0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n087.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 18:38:09 CST 2018
0.00/0.26	% done 68 iterations in 0.065s
0.00/0.26	% SZS status Theorem for 'stdin'
0.00/0.26	% SZS output start Refutation
0.00/0.27	tff(zf_stmt_13, conjecture,
0.00/0.27	  (![A:'type/realax/real',A0:app_encode_fun('type/realax/real',$o)]:
0.00/0.27	     ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.27	                      'const/sets/FINITE'('type/realax/real'),A0) & 
0.00/0.27	       (A0 != 'const/sets/EMPTY'('type/realax/real'))) =>
0.00/0.27	      ((app_encode_app(app_encode_fun('type/realax/real',$o),
0.00/0.27	                       'type/realax/real','const/sets/sup',A0) =
0.00/0.27	        A) <=>
0.00/0.27	       (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.27	                       app_encode_app('type/realax/real',
0.00/0.27	                                      app_encode_fun(app_encode_fun('type/realax/real',
0.00/0.27	                                                                    $o),
0.00/0.27	                                                     $o),
0.00/0.27	                                      'const/sets/IN'('type/realax/real'),A),
0.00/0.27	                       A0) & 
0.00/0.27	        (![A1:'type/realax/real']:
0.00/0.27	           (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.27	                           app_encode_app('type/realax/real',
0.00/0.27	                                          app_encode_fun(app_encode_fun(
0.00/0.27	                                                         'type/realax/real',
0.00/0.27	                                                         $o),$o),
0.00/0.27	                                          'const/sets/IN'('type/realax/real'),
0.00/0.27	                                          A1),
0.00/0.27	                           A0) =>
0.00/0.27	            app_encode_app('type/realax/real',$o,
0.00/0.27	                           app_encode_app('type/realax/real',
0.00/0.27	                                          app_encode_fun('type/realax/real',
0.00/0.27	                                                         $o),
0.00/0.27	                                          'const/realax/real_le',A1),
0.00/0.27	                           A)))))))).
0.00/0.27	tff(zf_stmt_0, negated_conjecture,
0.00/0.27	  (~
0.00/0.27	    (![A:'type/realax/real',A0:app_encode_fun('type/realax/real',$o)]:
0.00/0.27	       ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.27	                        'const/sets/FINITE'('type/realax/real'),A0) & 
0.00/0.27	         (A0 != 'const/sets/EMPTY'('type/realax/real'))) =>
0.00/0.27	        ((app_encode_app(app_encode_fun('type/realax/real',$o),
0.00/0.27	                         'type/realax/real','const/sets/sup',A0) =
0.00/0.27	          A) <=>
0.00/0.27	         (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.27	                         app_encode_app('type/realax/real',
0.00/0.27	                                        app_encode_fun(app_encode_fun(
0.00/0.27	                                                       'type/realax/real',$o),
0.00/0.27	                                                       $o),
0.00/0.27	                                        'const/sets/IN'('type/realax/real'),A),
0.00/0.27	                         A0) & 
0.00/0.27	          (![A1:'type/realax/real']:
0.00/0.27	             (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.27	                             app_encode_app('type/realax/real',
0.00/0.27	                                            app_encode_fun(app_encode_fun(
0.00/0.27	                                                           'type/realax/real',
0.00/0.27	                                                           $o),$o),
0.00/0.27	                                            'const/sets/IN'('type/realax/real'),
0.00/0.27	                                            A1),
0.00/0.27	                             A0) =>
0.00/0.27	              app_encode_app('type/realax/real',$o,
0.00/0.27	                             app_encode_app('type/realax/real',
0.00/0.27	                                            app_encode_fun('type/realax/real',
0.00/0.27	                                                           $o),
0.00/0.27	                                            'const/realax/real_le',A1),
0.00/0.27	                             A))))))))).
0.00/0.27	tff('0', plain,
0.00/0.27	    (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	       app_encode_app('type/realax/real', 
0.00/0.27	         app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	         'const/sets/IN'('type/realax/real'), sk_A12), sk_A0)
0.00/0.27	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	             'const/sets/IN'('type/realax/real'), sk_A), sk_A0)
0.00/0.27	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	        != sk_A),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.27	tff('1', plain,
0.00/0.27	    (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	       app_encode_app('type/realax/real', 
0.00/0.27	         app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	         'const/sets/IN'('type/realax/real'), sk_A), sk_A0)
0.00/0.27	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	        = sk_A),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.27	tff(zf_stmt_10, axiom,
0.00/0.27	  (![A:'type/realax/real']:
0.00/0.27	     app_encode_app('type/realax/real',$o,
0.00/0.27	                    app_encode_app('type/realax/real',
0.00/0.27	                                   app_encode_fun('type/realax/real',$o),
0.00/0.27	                                   'const/realax/real_le',A),
0.00/0.27	                    A))).
0.00/0.27	tff('2', plain,
0.00/0.27	    ![X6 : 'type/realax/real']:
0.00/0.27	      app_encode_app('type/realax/real', $o, 
0.00/0.27	        app_encode_app('type/realax/real', 
0.00/0.27	          app_encode_fun('type/realax/real', $o), 'const/realax/real_le', X6), 
0.00/0.27	        X6),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_10])).
0.00/0.27	tff('3', plain,
0.00/0.27	    app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	      'const/sets/FINITE'('type/realax/real'), sk_A0),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.27	tff(zf_stmt_11, axiom,
0.00/0.27	  (![A:app_encode_fun('type/realax/real',$o),A0:'type/realax/real']:
0.00/0.27	     ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.27	                      'const/sets/FINITE'('type/realax/real'),A) & 
0.00/0.27	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
0.00/0.27	      (app_encode_app('type/realax/real',$o,
0.00/0.27	                      app_encode_app('type/realax/real',
0.00/0.27	                                     app_encode_fun('type/realax/real',$o),
0.00/0.27	                                     'const/realax/real_le',A0),
0.00/0.27	                      app_encode_app(app_encode_fun('type/realax/real',$o),
0.00/0.27	                                     'type/realax/real','const/sets/sup',A)) <=>
0.00/0.27	       (?[A1:'type/realax/real']:
0.00/0.27	          (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.27	                          app_encode_app('type/realax/real',
0.00/0.27	                                         app_encode_fun(app_encode_fun(
0.00/0.27	                                                        'type/realax/real',$o),
0.00/0.27	                                                        $o),
0.00/0.27	                                         'const/sets/IN'('type/realax/real'),
0.00/0.27	                                         A1),
0.00/0.27	                          A) & 
0.00/0.27	           app_encode_app('type/realax/real',$o,
0.00/0.27	                          app_encode_app('type/realax/real',
0.00/0.27	                                         app_encode_fun('type/realax/real',$o),
0.00/0.27	                                         'const/realax/real_le',A0),
0.00/0.27	                          A1))))))).
0.00/0.27	tff('4', plain,
0.00/0.27	    ![X7 : app_encode_fun('type/realax/real', $o), X8 : 'type/realax/real', 
0.00/0.27	      X9 : 'type/realax/real']:
0.00/0.27	      (X7 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	             'const/sets/FINITE'('type/realax/real'), X7)
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             X8), 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', X7))
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', X8), X9)
0.00/0.27	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	               'const/sets/IN'('type/realax/real'), X9), X7)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_11])).
0.00/0.27	tff('5', plain,
0.00/0.27	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
0.00/0.27	      (~ $true
0.00/0.27	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	               'const/sets/IN'('type/realax/real'), X0), sk_A0)
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', X1), X0)
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             X1), 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.27	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.27	    inference('sup-', [status(thm)], ['3', '4'])).
0.00/0.27	tff('6', plain,
0.00/0.27	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
0.00/0.27	      (sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             X1), 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', X1), X0)
0.00/0.27	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	               'const/sets/IN'('type/realax/real'), X0), sk_A0)),
0.00/0.27	    inference('simplify', [status(thm)], ['5'])).
0.00/0.27	tff('7', plain, sk_A0 != 'const/sets/EMPTY'('type/realax/real'),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.27	tff('8', plain,
0.00/0.27	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
0.00/0.27	      (app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           X1), 
0.00/0.27	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', X1), X0)
0.00/0.27	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	               'const/sets/IN'('type/realax/real'), X0), sk_A0)),
0.00/0.27	    inference('simplify_reflect-', [status(thm)], ['6', '7'])).
0.00/0.27	tff('9', plain,
0.00/0.27	    ![X0 : 'type/realax/real']:
0.00/0.27	      (~ $true
0.00/0.27	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	               'const/sets/IN'('type/realax/real'), X0), sk_A0)
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             X0), 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0))),
0.00/0.27	    inference('sup-', [status(thm)], ['2', '8'])).
0.00/0.27	tff('10', plain,
0.00/0.27	    ![X0 : 'type/realax/real']:
0.00/0.27	      (app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           X0), 
0.00/0.27	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.27	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	               'const/sets/IN'('type/realax/real'), X0), sk_A0)),
0.00/0.27	    inference('simplify', [status(thm)], ['9'])).
0.00/0.27	tff('11', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	        = sk_A
0.00/0.27	     | app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           sk_A), 
0.00/0.27	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0))),
0.00/0.27	    inference('sup-', [status(thm)], ['1', '10'])).
0.00/0.27	tff('12', plain,
0.00/0.27	    (app_encode_app('type/realax/real', $o, 
0.00/0.27	       app_encode_app('type/realax/real', 
0.00/0.27	         app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	         sk_A), 
0.00/0.27	       app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	         'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.27	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	        = sk_A),
0.00/0.27	    inference('simplify', [status(thm)], ['11'])).
0.00/0.27	tff(zf_stmt_12, axiom,
0.00/0.27	  (![A:app_encode_fun('type/realax/real',$o),A0:'type/realax/real']:
0.00/0.27	     ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.27	                      'const/sets/FINITE'('type/realax/real'),A) & 
0.00/0.27	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
0.00/0.27	      (app_encode_app('type/realax/real',$o,
0.00/0.27	                      app_encode_app('type/realax/real',
0.00/0.27	                                     app_encode_fun('type/realax/real',$o),
0.00/0.27	                                     'const/realax/real_le',
0.00/0.27	                                     app_encode_app(app_encode_fun('type/realax/real',
0.00/0.27	                                                                   $o),
0.00/0.27	                                                    'type/realax/real',
0.00/0.27	                                                    'const/sets/sup',A)),
0.00/0.27	                      A0) <=>
0.00/0.27	       (![A1:'type/realax/real']:
0.00/0.27	          (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.27	                          app_encode_app('type/realax/real',
0.00/0.27	                                         app_encode_fun(app_encode_fun(
0.00/0.27	                                                        'type/realax/real',$o),
0.00/0.27	                                                        $o),
0.00/0.27	                                         'const/sets/IN'('type/realax/real'),
0.00/0.27	                                         A1),
0.00/0.27	                          A) =>
0.00/0.27	           app_encode_app('type/realax/real',$o,
0.00/0.27	                          app_encode_app('type/realax/real',
0.00/0.27	                                         app_encode_fun('type/realax/real',$o),
0.00/0.27	                                         'const/realax/real_le',A1),
0.00/0.27	                          A0))))))).
0.00/0.27	tff('13', plain,
0.00/0.27	    ![X10 : app_encode_fun('type/realax/real', $o), X12 : 'type/realax/real']:
0.00/0.27	      (X10 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	             'const/sets/FINITE'('type/realax/real'), X10)
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', X10)), X12)
0.00/0.27	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	             'const/sets/IN'('type/realax/real'), sk_A11(X12, X10)), X10)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_12])).
0.00/0.27	tff('14', plain,
0.00/0.27	    ![X13 : 'type/realax/real']:
0.00/0.27	      (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	             'const/sets/IN'('type/realax/real'), X13), sk_A0)
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             X13), sk_A)
0.00/0.27	       | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	          = sk_A),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.27	tff('15', plain,
0.00/0.27	    ![X0 : 'type/realax/real']:
0.00/0.27	      (~ $true
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', sk_A0)), X0)
0.00/0.27	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	             'const/sets/FINITE'('type/realax/real'), sk_A0)
0.00/0.27	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	       | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	          = sk_A
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             sk_A11(X0, sk_A0)), sk_A)),
0.00/0.27	    inference('sup-', [status(thm)], ['13', '14'])).
0.00/0.27	tff('16', plain,
0.00/0.27	    ![X0 : 'type/realax/real']:
0.00/0.27	      (~ $true
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', sk_A0)), X0)
0.00/0.27	       | ~ $true
0.00/0.27	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	       | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	          = sk_A
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             sk_A11(X0, sk_A0)), sk_A)),
0.00/0.27	    inference('demod', [status(thm)], ['15', '3'])).
0.00/0.27	tff('17', plain,
0.00/0.27	    ![X0 : 'type/realax/real']:
0.00/0.27	      (app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           sk_A11(X0, sk_A0)), sk_A)
0.00/0.27	       | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	          = sk_A
0.00/0.27	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', sk_A0)), X0)),
0.00/0.27	    inference('simplify', [status(thm)], ['16'])).
0.00/0.27	tff('18', plain,
0.00/0.27	    ![X0 : 'type/realax/real']:
0.00/0.27	      (app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           sk_A11(X0, sk_A0)), sk_A)
0.00/0.27	       | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	          = sk_A
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', sk_A0)), X0)),
0.00/0.27	    inference('simplify_reflect-', [status(thm)], ['17', '7'])).
0.00/0.27	tff('19', plain,
0.00/0.27	    ![X10 : app_encode_fun('type/realax/real', $o), X12 : 'type/realax/real']:
0.00/0.27	      (X10 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	             'const/sets/FINITE'('type/realax/real'), X10)
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', X10)), X12)
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', sk_A11(X12, X10)), X12)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_12])).
0.00/0.27	tff('20', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0)), sk_A)
0.00/0.27	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	        = sk_A
0.00/0.27	     | app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0)), sk_A)
0.00/0.27	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	           'const/sets/FINITE'('type/realax/real'), sk_A0)
0.00/0.27	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.27	    inference('sup-', [status(thm)], ['18', '19'])).
0.00/0.27	tff('21', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0)), sk_A)
0.00/0.27	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	        = sk_A
0.00/0.27	     | app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0)), sk_A)
0.00/0.27	     | ~ $true
0.00/0.27	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.27	    inference('demod', [status(thm)], ['20', '3'])).
0.00/0.27	tff('22', plain,
0.00/0.27	    (sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	        = sk_A
0.00/0.27	     | app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0)), sk_A)),
0.00/0.27	    inference('simplify', [status(thm)], ['21'])).
0.00/0.27	tff('23', plain,
0.00/0.27	    (app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	       'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	      = sk_A
0.00/0.27	     | app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0)), sk_A)),
0.00/0.27	    inference('simplify_reflect-', [status(thm)], ['22', '7'])).
0.00/0.27	tff(zf_stmt_8, axiom,
0.00/0.27	  (![A:'type/realax/real',A0:'type/realax/real']:
0.00/0.27	     ((app_encode_app('type/realax/real',$o,
0.00/0.27	                      app_encode_app('type/realax/real',
0.00/0.27	                                     app_encode_fun('type/realax/real',$o),
0.00/0.27	                                     'const/realax/real_le',A),
0.00/0.27	                      A0) & 
0.00/0.27	       app_encode_app('type/realax/real',$o,
0.00/0.27	                      app_encode_app('type/realax/real',
0.00/0.27	                                     app_encode_fun('type/realax/real',$o),
0.00/0.27	                                     'const/realax/real_le',A0),
0.00/0.27	                      A)) <=>
0.00/0.27	      (A = A0)))).
0.00/0.27	tff('24', plain,
0.00/0.27	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
0.00/0.27	      (X1 = X0
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', X0), X1)
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', X1), X0)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_8])).
0.00/0.27	tff('25', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	        = sk_A
0.00/0.27	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             sk_A), 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.27	     | sk_A
0.00/0.27	        = app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	            'type/realax/real', 'const/sets/sup', sk_A0)),
0.00/0.27	    inference('sup-', [status(thm)], ['23', '24'])).
0.00/0.27	tff('26', plain,
0.00/0.27	    (~ app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           sk_A), 
0.00/0.27	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.27	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	        = sk_A),
0.00/0.27	    inference('simplify', [status(thm)], ['25'])).
0.00/0.27	tff('27', plain,
0.00/0.27	    app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	      'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	     = sk_A,
0.00/0.27	    inference('clc', [status(thm)], ['12', '26'])).
0.00/0.27	tff('28', plain,
0.00/0.27	    (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	       app_encode_app('type/realax/real', 
0.00/0.27	         app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	         'const/sets/IN'('type/realax/real'), sk_A12), sk_A0)
0.00/0.27	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	             'const/sets/IN'('type/realax/real'), 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', sk_A0)), sk_A0)
0.00/0.27	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	        != app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0)),
0.00/0.27	    inference('demod', [status(thm)], ['0', '27', '27'])).
0.00/0.27	tff('29', plain,
0.00/0.27	    (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	           'const/sets/IN'('type/realax/real'), 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0)), sk_A0)
0.00/0.27	     | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	           'const/sets/IN'('type/realax/real'), sk_A12), sk_A0)),
0.00/0.27	    inference('simplify', [status(thm)], ['28'])).
0.00/0.27	tff('30', plain,
0.00/0.27	    ![X7 : app_encode_fun('type/realax/real', $o), X8 : 'type/realax/real']:
0.00/0.27	      (X7 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	             'const/sets/FINITE'('type/realax/real'), X7)
0.00/0.27	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	             'const/sets/IN'('type/realax/real'), sk_A1(X8, X7)), X7)
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', X8), 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', X7))),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_11])).
0.00/0.27	tff('31', plain,
0.00/0.27	    ![X0 : 'type/realax/real']:
0.00/0.27	      (~ $true
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', X0), 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.27	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	             'const/sets/FINITE'('type/realax/real'), sk_A0)
0.00/0.27	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             sk_A1(X0, sk_A0)), 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0))),
0.00/0.27	    inference('sup-', [status(thm)], ['30', '10'])).
0.00/0.27	tff('32', plain,
0.00/0.27	    ![X0 : 'type/realax/real']:
0.00/0.27	      (~ $true
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', X0), 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.27	       | ~ $true
0.00/0.27	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             sk_A1(X0, sk_A0)), 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0))),
0.00/0.27	    inference('demod', [status(thm)], ['31', '3'])).
0.00/0.27	tff('33', plain,
0.00/0.27	    ![X0 : 'type/realax/real']:
0.00/0.27	      (app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           sk_A1(X0, sk_A0)), 
0.00/0.27	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.27	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', X0), 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', sk_A0))),
0.00/0.27	    inference('simplify', [status(thm)], ['32'])).
0.00/0.27	tff('34', plain,
0.00/0.27	    ![X0 : 'type/realax/real']:
0.00/0.27	      (app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           sk_A1(X0, sk_A0)), 
0.00/0.27	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', X0), 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', sk_A0))),
0.00/0.27	    inference('simplify_reflect-', [status(thm)], ['33', '7'])).
0.00/0.27	tff('35', plain,
0.00/0.27	    ![X7 : app_encode_fun('type/realax/real', $o), X8 : 'type/realax/real']:
0.00/0.27	      (X7 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	             'const/sets/FINITE'('type/realax/real'), X7)
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             X8), sk_A1(X8, X7))
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', X8), 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', X7))),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_11])).
0.00/0.27	tff('36', plain,
0.00/0.27	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.27	      (~ $true
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', X1), 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', X0))
0.00/0.27	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.27	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', sk_A1(X1, X0)), X1)
0.00/0.27	       | sk_A1(X1, X0) = X1),
0.00/0.27	    inference('sup-', [status(thm)], ['35', '24'])).
0.00/0.27	tff('37', plain,
0.00/0.27	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.27	      (sk_A1(X1, X0) = X1
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', sk_A1(X1, X0)), X1)
0.00/0.27	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', X1), 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', X0))),
0.00/0.27	    inference('simplify', [status(thm)], ['36'])).
0.00/0.27	tff('38', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', sk_A0)), 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.27	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', sk_A0)), 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.27	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	           'const/sets/FINITE'('type/realax/real'), sk_A0)
0.00/0.27	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	     | sk_A1(
0.00/0.27	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0), sk_A0)
0.00/0.27	        = app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	            'type/realax/real', 'const/sets/sup', sk_A0)),
0.00/0.27	    inference('sup-', [status(thm)], ['34', '37'])).
0.00/0.27	tff('39', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | ~ $true
0.00/0.27	     | ~ $true
0.00/0.27	     | ~ $true
0.00/0.27	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	     | sk_A1(
0.00/0.27	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0), sk_A0)
0.00/0.27	        = app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	            'type/realax/real', 'const/sets/sup', sk_A0)),
0.00/0.27	    inference('demod', [status(thm)], ['38', '2', '2', '3'])).
0.00/0.27	tff('40', plain,
0.00/0.27	    (sk_A1(
0.00/0.27	       app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	         'type/realax/real', 'const/sets/sup', sk_A0), sk_A0)
0.00/0.27	      = app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	          'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.27	    inference('simplify', [status(thm)], ['39'])).
0.00/0.27	tff('41', plain,
0.00/0.27	    sk_A1(
0.00/0.27	      app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	        'type/realax/real', 'const/sets/sup', sk_A0), sk_A0)
0.00/0.27	     = app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	         'type/realax/real', 'const/sets/sup', sk_A0),
0.00/0.27	    inference('simplify_reflect-', [status(thm)], ['40', '7'])).
0.00/0.27	tff('42', plain,
0.00/0.27	    (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	       app_encode_app('type/realax/real', 
0.00/0.27	         app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	         'const/sets/IN'('type/realax/real'), 
0.00/0.27	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0)), sk_A0)
0.00/0.27	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', sk_A0)), 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.27	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	           'const/sets/FINITE'('type/realax/real'), sk_A0)
0.00/0.27	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.27	    inference('sup+', [status(thm)], ['41', '30'])).
0.00/0.27	tff('43', plain,
0.00/0.27	    (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	       app_encode_app('type/realax/real', 
0.00/0.27	         app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	         'const/sets/IN'('type/realax/real'), 
0.00/0.27	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0)), sk_A0)
0.00/0.27	     | ~ $true
0.00/0.27	     | ~ $true
0.00/0.27	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.27	    inference('demod', [status(thm)], ['42', '2', '3'])).
0.00/0.27	tff('44', plain,
0.00/0.27	    (sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.27	     | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	           'const/sets/IN'('type/realax/real'), 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0)), sk_A0)),
0.00/0.27	    inference('simplify', [status(thm)], ['43'])).
0.00/0.27	tff('45', plain,
0.00/0.27	    app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	      app_encode_app('type/realax/real', 
0.00/0.27	        app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	        'const/sets/IN'('type/realax/real'), 
0.00/0.27	        app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	          'type/realax/real', 'const/sets/sup', sk_A0)), sk_A0),
0.00/0.27	    inference('simplify_reflect-', [status(thm)], ['44', '7'])).
0.00/0.27	tff('46', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	           'const/sets/IN'('type/realax/real'), sk_A12), sk_A0)),
0.00/0.27	    inference('demod', [status(thm)], ['29', '45'])).
0.00/0.27	tff('47', plain,
0.00/0.27	    app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	      app_encode_app('type/realax/real', 
0.00/0.27	        app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	        'const/sets/IN'('type/realax/real'), sk_A12), sk_A0),
0.00/0.27	    inference('simplify', [status(thm)], ['46'])).
0.00/0.27	tff('48', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           sk_A12), 
0.00/0.27	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0))),
0.00/0.27	    inference('sup-', [status(thm)], ['47', '10'])).
0.00/0.27	tff('49', plain,
0.00/0.27	    app_encode_app('type/realax/real', $o, 
0.00/0.27	      app_encode_app('type/realax/real', 
0.00/0.27	        app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	        sk_A12), 
0.00/0.27	      app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	        'type/realax/real', 'const/sets/sup', sk_A0)),
0.00/0.27	    inference('simplify', [status(thm)], ['48'])).
0.00/0.27	tff('50', plain,
0.00/0.27	    (~ app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           sk_A12), sk_A)
0.00/0.27	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	             'const/sets/IN'('type/realax/real'), sk_A), sk_A0)
0.00/0.27	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	        != sk_A),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.27	tff('51', plain,
0.00/0.27	    (~ app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           sk_A12), 
0.00/0.27	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	           'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.27	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	             'const/sets/IN'('type/realax/real'), 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', sk_A0)), sk_A0)
0.00/0.27	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.27	        != app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0)),
0.00/0.27	    inference('demod', [status(thm)], ['50', '27', '27', '27'])).
0.00/0.27	tff('52', plain,
0.00/0.27	    (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	           'const/sets/IN'('type/realax/real'), 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0)), sk_A0)
0.00/0.27	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             sk_A12), 
0.00/0.27	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	             'type/realax/real', 'const/sets/sup', sk_A0))),
0.00/0.27	    inference('simplify', [status(thm)], ['51'])).
0.00/0.27	tff('53', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.27	             'const/sets/IN'('type/realax/real'), 
0.00/0.27	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'type/realax/real', 'const/sets/sup', sk_A0)), sk_A0)),
0.00/0.27	    inference('sup-', [status(thm)], ['49', '52'])).
0.00/0.27	tff('54', plain, (~ $true | ~ $true),
0.00/0.27	    inference('demod', [status(thm)], ['53', '45'])).
0.00/0.27	tff('55', plain, $false, inference('simplify', [status(thm)], ['54'])).
0.00/0.27	
0.00/0.27	% SZS output end Refutation
0.00/0.27	EOF
