.36	  ((l_or @ (iii @ X0 @ X1) @ (n_is @ X0 @ X1))))).
21.43/3.36	thf('10', plain,
21.43/3.36	    (![X1:$i,X0:$i]:
21.43/3.36	     ( ( lessis @ X0 @ X1 ) =
21.43/3.36	       ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
21.43/3.36	    define([status(thm)])).
21.43/3.36	thf(zip_derived_cl181, plain,
21.43/3.36	    (~ (((in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
21.43/3.36	         (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	           (diffprop @ '#sk1' @ '#sk2')) => (imp @ 
21.43/3.36	           (imp @ 
21.43/3.36	            (imp @ 
21.43/3.36	             (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	              (diffprop @ '#sk2' @ '#sk1')) @ 
21.43/3.36	             ($false)) @ 
21.43/3.36	            ((('#sk1') = ('#sk2')))) @ 
21.43/3.36	           ($false))))))),
21.43/3.36	    inference('rw', [status(thm)],
21.43/3.36	              [zip_derived_cl180, '2', '3', '3', '4', '5', '0', '6', '7', 
21.43/3.36	               '7', '8', '9', '10'])).
21.43/3.36	thf(zip_derived_cl183, plain,
21.43/3.36	    (~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	         (diffprop @ '#sk1' @ '#sk2')) => (imp @ 
21.43/3.36	         (imp @ 
21.43/3.36	          (imp @ 
21.43/3.36	           (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	            (diffprop @ '#sk2' @ '#sk1')) @ 
21.43/3.36	           ($false)) @ 
21.43/3.36	          ((('#sk1') = ('#sk2')))) @ 
21.43/3.36	         ($false))))),
21.43/3.36	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl181])).
21.43/3.36	thf(zip_derived_cl185, plain,
21.43/3.36	    (~ (imp @ 
21.43/3.36	        (imp @ 
21.43/3.36	         (imp @ 
21.43/3.36	          (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	           (diffprop @ '#sk2' @ '#sk1')) @ 
21.43/3.36	          ($false)) @ 
21.43/3.36	         ((('#sk1') = ('#sk2')))) @ 
21.43/3.36	        ($false))),
21.43/3.36	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl183])).
21.43/3.36	thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))).
21.43/3.36	thf('11', plain,
21.43/3.36	    (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )),
21.43/3.36	    inference('rw.lit', [status(esa)], [def_imp])).
21.43/3.36	thf(zip_derived_cl186, plain,
21.43/3.36	    (~ (((imp @ 
21.43/3.36	         (imp @ 
21.43/3.36	          (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	           (diffprop @ '#sk2' @ '#sk1')) @ 
21.43/3.36	          ($false)) @ 
21.43/3.36	         ((('#sk1') = ('#sk2')))) => ($false)))),
21.43/3.36	    inference('rw_clause', [status(thm)], [zip_derived_cl185, '11'])).
21.43/3.36	thf(zip_derived_cl187, plain,
21.43/3.36	    (~ (((~) @ (imp @ 
21.43/3.36	                (imp @ 
21.43/3.36	                 (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	                  (diffprop @ '#sk2' @ '#sk1')) @ 
21.43/3.36	                 ($false)) @ 
21.43/3.36	                ((('#sk1') = ('#sk2'))))))),
21.43/3.36	    inference('simplify boolean subterms', [status(thm)], [zip_derived_cl186])).
21.43/3.36	thf(zip_derived_cl188, plain,
21.43/3.36	    ( (imp @ 
21.43/3.36	       (imp @ 
21.43/3.36	        (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	         (diffprop @ '#sk2' @ '#sk1')) @ 
21.43/3.36	        ($false)) @ 
21.43/3.36	       ((('#sk1') = ('#sk2'))))),
21.43/3.36	    inference('simplify nested equalities', [status(thm)],
21.43/3.36	              [zip_derived_cl187])).
21.43/3.36	thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))).
21.43/3.36	thf('12', plain,
21.43/3.36	    (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )),
21.43/3.36	    inference('rw.lit', [status(esa)], [def_imp])).
21.43/3.36	thf(zip_derived_cl189, plain,
21.43/3.36	    ( (((imp @ 
21.43/3.36	        (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	         (diffprop @ '#sk2' @ '#sk1')) @ 
21.43/3.36	        ($false)) => ((('#sk1') = ('#sk2')))))),
21.43/3.36	    inference('rw_clause', [status(thm)], [zip_derived_cl188, '12'])).
21.43/3.36	thf(zip_derived_cl190, plain,
21.43/3.36	    ((~ (imp @ 
21.43/3.36	         (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	          (diffprop @ '#sk2' @ '#sk1')) @ 
21.43/3.36	         ($false))
21.43/3.36	      |  ((('#sk1') = ('#sk2'))))),
21.43/3.36	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl189])).
21.43/3.36	thf(zip_derived_cl191, plain,
21.43/3.36	    ((~ (imp @ 
21.43/3.36	         (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	          (diffprop @ '#sk2' @ '#sk1')) @ 
21.43/3.36	         ($false))
21.43/3.36	      | (('#sk1') = ('#sk2')))),
21.43/3.36	    inference('simplify nested equalities', [status(thm)],
21.43/3.36	              [zip_derived_cl190])).
21.43/3.36	thf(zip_derived_cl192, plain,
21.43/3.36	    ((~ (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	          (diffprop @ '#sk2' @ '#sk1')) => ($false)))
21.43/3.36	      | (('#sk1') = ('#sk2')))),
21.43/3.36	    inference('rw_clause', [status(thm)], [zip_derived_cl191, '11'])).
21.43/3.36	thf(zip_derived_cl193, plain,
21.43/3.36	    ((~ (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	                 (diffprop @ '#sk2' @ '#sk1'))))
21.43/3.36	      | (('#sk1') = ('#sk2')))),
21.43/3.36	    inference('simplify boolean subterms', [status(thm)], [zip_derived_cl192])).
21.43/3.36	thf(zip_derived_cl194, plain,
21.43/3.36	    (( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	        (diffprop @ '#sk2' @ '#sk1'))
21.43/3.36	      | (('#sk1') = ('#sk2')))),
21.43/3.36	    inference('simplify nested equalities', [status(thm)],
21.43/3.36	              [zip_derived_cl193])).
21.43/3.36	thf(satz10d, axiom,
21.43/3.36	  (all_of @
21.43/3.36	   ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 
21.43/3.36	   ( ^[X0:$i]:
21.43/3.36	     ( all_of @
21.43/3.36	       ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 
21.43/3.36	       ( ^[X1:$i]:
21.43/3.36	         ( ( lessis @ X0 @ X1 ) => ( d_not @ ( d_29_ii @ X0 @ X1 ) ) ) ) ) ))).
21.43/3.36	thf(zip_derived_cl47, plain,
21.43/3.36	    ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ 
21.43/3.36	       (^[Y0 : $i]:
21.43/3.36	          (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 
21.43/3.36	           (^[Y1 : $i]:
21.43/3.36	              (((lessis @ Y0 @ Y1) => (d_not @ (d_29_ii @ Y0 @ Y1))))))))),
21.43/3.36	    inference('cnf', [status(esa)], [satz10d])).
21.43/3.36	thf(zip_derived_cl48, plain,
21.43/3.36	    ( (all_of @ ((('#C') @ in @ nat)) @ 
21.43/3.36	       ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 
21.43/3.36	         ((('#S') @ ((('#B') @ ('#S') @ 
21.43/3.36	                      ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @ 
21.43/3.36	           ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))))),
21.43/3.36	    inference('lams2combs', [status(thm)], [zip_derived_cl47])).
21.43/3.36	thf(zip_derived_cl329, plain,
21.43/3.36	    ( (all_of @ 
21.43/3.36	       ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 
21.43/3.36	       ((('#B') @ (all_of @ 
21.43/3.36	                   ((('#C') @ in @ 
21.43/3.36	                     (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 
21.43/3.36	         ((('#S') @ ((('#B') @ ('#S') @ 
21.43/3.36	                      ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @ 
21.43/3.36	           ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))))))),
21.43/3.36	    inference('rw', [status(thm)], [zip_derived_cl48, '0'])).
21.43/3.36	thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
21.43/3.36	  ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
21.43/3.36	thf('13', plain,
21.43/3.36	    (![X0:( $i > $o ),X1:( $i > $o )]:
21.43/3.36	     ( ( all_of @ X0 @ X1 ) <=>
21.43/3.36	       ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
21.43/3.36	    inference('rw.lit', [status(esa)], [def_all_of])).
21.43/3.36	thf(zip_derived_cl330, plain,
21.43/3.36	    ( (((!!) @ (^[Y0 : $i]:
21.43/3.36	                  (((is_of @ Y0 @ 
21.43/3.36	                    ((('#C') @ in @ 
21.43/3.36	                      (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
21.43/3.36	                    ((('#B') @ (all_of @ 
21.43/3.36	                                ((('#C') @ in @ 
21.43/3.36	                                  (d_Sep @ omega @ 
21.43/3.36	                                   ((('#C') @ (!=) @ emptyset)))))) @ 
21.43/3.36	                      ((('#S') @ ((('#B') @ ('#S') @ 
21.43/3.36	                                   ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @ 
21.43/3.36	                        ((('#B') @ ((('#B') @ d_not)) @ d_29_ii)))) @ 
21.43/3.36	                      Y0)))))))),
21.43/3.36	    inference('rw_clause', [status(thm)], [zip_derived_cl329, '13'])).
21.43/3.36	thf(zip_derived_cl331, plain,
21.43/3.36	    ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 
21.43/3.36	                            ((('#C') @ is_of @ 
21.43/3.36	                              ((('#C') @ in @ 
21.43/3.36	                                (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))) @ 
21.43/3.36	                 ((('#B') @ (all_of @ 
21.43/3.36	                             ((('#C') @ in @ 
21.43/3.36	                               (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 
21.43/3.36	                   ((('#S') @ ((('#B') @ ('#S') @ 
21.43/3.36	                                ((('#B') @ ((('#B') @ (=>))) @ lessis)))) @ 
21.43/3.36	                     ((('#B') @ ((('#B') @ d_not)) @ d_29_ii))))))))))),
21.43/3.36	    inference('comb-normalize', [status(thm)], [zip_derived_cl330])).
21.43/3.36	thf(zip_derived_cl332, plain,
21.43/3.36	    (![X2 : $i]:
21.43/3.36	        (((is_of @ X2 @ 
21.43/3.36	          ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
21.43/3.36	          (all_of @ 
21.43/3.36	          ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 
21.43/3.36	          ((('#S') @ ((('#B') @ (=>) @ (lessis @ X2))) @ 
21.43/3.36	            ((('#B') @ d_not @ (d_29_ii @ X2))))))))),
21.43/3.36	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl331])).
21.43/3.36	thf(zip_derived_cl333, plain,
21.43/3.36	    (![X2 : $i]:
21.43/3.36	        (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
21.43/3.36	          (all_of @ 
21.43/3.36	          ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 
21.43/3.36	          ((('#S') @ ((('#B') @ (=>) @ (lessis @ X2))) @ 
21.43/3.36	            ((('#B') @ d_not @ (d_29_ii @ X2))))))))),
21.43/3.36	    inference('rw', [status(thm)], [zip_derived_cl332, '2'])).
21.43/3.36	thf(zip_derived_cl334, plain,
21.43/3.36	    (![X2 : $i]:
21.43/3.36	       (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        |  (all_of @ 
21.43/3.36	            ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 
21.43/3.36	            ((('#S') @ ((('#B') @ (=>) @ (lessis @ X2))) @ 
21.43/3.36	              ((('#B') @ d_not @ (d_29_ii @ X2)))))))),
21.43/3.36	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl333])).
21.43/3.36	thf(zip_derived_cl335, plain,
21.43/3.36	    (![X0 : $i]:
21.43/3.36	       ( (((!!) @ (^[Y0 : $i]:
21.43/3.36	                     (((is_of @ Y0 @ 
21.43/3.36	                       ((('#C') @ in @ 
21.43/3.36	                         (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
21.43/3.36	                       ((('#S') @ ((('#B') @ (=>) @ (lessis @ X0))) @ 
21.43/3.36	                         ((('#B') @ d_not @ (d_29_ii @ X0))) @ Y0)))))))
21.43/3.36	        | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
21.43/3.36	    inference('rw_clause', [status(thm)], [zip_derived_cl334, '13'])).
21.43/3.36	thf(zip_derived_cl336, plain,
21.43/3.36	    (![X0 : $i]:
21.43/3.36	       ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 
21.43/3.36	                               ((('#C') @ is_of @ 
21.43/3.36	                                 ((('#C') @ in @ 
21.43/3.36	                                   (d_Sep @ omega @ 
21.43/3.36	                                    ((('#C') @ (!=) @ emptyset))))))))) @ 
21.43/3.36	                    ((('#S') @ ((('#B') @ (=>) @ (lessis @ X0))) @ 
21.43/3.36	                      ((('#B') @ d_not @ (d_29_ii @ X0)))))))))
21.43/3.36	        | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
21.43/3.36	    inference('comb-normalize', [status(thm)], [zip_derived_cl335])).
21.43/3.36	thf(zip_derived_cl337, plain,
21.43/3.36	    (![X0 : $i, X2 : $i]:
21.43/3.36	       ( (((is_of @ X2 @ 
21.43/3.36	           ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
21.43/3.36	           (((lessis @ X0 @ X2) => (d_not @ (d_29_ii @ X0 @ X2))))))
21.43/3.36	        | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
21.43/3.36	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl336])).
21.43/3.36	thf(zip_derived_cl338, plain,
21.43/3.36	    (![X0 : $i, X2 : $i]:
21.43/3.36	       ( (((in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))) =>
21.43/3.36	           (((imp @ 
21.43/3.36	             (imp @ 
21.43/3.36	              (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	               (diffprop @ X2 @ X0)) @ 
21.43/3.36	              ($false)) @ 
21.43/3.36	             (((X0) = (X2)))) => (imp @ 
21.43/3.36	             (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	              (diffprop @ X0 @ X2)) @ 
21.43/3.36	             ($false))))))
21.43/3.36	        | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
21.43/3.36	    inference('rw', [status(thm)],
21.43/3.36	              [zip_derived_cl337, '2', '3', '3', '4', '5', '0', '6', '7', 
21.43/3.36	               '7', '8', '9', '10'])).
21.43/3.36	thf(zip_derived_cl339, plain,
21.43/3.36	    (![X0 : $i, X2 : $i]:
21.43/3.36	       (~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        |  (((imp @ 
21.43/3.36	             (imp @ 
21.43/3.36	              (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	               (diffprop @ X2 @ X0)) @ 
21.43/3.36	              ($false)) @ 
21.43/3.36	             (((X0) = (X2)))) => (imp @ 
21.43/3.36	             (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	              (diffprop @ X0 @ X2)) @ 
21.43/3.36	             ($false))))
21.43/3.36	        | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
21.43/3.36	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl338])).
21.43/3.36	thf(zip_derived_cl340, plain,
21.43/3.36	    (![X0 : $i, X2 : $i]:
21.43/3.36	       (~ (imp @ 
21.43/3.36	           (imp @ 
21.43/3.36	            (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	             (diffprop @ X2 @ X0)) @ 
21.43/3.36	            ($false)) @ 
21.43/3.36	           (((X0) = (X2))))
21.43/3.36	        |  (imp @ 
21.43/3.36	            (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	             (diffprop @ X0 @ X2)) @ 
21.43/3.36	            ($false))
21.43/3.36	        | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (in @ X2 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
21.43/3.36	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl339])).
21.43/3.36	thf(zip_derived_cl341, plain,
21.43/3.36	    (![X0 : $i, X1 : $i]:
21.43/3.36	       (~ (((imp @ 
21.43/3.36	            (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	             (diffprop @ X0 @ X1)) @ 
21.43/3.36	            ($false)) => (((X1) = (X0)))))
21.43/3.36	        | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        |  (imp @ 
21.43/3.36	            (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	             (diffprop @ X1 @ X0)) @ 
21.43/3.36	            ($false)))),
21.43/3.36	    inference('rw_clause', [status(thm)], [zip_derived_cl340, '11'])).
21.43/3.36	thf(zip_derived_cl342, plain,
21.43/3.36	    (![X0 : $i, X1 : $i]:
21.43/3.36	       ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	           (diffprop @ X0 @ X1)) => ($false)))
21.43/3.36	        | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (((imp @ 
21.43/3.36	              (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	               (diffprop @ X1 @ X0)) @ 
21.43/3.36	              ($false)) => (((X0) = (X1))))))),
21.43/3.36	    inference('rw_clause', [status(thm)], [zip_derived_cl341, '12'])).
21.43/3.36	thf(zip_derived_cl343, plain,
21.43/3.36	    (![X0 : $i, X1 : $i]:
21.43/3.36	       ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	                  (diffprop @ X0 @ X1))))
21.43/3.36	        | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (((imp @ 
21.43/3.36	              (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	               (diffprop @ X1 @ X0)) @ 
21.43/3.36	              ($false)) => (((X0) = (X1))))))),
21.43/3.36	    inference('simplify boolean subterms', [status(thm)], [zip_derived_cl342])).
21.43/3.36	thf(zip_derived_cl344, plain,
21.43/3.36	    (![X0 : $i, X1 : $i]:
21.43/3.36	       (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	           (diffprop @ X0 @ X1))
21.43/3.36	        | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (((imp @ 
21.43/3.36	              (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	               (diffprop @ X1 @ X0)) @ 
21.43/3.36	              ($false)) => (((X0) = (X1))))))),
21.43/3.36	    inference('simplify nested equalities', [status(thm)],
21.43/3.36	              [zip_derived_cl343])).
21.43/3.36	thf(zip_derived_cl345, plain,
21.43/3.36	    (![X0 : $i, X1 : $i]:
21.43/3.36	       ( (imp @ 
21.43/3.36	          (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	           (diffprop @ X1 @ X0)) @ 
21.43/3.36	          ($false))
21.43/3.36	        | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	             (diffprop @ X0 @ X1)))),
21.43/3.36	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl344])).
21.43/3.36	thf(zip_derived_cl347, plain,
21.43/3.36	    (![X0 : $i, X1 : $i]:
21.43/3.36	       ( (((l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	           (diffprop @ X0 @ X1)) => ($false)))
21.43/3.36	        | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	             (diffprop @ X1 @ X0))
21.43/3.36	        | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
21.43/3.36	    inference('rw_clause', [status(thm)], [zip_derived_cl345, '12'])).
21.43/3.36	thf(zip_derived_cl349, plain,
21.43/3.36	    (![X0 : $i, X1 : $i]:
21.43/3.36	       ( (((~) @ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	                  (diffprop @ X0 @ X1))))
21.43/3.36	        | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	             (diffprop @ X1 @ X0))
21.43/3.36	        | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
21.43/3.36	    inference('simplify boolean subterms', [status(thm)], [zip_derived_cl347])).
21.43/3.36	thf(zip_derived_cl350, plain,
21.43/3.36	    (![X0 : $i, X1 : $i]:
21.43/3.36	       (~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	           (diffprop @ X0 @ X1))
21.43/3.36	        | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	             (diffprop @ X1 @ X0))
21.43/3.36	        | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))),
21.43/3.36	    inference('simplify nested equalities', [status(thm)],
21.43/3.36	              [zip_derived_cl349])).
21.43/3.36	thf(zip_derived_cl2270, plain,
21.43/3.36	    (((('#sk1') = ('#sk2'))
21.43/3.36	      | ~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	      | ~ (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	      | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	           (diffprop @ '#sk1' @ '#sk2')))),
21.43/3.36	    inference('sup-', [status(thm)], [zip_derived_cl194, zip_derived_cl350])).
21.43/3.36	thf(zip_derived_cl182, plain,
21.43/3.36	    ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
21.43/3.36	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl181])).
21.43/3.36	thf(zip_derived_cl176, plain,
21.43/3.36	    ( (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
21.43/3.36	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl175])).
21.43/3.36	thf(zip_derived_cl184, plain,
21.43/3.36	    ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	       (diffprop @ '#sk1' @ '#sk2'))),
21.43/3.36	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl183])).
21.43/3.36	thf(zip_derived_cl2286, plain, ((('#sk1') = ('#sk2'))),
21.43/3.36	    inference('demod', [status(thm)],
21.43/3.36	              [zip_derived_cl2270, zip_derived_cl182, zip_derived_cl176, 
21.43/3.36	               zip_derived_cl184])).
21.43/3.36	thf(zip_derived_cl184, plain,
21.43/3.36	    ( (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	       (diffprop @ '#sk1' @ '#sk2'))),
21.43/3.36	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl183])).
21.43/3.36	thf(zip_derived_cl346, plain,
21.43/3.36	    (![X0 : $i, X1 : $i]:
21.43/3.36	       (~ (((X0) = (X1)))
21.43/3.36	        | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	             (diffprop @ X0 @ X1)))),
21.43/3.36	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl344])).
21.43/3.36	thf(zip_derived_cl348, plain,
21.43/3.36	    (![X0 : $i, X1 : $i]:
21.43/3.36	       (((X0) != (X1))
21.43/3.36	        | ~ (in @ X1 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (in @ X0 @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	        | ~ (l_some @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 
21.43/3.36	             (diffprop @ X0 @ X1)))),
21.43/3.36	    inference('simplify nested equalities', [status(thm)],
21.43/3.36	              [zip_derived_cl346])).
21.43/3.36	thf(zip_derived_cl2153, plain,
21.43/3.36	    ((~ (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	      | ~ (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))
21.43/3.36	      | (('#sk1') != ('#sk2')))),
21.43/3.36	    inference('sup-', [status(thm)], [zip_derived_cl184, zip_derived_cl348])).
21.43/3.36	thf(zip_derived_cl176, plain,
21.43/3.36	    ( (in @ '#sk1' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
21.43/3.36	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl175])).
21.43/3.36	thf(zip_derived_cl182, plain,
21.43/3.36	    ( (in @ '#sk2' @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))),
21.43/3.36	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl181])).
21.43/3.36	thf(zip_derived_cl2159, plain, ((('#sk1') != ('#sk2'))),
21.43/3.36	    inference('demod', [status(thm)],
21.43/3.36	              [zip_derived_cl2153, zip_derived_cl176, zip_derived_cl182])).
21.43/3.36	thf(zip_derived_cl2287, plain, ($false),
21.43/3.36	    inference('simplify_reflect-', [status(thm)],
21.43/3.36	              [zip_derived_cl2286, zip_derived_cl2159])).
21.43/3.36	
21.43/3.36	% SZS output end Refutation
21.43/3.36	
21.43/3.36	
21.43/3.36	% Terminating...
5.20/3.40	% Runner terminated.
5.20/3.43	% Zipperpin 1.5 exiting
5.20/3.44	EOF