0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n087.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:37:09 CST 2018
0.00/0.23	% done 46 iterations in 0.031s
0.00/0.23	% SZS status Theorem for 'stdin'
0.00/0.23	% SZS output start Refutation
0.00/0.24	tff(zf_stmt_13, conjecture,
0.00/0.24	  (![A:app_encode_fun('type/realax/real',$o)]:
0.00/0.24	     ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.24	                      'const/sets/FINITE'('type/realax/real'),A) & 
0.00/0.24	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
0.00/0.24	      (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.24	                      app_encode_app('type/realax/real',
0.00/0.24	                                     app_encode_fun(app_encode_fun('type/realax/real',
0.00/0.24	                                                                   $o),
0.00/0.24	                                                    $o),
0.00/0.24	                                     'const/sets/IN'('type/realax/real'),
0.00/0.24	                                     app_encode_app(app_encode_fun('type/realax/real',
0.00/0.24	                                                                   $o),
0.00/0.24	                                                    'type/realax/real',
0.00/0.24	                                                    'const/sets/inf',A)),
0.00/0.24	                      A) & 
0.00/0.24	       (![A0:'type/realax/real']:
0.00/0.24	          (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.24	                          app_encode_app('type/realax/real',
0.00/0.24	                                         app_encode_fun(app_encode_fun(
0.00/0.24	                                                        'type/realax/real',$o),
0.00/0.24	                                                        $o),
0.00/0.24	                                         'const/sets/IN'('type/realax/real'),
0.00/0.24	                                         A0),
0.00/0.24	                          A) =>
0.00/0.24	           app_encode_app('type/realax/real',$o,
0.00/0.24	                          app_encode_app('type/realax/real',
0.00/0.24	                                         app_encode_fun('type/realax/real',$o),
0.00/0.24	                                         'const/realax/real_le',
0.00/0.24	                                         app_encode_app(app_encode_fun(
0.00/0.24	                                                        'type/realax/real',$o),
0.00/0.24	                                                        'type/realax/real',
0.00/0.24	                                                        'const/sets/inf',A)),
0.00/0.24	                          A0))))))).
0.00/0.24	tff(zf_stmt_0, negated_conjecture,
0.00/0.24	  (~
0.00/0.24	    (![A:app_encode_fun('type/realax/real',$o)]:
0.00/0.24	       ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.24	                        'const/sets/FINITE'('type/realax/real'),A) & 
0.00/0.24	         (A != 'const/sets/EMPTY'('type/realax/real'))) =>
0.00/0.24	        (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.24	                        app_encode_app('type/realax/real',
0.00/0.24	                                       app_encode_fun(app_encode_fun(
0.00/0.24	                                                      'type/realax/real',$o),
0.00/0.24	                                                      $o),
0.00/0.24	                                       'const/sets/IN'('type/realax/real'),
0.00/0.24	                                       app_encode_app(app_encode_fun(
0.00/0.24	                                                      'type/realax/real',$o),
0.00/0.24	                                                      'type/realax/real',
0.00/0.24	                                                      'const/sets/inf',A)),
0.00/0.24	                        A) & 
0.00/0.24	         (![A0:'type/realax/real']:
0.00/0.24	            (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.24	                            app_encode_app('type/realax/real',
0.00/0.24	                                           app_encode_fun(app_encode_fun(
0.00/0.24	                                                          'type/realax/real',
0.00/0.24	                                                          $o),$o),
0.00/0.24	                                           'const/sets/IN'('type/realax/real'),
0.00/0.24	                                           A0),
0.00/0.24	                            A) =>
0.00/0.24	             app_encode_app('type/realax/real',$o,
0.00/0.24	                            app_encode_app('type/realax/real',
0.00/0.24	                                           app_encode_fun('type/realax/real',
0.00/0.24	                                                          $o),
0.00/0.24	                                           'const/realax/real_le',
0.00/0.24	                                           app_encode_app(app_encode_fun(
0.00/0.24	                                                          'type/realax/real',
0.00/0.24	                                                          $o),
0.00/0.24	                                                          'type/realax/real',
0.00/0.24	                                                          'const/sets/inf',A)),
0.00/0.24	                            A0)))))))).
0.00/0.24	tff('0', plain,
0.00/0.24	    app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	      'const/sets/FINITE'('type/realax/real'), sk_A),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.24	tff(zf_stmt_9, axiom,
0.00/0.24	  (![A:app_encode_fun('type/realax/real',$o)]:
0.00/0.24	     (((?[A0:'type/realax/real']:
0.00/0.24	          (![A1:'type/realax/real']:
0.00/0.24	             (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.24	                             app_encode_app('type/realax/real',
0.00/0.24	                                            app_encode_fun(app_encode_fun(
0.00/0.24	                                                           'type/realax/real',
0.00/0.24	                                                           $o),$o),
0.00/0.24	                                            'const/sets/IN'('type/realax/real'),
0.00/0.24	                                            A1),
0.00/0.24	                             A) =>
0.00/0.24	              app_encode_app('type/realax/real',$o,
0.00/0.24	                             app_encode_app('type/realax/real',
0.00/0.24	                                            app_encode_fun('type/realax/real',
0.00/0.24	                                                           $o),
0.00/0.24	                                            'const/realax/real_le',A0),
0.00/0.24	                             A1)))) & 
0.00/0.24	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
0.00/0.24	      ((![A0:'type/realax/real']:
0.00/0.24	          ((![A1:'type/realax/real']:
0.00/0.24	              (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.24	                              app_encode_app('type/realax/real',
0.00/0.24	                                             app_encode_fun(app_encode_fun(
0.00/0.24	                                                            'type/realax/real',
0.00/0.24	                                                            $o),$o),
0.00/0.24	                                             'const/sets/IN'('type/realax/real'),
0.00/0.24	                                             A1),
0.00/0.24	                              A) =>
0.00/0.24	               app_encode_app('type/realax/real',$o,
0.00/0.24	                              app_encode_app('type/realax/real',
0.00/0.24	                                             app_encode_fun('type/realax/real',
0.00/0.24	                                                            $o),
0.00/0.24	                                             'const/realax/real_le',A0),
0.00/0.24	                              A1))) =>
0.00/0.24	           app_encode_app('type/realax/real',$o,
0.00/0.24	                          app_encode_app('type/realax/real',
0.00/0.24	                                         app_encode_fun('type/realax/real',$o),
0.00/0.24	                                         'const/realax/real_le',A0),
0.00/0.24	                          app_encode_app(app_encode_fun('type/realax/real',$o),
0.00/0.24	                                         'type/realax/real','const/sets/inf',
0.00/0.24	                                         A)))) & 
0.00/0.24	       (![A0:'type/realax/real']:
0.00/0.24	          (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.24	                          app_encode_app('type/realax/real',
0.00/0.24	                                         app_encode_fun(app_encode_fun(
0.00/0.24	                                                        'type/realax/real',$o),
0.00/0.24	                                                        $o),
0.00/0.24	                                         'const/sets/IN'('type/realax/real'),
0.00/0.24	                                         A0),
0.00/0.24	                          A) =>
0.00/0.24	           app_encode_app('type/realax/real',$o,
0.00/0.24	                          app_encode_app('type/realax/real',
0.00/0.24	                                         app_encode_fun('type/realax/real',$o),
0.00/0.24	                                         'const/realax/real_le',
0.00/0.24	                                         app_encode_app(app_encode_fun(
0.00/0.24	                                                        'type/realax/real',$o),
0.00/0.24	                                                        'type/realax/real',
0.00/0.24	                                                        'const/sets/inf',A)),
0.00/0.24	                          A0))))))).
0.00/0.24	tff(zf_stmt_1, axiom,
0.00/0.24	  ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.24	                   app_encode_app('type/realax/real',
0.00/0.24	                                  app_encode_fun(app_encode_fun('type/realax/real',
0.00/0.24	                                                                $o),
0.00/0.24	                                                 $o),
0.00/0.24	                                  'const/sets/IN'('type/realax/real'),A1),
0.00/0.24	                   A) =>
0.00/0.24	    app_encode_app('type/realax/real',$o,
0.00/0.24	                   app_encode_app('type/realax/real',
0.00/0.24	                                  app_encode_fun('type/realax/real',$o),
0.00/0.24	                                  'const/realax/real_le',A0),
0.00/0.24	                   A1)) =>
0.00/0.24	   zip_tseitin1(A1,A0,A))).
0.00/0.24	tff('1', plain,
0.00/0.24	    ![X6 : app_encode_fun('type/realax/real', $o), X7 : 'type/realax/real', 
0.00/0.24	      X8 : 'type/realax/real']:
0.00/0.24	      (zip_tseitin1(X7, X8, X6)
0.00/0.24	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	             'const/sets/IN'('type/realax/real'), X7), X6)),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.00/0.24	tff(zf_stmt_2, axiom,
0.00/0.24	  (zip_tseitin2(A) =>
0.00/0.24	   ((![A0:'type/realax/real']:
0.00/0.24	       (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.24	                       app_encode_app('type/realax/real',
0.00/0.24	                                      app_encode_fun(app_encode_fun('type/realax/real',
0.00/0.24	                                                                    $o),
0.00/0.24	                                                     $o),
0.00/0.24	                                      'const/sets/IN'('type/realax/real'),A0),
0.00/0.24	                       A) =>
0.00/0.24	        app_encode_app('type/realax/real',$o,
0.00/0.24	                       app_encode_app('type/realax/real',
0.00/0.24	                                      app_encode_fun('type/realax/real',$o),
0.00/0.24	                                      'const/realax/real_le',
0.00/0.24	                                      app_encode_app(app_encode_fun('type/realax/real',
0.00/0.24	                                                                    $o),
0.00/0.24	                                                     'type/realax/real',
0.00/0.24	                                                     'const/sets/inf',A)),
0.00/0.24	                       A0))) & 
0.00/0.24	    (![A0:'type/realax/real']:
0.00/0.24	       ((![A1:'type/realax/real']: zip_tseitin1(A1,A0,A)) =>
0.00/0.24	        app_encode_app('type/realax/real',$o,
0.00/0.24	                       app_encode_app('type/realax/real',
0.00/0.24	                                      app_encode_fun('type/realax/real',$o),
0.00/0.24	                                      'const/realax/real_le',A0),
0.00/0.24	                       app_encode_app(app_encode_fun('type/realax/real',$o),
0.00/0.24	                                      'type/realax/real','const/sets/inf',A))))))).
0.00/0.24	tff('2', plain,
0.00/0.24	    ![X6 : app_encode_fun('type/realax/real', $o), X10 : 'type/realax/real']:
0.00/0.24	      (~ zip_tseitin1(sk_A1(X10, X6), X10, X6)
0.00/0.24	       | app_encode_app('type/realax/real', $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	             X10), 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', X6))
0.00/0.24	       | ~ zip_tseitin2(X6)),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_2])).
0.00/0.24	tff('3', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.24	      (~ $true
0.00/0.24	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	             'const/sets/IN'('type/realax/real'), sk_A1(X1, X0)), X0)
0.00/0.24	       | ~ zip_tseitin2(X0)
0.00/0.24	       | app_encode_app('type/realax/real', $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	             X1), 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', X0))),
0.00/0.24	    inference('sup-', [status(thm)], ['1', '2'])).
0.00/0.24	tff('4', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.24	      (app_encode_app('type/realax/real', $o, 
0.00/0.24	         app_encode_app('type/realax/real', 
0.00/0.24	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	           X1), 
0.00/0.24	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	           'type/realax/real', 'const/sets/inf', X0))
0.00/0.24	       | ~ zip_tseitin2(X0)
0.00/0.24	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	             'const/sets/IN'('type/realax/real'), sk_A1(X1, X0)), X0)),
0.00/0.24	    inference('simplify', [status(thm)], ['3'])).
0.00/0.24	tff(zf_stmt_12, axiom,
0.00/0.24	  (![A:app_encode_fun('type/realax/real',$o)]:
0.00/0.24	     ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.24	                      'const/sets/FINITE'('type/realax/real'),A) & 
0.00/0.24	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
0.00/0.24	      (?[A0:'type/realax/real']:
0.00/0.24	         (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.24	                         app_encode_app('type/realax/real',
0.00/0.24	                                        app_encode_fun(app_encode_fun(
0.00/0.24	                                                       'type/realax/real',$o),
0.00/0.24	                                                       $o),
0.00/0.24	                                        'const/sets/IN'('type/realax/real'),
0.00/0.24	                                        A0),
0.00/0.24	                         A) & 
0.00/0.24	          (![A1:'type/realax/real']:
0.00/0.24	             (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.24	                             app_encode_app('type/realax/real',
0.00/0.24	                                            app_encode_fun(app_encode_fun(
0.00/0.24	                                                           'type/realax/real',
0.00/0.24	                                                           $o),$o),
0.00/0.24	                                            'const/sets/IN'('type/realax/real'),
0.00/0.24	                                            A1),
0.00/0.24	                             A) =>
0.00/0.24	              app_encode_app('type/realax/real',$o,
0.00/0.24	                             app_encode_app('type/realax/real',
0.00/0.24	                                            app_encode_fun('type/realax/real',
0.00/0.24	                                                           $o),
0.00/0.24	                                            'const/realax/real_le',A0),
0.00/0.24	                             A1)))))))).
0.00/0.24	tff('5', plain,
0.00/0.24	    ![X18 : app_encode_fun('type/realax/real', $o), X19 : 'type/realax/real']:
0.00/0.24	      (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	             'const/sets/IN'('type/realax/real'), X19), X18)
0.00/0.24	       | app_encode_app('type/realax/real', $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	             sk_A0(X18)), X19)
0.00/0.24	       | X18 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X18)),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_12])).
0.00/0.24	tff('6', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.24	      (~ $true
0.00/0.24	       | ~ zip_tseitin2(X0)
0.00/0.24	       | app_encode_app('type/realax/real', $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	             X1), 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', X0))
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | app_encode_app('type/realax/real', $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	             sk_A0(X0)), sk_A1(X1, X0))),
0.00/0.24	    inference('sup-', [status(thm)], ['4', '5'])).
0.00/0.24	tff('7', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.24	      (app_encode_app('type/realax/real', $o, 
0.00/0.24	         app_encode_app('type/realax/real', 
0.00/0.24	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	           sk_A0(X0)), sk_A1(X1, X0))
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | app_encode_app('type/realax/real', $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	             X1), 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', X0))
0.00/0.24	       | ~ zip_tseitin2(X0)),
0.00/0.24	    inference('simplify', [status(thm)], ['6'])).
0.00/0.24	tff(zf_stmt_3, axiom,
0.00/0.24	  ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.24	                   app_encode_app('type/realax/real',
0.00/0.24	                                  app_encode_fun(app_encode_fun('type/realax/real',
0.00/0.24	                                                                $o),
0.00/0.24	                                                 $o),
0.00/0.24	                                  'const/sets/IN'('type/realax/real'),A1),
0.00/0.24	                   A) =>
0.00/0.24	    app_encode_app('type/realax/real',$o,
0.00/0.24	                   app_encode_app('type/realax/real',
0.00/0.24	                                  app_encode_fun('type/realax/real',$o),
0.00/0.24	                                  'const/realax/real_le',A0),
0.00/0.24	                   A1)) =>
0.00/0.24	   zip_tseitin0(A1,A0,A))).
0.00/0.24	tff('8', plain,
0.00/0.24	    ![X4 : 'type/realax/real', X5 : 'type/realax/real', 
0.00/0.24	      X6 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (zip_tseitin0(X4, X5, X6)
0.00/0.24	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	             'const/sets/IN'('type/realax/real'), X4), X6)),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_3])).
0.00/0.24	tff(zf_stmt_4, type, zip_tseitin2 :
0.00/0.24	    app_encode_fun('type/realax/real',$o) > $o).
0.00/0.24	tff(zf_stmt_5, type, zip_tseitin1 :
0.00/0.24	    ('type/realax/real' * 
0.00/0.24	     'type/realax/real' * 
0.00/0.24	     app_encode_fun('type/realax/real',$o)) > $o).
0.00/0.24	tff(zf_stmt_6, type, zip_tseitin0 :
0.00/0.24	    ('type/realax/real' * 
0.00/0.24	     'type/realax/real' * 
0.00/0.24	     app_encode_fun('type/realax/real',$o)) > $o).
0.00/0.24	tff(zf_stmt_7, axiom,
0.00/0.24	  (![A:app_encode_fun('type/realax/real',$o)]:
0.00/0.24	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
0.00/0.24	       (?[A0:'type/realax/real']:
0.00/0.24	          (![A1:'type/realax/real']: zip_tseitin0(A1,A0,A)))) =>
0.00/0.24	      zip_tseitin2(A)))).
0.00/0.24	tff('9', plain,
0.00/0.24	    ![X11 : app_encode_fun('type/realax/real', $o), X12 : 'type/realax/real']:
0.00/0.24	      (zip_tseitin2(X11)
0.00/0.24	       | ~ zip_tseitin0(sk_A11(X12, X11), X12, X11)
0.00/0.24	       | X11 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_7])).
0.00/0.24	tff('10', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.24	      (~ $true
0.00/0.24	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	             'const/sets/IN'('type/realax/real'), sk_A11(X1, X0)), X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | zip_tseitin2(X0)),
0.00/0.24	    inference('sup-', [status(thm)], ['8', '9'])).
0.00/0.24	tff('11', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.24	      (zip_tseitin2(X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	             'const/sets/IN'('type/realax/real'), sk_A11(X1, X0)), X0)),
0.00/0.24	    inference('simplify', [status(thm)], ['10'])).
0.00/0.24	tff('12', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.24	      (~ $true
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | zip_tseitin2(X0)
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | app_encode_app('type/realax/real', $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	             sk_A0(X0)), sk_A11(X1, X0))),
0.00/0.24	    inference('sup-', [status(thm)], ['11', '5'])).
0.00/0.24	tff('13', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.24	      (app_encode_app('type/realax/real', $o, 
0.00/0.24	         app_encode_app('type/realax/real', 
0.00/0.24	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	           sk_A0(X0)), sk_A11(X1, X0))
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | zip_tseitin2(X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.24	    inference('simplify', [status(thm)], ['12'])).
0.00/0.24	tff('14', plain,
0.00/0.24	    ![X4 : 'type/realax/real', X5 : 'type/realax/real', 
0.00/0.24	      X6 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (zip_tseitin0(X4, X5, X6)
0.00/0.24	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.24	             app_encode_app('type/realax/real', 
0.00/0.24	               app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'const/realax/real_le', X5), X4)),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_3])).
0.00/0.24	tff('15', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.24	      (~ $true
0.00/0.24	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.24	             app_encode_app('type/realax/real', 
0.00/0.24	               app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'const/realax/real_le', X1), sk_A11(X1, X0))
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | zip_tseitin2(X0)),
0.00/0.24	    inference('sup-', [status(thm)], ['14', '9'])).
0.00/0.24	tff('16', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.24	      (zip_tseitin2(X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.24	             app_encode_app('type/realax/real', 
0.00/0.24	               app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'const/realax/real_le', X1), sk_A11(X1, X0))),
0.00/0.24	    inference('simplify', [status(thm)], ['15'])).
0.00/0.24	tff('17', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (~ $true
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | zip_tseitin2(X0)
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | zip_tseitin2(X0)),
0.00/0.24	    inference('sup-', [status(thm)], ['13', '16'])).
0.00/0.24	tff('18', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	           'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | zip_tseitin2(X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.24	    inference('simplify', [status(thm)], ['17'])).
0.00/0.24	tff('19', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.24	      (app_encode_app('type/realax/real', $o, 
0.00/0.24	         app_encode_app('type/realax/real', 
0.00/0.24	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	           X1), 
0.00/0.24	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	           'type/realax/real', 'const/sets/inf', X0))
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | app_encode_app('type/realax/real', $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	             sk_A0(X0)), sk_A1(X1, X0))),
0.00/0.24	    inference('clc', [status(thm)], ['7', '18'])).
0.00/0.24	tff('20', plain,
0.00/0.24	    ![X6 : app_encode_fun('type/realax/real', $o), X7 : 'type/realax/real', 
0.00/0.24	      X8 : 'type/realax/real']:
0.00/0.24	      (zip_tseitin1(X7, X8, X6)
0.00/0.24	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.24	             app_encode_app('type/realax/real', 
0.00/0.24	               app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'const/realax/real_le', X8), X7)),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.00/0.24	tff('21', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.24	      (~ $true
0.00/0.24	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.24	             app_encode_app('type/realax/real', 
0.00/0.24	               app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'const/realax/real_le', X1), sk_A1(X1, X0))
0.00/0.24	       | ~ zip_tseitin2(X0)
0.00/0.24	       | app_encode_app('type/realax/real', $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	             X1), 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', X0))),
0.00/0.24	    inference('sup-', [status(thm)], ['20', '2'])).
0.00/0.24	tff('22', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.24	      (app_encode_app('type/realax/real', $o, 
0.00/0.24	         app_encode_app('type/realax/real', 
0.00/0.24	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	           X1), 
0.00/0.24	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	           'type/realax/real', 'const/sets/inf', X0))
0.00/0.24	       | ~ zip_tseitin2(X0)
0.00/0.24	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.24	             app_encode_app('type/realax/real', 
0.00/0.24	               app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'const/realax/real_le', X1), sk_A1(X1, X0))),
0.00/0.24	    inference('simplify', [status(thm)], ['21'])).
0.00/0.24	tff('23', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (~ $true
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | app_encode_app('type/realax/real', $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	             sk_A0(X0)), 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', X0))
0.00/0.24	       | ~ zip_tseitin2(X0)
0.00/0.24	       | app_encode_app('type/realax/real', $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	             sk_A0(X0)), 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', X0))),
0.00/0.24	    inference('sup-', [status(thm)], ['19', '22'])).
0.00/0.24	tff('24', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (~ zip_tseitin2(X0)
0.00/0.24	       | app_encode_app('type/realax/real', $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	             sk_A0(X0)), 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', X0))
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.24	    inference('simplify', [status(thm)], ['23'])).
0.00/0.24	tff('25', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | app_encode_app('type/realax/real', $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	             sk_A0(X0)), 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', X0))),
0.00/0.24	    inference('clc', [status(thm)], ['24', '18'])).
0.00/0.24	tff('26', plain,
0.00/0.24	    ![X18 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	         app_encode_app('type/realax/real', 
0.00/0.24	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	           'const/sets/IN'('type/realax/real'), sk_A0(X18)), X18)
0.00/0.24	       | X18 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X18)),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_12])).
0.00/0.24	tff('27', plain,
0.00/0.24	    ![X6 : app_encode_fun('type/realax/real', $o), X9 : 'type/realax/real']:
0.00/0.24	      (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	             'const/sets/IN'('type/realax/real'), X9), X6)
0.00/0.24	       | app_encode_app('type/realax/real', $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'type/realax/real', 'const/sets/inf', X6)), X9)
0.00/0.24	       | ~ zip_tseitin2(X6)),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_2])).
0.00/0.24	tff('28', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (~ $true
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | ~ zip_tseitin2(X0)
0.00/0.24	       | app_encode_app('type/realax/real', $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'type/realax/real', 'const/sets/inf', X0)), sk_A0(X0))),
0.00/0.24	    inference('sup-', [status(thm)], ['26', '27'])).
0.00/0.24	tff('29', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (app_encode_app('type/realax/real', $o, 
0.00/0.24	         app_encode_app('type/realax/real', 
0.00/0.24	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', X0)), sk_A0(X0))
0.00/0.24	       | ~ zip_tseitin2(X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)),
0.00/0.24	    inference('simplify', [status(thm)], ['28'])).
0.00/0.24	tff(zf_stmt_11, axiom,
0.00/0.24	  (![A:'type/realax/real',A0:'type/realax/real']:
0.00/0.24	     ((app_encode_app('type/realax/real',$o,
0.00/0.24	                      app_encode_app('type/realax/real',
0.00/0.24	                                     app_encode_fun('type/realax/real',$o),
0.00/0.24	                                     'const/realax/real_le',A),
0.00/0.24	                      A0) & 
0.00/0.24	       app_encode_app('type/realax/real',$o,
0.00/0.24	                      app_encode_app('type/realax/real',
0.00/0.24	                                     app_encode_fun('type/realax/real',$o),
0.00/0.24	                                     'const/realax/real_le',A0),
0.00/0.24	                      A)) <=>
0.00/0.24	      (A = A0)))).
0.00/0.24	tff('30', plain,
0.00/0.24	    ![X15 : 'type/realax/real', X16 : 'type/realax/real']:
0.00/0.24	      (X16 = X15
0.00/0.24	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.24	             app_encode_app('type/realax/real', 
0.00/0.24	               app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'const/realax/real_le', X15), X16)
0.00/0.24	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.24	             app_encode_app('type/realax/real', 
0.00/0.24	               app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'const/realax/real_le', X16), X15)),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_11])).
0.00/0.24	tff('31', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (~ $true
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | ~ zip_tseitin2(X0)
0.00/0.24	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.24	             app_encode_app('type/realax/real', 
0.00/0.24	               app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'const/realax/real_le', sk_A0(X0)), 
0.00/0.24	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'type/realax/real', 'const/sets/inf', X0))
0.00/0.24	       | sk_A0(X0)
0.00/0.24	          = app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	              'type/realax/real', 'const/sets/inf', X0)),
0.00/0.24	    inference('sup-', [status(thm)], ['29', '30'])).
0.00/0.24	tff('32', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (sk_A0(X0)
0.00/0.24	        = app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	            'type/realax/real', 'const/sets/inf', X0)
0.00/0.24	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.24	             app_encode_app('type/realax/real', 
0.00/0.24	               app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'const/realax/real_le', sk_A0(X0)), 
0.00/0.24	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'type/realax/real', 'const/sets/inf', X0))
0.00/0.24	       | ~ zip_tseitin2(X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)),
0.00/0.24	    inference('simplify', [status(thm)], ['31'])).
0.00/0.24	tff('33', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	           'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.24	             app_encode_app('type/realax/real', 
0.00/0.24	               app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'const/realax/real_le', sk_A0(X0)), 
0.00/0.24	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'type/realax/real', 'const/sets/inf', X0))
0.00/0.24	       | sk_A0(X0)
0.00/0.24	          = app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	              'type/realax/real', 'const/sets/inf', X0)),
0.00/0.24	    inference('clc', [status(thm)], ['32', '18'])).
0.00/0.24	tff('34', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (~ $true
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | sk_A0(X0)
0.00/0.24	          = app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	              'type/realax/real', 'const/sets/inf', X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)),
0.00/0.24	    inference('sup-', [status(thm)], ['25', '33'])).
0.00/0.24	tff('35', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (sk_A0(X0)
0.00/0.24	        = app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	            'type/realax/real', 'const/sets/inf', X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)),
0.00/0.24	    inference('simplify', [status(thm)], ['34'])).
0.00/0.24	tff('36', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	         app_encode_app('type/realax/real', 
0.00/0.24	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	           'const/sets/IN'('type/realax/real'), 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', X0)), X0)
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | X0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.24	    inference('sup+', [status(thm)], ['35', '26'])).
0.00/0.24	tff('37', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.24	      (X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.24	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	             'const/sets/IN'('type/realax/real'), 
0.00/0.24	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'type/realax/real', 'const/sets/inf', X0)), X0)),
0.00/0.24	    inference('simplify', [status(thm)], ['36'])).
0.00/0.24	tff('38', plain,
0.00/0.24	    (~ $true
0.00/0.24	     | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	         app_encode_app('type/realax/real', 
0.00/0.24	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	           'const/sets/IN'('type/realax/real'), 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', sk_A)), sk_A)
0.00/0.24	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.24	    inference('sup-', [status(thm)], ['0', '37'])).
0.00/0.24	tff('39', plain,
0.00/0.24	    (sk_A = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	     | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	         app_encode_app('type/realax/real', 
0.00/0.24	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	           'const/sets/IN'('type/realax/real'), 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', sk_A)), sk_A)),
0.00/0.24	    inference('simplify', [status(thm)], ['38'])).
0.00/0.24	tff('40', plain, sk_A != 'const/sets/EMPTY'('type/realax/real'),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.24	tff('41', plain,
0.00/0.24	    app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	      app_encode_app('type/realax/real', 
0.00/0.24	        app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	        'const/sets/IN'('type/realax/real'), 
0.00/0.24	        app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	          'type/realax/real', 'const/sets/inf', sk_A)), sk_A),
0.00/0.24	    inference('simplify_reflect-', [status(thm)], ['39', '40'])).
0.00/0.24	tff('42', plain,
0.00/0.24	    (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	         app_encode_app('type/realax/real', 
0.00/0.24	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	           'const/sets/IN'('type/realax/real'), 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', sk_A)), sk_A)
0.00/0.24	     | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	         app_encode_app('type/realax/real', 
0.00/0.24	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	           'const/sets/IN'('type/realax/real'), sk_A01), sk_A)),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.24	tff('43', plain,
0.00/0.24	    (~ $true
0.00/0.24	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	             'const/sets/IN'('type/realax/real'), 
0.00/0.24	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'type/realax/real', 'const/sets/inf', sk_A)), sk_A)
0.00/0.24	     | ~ zip_tseitin2(sk_A)
0.00/0.24	     | app_encode_app('type/realax/real', $o, 
0.00/0.24	         app_encode_app('type/realax/real', 
0.00/0.24	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', sk_A)), sk_A01)),
0.00/0.24	    inference('sup-', [status(thm)], ['42', '27'])).
0.00/0.24	tff('44', plain,
0.00/0.24	    (app_encode_app('type/realax/real', $o, 
0.00/0.24	       app_encode_app('type/realax/real', 
0.00/0.24	         app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	           'type/realax/real', 'const/sets/inf', sk_A)), sk_A01)
0.00/0.24	     | ~ zip_tseitin2(sk_A)
0.00/0.24	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	             'const/sets/IN'('type/realax/real'), 
0.00/0.24	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'type/realax/real', 'const/sets/inf', sk_A)), sk_A)),
0.00/0.24	    inference('simplify', [status(thm)], ['43'])).
0.00/0.24	tff('45', plain,
0.00/0.24	    (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	         app_encode_app('type/realax/real', 
0.00/0.24	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	           'const/sets/IN'('type/realax/real'), 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', sk_A)), sk_A)
0.00/0.24	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.24	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'type/realax/real', 'const/sets/inf', sk_A)), sk_A01)),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.24	tff('46', plain,
0.00/0.24	    (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	         app_encode_app('type/realax/real', 
0.00/0.24	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	           'const/sets/IN'('type/realax/real'), 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', sk_A)), sk_A)
0.00/0.24	     | ~ zip_tseitin2(sk_A)),
0.00/0.24	    inference('clc', [status(thm)], ['44', '45'])).
0.00/0.24	tff('47', plain,
0.00/0.24	    (~ $true
0.00/0.24	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	           'const/sets/FINITE'('type/realax/real'), sk_A)
0.00/0.24	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	             'const/sets/IN'('type/realax/real'), 
0.00/0.24	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'type/realax/real', 'const/sets/inf', sk_A)), sk_A)),
0.00/0.24	    inference('sup-', [status(thm)], ['18', '46'])).
0.00/0.24	tff('48', plain,
0.00/0.24	    (~ $true
0.00/0.24	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
0.00/0.24	     | ~ $true
0.00/0.24	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	           app_encode_app('type/realax/real', 
0.00/0.24	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	             'const/sets/IN'('type/realax/real'), 
0.00/0.24	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	               'type/realax/real', 'const/sets/inf', sk_A)), sk_A)),
0.00/0.24	    inference('demod', [status(thm)], ['47', '0'])).
0.00/0.24	tff('49', plain,
0.00/0.24	    (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	         app_encode_app('type/realax/real', 
0.00/0.24	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	           'const/sets/IN'('type/realax/real'), 
0.00/0.24	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	             'type/realax/real', 'const/sets/inf', sk_A)), sk_A)
0.00/0.24	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.24	    inference('simplify', [status(thm)], ['48'])).
0.00/0.24	tff('50', plain,
0.00/0.24	    ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.24	        app_encode_app('type/realax/real', 
0.00/0.24	          app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.24	          'const/sets/IN'('type/realax/real'), 
0.00/0.24	          app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.24	            'type/realax/real', 'const/sets/inf', sk_A)), sk_A),
0.00/0.24	    inference('simplify_reflect-', [status(thm)], ['49', '40'])).
0.00/0.24	tff('51', plain, ~ $true, inference('sup-', [status(thm)], ['41', '50'])).
0.00/0.24	tff('52', plain, $false, inference('simplify', [status(thm)], ['51'])).
0.00/0.24	
0.00/0.24	% SZS output end Refutation
0.00/0.24	EOF
