0.00/0.10	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.12	% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.V4GAWtQP4U true
0.12/0.33	% Computer : n006.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit : 1440
0.12/0.33	% WCLimit  : 180
0.12/0.33	% DateTime : Thu Jul  4 10:56:09 EDT 2024
0.12/0.33	% CPUTime  : 
0.12/0.33	% Running portfolio for 1440 s
0.12/0.33	% File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.18/0.33	% Number of cores: 8
0.18/0.33	% Python version: Python 3.6.8
0.18/0.34	% Running in HO mode
0.71/0.61	% Total configuration time : 828
0.71/0.61	% Estimated wc time : 1656
0.71/0.61	% Estimated cpu time (8 cpus) : 207.0
0.71/0.63	% /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
0.95/0.64	% /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
0.95/0.67	% /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
0.95/0.69	% /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
0.95/0.69	% /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
0.95/0.70	% /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
0.95/0.70	% /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
0.95/0.70	% /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
83.60/11.07	% Solved by lams/35_full_unif4.sh.
83.60/11.07	% done 896 iterations in 10.400s
83.60/11.07	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
83.60/11.07	% SZS output start Refutation
83.60/11.07	thf(emptyset_type, type, emptyset: $i).
83.60/11.07	thf(lessis_type, type, lessis: $i > $i > $o).
83.60/11.07	thf(orec3_type, type, orec3: $o > $o > $o > $o).
83.60/11.07	thf(diffprop_type, type, diffprop: $i > $i > $i > $o).
83.60/11.07	thf(ec3_type, type, ec3: $o > $o > $o > $o).
83.60/11.07	thf(l_ec_type, type, l_ec: $o > $o > $o).
83.60/11.07	thf(d_not_type, type, d_not: $o > $o).
83.60/11.07	thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
83.60/11.07	thf(in_type, type, in: $i > $i > $o).
83.60/11.07	thf(moreis_type, type, moreis: $i > $i > $o).
83.60/11.07	thf(n_1_type, type, n_1: $i).
83.60/11.07	thf('#sk7506_type', type, '#sk7506': $i > $i > $i).
83.60/11.07	thf(and3_type, type, and3: $o > $o > $o > $o).
83.60/11.07	thf('#form7507_type', type, '#form7507': $i > $i > $o).
83.60/11.07	thf(e_is_type, type, e_is: $i > $i > $i > $o).
83.60/11.07	thf(nat_type, type, nat: $i).
83.60/11.07	thf(iii_type, type, iii: $i > $i > $o).
83.60/11.07	thf(l_or_type, type, l_or: $o > $o > $o).
83.60/11.07	thf(non_type, type, non: $i > ($i > $o) > $i > $o).
83.60/11.07	thf('#sk3561_type', type, '#sk3561': $i).
83.60/11.07	thf(l_some_type, type, l_some: $i > ($i > $o) > $o).
83.60/11.07	thf(d_and_type, type, d_and: $o > $o > $o).
83.60/11.07	thf(imp_type, type, imp: $o > $o > $o).
83.60/11.07	thf('#sk8789_type', type, '#sk8789': $i).
83.60/11.07	thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
83.60/11.07	thf(n_is_type, type, n_is: $i > $i > $o).
83.60/11.07	thf(or3_type, type, or3: $o > $o > $o > $o).
83.60/11.07	thf(n_some_type, type, n_some: ($i > $o) > $o).
83.60/11.07	thf(ordsucc_type, type, ordsucc: $i > $i).
83.60/11.07	thf(d_29_ii_type, type, d_29_ii: $i > $i > $o).
83.60/11.07	thf(n_pl_type, type, n_pl: $i > $i > $i).
83.60/11.07	thf('#sk8788_type', type, '#sk8788': $i).
83.60/11.07	thf(def_lessis, axiom,(( lessis  ) =
83.60/11.07	  (^[X0:$i,X1:$i]: ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) )))).
83.60/11.07	thf(def_iii, axiom,(( iii  ) =
83.60/11.07	  (^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X1 @ X0 ) )))).
83.60/11.07	thf(def_diffprop, axiom,(( diffprop  ) =
83.60/11.07	  (^[X0:$i,X1:$i,X2:$i]: ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) )))).
83.60/11.07	thf(def_n_is, axiom,(( n_is  ) = (e_is @ nat))).
83.60/11.07	thf(def_e_is, axiom,(( e_is  ) = (^[X0:$i,X:$i,Y:$i]: ( ( X ) = ( Y ) )))).
83.60/11.07	thf('0', plain, (( e_is ) = ( ^[X0:$i,X:$i,Y:$i]: ( ( X ) = ( Y ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)], [def_e_is])).
83.60/11.07	thf('1', plain,
83.60/11.07	    (( e_is ) = ( ^[V_1:$i,V_2:$i,V_3:$i]: ( ( V_2 ) = ( V_3 ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf('2', plain, (( n_is ) = ( e_is @ nat )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)], [def_n_is, '1'])).
83.60/11.07	thf('3', plain, (( n_is ) = ( e_is @ nat )), define([status(thm)])).
83.60/11.07	thf('4', plain,
83.60/11.07	    (( diffprop ) =
83.60/11.07	     ( ^[X0:$i,X1:$i,X2:$i]: ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)], [def_diffprop, '3', '1'])).
83.60/11.07	thf('5', plain,
83.60/11.07	    (( diffprop ) =
83.60/11.07	     ( ^[V_1:$i,V_2:$i,V_3:$i]: ( n_is @ V_1 @ ( n_pl @ V_2 @ V_3 ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf(def_n_some, axiom,(( n_some  ) = (l_some @ nat))).
83.60/11.07	thf(def_l_some, axiom,(( l_some  ) =
83.60/11.07	  (^[X0:$i,X1:( $i > $o )]:
83.60/11.07	   ( d_not @ ( all_of @ ( ^[X2:$i]: ( in @ X2 @ X0 ) ) @ ( non @ X0 @ X1 ) ) )))).
83.60/11.07	thf(def_non, axiom,(( non  ) =
83.60/11.07	  (^[X0:$i,X1:( $i > $o ),X2:$i]: ( d_not @ ( X1 @ X2 ) )))).
83.60/11.07	thf(def_d_not, axiom,(( d_not  ) = (^[X0:$o]: ( imp @ X0 @ $false )))).
83.60/11.07	thf(def_imp, axiom,(( imp  ) = (^[X0:$o,X1:$o]: ( ( X0 ) => ( X1 ) )))).
83.60/11.07	thf('6', plain, (( imp ) = ( ^[X0:$o,X1:$o]: ( ( X0 ) => ( X1 ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)], [def_imp])).
83.60/11.07	thf('7', plain, (( imp ) = ( ^[V_1:$o,V_2:$o]: ( ( V_1 ) => ( V_2 ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf('8', plain, (( d_not ) = ( ^[X0:$o]: ( imp @ X0 @ $false ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)], [def_d_not, '7'])).
83.60/11.07	thf('9', plain, (( d_not ) = ( ^[V_1:$o]: ( imp @ V_1 @ $false ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf('10', plain,
83.60/11.07	    (( non ) = ( ^[X0:$i,X1:( $i > $o ),X2:$i]: ( d_not @ ( X1 @ X2 ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)], [def_non, '9', '7'])).
83.60/11.07	thf('11', plain,
83.60/11.07	    (( non ) =
83.60/11.07	     ( ^[V_1:$i,V_2:( $i > $o ),V_3:$i]: ( d_not @ ( V_2 @ V_3 ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf(def_all_of, axiom,(( all_of  ) =
83.60/11.07	  (^[X0:( $i > $o ),X1:( $i > $o )]:
83.60/11.07	   ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) )))).
83.60/11.07	thf(def_is_of, axiom,(( is_of  ) = (^[X0:$i,X1:( $i > $o )]: ( X1 @ X0 )))).
83.60/11.07	thf('12', plain, (( is_of ) = ( ^[X0:$i,X1:( $i > $o )]: ( X1 @ X0 ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)], [def_is_of])).
83.60/11.07	thf('13', plain, (( is_of ) = ( ^[V_1:$i,V_2:( $i > $o )]: ( V_2 @ V_1 ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf('14', plain,
83.60/11.07	    (( all_of ) =
83.60/11.07	     ( ^[X0:( $i > $o ),X1:( $i > $o )]:
83.60/11.07	       ( ![X2:$i]: ( ( is_of @ X2 @ X0 ) => ( X1 @ X2 ) ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)], [def_all_of, '13'])).
83.60/11.07	thf('15', plain,
83.60/11.07	    (( all_of ) =
83.60/11.07	     ( ^[V_1:( $i > $o ),V_2:( $i > $o )]:
83.60/11.07	       ( ![X4:$i]: ( ( is_of @ X4 @ V_1 ) => ( V_2 @ X4 ) ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf('16', plain,
83.60/11.07	    (( l_some ) =
83.60/11.07	     ( ^[X0:$i,X1:( $i > $o )]:
83.60/11.07	       ( d_not @
83.60/11.07	         ( all_of @ ( ^[X2:$i]: ( in @ X2 @ X0 ) ) @ ( non @ X0 @ X1 ) ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)],
83.60/11.07	              [def_l_some, '11', '9', '7', '15', '13'])).
83.60/11.07	thf('17', plain,
83.60/11.07	    (( l_some ) =
83.60/11.07	     ( ^[V_1:$i,V_2:( $i > $o )]:
83.60/11.07	       ( d_not @
83.60/11.07	         ( all_of @ ( ^[V_3:$i]: ( in @ V_3 @ V_1 ) ) @ ( non @ V_1 @ V_2 ) ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf('18', plain, (( n_some ) = ( l_some @ nat )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)],
83.60/11.07	              [def_n_some, '17', '11', '9', '7', '15', '13'])).
83.60/11.07	thf('19', plain, (( n_some ) = ( l_some @ nat )), define([status(thm)])).
83.60/11.07	thf('20', plain,
83.60/11.07	    (( iii ) = ( ^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X1 @ X0 ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)],
83.60/11.07	              [def_iii, '5', '19', '3', '1', '17', '11', '9', '7', '15', '13'])).
83.60/11.07	thf('21', plain,
83.60/11.07	    (( iii ) = ( ^[V_1:$i,V_2:$i]: ( n_some @ ( diffprop @ V_2 @ V_1 ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf(def_l_or, axiom,(( l_or  ) = (^[X0:$o]: ( imp @ ( d_not @ X0 ) )))).
83.60/11.07	thf('22', plain, (( l_or ) = ( ^[X0:$o]: ( imp @ ( d_not @ X0 ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)], [def_l_or, '9', '7'])).
83.60/11.07	thf('23', plain, (( l_or ) = ( ^[V_1:$o]: ( imp @ ( d_not @ V_1 ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf('24', plain,
83.60/11.07	    (( lessis ) =
83.60/11.07	     ( ^[X0:$i,X1:$i]: ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)],
83.60/11.07	              [def_lessis, '21', '5', '19', '3', '1', '17', '11', '23', '9', 
83.60/11.07	               '7', '15', '13'])).
83.60/11.07	thf('25', plain,
83.60/11.07	    (( lessis ) =
83.60/11.07	     ( ^[V_1:$i,V_2:$i]:
83.60/11.07	       ( l_or @ ( iii @ V_1 @ V_2 ) @ ( n_is @ V_1 @ V_2 ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf(satz25b, conjecture,
83.60/11.07	  (all_of @
83.60/11.07	   ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 
83.60/11.07	   ( ^[X0:$i]:
83.60/11.07	     ( all_of @
83.60/11.07	       ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 
83.60/11.07	       ( ^[X1:$i]:
83.60/11.07	         ( ( iii @ X1 @ X0 ) => ( lessis @ ( n_pl @ X1 @ n_1 ) @ X0 ) ) ) ) ))).
83.60/11.07	thf(zf_stmt_0, conjecture,
83.60/11.07	  (![X4:$i]:
83.60/11.07	   ( ( in @ X4 @ nat ) =>
83.60/11.07	     ( ![X6:$i]:
83.60/11.07	       ( ( in @ X6 @ nat ) =>
83.60/11.07	         ( ( ~( ![X8:$i]:
83.60/11.07	                ( ( in @ X8 @ nat ) => ( ( X4 ) != ( n_pl @ X6 @ X8 ) ) ) ) ) =>
83.60/11.07	           ( ( ![X10:$i]:
83.60/11.07	               ( ( in @ X10 @ nat ) =>
83.60/11.07	                 ( ( X4 ) != ( n_pl @ ( n_pl @ X6 @ n_1 ) @ X10 ) ) ) ) =>
83.60/11.07	             ( ( n_pl @ X6 @ n_1 ) = ( X4 ) ) ) ) ) ) ))).
83.60/11.07	thf(zf_stmt_1, negated_conjecture,
83.60/11.07	  (~( ![X4:$i]:
83.60/11.07	      ( ( in @ X4 @ nat ) =>
83.60/11.07	        ( ![X6:$i]:
83.60/11.07	          ( ( in @ X6 @ nat ) =>
83.60/11.07	            ( ( ~( ![X8:$i]:
83.60/11.07	                   ( ( in @ X8 @ nat ) => ( ( X4 ) != ( n_pl @ X6 @ X8 ) ) ) ) ) =>
83.60/11.07	              ( ( ![X10:$i]:
83.60/11.07	                  ( ( in @ X10 @ nat ) =>
83.60/11.07	                    ( ( X4 ) != ( n_pl @ ( n_pl @ X6 @ n_1 ) @ X10 ) ) ) ) =>
83.60/11.07	                ( ( n_pl @ X6 @ n_1 ) = ( X4 ) ) ) ) ) ) ) )),
83.60/11.07	  inference('cnf.neg', [status(esa)], [zf_stmt_0])).
83.60/11.07	thf(zip_derived_cl154, plain,
83.60/11.07	    (~ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                   (((in @ Y0 @ nat) =>
83.60/11.07	                     (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                 (((in @ Y1 @ nat) =>
83.60/11.07	                                   (((((~) @ (((!!) @ (^[Y2 : $i]:
83.60/11.07	                                                         (((in @ Y2 @ nat) =>
83.60/11.07	                                                           (((Y0) != (n_pl @ 
83.60/11.07	                                                             Y1 @ Y2)))))))))) =>
83.60/11.07	                                     (((((!!) @ (^[Y2 : $i]:
83.60/11.07	                                                   (((in @ Y2 @ nat) =>
83.60/11.07	                                                     (((Y0) != (n_pl @ 
83.60/11.07	                                                       (n_pl @ Y1 @ n_1) @ 
83.60/11.07	                                                       Y2)))))))) =>
83.60/11.07	                                       (((n_pl @ Y1 @ n_1) = (Y0)))))))))))))))))),
83.60/11.07	    inference('cnf', [status(esa)], [zf_stmt_1])).
83.60/11.07	thf(zip_derived_cl7069, plain,
83.60/11.07	    (~ (((in @ '#sk8788' @ nat) =>
83.60/11.07	         (((!!) @ (^[Y0 : $i]:
83.60/11.07	                     (((in @ Y0 @ nat) =>
83.60/11.07	                       (((((~) @ (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                             (((in @ Y1 @ nat) =>
83.60/11.07	                                               ((('#sk8788') != (n_pl @ Y0 @ 
83.60/11.07	                                                 Y1)))))))))) =>
83.60/11.07	                         (((((!!) @ (^[Y1 : $i]:
83.60/11.07	                                       (((in @ Y1 @ nat) =>
83.60/11.07	                                         ((('#sk8788') != (n_pl @ 
83.60/11.07	                                           (n_pl @ Y0 @ n_1) @ Y1)))))))) =>
83.60/11.07	                           (((n_pl @ Y0 @ n_1) = ('#sk8788'))))))))))))))),
83.60/11.07	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl154])).
83.60/11.07	thf(zip_derived_cl7071, plain,
83.60/11.07	    (~ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                   (((in @ Y0 @ nat) =>
83.60/11.07	                     (((((~) @ (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                           (((in @ Y1 @ nat) =>
83.60/11.07	                                             ((('#sk8788') != (n_pl @ Y0 @ 
83.60/11.07	                                               Y1)))))))))) =>
83.60/11.07	                       (((((!!) @ (^[Y1 : $i]:
83.60/11.07	                                     (((in @ Y1 @ nat) =>
83.60/11.07	                                       ((('#sk8788') != (n_pl @ 
83.60/11.07	                                         (n_pl @ Y0 @ n_1) @ Y1)))))))) =>
83.60/11.07	                         (((n_pl @ Y0 @ n_1) = ('#sk8788'))))))))))))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7069])).
83.60/11.07	thf(zip_derived_cl7072, plain,
83.60/11.07	    (~ (((in @ '#sk8789' @ nat) =>
83.60/11.07	         (((((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                               (((in @ Y0 @ nat) =>
83.60/11.07	                                 ((('#sk8788') != (n_pl @ '#sk8789' @ Y0)))))))))) =>
83.60/11.07	           (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                         (((in @ Y0 @ nat) =>
83.60/11.07	                           ((('#sk8788') != (n_pl @ 
83.60/11.07	                             (n_pl @ '#sk8789' @ n_1) @ Y0)))))))) =>
83.60/11.07	             (((n_pl @ '#sk8789' @ n_1) = ('#sk8788')))))))))),
83.60/11.07	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl7071])).
83.60/11.07	thf(def_n_1, axiom, (( n_1 ) = ( ordsucc @ emptyset ))).
83.60/11.07	thf(zip_derived_cl47, plain, (((n_1) = (ordsucc @ emptyset))),
83.60/11.07	    inference('cnf', [status(esa)], [def_n_1])).
83.60/11.07	thf(k_In_ind, axiom,
83.60/11.07	  (![X0:( $i > $o )]:
83.60/11.07	   ( ( ![X1:$i]:
83.60/11.07	       ( ( ![X2:$i]: ( ( in @ X2 @ X1 ) => ( X0 @ X2 ) ) ) => ( X0 @ X1 ) ) ) =>
83.60/11.07	     ( ![X1:$i]: ( X0 @ X1 ) ) ))).
83.60/11.07	thf(zip_derived_cl83, plain,
83.60/11.07	    ( (((!!) @ (^[Y0 : $i > $o]:
83.60/11.07	                  (((((!!) @ (^[Y1 : $i]:
83.60/11.07	                                (((((!!) @ (^[Y2 : $i]:
83.60/11.07	                                              (((in @ Y2 @ Y1) => (Y0 @ Y2)))))) =>
83.60/11.07	                                  (Y0 @ Y1)))))) =>
83.60/11.07	                    (((!!) @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
83.60/11.07	    inference('cnf', [status(esa)], [k_In_ind])).
83.60/11.07	thf(zip_derived_cl2418, plain,
83.60/11.07	    (![X2 : $i > $o]:
83.60/11.07	        (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                      (((((!!) @ (^[Y1 : $i]: (((in @ Y1 @ Y0) => (X2 @ Y1)))))) =>
83.60/11.07	                        (X2 @ Y0)))))) =>
83.60/11.07	          (((!!) @ (^[Y0 : $i]: (X2 @ Y0))))))),
83.60/11.07	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl83])).
83.60/11.07	thf(zip_derived_cl2420, plain,
83.60/11.07	    ( (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                    (((((!!) @ (^[Y1 : $i]:
83.60/11.07	                                  (((in @ Y1 @ Y0) => (((Y1) != (emptyset)))))))) =>
83.60/11.07	                      (((Y0) != (emptyset)))))))) =>
83.60/11.07	        (((!!) @ (^[Y0 : $i]: (((Y0) != (emptyset))))))))),
83.60/11.07	    inference('triggered_bool_instantiation', [status(thm)],
83.60/11.07	              [zip_derived_cl2418])).
83.60/11.07	thf(zip_derived_cl2893, plain,
83.60/11.07	    ((~ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                    (((((!!) @ (^[Y1 : $i]:
83.60/11.07	                                  (((in @ Y1 @ Y0) => (((Y1) != (emptyset)))))))) =>
83.60/11.07	                      (((Y0) != (emptyset))))))))
83.60/11.07	      |  (((!!) @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2420])).
83.60/11.07	thf(zip_derived_cl2894, plain,
83.60/11.07	    ((~ (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                      (((in @ Y0 @ '#sk3561') => (((Y0) != (emptyset)))))))) =>
83.60/11.07	          ((('#sk3561') != (emptyset)))))
83.60/11.07	      |  (((!!) @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))),
83.60/11.07	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2893])).
83.60/11.07	thf(zip_derived_cl2896, plain,
83.60/11.07	    ((~ ((('#sk3561') != (emptyset)))
83.60/11.07	      |  (((!!) @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2894])).
83.60/11.07	thf(zip_derived_cl2898, plain,
83.60/11.07	    (((('#sk3561') = (emptyset))
83.60/11.07	      |  (((!!) @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))),
83.60/11.07	    inference('simplify nested equalities', [status(thm)],
83.60/11.07	              [zip_derived_cl2896])).
83.60/11.07	thf(zip_derived_cl2899, plain,
83.60/11.07	    (![X2 : $i]: ( (((X2) != (emptyset))) | (('#sk3561') = (emptyset)))),
83.60/11.07	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2898])).
83.60/11.07	thf(zip_derived_cl2901, plain,
83.60/11.07	    (![X2 : $i]: (((X2) != (emptyset)) | (('#sk3561') = (emptyset)))),
83.60/11.07	    inference('simplify nested equalities', [status(thm)],
83.60/11.07	              [zip_derived_cl2899])).
83.60/11.07	thf(zip_derived_cl2902, plain, ((('#sk3561') = (emptyset))),
83.60/11.07	    inference('simplify', [status(thm)], [zip_derived_cl2901])).
83.60/11.07	thf(zip_derived_cl2909, plain, (((n_1) = (ordsucc @ '#sk3561'))),
83.60/11.07	    inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl2902])).
83.60/11.07	thf(zip_derived_cl7073, plain,
83.60/11.07	    (~ (((in @ '#sk8789' @ nat) =>
83.60/11.07	         (((((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                               (((in @ Y0 @ nat) =>
83.60/11.07	                                 ((('#sk8788') != (n_pl @ '#sk8789' @ Y0)))))))))) =>
83.60/11.07	           (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                         (((in @ Y0 @ nat) =>
83.60/11.07	                           ((('#sk8788') != (n_pl @ 
83.60/11.07	                             (n_pl @ '#sk8789' @ n_1) @ Y0)))))))) =>
83.60/11.07	             (((n_pl @ '#sk8789' @ (ordsucc @ '#sk3561')) = ('#sk8788')))))))))),
83.60/11.07	    inference('demod', [status(thm)],
83.60/11.07	              [zip_derived_cl7072, zip_derived_cl2909])).
83.60/11.07	thf(zip_derived_cl7075, plain,
83.60/11.07	    (~ (((((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                             (((in @ Y0 @ nat) =>
83.60/11.07	                               ((('#sk8788') != (n_pl @ '#sk8789' @ Y0)))))))))) =>
83.60/11.07	         (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                       (((in @ Y0 @ nat) =>
83.60/11.07	                         ((('#sk8788') != (n_pl @ (n_pl @ '#sk8789' @ n_1) @ 
83.60/11.07	                           Y0)))))))) =>
83.60/11.07	           (((n_pl @ '#sk8789' @ (ordsucc @ '#sk3561')) = ('#sk8788')))))))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7073])).
83.60/11.07	thf(zip_derived_cl7077, plain,
83.60/11.07	    (~ (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                     (((in @ Y0 @ nat) =>
83.60/11.07	                       ((('#sk8788') != (n_pl @ (n_pl @ '#sk8789' @ n_1) @ 
83.60/11.07	                         Y0)))))))) =>
83.60/11.07	         (((n_pl @ '#sk8789' @ (ordsucc @ '#sk3561')) = ('#sk8788')))))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7075])).
83.60/11.07	thf(zip_derived_cl7079, plain,
83.60/11.07	    ( (((!!) @ (^[Y0 : $i]:
83.60/11.07	                  (((in @ Y0 @ nat) =>
83.60/11.07	                    ((('#sk8788') != (n_pl @ (n_pl @ '#sk8789' @ n_1) @ Y0))))))))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7077])).
83.60/11.07	thf(def_orec3, axiom,(( orec3  ) =
83.60/11.07	  (^[X0:$o,X1:$o,X2:$o]:
83.60/11.07	   ( d_and @ ( or3 @ X0 @ X1 @ X2 ) @ ( ec3 @ X0 @ X1 @ X2 ) )))).
83.60/11.07	thf(def_ec3, axiom,(( ec3  ) =
83.60/11.07	  (^[X0:$o,X1:$o,X2:$o]:
83.60/11.07	   ( and3 @ ( l_ec @ X0 @ X1 ) @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X0 ) )))).
83.60/11.07	thf(def_and3, axiom,(( and3  ) =
83.60/11.07	  (^[X0:$o,X1:$o,X2:$o]: ( d_and @ X0 @ ( d_and @ X1 @ X2 ) )))).
83.60/11.07	thf(def_d_and, axiom,(( d_and  ) =
83.60/11.07	  (^[X0:$o,X1:$o]: ( d_not @ ( l_ec @ X0 @ X1 ) )))).
83.60/11.07	thf(def_l_ec, axiom,(( l_ec  ) =
83.60/11.07	  (^[X0:$o,X1:$o]: ( imp @ X0 @ ( d_not @ X1 ) )))).
83.60/11.07	thf('26', plain,
83.60/11.07	    (( l_ec ) = ( ^[X0:$o,X1:$o]: ( imp @ X0 @ ( d_not @ X1 ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)], [def_l_ec, '9', '7'])).
83.60/11.07	thf('27', plain,
83.60/11.07	    (( l_ec ) = ( ^[V_1:$o,V_2:$o]: ( imp @ V_1 @ ( d_not @ V_2 ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf('28', plain,
83.60/11.07	    (( d_and ) = ( ^[X0:$o,X1:$o]: ( d_not @ ( l_ec @ X0 @ X1 ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)], [def_d_and, '27', '9', '7'])).
83.60/11.07	thf('29', plain,
83.60/11.07	    (( d_and ) = ( ^[V_1:$o,V_2:$o]: ( d_not @ ( l_ec @ V_1 @ V_2 ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf('30', plain,
83.60/11.07	    (( and3 ) =
83.60/11.07	     ( ^[X0:$o,X1:$o,X2:$o]: ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)],
83.60/11.07	              [def_and3, '29', '27', '9', '7'])).
83.60/11.07	thf('31', plain,
83.60/11.07	    (( and3 ) =
83.60/11.07	     ( ^[V_1:$o,V_2:$o,V_3:$o]: ( d_and @ V_1 @ ( d_and @ V_2 @ V_3 ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf('32', plain,
83.60/11.07	    (( ec3 ) =
83.60/11.07	     ( ^[X0:$o,X1:$o,X2:$o]:
83.60/11.07	       ( and3 @ ( l_ec @ X0 @ X1 ) @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X0 ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)],
83.60/11.07	              [def_ec3, '31', '29', '27', '9', '7'])).
83.60/11.07	thf('33', plain,
83.60/11.07	    (( ec3 ) =
83.60/11.07	     ( ^[V_1:$o,V_2:$o,V_3:$o]:
83.60/11.07	       ( and3 @
83.60/11.07	         ( l_ec @ V_1 @ V_2 ) @ ( l_ec @ V_2 @ V_3 ) @ ( l_ec @ V_3 @ V_1 ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf(def_or3, axiom,(( or3  ) =
83.60/11.07	  (^[X0:$o,X1:$o,X2:$o]: ( l_or @ X0 @ ( l_or @ X1 @ X2 ) )))).
83.60/11.07	thf('34', plain,
83.60/11.07	    (( or3 ) = ( ^[X0:$o,X1:$o,X2:$o]: ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)], [def_or3, '23', '9', '7'])).
83.60/11.07	thf('35', plain,
83.60/11.07	    (( or3 ) =
83.60/11.07	     ( ^[V_1:$o,V_2:$o,V_3:$o]: ( l_or @ V_1 @ ( l_or @ V_2 @ V_3 ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf('36', plain,
83.60/11.07	    (( orec3 ) =
83.60/11.07	     ( ^[X0:$o,X1:$o,X2:$o]:
83.60/11.07	       ( d_and @ ( or3 @ X0 @ X1 @ X2 ) @ ( ec3 @ X0 @ X1 @ X2 ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)],
83.60/11.07	              [def_orec3, '33', '31', '35', '23', '29', '27', '9', '7'])).
83.60/11.07	thf('37', plain,
83.60/11.07	    (( orec3 ) =
83.60/11.07	     ( ^[V_1:$o,V_2:$o,V_3:$o]:
83.60/11.07	       ( d_and @ ( or3 @ V_1 @ V_2 @ V_3 ) @ ( ec3 @ V_1 @ V_2 @ V_3 ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf(satz9, axiom,
83.60/11.07	  (all_of @
83.60/11.07	   ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 
83.60/11.07	   ( ^[X0:$i]:
83.60/11.07	     ( all_of @
83.60/11.07	       ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 
83.60/11.07	       ( ^[X1:$i]:
83.60/11.07	         ( orec3 @
83.60/11.07	           ( n_is @ X0 @ X1 ) @ 
83.60/11.07	           ( n_some @ ( ^[X2:$i]: ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ) @ 
83.60/11.07	           ( n_some @ ( ^[X2:$i]: ( n_is @ X1 @ ( n_pl @ X0 @ X2 ) ) ) ) ) ) ) ))).
83.60/11.07	thf(zf_stmt_2, axiom,
83.60/11.07	  (![X4:$i]:
83.60/11.07	   ( ( in @ X4 @ nat ) =>
83.60/11.07	     ( ![X6:$i]:
83.60/11.07	       ( ( in @ X6 @ nat ) =>
83.60/11.07	         ( ~( ( ( ( X4 ) != ( X6 ) ) =>
83.60/11.07	                ( ( ![X8:$i]:
83.60/11.07	                    ( ( in @ X8 @ nat ) => ( ( X4 ) != ( n_pl @ X6 @ X8 ) ) ) ) =>
83.60/11.07	                  ( ~( ![X10:$i]:
83.60/11.07	                       ( ( in @ X10 @ nat ) =>
83.60/11.07	                         ( ( X6 ) != ( n_pl @ X4 @ X10 ) ) ) ) ) ) ) =>
83.60/11.07	              ( ( ( ( X4 ) = ( X6 ) ) =>
83.60/11.07	                  ( ![X12:$i]:
83.60/11.07	                    ( ( in @ X12 @ nat ) => ( ( X4 ) != ( n_pl @ X6 @ X12 ) ) ) ) ) =>
83.60/11.07	                ( ( ( ~( ![X14:$i]:
83.60/11.07	                         ( ( in @ X14 @ nat ) =>
83.60/11.07	                           ( ( X4 ) != ( n_pl @ X6 @ X14 ) ) ) ) ) =>
83.60/11.07	                    ( ![X16:$i]:
83.60/11.07	                      ( ( in @ X16 @ nat ) =>
83.60/11.07	                        ( ( X6 ) != ( n_pl @ X4 @ X16 ) ) ) ) ) =>
83.60/11.07	                  ( ~( ( ~( ![X18:$i]:
83.60/11.07	                            ( ( in @ X18 @ nat ) =>
83.60/11.07	                              ( ( X6 ) != ( n_pl @ X4 @ X18 ) ) ) ) ) =>
83.60/11.07	                       ( ( X4 ) != ( X6 ) ) ) ) ) ) ) ) ) ) ))).
83.60/11.07	thf(zip_derived_cl120, plain,
83.60/11.07	    ( (((!!) @ (^[Y0 : $i]:
83.60/11.07	                  (((in @ Y0 @ nat) =>
83.60/11.07	                    (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                (((in @ Y1 @ nat) =>
83.60/11.07	                                  (((~) @ (((((((Y0) != (Y1))) =>
83.60/11.07	                                              (((((!!) @ (^[Y2 : $i]:
83.60/11.07	                                                            (((in @ Y2 @ 
83.60/11.07	                                                              nat) =>
83.60/11.07	                                                              (((Y0) !=
83.60/11.07	                                                                (n_pl @ Y1 @ 
83.60/11.07	                                                                Y2)))))))) =>
83.60/11.07	                                                (((~) @ (((!!) @ (^[Y2 : $i]:
83.60/11.07	                                                                    (
83.60/11.07	                                                                    (
83.60/11.07	                                                                    (in @ 
83.60/11.07	                                                                    Y2 @ 
83.60/11.07	                                                                    nat) =>
83.60/11.07	                                                                    ((
83.60/11.07	                                                                    (Y1) !=
83.60/11.07	                                                                    (n_pl @ 
83.60/11.07	                                                                    Y0 @ Y2)))))))))))))) =>
83.60/11.07	                                            (((((((Y0) = (Y1))) =>
83.60/11.07	                                                (((!!) @ (^[Y2 : $i]:
83.60/11.07	                                                            (((in @ Y2 @ 
83.60/11.07	                                                              nat) =>
83.60/11.07	                                                              (((Y0) !=
83.60/11.07	                                                                (n_pl @ Y1 @ 
83.60/11.07	                                                                Y2)))))))))) =>
83.60/11.07	                                              (((((((~) @ (((!!) @ (^[Y2 : $i]:
83.60/11.07	                                                                    ((
83.60/11.07	                                                                    (in @ 
83.60/11.07	                                                                    Y2 @ 
83.60/11.07	                                                                    nat) =>
83.60/11.07	                                                                    ((
83.60/11.07	                                                                    (Y0) !=
83.60/11.07	                                                                    (n_pl @ 
83.60/11.07	                                                                    Y1 @ Y2)))))))))) =>
83.60/11.07	                                                  (((!!) @ (^[Y2 : $i]:
83.60/11.07	                                                              (((in @ Y2 @ 
83.60/11.07	                                                                nat) =>
83.60/11.07	                                                                (((Y1) !=
83.60/11.07	                                                                  (n_pl @ 
83.60/11.07	                                                                  Y0 @ Y2)))))))))) =>
83.60/11.07	                                                (((~) @ (((((~) @ (((!!) @ (
83.60/11.07	                                                                    ^[Y2 : $i]:
83.60/11.07	                                                                    ((
83.60/11.07	                                                                    (in @ 
83.60/11.07	                                                                    Y2 @ 
83.60/11.07	                                                                    nat) =>
83.60/11.07	                                                                    ((
83.60/11.07	                                                                    (Y1) !=
83.60/11.07	                                                                    (n_pl @ 
83.60/11.07	                                                                    Y0 @ Y2)))))))))) =>
83.60/11.07	                                                          (((Y0) != (Y1)))))))))))))))))))))))))),
83.60/11.07	    inference('cnf', [status(esa)], [zf_stmt_2])).
83.60/11.07	thf(zip_derived_cl5687, plain,
83.60/11.07	    (![X2 : $i]:
83.60/11.07	        (((in @ X2 @ nat) =>
83.60/11.07	          (((!!) @ (^[Y0 : $i]:
83.60/11.07	                      (((in @ Y0 @ nat) =>
83.60/11.07	                        (((~) @ (((((((X2) != (Y0))) =>
83.60/11.07	                                    (((((!!) @ (^[Y1 : $i]:
83.60/11.07	                                                  (((in @ Y1 @ nat) =>
83.60/11.07	                                                    (((X2) != (n_pl @ Y0 @ 
83.60/11.07	                                                      Y1)))))))) =>
83.60/11.07	                                      (((~) @ (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                                          (((in @ Y1 @ 
83.60/11.07	                                                            nat) =>
83.60/11.07	                                                            (((Y0) !=
83.60/11.07	                                                              (n_pl @ X2 @ 
83.60/11.07	                                                              Y1)))))))))))))) =>
83.60/11.07	                                  (((((((X2) = (Y0))) =>
83.60/11.07	                                      (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                                  (((in @ Y1 @ nat) =>
83.60/11.07	                                                    (((X2) != (n_pl @ Y0 @ 
83.60/11.07	                                                      Y1)))))))))) =>
83.60/11.07	                                    (((((((~) @ (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                                            (((in @ Y1 @ 
83.60/11.07	                                                              nat) =>
83.60/11.07	                                                              (((X2) !=
83.60/11.07	                                                                (n_pl @ Y0 @ 
83.60/11.07	                                                                Y1)))))))))) =>
83.60/11.07	                                        (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                                    (((in @ Y1 @ nat) =>
83.60/11.07	                                                      (((Y0) != (n_pl @ X2 @ 
83.60/11.07	                                                        Y1)))))))))) =>
83.60/11.07	                                      (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                                                    (
83.60/11.07	                                                                    (
83.60/11.07	                                                                    (in @ 
83.60/11.07	                                                                    Y1 @ 
83.60/11.07	                                                                    nat) =>
83.60/11.07	                                                                    ((
83.60/11.07	                                                                    (Y0) !=
83.60/11.07	                                                                    (n_pl @ 
83.60/11.07	                                                                    X2 @ Y1)))))))))) =>
83.60/11.07	                                                (((X2) != (Y0))))))))))))))))))))))),
83.60/11.07	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl120])).
83.60/11.07	thf(zip_derived_cl5688, plain,
83.60/11.07	    (![X2 : $i]:
83.60/11.07	       (~ (in @ X2 @ nat)
83.60/11.07	        |  (((!!) @ (^[Y0 : $i]:
83.60/11.07	                       (((in @ Y0 @ nat) =>
83.60/11.07	                         (((~) @ (((((((X2) != (Y0))) =>
83.60/11.07	                                     (((((!!) @ (^[Y1 : $i]:
83.60/11.07	                                                   (((in @ Y1 @ nat) =>
83.60/11.07	                                                     (((X2) != (n_pl @ Y0 @ 
83.60/11.07	                                                       Y1)))))))) =>
83.60/11.07	                                       (((~) @ (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                                           (((in @ Y1 @ 
83.60/11.07	                                                             nat) =>
83.60/11.07	                                                             (((Y0) !=
83.60/11.07	                                                               (n_pl @ X2 @ 
83.60/11.07	                                                               Y1)))))))))))))) =>
83.60/11.07	                                   (((((((X2) = (Y0))) =>
83.60/11.07	                                       (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                                   (((in @ Y1 @ nat) =>
83.60/11.07	                                                     (((X2) != (n_pl @ Y0 @ 
83.60/11.07	                                                       Y1)))))))))) =>
83.60/11.07	                                     (((((((~) @ (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                                             (((in @ Y1 @ 
83.60/11.07	                                                               nat) =>
83.60/11.07	                                                               (((X2) !=
83.60/11.07	                                                                 (n_pl @ 
83.60/11.07	                                                                 Y0 @ Y1)))))))))) =>
83.60/11.07	                                         (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                                     (((in @ Y1 @ nat) =>
83.60/11.07	                                                       (((Y0) != (n_pl @ 
83.60/11.07	                                                         X2 @ Y1)))))))))) =>
83.60/11.07	                                       (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                                                    ((
83.60/11.07	                                                                    (in @ 
83.60/11.07	                                                                    Y1 @ 
83.60/11.07	                                                                    nat) =>
83.60/11.07	                                                                    ((
83.60/11.07	                                                                    (Y0) !=
83.60/11.07	                                                                    (n_pl @ 
83.60/11.07	                                                                    X2 @ Y1)))))))))) =>
83.60/11.07	                                                 (((X2) != (Y0)))))))))))))))))))))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5687])).
83.60/11.07	thf(zip_derived_cl5689, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       ( (((in @ X4 @ nat) =>
83.60/11.07	           (((~) @ (((((((X2) != (X4))) =>
83.60/11.07	                       (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                                     (((in @ Y0 @ nat) =>
83.60/11.07	                                       (((X2) != (n_pl @ X4 @ Y0)))))))) =>
83.60/11.07	                         (((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                             (((in @ Y0 @ nat) =>
83.60/11.07	                                               (((X4) != (n_pl @ X2 @ Y0)))))))))))))) =>
83.60/11.07	                     (((((((X2) = (X4))) =>
83.60/11.07	                         (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                     (((in @ Y0 @ nat) =>
83.60/11.07	                                       (((X2) != (n_pl @ X4 @ Y0)))))))))) =>
83.60/11.07	                       (((((((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                               (((in @ Y0 @ nat) =>
83.60/11.07	                                                 (((X2) != (n_pl @ X4 @ Y0)))))))))) =>
83.60/11.07	                           (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                       (((in @ Y0 @ nat) =>
83.60/11.07	                                         (((X4) != (n_pl @ X2 @ Y0)))))))))) =>
83.60/11.07	                         (((~) @ (((((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                                       (((in @ Y0 @ nat) =>
83.60/11.07	                                                         (((X4) != (n_pl @ 
83.60/11.07	                                                           X2 @ Y0)))))))))) =>
83.60/11.07	                                   (((X2) != (X4)))))))))))))))))
83.60/11.07	        | ~ (in @ X2 @ nat))),
83.60/11.07	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5688])).
83.60/11.07	thf(zip_derived_cl5690, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       (~ (in @ X4 @ nat)
83.60/11.07	        | ~ (((((((X2) != (X4))) =>
83.60/11.07	                (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                              (((in @ Y0 @ nat) =>
83.60/11.07	                                (((X2) != (n_pl @ X4 @ Y0)))))))) =>
83.60/11.07	                  (((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                      (((in @ Y0 @ nat) =>
83.60/11.07	                                        (((X4) != (n_pl @ X2 @ Y0)))))))))))))) =>
83.60/11.07	              (((((((X2) = (X4))) =>
83.60/11.07	                  (((!!) @ (^[Y0 : $i]:
83.60/11.07	                              (((in @ Y0 @ nat) =>
83.60/11.07	                                (((X2) != (n_pl @ X4 @ Y0)))))))))) =>
83.60/11.07	                (((((((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                        (((in @ Y0 @ nat) =>
83.60/11.07	                                          (((X2) != (n_pl @ X4 @ Y0)))))))))) =>
83.60/11.07	                    (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                (((in @ Y0 @ nat) =>
83.60/11.07	                                  (((X4) != (n_pl @ X2 @ Y0)))))))))) =>
83.60/11.07	                  (((~) @ (((((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                                (((in @ Y0 @ nat) =>
83.60/11.07	                                                  (((X4) != (n_pl @ X2 @ Y0)))))))))) =>
83.60/11.07	                            (((X2) != (X4)))))))))))))
83.60/11.07	        | ~ (in @ X2 @ nat))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5689])).
83.60/11.07	thf(zip_derived_cl5692, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       (~ (((((((X2) = (X4))) =>
83.60/11.07	              (((!!) @ (^[Y0 : $i]:
83.60/11.07	                          (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))))) =>
83.60/11.07	            (((((((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                    (((in @ Y0 @ nat) =>
83.60/11.07	                                      (((X2) != (n_pl @ X4 @ Y0)))))))))) =>
83.60/11.07	                (((!!) @ (^[Y0 : $i]:
83.60/11.07	                            (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))))) =>
83.60/11.07	              (((~) @ (((((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                            (((in @ Y0 @ nat) =>
83.60/11.07	                                              (((X4) != (n_pl @ X2 @ Y0)))))))))) =>
83.60/11.07	                        (((X2) != (X4)))))))))))
83.60/11.07	        | ~ (in @ X2 @ nat)
83.60/11.07	        | ~ (in @ X4 @ nat))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5690])).
83.60/11.07	thf(zip_derived_cl5695, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       (~ (((((((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                  (((in @ Y0 @ nat) =>
83.60/11.07	                                    (((X2) != (n_pl @ X4 @ Y0)))))))))) =>
83.60/11.07	              (((!!) @ (^[Y0 : $i]:
83.60/11.07	                          (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))))) =>
83.60/11.07	            (((~) @ (((((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                          (((in @ Y0 @ nat) =>
83.60/11.07	                                            (((X4) != (n_pl @ X2 @ Y0)))))))))) =>
83.60/11.07	                      (((X2) != (X4)))))))))
83.60/11.07	        | ~ (in @ X4 @ nat)
83.60/11.07	        | ~ (in @ X2 @ nat))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5692])).
83.60/11.07	thf(zip_derived_cl5699, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       ( (((((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                               (((in @ Y0 @ nat) =>
83.60/11.07	                                 (((X2) != (n_pl @ X4 @ Y0)))))))))) =>
83.60/11.07	           (((!!) @ (^[Y0 : $i]:
83.60/11.07	                       (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0))))))))))
83.60/11.07	        | ~ (in @ X2 @ nat)
83.60/11.07	        | ~ (in @ X4 @ nat))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5695])).
83.60/11.07	thf(zip_derived_cl5705, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       ( (((!!) @ (^[Y0 : $i]:
83.60/11.07	                     (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0))))))))
83.60/11.07	        |  (((!!) @ (^[Y0 : $i]:
83.60/11.07	                       (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0))))))))
83.60/11.07	        | ~ (in @ X4 @ nat)
83.60/11.07	        | ~ (in @ X2 @ nat))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5699])).
83.60/11.07	thf(zip_derived_cl5710, plain,
83.60/11.07	    (![X2 : $i, X4 : $i, X6 : $i]:
83.60/11.07	       ( (((in @ X6 @ nat) => (((X2) != (n_pl @ X4 @ X6)))))
83.60/11.07	        | ~ (in @ X2 @ nat)
83.60/11.07	        | ~ (in @ X4 @ nat)
83.60/11.07	        |  (((!!) @ (^[Y0 : $i]:
83.60/11.07	                       (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))))),
83.60/11.07	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5705])).
83.60/11.07	thf(zip_derived_cl5720, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       (~ ('#form7507' @ X2 @ X4)
83.60/11.07	        |  (((!!) @ (^[Y0 : $i]:
83.60/11.07	                       (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))))),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf(zip_derived_cl5691, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       ( (((((X2) != (X4))) =>
83.60/11.07	           (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                         (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))) =>
83.60/11.07	             (((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                 (((in @ Y0 @ nat) =>
83.60/11.07	                                   (((X4) != (n_pl @ X2 @ Y0))))))))))))))
83.60/11.07	        | ~ (in @ X2 @ nat)
83.60/11.07	        | ~ (in @ X4 @ nat))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5690])).
83.60/11.07	thf(zip_derived_cl5693, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       (~ (((X2) != (X4)))
83.60/11.07	        |  (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                         (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))) =>
83.60/11.07	             (((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                 (((in @ Y0 @ nat) =>
83.60/11.07	                                   (((X4) != (n_pl @ X2 @ Y0))))))))))))
83.60/11.07	        | ~ (in @ X4 @ nat)
83.60/11.07	        | ~ (in @ X2 @ nat))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5691])).
83.60/11.07	thf(zip_derived_cl5696, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       (((X2) = (X4))
83.60/11.07	        |  (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                         (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0)))))))) =>
83.60/11.07	             (((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                 (((in @ Y0 @ nat) =>
83.60/11.07	                                   (((X4) != (n_pl @ X2 @ Y0))))))))))))
83.60/11.07	        | ~ (in @ X4 @ nat)
83.60/11.07	        | ~ (in @ X2 @ nat))),
83.60/11.07	    inference('simplify nested equalities', [status(thm)],
83.60/11.07	              [zip_derived_cl5693])).
83.60/11.07	thf(zip_derived_cl5697, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       (~ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                      (((in @ Y0 @ nat) => (((X2) != (n_pl @ X4 @ Y0))))))))
83.60/11.07	        | ~ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                        (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0))))))))
83.60/11.07	        | ~ (in @ X2 @ nat)
83.60/11.07	        | ~ (in @ X4 @ nat)
83.60/11.07	        | ((X2) = (X4)))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5696])).
83.60/11.07	thf(zip_derived_cl5701, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       (~ (((in @ ('#sk7506' @ X2 @ X4) @ nat) =>
83.60/11.07	            (((X2) != (n_pl @ X4 @ ('#sk7506' @ X2 @ X4))))))
83.60/11.07	        | ((X2) = (X4))
83.60/11.07	        | ~ (in @ X4 @ nat)
83.60/11.07	        | ~ (in @ X2 @ nat)
83.60/11.07	        | ~ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                        (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))))),
83.60/11.07	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl5697])).
83.60/11.07	thf(zip_derived_cl5707, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       ( (in @ ('#sk7506' @ X2 @ X4) @ nat)
83.60/11.07	        | ~ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                        (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0))))))))
83.60/11.07	        | ~ (in @ X2 @ nat)
83.60/11.07	        | ~ (in @ X4 @ nat)
83.60/11.07	        | ((X2) = (X4)))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5701])).
83.60/11.07	thf(zip_derived_cl5714, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       ( ('#form7507' @ X2 @ X4)
83.60/11.07	        | ~ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                        (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))))),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf(zip_derived_cl7081, plain,
83.60/11.07	    ( ('#form7507' @ (n_pl @ '#sk8789' @ n_1) @ '#sk8788')),
83.60/11.07	    inference('renaming', [status(thm)],
83.60/11.07	              [zip_derived_cl7079, zip_derived_cl5720, zip_derived_cl5714])).
83.60/11.07	thf(zip_derived_cl2909, plain, (((n_1) = (ordsucc @ '#sk3561'))),
83.60/11.07	    inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl2902])).
83.60/11.07	thf(zip_derived_cl7083, plain,
83.60/11.07	    ( ('#form7507' @ (n_pl @ '#sk8789' @ (ordsucc @ '#sk3561')) @ '#sk8788')),
83.60/11.07	    inference('demod', [status(thm)],
83.60/11.07	              [zip_derived_cl7081, zip_derived_cl2909])).
83.60/11.07	thf(def_moreis, axiom,(( moreis  ) =
83.60/11.07	  (^[X0:$i,X1:$i]: ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) )))).
83.60/11.07	thf(def_d_29_ii, axiom,(( d_29_ii  ) =
83.60/11.07	  (^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X0 @ X1 ) )))).
83.60/11.07	thf('38', plain,
83.60/11.07	    (( d_29_ii ) = ( ^[X0:$i,X1:$i]: ( n_some @ ( diffprop @ X0 @ X1 ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)],
83.60/11.07	              [def_d_29_ii, '5', '19', '3', '1', '17', '11', '9', '7', '15', 
83.60/11.07	               '13'])).
83.60/11.07	thf('39', plain,
83.60/11.07	    (( d_29_ii ) =
83.60/11.07	     ( ^[V_1:$i,V_2:$i]: ( n_some @ ( diffprop @ V_1 @ V_2 ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf('40', plain,
83.60/11.07	    (( moreis ) =
83.60/11.07	     ( ^[X0:$i,X1:$i]: ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) )),
83.60/11.07	    inference('simplify_rw_rule', [status(thm)],
83.60/11.07	              [def_moreis, '39', '5', '19', '3', '1', '17', '11', '23', '9', 
83.60/11.07	               '7', '15', '13'])).
83.60/11.07	thf('41', plain,
83.60/11.07	    (( moreis ) =
83.60/11.07	     ( ^[V_1:$i,V_2:$i]:
83.60/11.07	       ( l_or @ ( d_29_ii @ V_1 @ V_2 ) @ ( n_is @ V_1 @ V_2 ) ) )),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf(satz25, axiom,
83.60/11.07	  (all_of @
83.60/11.07	   ( ^[X0:$i]: ( in @ X0 @ nat ) ) @ 
83.60/11.07	   ( ^[X0:$i]:
83.60/11.07	     ( all_of @
83.60/11.07	       ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 
83.60/11.07	       ( ^[X1:$i]:
83.60/11.07	         ( ( d_29_ii @ X1 @ X0 ) => ( moreis @ X1 @ ( n_pl @ X0 @ n_1 ) ) ) ) ) ))).
83.60/11.07	thf(zf_stmt_3, axiom,
83.60/11.07	  (![X4:$i]:
83.60/11.07	   ( ( in @ X4 @ nat ) =>
83.60/11.07	     ( ![X6:$i]:
83.60/11.07	       ( ( in @ X6 @ nat ) =>
83.60/11.07	         ( ( ~( ![X8:$i]:
83.60/11.07	                ( ( in @ X8 @ nat ) => ( ( X6 ) != ( n_pl @ X4 @ X8 ) ) ) ) ) =>
83.60/11.07	           ( ( ![X10:$i]:
83.60/11.07	               ( ( in @ X10 @ nat ) =>
83.60/11.07	                 ( ( X6 ) != ( n_pl @ ( n_pl @ X4 @ n_1 ) @ X10 ) ) ) ) =>
83.60/11.07	             ( ( X6 ) = ( n_pl @ X4 @ n_1 ) ) ) ) ) ) ))).
83.60/11.07	thf(zip_derived_cl171, plain,
83.60/11.07	    ( (((!!) @ (^[Y0 : $i]:
83.60/11.07	                  (((in @ Y0 @ nat) =>
83.60/11.07	                    (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                (((in @ Y1 @ nat) =>
83.60/11.07	                                  (((((~) @ (((!!) @ (^[Y2 : $i]:
83.60/11.07	                                                        (((in @ Y2 @ nat) =>
83.60/11.07	                                                          (((Y1) != (n_pl @ 
83.60/11.07	                                                            Y0 @ Y2)))))))))) =>
83.60/11.07	                                    (((((!!) @ (^[Y2 : $i]:
83.60/11.07	                                                  (((in @ Y2 @ nat) =>
83.60/11.07	                                                    (((Y1) != (n_pl @ 
83.60/11.07	                                                      (n_pl @ Y0 @ n_1) @ Y2)))))))) =>
83.60/11.07	                                      (((Y1) = (n_pl @ Y0 @ n_1)))))))))))))))))),
83.60/11.07	    inference('cnf', [status(esa)], [zf_stmt_3])).
83.60/11.07	thf(zip_derived_cl10250, plain,
83.60/11.07	    (![X2 : $i]:
83.60/11.07	        (((in @ X2 @ nat) =>
83.60/11.07	          (((!!) @ (^[Y0 : $i]:
83.60/11.07	                      (((in @ Y0 @ nat) =>
83.60/11.07	                        (((((~) @ (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                              (((in @ Y1 @ nat) =>
83.60/11.07	                                                (((Y0) != (n_pl @ X2 @ Y1)))))))))) =>
83.60/11.07	                          (((((!!) @ (^[Y1 : $i]:
83.60/11.07	                                        (((in @ Y1 @ nat) =>
83.60/11.07	                                          (((Y0) != (n_pl @ 
83.60/11.07	                                            (n_pl @ X2 @ n_1) @ Y1)))))))) =>
83.60/11.07	                            (((Y0) = (n_pl @ X2 @ n_1))))))))))))))),
83.60/11.07	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl171])).
83.60/11.07	thf(zip_derived_cl10251, plain,
83.60/11.07	    (![X2 : $i]:
83.60/11.07	       (~ (in @ X2 @ nat)
83.60/11.07	        |  (((!!) @ (^[Y0 : $i]:
83.60/11.07	                       (((in @ Y0 @ nat) =>
83.60/11.07	                         (((((~) @ (((!!) @ (^[Y1 : $i]:
83.60/11.07	                                               (((in @ Y1 @ nat) =>
83.60/11.07	                                                 (((Y0) != (n_pl @ X2 @ Y1)))))))))) =>
83.60/11.07	                           (((((!!) @ (^[Y1 : $i]:
83.60/11.07	                                         (((in @ Y1 @ nat) =>
83.60/11.07	                                           (((Y0) != (n_pl @ 
83.60/11.07	                                             (n_pl @ X2 @ n_1) @ Y1)))))))) =>
83.60/11.07	                             (((Y0) = (n_pl @ X2 @ n_1)))))))))))))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl10250])).
83.60/11.07	thf(zip_derived_cl10252, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       ( (((in @ X4 @ nat) =>
83.60/11.07	           (((((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                 (((in @ Y0 @ nat) =>
83.60/11.07	                                   (((X4) != (n_pl @ X2 @ Y0)))))))))) =>
83.60/11.07	             (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                           (((in @ Y0 @ nat) =>
83.60/11.07	                             (((X4) != (n_pl @ (n_pl @ X2 @ n_1) @ Y0)))))))) =>
83.60/11.07	               (((X4) = (n_pl @ X2 @ n_1)))))))))
83.60/11.07	        | ~ (in @ X2 @ nat))),
83.60/11.07	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10251])).
83.60/11.07	thf(zip_derived_cl2909, plain, (((n_1) = (ordsucc @ '#sk3561'))),
83.60/11.07	    inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl2902])).
83.60/11.07	thf(zip_derived_cl10253, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       ( (((in @ X4 @ nat) =>
83.60/11.07	           (((((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                 (((in @ Y0 @ nat) =>
83.60/11.07	                                   (((X4) != (n_pl @ X2 @ Y0)))))))))) =>
83.60/11.07	             (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                           (((in @ Y0 @ nat) =>
83.60/11.07	                             (((X4) != (n_pl @ (n_pl @ X2 @ n_1) @ Y0)))))))) =>
83.60/11.07	               (((X4) = (n_pl @ X2 @ (ordsucc @ '#sk3561'))))))))))
83.60/11.07	        | ~ (in @ X2 @ nat))),
83.60/11.07	    inference('demod', [status(thm)],
83.60/11.07	              [zip_derived_cl10252, zip_derived_cl2909])).
83.60/11.07	thf(zip_derived_cl10254, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       (~ (in @ X4 @ nat)
83.60/11.07	        |  (((((~) @ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                                 (((in @ Y0 @ nat) =>
83.60/11.07	                                   (((X4) != (n_pl @ X2 @ Y0)))))))))) =>
83.60/11.07	             (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                           (((in @ Y0 @ nat) =>
83.60/11.07	                             (((X4) != (n_pl @ (n_pl @ X2 @ n_1) @ Y0)))))))) =>
83.60/11.07	               (((X4) = (n_pl @ X2 @ (ordsucc @ '#sk3561'))))))))
83.60/11.07	        | ~ (in @ X2 @ nat))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl10253])).
83.60/11.07	thf(zip_derived_cl10255, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       ( (((!!) @ (^[Y0 : $i]:
83.60/11.07	                     (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0))))))))
83.60/11.07	        |  (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                         (((in @ Y0 @ nat) =>
83.60/11.07	                           (((X4) != (n_pl @ (n_pl @ X2 @ n_1) @ Y0)))))))) =>
83.60/11.07	             (((X4) = (n_pl @ X2 @ (ordsucc @ '#sk3561'))))))
83.60/11.07	        | ~ (in @ X2 @ nat)
83.60/11.07	        | ~ (in @ X4 @ nat))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl10254])).
83.60/11.07	thf(zip_derived_cl5720, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       (~ ('#form7507' @ X2 @ X4)
83.60/11.07	        |  (((!!) @ (^[Y0 : $i]:
83.60/11.07	                       (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))))),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf(zip_derived_cl5714, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       ( ('#form7507' @ X2 @ X4)
83.60/11.07	        | ~ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                        (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))))),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf(zip_derived_cl10256, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       ( ('#form7507' @ X2 @ X4)
83.60/11.07	        | ~ (in @ X4 @ nat)
83.60/11.07	        | ~ (in @ X2 @ nat)
83.60/11.07	        |  (((((!!) @ (^[Y0 : $i]:
83.60/11.07	                         (((in @ Y0 @ nat) =>
83.60/11.07	                           (((X4) != (n_pl @ (n_pl @ X2 @ n_1) @ Y0)))))))) =>
83.60/11.07	             (((X4) = (n_pl @ X2 @ (ordsucc @ '#sk3561')))))))),
83.60/11.07	    inference('renaming', [status(thm)],
83.60/11.07	              [zip_derived_cl10255, zip_derived_cl5720, zip_derived_cl5714])).
83.60/11.07	thf(zip_derived_cl10257, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       (~ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                      (((in @ Y0 @ nat) =>
83.60/11.07	                        (((X4) != (n_pl @ (n_pl @ X2 @ n_1) @ Y0))))))))
83.60/11.07	        |  (((X4) = (n_pl @ X2 @ (ordsucc @ '#sk3561'))))
83.60/11.07	        | ~ (in @ X2 @ nat)
83.60/11.07	        | ~ (in @ X4 @ nat)
83.60/11.07	        |  ('#form7507' @ X2 @ X4))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl10256])).
83.60/11.07	thf(zip_derived_cl10258, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       (~ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                      (((in @ Y0 @ nat) =>
83.60/11.07	                        (((X4) != (n_pl @ (n_pl @ X2 @ n_1) @ Y0))))))))
83.60/11.07	        | ((X4) = (n_pl @ X2 @ (ordsucc @ '#sk3561')))
83.60/11.07	        | ~ (in @ X2 @ nat)
83.60/11.07	        | ~ (in @ X4 @ nat)
83.60/11.07	        |  ('#form7507' @ X2 @ X4))),
83.60/11.07	    inference('simplify nested equalities', [status(thm)],
83.60/11.07	              [zip_derived_cl10257])).
83.60/11.07	thf(zip_derived_cl5720, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       (~ ('#form7507' @ X2 @ X4)
83.60/11.07	        |  (((!!) @ (^[Y0 : $i]:
83.60/11.07	                       (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))))),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf(zip_derived_cl5714, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       ( ('#form7507' @ X2 @ X4)
83.60/11.07	        | ~ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                        (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))))),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf(zip_derived_cl10259, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       (~ ('#form7507' @ (n_pl @ X2 @ n_1) @ X4)
83.60/11.07	        |  ('#form7507' @ X2 @ X4)
83.60/11.07	        | ~ (in @ X4 @ nat)
83.60/11.07	        | ~ (in @ X2 @ nat)
83.60/11.07	        | ((X4) = (n_pl @ X2 @ (ordsucc @ '#sk3561'))))),
83.60/11.07	    inference('renaming', [status(thm)],
83.60/11.07	              [zip_derived_cl10258, zip_derived_cl5720, zip_derived_cl5714])).
83.60/11.07	thf(zip_derived_cl2909, plain, (((n_1) = (ordsucc @ '#sk3561'))),
83.60/11.07	    inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl2902])).
83.60/11.07	thf(zip_derived_cl10260, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       (~ ('#form7507' @ (n_pl @ X2 @ (ordsucc @ '#sk3561')) @ X4)
83.60/11.07	        |  ('#form7507' @ X2 @ X4)
83.60/11.07	        | ~ (in @ X4 @ nat)
83.60/11.07	        | ~ (in @ X2 @ nat)
83.60/11.07	        | ((X4) = (n_pl @ X2 @ (ordsucc @ '#sk3561'))))),
83.60/11.07	    inference('demod', [status(thm)],
83.60/11.07	              [zip_derived_cl10259, zip_derived_cl2909])).
83.60/11.07	thf(zip_derived_cl10280, plain,
83.60/11.07	    (((('#sk8788') = (n_pl @ '#sk8789' @ (ordsucc @ '#sk3561')))
83.60/11.07	      | ~ (in @ '#sk8789' @ nat)
83.60/11.07	      | ~ (in @ '#sk8788' @ nat)
83.60/11.07	      |  ('#form7507' @ '#sk8789' @ '#sk8788'))),
83.60/11.07	    inference('sup-', [status(thm)],
83.60/11.07	              [zip_derived_cl7083, zip_derived_cl10260])).
83.60/11.07	thf(zip_derived_cl7074, plain, ( (in @ '#sk8789' @ nat)),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7073])).
83.60/11.07	thf(zip_derived_cl7070, plain, ( (in @ '#sk8788' @ nat)),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7069])).
83.60/11.07	thf(zip_derived_cl7076, plain,
83.60/11.07	    (~ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                   (((in @ Y0 @ nat) =>
83.60/11.07	                     ((('#sk8788') != (n_pl @ '#sk8789' @ Y0))))))))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7075])).
83.60/11.07	thf(zip_derived_cl5720, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       (~ ('#form7507' @ X2 @ X4)
83.60/11.07	        |  (((!!) @ (^[Y0 : $i]:
83.60/11.07	                       (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))))),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf(zip_derived_cl5714, plain,
83.60/11.07	    (![X2 : $i, X4 : $i]:
83.60/11.07	       ( ('#form7507' @ X2 @ X4)
83.60/11.07	        | ~ (((!!) @ (^[Y0 : $i]:
83.60/11.07	                        (((in @ Y0 @ nat) => (((X4) != (n_pl @ X2 @ Y0)))))))))),
83.60/11.07	    define([status(thm)])).
83.60/11.07	thf(zip_derived_cl7078, plain, (~ ('#form7507' @ '#sk8789' @ '#sk8788')),
83.60/11.07	    inference('renaming', [status(thm)],
83.60/11.07	              [zip_derived_cl7076, zip_derived_cl5720, zip_derived_cl5714])).
83.60/11.07	thf(zip_derived_cl10316, plain,
83.60/11.07	    ((('#sk8788') = (n_pl @ '#sk8789' @ (ordsucc @ '#sk3561')))),
83.60/11.07	    inference('demod', [status(thm)],
83.60/11.07	              [zip_derived_cl10280, zip_derived_cl7074, zip_derived_cl7070, 
83.60/11.07	               zip_derived_cl7078])).
83.60/11.07	thf(zip_derived_cl7080, plain,
83.60/11.07	    (~ (((n_pl @ '#sk8789' @ (ordsucc @ '#sk3561')) = ('#sk8788')))),
83.60/11.07	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7077])).
83.60/11.07	thf(zip_derived_cl7082, plain,
83.60/11.07	    (((n_pl @ '#sk8789' @ (ordsucc @ '#sk3561')) != ('#sk8788'))),
83.60/11.07	    inference('simplify nested equalities', [status(thm)],
83.60/11.07	              [zip_derived_cl7080])).
83.60/11.07	thf(zip_derived_cl10317, plain, ($false),
83.60/11.07	    inference('simplify_reflect-', [status(thm)],
83.60/11.07	              [zip_derived_cl10316, zip_derived_cl7082])).
83.60/11.07	
83.60/11.07	% SZS output end Refutation
83.60/11.07	
83.60/11.07	
83.60/11.07	% Terminating...
83.94/11.14	% Runner terminated.
83.94/11.14	% Zipperpin 1.5 exiting
83.94/11.14	EOF