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    : kbo
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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n098.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 18:38:09 CST 2018
0.00/0.27	% done 83 iterations in 0.078s
0.00/0.27	% SZS status Theorem for 'stdin'
0.00/0.27	% SZS output start Refutation
0.00/0.28	tff(zf_stmt_13, conjecture,
0.00/0.28	  (![A:'type/realax/real',A0:app_encode_fun('type/realax/real',$o)]:
0.00/0.28	     ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.28	                      'const/sets/FINITE'('type/realax/real'),A0) & 
0.00/0.28	       (A0 != 'const/sets/EMPTY'('type/realax/real'))) =>
0.00/0.28	      ((app_encode_app(app_encode_fun('type/realax/real',$o),
0.00/0.28	                       'type/realax/real','const/sets/sup',A0) =
0.00/0.28	        A) <=>
0.00/0.28	       (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.28	                       app_encode_app('type/realax/real',
0.00/0.28	                                      app_encode_fun(app_encode_fun('type/realax/real',
0.00/0.28	                                                                    $o),
0.00/0.28	                                                     $o),
0.00/0.28	                                      'const/sets/IN'('type/realax/real'),A),
0.00/0.28	                       A0) & 
0.00/0.28	        (![A1:'type/realax/real']:
0.00/0.28	           (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.28	                           app_encode_app('type/realax/real',
0.00/0.28	                                          app_encode_fun(app_encode_fun(
0.00/0.28	                                                         'type/realax/real',
0.00/0.28	                                                         $o),$o),
0.00/0.28	                                          'const/sets/IN'('type/realax/real'),
0.00/0.28	                                          A1),
0.00/0.28	                           A0) =>
0.00/0.28	            app_encode_app('type/realax/real',$o,
0.00/0.28	                           app_encode_app('type/realax/real',
0.00/0.28	                                          app_encode_fun('type/realax/real',
0.00/0.28	                                                         $o),
0.00/0.28	                                          'const/realax/real_le',A1),
0.00/0.28	                           A)))))))).
0.00/0.28	tff(zf_stmt_0, negated_conjecture,
0.00/0.28	  (~
0.00/0.28	    (![A:'type/realax/real',A0:app_encode_fun('type/realax/real',$o)]:
0.00/0.28	       ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.28	                        'const/sets/FINITE'('type/realax/real'),A0) & 
0.00/0.28	         (A0 != 'const/sets/EMPTY'('type/realax/real'))) =>
0.00/0.28	        ((app_encode_app(app_encode_fun('type/realax/real',$o),
0.00/0.28	                         'type/realax/real','const/sets/sup',A0) =
0.00/0.28	          A) <=>
0.00/0.28	         (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.28	                         app_encode_app('type/realax/real',
0.00/0.28	                                        app_encode_fun(app_encode_fun(
0.00/0.28	                                                       'type/realax/real',$o),
0.00/0.28	                                                       $o),
0.00/0.28	                                        'const/sets/IN'('type/realax/real'),A),
0.00/0.28	                         A0) & 
0.00/0.28	          (![A1:'type/realax/real']:
0.00/0.28	             (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.28	                             app_encode_app('type/realax/real',
0.00/0.28	                                            app_encode_fun(app_encode_fun(
0.00/0.28	                                                           'type/realax/real',
0.00/0.28	                                                           $o),$o),
0.00/0.28	                                            'const/sets/IN'('type/realax/real'),
0.00/0.28	                                            A1),
0.00/0.28	                             A0) =>
0.00/0.28	              app_encode_app('type/realax/real',$o,
0.00/0.28	                             app_encode_app('type/realax/real',
0.00/0.28	                                            app_encode_fun('type/realax/real',
0.00/0.28	                                                           $o),
0.00/0.28	                                            'const/realax/real_le',A1),
0.00/0.28	                             A))))))))).
0.00/0.28	tff('0', plain,
0.00/0.28	    (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	       app_encode_app('type/realax/real', 
0.00/0.28	         app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	         'const/sets/IN'('type/realax/real'), sk_A12), sk_A0)
0.00/0.28	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	             'const/sets/IN'('type/realax/real'), sk_A), sk_A0)
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	        != sk_A),
0.00/0.28	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.28	tff(zf_stmt_10, axiom,
0.00/0.28	  (![A:'type/realax/real']:
0.00/0.28	     app_encode_app('type/realax/real',$o,
0.00/0.28	                    app_encode_app('type/realax/real',
0.00/0.28	                                   app_encode_fun('type/realax/real',$o),
0.00/0.28	                                   'const/realax/real_le',A),
0.00/0.28	                    A))).
0.00/0.28	tff('1', plain,
0.00/0.28	    ![X6 : 'type/realax/real']:
0.00/0.28	      app_encode_app('type/realax/real', $o, 
0.00/0.28	        app_encode_app('type/realax/real', 
0.00/0.28	          app_encode_fun('type/realax/real', $o), 'const/realax/real_le', X6), 
0.00/0.28	        X6),
0.00/0.28	    inference('cnf', [status(esa)], [zf_stmt_10])).
0.00/0.28	tff(zf_stmt_11, axiom,
0.00/0.28	  (![A:app_encode_fun('type/realax/real',$o),A0:'type/realax/real']:
0.00/0.28	     ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.28	                      'const/sets/FINITE'('type/realax/real'),A) & 
0.00/0.28	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
0.00/0.28	      (app_encode_app('type/realax/real',$o,
0.00/0.28	                      app_encode_app('type/realax/real',
0.00/0.28	                                     app_encode_fun('type/realax/real',$o),
0.00/0.28	                                     'const/realax/real_le',A0),
0.00/0.28	                      app_encode_app(app_encode_fun('type/realax/real',$o),
0.00/0.28	                                     'type/realax/real','const/sets/sup',A)) <=>
0.00/0.28	       (?[A1:'type/realax/real']:
0.00/0.28	          (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.28	                          app_encode_app('type/realax/real',
0.00/0.28	                                         app_encode_fun(app_encode_fun(
0.00/0.28	                                                        'type/realax/real',$o),
0.00/0.28	                                                        $o),
0.00/0.28	                                         'const/sets/IN'('type/realax/real'),
0.00/0.28	                                         A1),
0.00/0.28	                          A) & 
0.00/0.28	           app_encode_app('type/realax/real',$o,
0.00/0.28	                          app_encode_app('type/realax/real',
0.00/0.28	                                         app_encode_fun('type/realax/real',$o),
0.00/0.28	                                         'const/realax/real_le',A0),
0.00/0.28	                          A1))))))).
0.00/0.28	tff('2', plain,
0.00/0.28	    ![X7 : app_encode_fun('type/realax/real', $o), X8 : 'type/realax/real', 
0.00/0.28	      X9 : 'type/realax/real']:
0.00/0.28	      (X7 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             'const/sets/FINITE'('type/realax/real'), X7)
0.00/0.28	       | app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             X8), 
0.00/0.28	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	             'type/realax/real', 'const/sets/sup', X7))
0.00/0.28	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'const/realax/real_le', X8), X9)
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	               'const/sets/IN'('type/realax/real'), X9), X7)),
0.00/0.28	    inference('cnf', [status(esa)], [zf_stmt_11])).
0.00/0.28	tff('3', plain,
0.00/0.28	    ![X0 : 'type/realax/real', X1 : app_encode_fun('type/realax/real', $o)]:
0.00/0.28	      (~ $true
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	               'const/sets/IN'('type/realax/real'), X0), X1)
0.00/0.28	       | app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             X0), 
0.00/0.28	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	             'type/realax/real', 'const/sets/sup', X1))
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             'const/sets/FINITE'('type/realax/real'), X1)
0.00/0.28	       | X1 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.28	    inference('sup-', [status(thm)], ['1', '2'])).
0.00/0.28	tff('4', plain,
0.00/0.28	    ![X0 : 'type/realax/real', X1 : app_encode_fun('type/realax/real', $o)]:
0.00/0.28	      (X1 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             'const/sets/FINITE'('type/realax/real'), X1)
0.00/0.28	       | app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             X0), 
0.00/0.28	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	             'type/realax/real', 'const/sets/sup', X1))
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	               'const/sets/IN'('type/realax/real'), X0), X1)),
0.00/0.28	    inference('simplify', [status(thm)], ['3'])).
0.00/0.28	tff('5', plain,
0.00/0.28	    ![X7 : app_encode_fun('type/realax/real', $o), X8 : 'type/realax/real']:
0.00/0.28	      (X7 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             'const/sets/FINITE'('type/realax/real'), X7)
0.00/0.28	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	             'const/sets/IN'('type/realax/real'), sk_A1(X8, X7)), X7)
0.00/0.28	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'const/realax/real_le', X8), 
0.00/0.28	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'type/realax/real', 'const/sets/sup', X7))),
0.00/0.28	    inference('cnf', [status(esa)], [zf_stmt_11])).
0.00/0.28	tff('6', plain,
0.00/0.28	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.28	      (~ $true
0.00/0.28	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	             'const/sets/IN'('type/realax/real'), 
0.00/0.28	             sk_A1(
0.00/0.28	               app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	                 'type/realax/real', 'const/sets/sup', X0), X0)), X0)
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.28	       | X0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.28	    inference('sup-', [status(thm)], ['1', '5'])).
0.00/0.28	tff('7', plain,
0.00/0.28	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.28	      (X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.28	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	             'const/sets/IN'('type/realax/real'), 
0.00/0.28	             sk_A1(
0.00/0.28	               app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	                 'type/realax/real', 'const/sets/sup', X0), X0)), X0)),
0.00/0.28	    inference('simplify', [status(thm)], ['6'])).
0.00/0.28	tff('8', plain,
0.00/0.28	    ![X13 : 'type/realax/real']:
0.00/0.28	      (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	             'const/sets/IN'('type/realax/real'), X13), sk_A0)
0.00/0.28	       | app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             X13), sk_A)
0.00/0.28	       | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	           'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	          = sk_A),
0.00/0.28	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.28	tff('9', plain,
0.00/0.28	    (~ $true
0.00/0.28	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           'const/sets/FINITE'('type/realax/real'), sk_A0)
0.00/0.28	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	        = sk_A
0.00/0.28	     | app_encode_app('type/realax/real', $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	           sk_A1(
0.00/0.28	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'type/realax/real', 'const/sets/sup', sk_A0), sk_A0)), sk_A)),
0.00/0.28	    inference('sup-', [status(thm)], ['7', '8'])).
0.00/0.28	tff('10', plain,
0.00/0.28	    app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	      'const/sets/FINITE'('type/realax/real'), sk_A0),
0.00/0.28	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.28	tff('11', plain,
0.00/0.28	    (~ $true
0.00/0.28	     | ~ $true
0.00/0.28	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	        = sk_A
0.00/0.28	     | app_encode_app('type/realax/real', $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	           sk_A1(
0.00/0.28	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'type/realax/real', 'const/sets/sup', sk_A0), sk_A0)), sk_A)),
0.00/0.28	    inference('demod', [status(thm)], ['9', '10'])).
0.00/0.28	tff('12', plain,
0.00/0.28	    (app_encode_app('type/realax/real', $o, 
0.00/0.28	       app_encode_app('type/realax/real', 
0.00/0.28	         app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	         sk_A1(
0.00/0.28	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	             'type/realax/real', 'const/sets/sup', sk_A0), sk_A0)), sk_A)
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	        = sk_A
0.00/0.28	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.28	    inference('simplify', [status(thm)], ['11'])).
0.00/0.28	tff('13', plain, sk_A0 != 'const/sets/EMPTY'('type/realax/real'),
0.00/0.28	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.28	tff('14', plain,
0.00/0.28	    (app_encode_app('type/realax/real', $o, 
0.00/0.28	       app_encode_app('type/realax/real', 
0.00/0.28	         app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	         sk_A1(
0.00/0.28	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	             'type/realax/real', 'const/sets/sup', sk_A0), sk_A0)), sk_A)
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	        = sk_A),
0.00/0.28	    inference('simplify_reflect-', [status(thm)], ['12', '13'])).
0.00/0.28	tff('15', plain,
0.00/0.28	    ![X7 : app_encode_fun('type/realax/real', $o), X8 : 'type/realax/real']:
0.00/0.28	      (X7 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             'const/sets/FINITE'('type/realax/real'), X7)
0.00/0.28	       | app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             X8), sk_A1(X8, X7))
0.00/0.28	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'const/realax/real_le', X8), 
0.00/0.28	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'type/realax/real', 'const/sets/sup', X7))),
0.00/0.28	    inference('cnf', [status(esa)], [zf_stmt_11])).
0.00/0.28	tff('16', plain,
0.00/0.28	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.28	      (~ $true
0.00/0.28	       | app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'type/realax/real', 'const/sets/sup', X0)), 
0.00/0.28	           sk_A1(
0.00/0.28	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'type/realax/real', 'const/sets/sup', X0), X0))
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.28	       | X0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.28	    inference('sup-', [status(thm)], ['1', '15'])).
0.00/0.28	tff('17', plain,
0.00/0.28	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.28	      (X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.28	       | app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'type/realax/real', 'const/sets/sup', X0)), 
0.00/0.28	           sk_A1(
0.00/0.28	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'type/realax/real', 'const/sets/sup', X0), X0))),
0.00/0.28	    inference('simplify', [status(thm)], ['16'])).
0.00/0.28	tff(zf_stmt_9, axiom,
0.00/0.28	  (![A:'type/realax/real',A0:'type/realax/real',A1:'type/realax/real']:
0.00/0.28	     ((app_encode_app('type/realax/real',$o,
0.00/0.28	                      app_encode_app('type/realax/real',
0.00/0.28	                                     app_encode_fun('type/realax/real',$o),
0.00/0.28	                                     'const/realax/real_le',A),
0.00/0.28	                      A0) & 
0.00/0.28	       app_encode_app('type/realax/real',$o,
0.00/0.28	                      app_encode_app('type/realax/real',
0.00/0.28	                                     app_encode_fun('type/realax/real',$o),
0.00/0.28	                                     'const/realax/real_le',A0),
0.00/0.28	                      A1)) =>
0.00/0.28	      app_encode_app('type/realax/real',$o,
0.00/0.28	                     app_encode_app('type/realax/real',
0.00/0.28	                                    app_encode_fun('type/realax/real',$o),
0.00/0.28	                                    'const/realax/real_le',A),
0.00/0.28	                     A1)))).
0.00/0.28	tff('18', plain,
0.00/0.28	    ![X3 : 'type/realax/real', X4 : 'type/realax/real', 
0.00/0.28	      X5 : 'type/realax/real']:
0.00/0.28	      (~ app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             X3), X4)
0.00/0.28	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'const/realax/real_le', X4), X5)
0.00/0.28	       | app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             X3), X5)),
0.00/0.28	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.00/0.28	tff('19', plain,
0.00/0.28	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.28	      (~ $true
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.28	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	       | app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'type/realax/real', 'const/sets/sup', X0)), X1)
0.00/0.28	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'const/realax/real_le', 
0.00/0.28	               sk_A1(
0.00/0.28	                 app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	                   'type/realax/real', 'const/sets/sup', X0), X0)), X1)),
0.00/0.28	    inference('sup-', [status(thm)], ['17', '18'])).
0.00/0.28	tff('20', plain,
0.00/0.28	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.28	      (~ app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             sk_A1(
0.00/0.28	               app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	                 'type/realax/real', 'const/sets/sup', X0), X0)), X1)
0.00/0.28	       | app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'type/realax/real', 'const/sets/sup', X0)), X1)
0.00/0.28	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             'const/sets/FINITE'('type/realax/real'), X0)),
0.00/0.28	    inference('simplify', [status(thm)], ['19'])).
0.00/0.28	tff('21', plain,
0.00/0.28	    (~ $true
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	        = sk_A
0.00/0.28	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           'const/sets/FINITE'('type/realax/real'), sk_A0)
0.00/0.28	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	     | app_encode_app('type/realax/real', $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	             'type/realax/real', 'const/sets/sup', sk_A0)), sk_A)),
0.00/0.28	    inference('sup-', [status(thm)], ['14', '20'])).
0.00/0.28	tff('22', plain,
0.00/0.28	    (~ $true
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	        = sk_A
0.00/0.28	     | ~ $true
0.00/0.28	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	     | app_encode_app('type/realax/real', $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	             'type/realax/real', 'const/sets/sup', sk_A0)), sk_A)),
0.00/0.28	    inference('demod', [status(thm)], ['21', '10'])).
0.00/0.28	tff('23', plain,
0.00/0.28	    (app_encode_app('type/realax/real', $o, 
0.00/0.28	       app_encode_app('type/realax/real', 
0.00/0.28	         app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	           'type/realax/real', 'const/sets/sup', sk_A0)), sk_A)
0.00/0.28	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	        = sk_A),
0.00/0.28	    inference('simplify', [status(thm)], ['22'])).
0.00/0.28	tff('24', plain,
0.00/0.28	    (app_encode_app('type/realax/real', $o, 
0.00/0.28	       app_encode_app('type/realax/real', 
0.00/0.28	         app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	           'type/realax/real', 'const/sets/sup', sk_A0)), sk_A)
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	        = sk_A),
0.00/0.28	    inference('simplify_reflect-', [status(thm)], ['23', '13'])).
0.00/0.28	tff(zf_stmt_8, axiom,
0.00/0.28	  (![A:'type/realax/real',A0:'type/realax/real']:
0.00/0.28	     ((app_encode_app('type/realax/real',$o,
0.00/0.28	                      app_encode_app('type/realax/real',
0.00/0.28	                                     app_encode_fun('type/realax/real',$o),
0.00/0.28	                                     'const/realax/real_le',A),
0.00/0.28	                      A0) & 
0.00/0.28	       app_encode_app('type/realax/real',$o,
0.00/0.28	                      app_encode_app('type/realax/real',
0.00/0.28	                                     app_encode_fun('type/realax/real',$o),
0.00/0.28	                                     'const/realax/real_le',A0),
0.00/0.28	                      A)) <=>
0.00/0.28	      (A = A0)))).
0.00/0.28	tff('25', plain,
0.00/0.28	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
0.00/0.28	      (X1 = X0
0.00/0.28	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'const/realax/real_le', X0), X1)
0.00/0.28	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'const/realax/real_le', X1), X0)),
0.00/0.28	    inference('cnf', [status(esa)], [zf_stmt_8])).
0.00/0.28	tff('26', plain,
0.00/0.28	    (~ $true
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	        = sk_A
0.00/0.28	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             sk_A), 
0.00/0.28	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	             'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.28	     | sk_A
0.00/0.28	        = app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	            'type/realax/real', 'const/sets/sup', sk_A0)),
0.00/0.28	    inference('sup-', [status(thm)], ['24', '25'])).
0.00/0.28	tff('27', plain,
0.00/0.28	    (~ app_encode_app('type/realax/real', $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	           sk_A), 
0.00/0.28	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	           'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	        = sk_A),
0.00/0.28	    inference('simplify', [status(thm)], ['26'])).
0.00/0.28	tff('28', plain,
0.00/0.28	    (~ $true
0.00/0.28	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	             'const/sets/IN'('type/realax/real'), sk_A), sk_A0)
0.00/0.28	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           'const/sets/FINITE'('type/realax/real'), sk_A0)
0.00/0.28	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	        = sk_A),
0.00/0.28	    inference('sup-', [status(thm)], ['4', '27'])).
0.00/0.28	tff('29', plain,
0.00/0.28	    (~ $true
0.00/0.28	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	             'const/sets/IN'('type/realax/real'), sk_A), sk_A0)
0.00/0.28	     | ~ $true
0.00/0.28	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	        = sk_A),
0.00/0.28	    inference('demod', [status(thm)], ['28', '10'])).
0.00/0.28	tff('30', plain,
0.00/0.28	    (app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	       'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	      = sk_A
0.00/0.28	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	             'const/sets/IN'('type/realax/real'), sk_A), sk_A0)),
0.00/0.28	    inference('simplify', [status(thm)], ['29'])).
0.00/0.28	tff('31', plain,
0.00/0.28	    (app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	       'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	      = sk_A
0.00/0.28	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	             'const/sets/IN'('type/realax/real'), sk_A), sk_A0)),
0.00/0.28	    inference('simplify_reflect-', [status(thm)], ['30', '13'])).
0.00/0.28	tff('32', plain,
0.00/0.28	    (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	       app_encode_app('type/realax/real', 
0.00/0.28	         app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	         'const/sets/IN'('type/realax/real'), sk_A), sk_A0)
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	        = sk_A),
0.00/0.28	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.28	tff('33', plain,
0.00/0.28	    app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	      'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	     = sk_A,
0.00/0.28	    inference('clc', [status(thm)], ['31', '32'])).
0.00/0.28	tff('34', plain,
0.00/0.28	    (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	       app_encode_app('type/realax/real', 
0.00/0.28	         app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	         'const/sets/IN'('type/realax/real'), sk_A12), sk_A0)
0.00/0.28	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	             'const/sets/IN'('type/realax/real'), sk_A), sk_A0)
0.00/0.28	     | sk_A != sk_A),
0.00/0.28	    inference('demod', [status(thm)], ['0', '33'])).
0.00/0.28	tff('35', plain,
0.00/0.28	    (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	           'const/sets/IN'('type/realax/real'), sk_A), sk_A0)
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	           'const/sets/IN'('type/realax/real'), sk_A12), sk_A0)),
0.00/0.28	    inference('simplify', [status(thm)], ['34'])).
0.00/0.28	tff('36', plain,
0.00/0.28	    (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	       app_encode_app('type/realax/real', 
0.00/0.28	         app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	         'const/sets/IN'('type/realax/real'), sk_A1(sk_A, sk_A0)), sk_A0)
0.00/0.28	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           'const/sets/FINITE'('type/realax/real'), sk_A0)
0.00/0.28	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.28	    inference('sup+', [status(thm)], ['33', '7'])).
0.00/0.28	tff('37', plain,
0.00/0.28	    (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	       app_encode_app('type/realax/real', 
0.00/0.28	         app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	         'const/sets/IN'('type/realax/real'), sk_A1(sk_A, sk_A0)), sk_A0)
0.00/0.28	     | ~ $true
0.00/0.28	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.28	    inference('demod', [status(thm)], ['36', '10'])).
0.00/0.28	tff('38', plain,
0.00/0.28	    (sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	           'const/sets/IN'('type/realax/real'), sk_A1(sk_A, sk_A0)), sk_A0)),
0.00/0.28	    inference('simplify', [status(thm)], ['37'])).
0.00/0.28	tff('39', plain,
0.00/0.28	    app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	      app_encode_app('type/realax/real', 
0.00/0.28	        app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	        'const/sets/IN'('type/realax/real'), sk_A1(sk_A, sk_A0)), sk_A0),
0.00/0.28	    inference('simplify_reflect-', [status(thm)], ['38', '13'])).
0.00/0.28	tff(zf_stmt_12, axiom,
0.00/0.28	  (![A:app_encode_fun('type/realax/real',$o),A0:'type/realax/real']:
0.00/0.28	     ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.28	                      'const/sets/FINITE'('type/realax/real'),A) & 
0.00/0.28	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
0.00/0.28	      (app_encode_app('type/realax/real',$o,
0.00/0.28	                      app_encode_app('type/realax/real',
0.00/0.28	                                     app_encode_fun('type/realax/real',$o),
0.00/0.28	                                     'const/realax/real_le',
0.00/0.28	                                     app_encode_app(app_encode_fun('type/realax/real',
0.00/0.28	                                                                   $o),
0.00/0.28	                                                    'type/realax/real',
0.00/0.28	                                                    'const/sets/sup',A)),
0.00/0.28	                      A0) <=>
0.00/0.28	       (![A1:'type/realax/real']:
0.00/0.28	          (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.28	                          app_encode_app('type/realax/real',
0.00/0.28	                                         app_encode_fun(app_encode_fun(
0.00/0.28	                                                        'type/realax/real',$o),
0.00/0.28	                                                        $o),
0.00/0.28	                                         'const/sets/IN'('type/realax/real'),
0.00/0.28	                                         A1),
0.00/0.28	                          A) =>
0.00/0.28	           app_encode_app('type/realax/real',$o,
0.00/0.28	                          app_encode_app('type/realax/real',
0.00/0.28	                                         app_encode_fun('type/realax/real',$o),
0.00/0.28	                                         'const/realax/real_le',A1),
0.00/0.28	                          A0))))))).
0.00/0.28	tff('40', plain,
0.00/0.28	    ![X10 : app_encode_fun('type/realax/real', $o), 
0.00/0.28	      X11 : 'type/realax/real', X12 : 'type/realax/real']:
0.00/0.28	      (X10 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             'const/sets/FINITE'('type/realax/real'), X10)
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	               'const/sets/IN'('type/realax/real'), X11), X10)
0.00/0.28	       | app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             X11), X12)
0.00/0.28	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'const/realax/real_le', 
0.00/0.28	               app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	                 'type/realax/real', 'const/sets/sup', X10)), X12)),
0.00/0.28	    inference('cnf', [status(esa)], [zf_stmt_12])).
0.00/0.28	tff('41', plain,
0.00/0.28	    ![X0 : 'type/realax/real']:
0.00/0.28	      (~ $true
0.00/0.28	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'const/realax/real_le', 
0.00/0.28	               app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	                 'type/realax/real', 'const/sets/sup', sk_A0)), X0)
0.00/0.28	       | app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             sk_A1(sk_A, sk_A0)), X0)
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             'const/sets/FINITE'('type/realax/real'), sk_A0)
0.00/0.28	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.28	    inference('sup-', [status(thm)], ['39', '40'])).
0.00/0.28	tff('42', plain,
0.00/0.28	    ![X0 : 'type/realax/real']:
0.00/0.28	      (~ $true
0.00/0.28	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'const/realax/real_le', sk_A), X0)
0.00/0.28	       | app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             sk_A1(sk_A, sk_A0)), X0)
0.00/0.28	       | ~ $true
0.00/0.28	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.28	    inference('demod', [status(thm)], ['41', '33', '10'])).
0.00/0.28	tff('43', plain,
0.00/0.28	    ![X0 : 'type/realax/real']:
0.00/0.28	      (sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	       | app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             sk_A1(sk_A, sk_A0)), X0)
0.00/0.28	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'const/realax/real_le', sk_A), X0)),
0.00/0.28	    inference('simplify', [status(thm)], ['42'])).
0.00/0.28	tff('44', plain,
0.00/0.28	    ![X0 : 'type/realax/real']:
0.00/0.28	      (app_encode_app('type/realax/real', $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	           sk_A1(sk_A, sk_A0)), X0)
0.00/0.28	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'const/realax/real_le', sk_A), X0)),
0.00/0.28	    inference('simplify_reflect-', [status(thm)], ['43', '13'])).
0.00/0.28	tff('45', plain,
0.00/0.28	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.28	      (~ $true
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             'const/sets/FINITE'('type/realax/real'), X0)
0.00/0.28	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'const/realax/real_le', 
0.00/0.28	               sk_A1(
0.00/0.28	                 app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	                   'type/realax/real', 'const/sets/sup', X0), X0)), 
0.00/0.28	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'type/realax/real', 'const/sets/sup', X0))
0.00/0.28	       | sk_A1(
0.00/0.28	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	             'type/realax/real', 'const/sets/sup', X0), X0)
0.00/0.28	          = app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	              'type/realax/real', 'const/sets/sup', X0)),
0.00/0.28	    inference('sup-', [status(thm)], ['17', '25'])).
0.00/0.28	tff('46', plain,
0.00/0.28	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.00/0.28	      (sk_A1(
0.00/0.28	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	           'type/realax/real', 'const/sets/sup', X0), X0)
0.00/0.28	        = app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	            'type/realax/real', 'const/sets/sup', X0)
0.00/0.28	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'const/realax/real_le', 
0.00/0.28	               sk_A1(
0.00/0.28	                 app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	                   'type/realax/real', 'const/sets/sup', X0), X0)), 
0.00/0.28	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'type/realax/real', 'const/sets/sup', X0))
0.00/0.28	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             'const/sets/FINITE'('type/realax/real'), X0)),
0.00/0.28	    inference('simplify', [status(thm)], ['45'])).
0.00/0.28	tff('47', plain,
0.00/0.28	    (~ app_encode_app('type/realax/real', $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	           sk_A1(
0.00/0.28	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	               'type/realax/real', 'const/sets/sup', sk_A0), sk_A0)), sk_A)
0.00/0.28	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           'const/sets/FINITE'('type/realax/real'), sk_A0)
0.00/0.28	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	     | sk_A1(
0.00/0.28	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	           'type/realax/real', 'const/sets/sup', sk_A0), sk_A0)
0.00/0.28	        = app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	            'type/realax/real', 'const/sets/sup', sk_A0)),
0.00/0.28	    inference('sup-', [status(thm)], ['33', '46'])).
0.00/0.28	tff('48', plain,
0.00/0.28	    (~ app_encode_app('type/realax/real', $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	           sk_A1(sk_A, sk_A0)), sk_A)
0.00/0.28	     | ~ $true
0.00/0.28	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	     | sk_A1(sk_A, sk_A0) = sk_A),
0.00/0.28	    inference('demod', [status(thm)], ['47', '33', '10', '33', '33'])).
0.00/0.28	tff('49', plain,
0.00/0.28	    (sk_A1(sk_A, sk_A0) = sk_A
0.00/0.28	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             sk_A1(sk_A, sk_A0)), sk_A)),
0.00/0.28	    inference('simplify', [status(thm)], ['48'])).
0.00/0.28	tff('50', plain,
0.00/0.28	    (sk_A1(sk_A, sk_A0) = sk_A
0.00/0.28	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             sk_A1(sk_A, sk_A0)), sk_A)),
0.00/0.28	    inference('simplify_reflect-', [status(thm)], ['49', '13'])).
0.00/0.28	tff('51', plain,
0.00/0.28	    (~ $true
0.00/0.28	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             sk_A), sk_A)
0.00/0.28	     | sk_A1(sk_A, sk_A0) = sk_A),
0.00/0.28	    inference('sup-', [status(thm)], ['44', '50'])).
0.00/0.28	tff('52', plain, (~ $true | ~ $true | sk_A1(sk_A, sk_A0) = sk_A),
0.00/0.28	    inference('demod', [status(thm)], ['51', '1'])).
0.00/0.28	tff('53', plain, sk_A1(sk_A, sk_A0) = sk_A,
0.00/0.28	    inference('simplify', [status(thm)], ['52'])).
0.00/0.28	tff('54', plain,
0.00/0.28	    app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	      app_encode_app('type/realax/real', 
0.00/0.28	        app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	        'const/sets/IN'('type/realax/real'), sk_A), sk_A0),
0.00/0.28	    inference('demod', [status(thm)], ['39', '53'])).
0.00/0.28	tff('55', plain,
0.00/0.28	    (~ $true
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	           'const/sets/IN'('type/realax/real'), sk_A12), sk_A0)),
0.00/0.28	    inference('demod', [status(thm)], ['35', '54'])).
0.00/0.28	tff('56', plain,
0.00/0.28	    app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	      app_encode_app('type/realax/real', 
0.00/0.28	        app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	        'const/sets/IN'('type/realax/real'), sk_A12), sk_A0),
0.00/0.28	    inference('simplify', [status(thm)], ['55'])).
0.00/0.28	tff('57', plain,
0.00/0.28	    ![X0 : 'type/realax/real']:
0.00/0.28	      (app_encode_app('type/realax/real', $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	           X0), sk_A)
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	               'const/sets/IN'('type/realax/real'), X0), sk_A0)
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             'const/sets/FINITE'('type/realax/real'), sk_A0)
0.00/0.28	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.28	    inference('sup+', [status(thm)], ['33', '4'])).
0.00/0.28	tff('58', plain,
0.00/0.28	    ![X0 : 'type/realax/real']:
0.00/0.28	      (app_encode_app('type/realax/real', $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	           X0), sk_A)
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	               'const/sets/IN'('type/realax/real'), X0), sk_A0)
0.00/0.28	       | ~ $true
0.00/0.28	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.28	    inference('demod', [status(thm)], ['57', '10'])).
0.00/0.28	tff('59', plain,
0.00/0.28	    ![X0 : 'type/realax/real']:
0.00/0.28	      (sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.28	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	             app_encode_app('type/realax/real', 
0.00/0.28	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	               'const/sets/IN'('type/realax/real'), X0), sk_A0)
0.00/0.28	       | app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             X0), sk_A)),
0.00/0.28	    inference('simplify', [status(thm)], ['58'])).
0.00/0.28	tff('60', plain,
0.00/0.28	    ![X0 : 'type/realax/real']:
0.00/0.28	      (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	             'const/sets/IN'('type/realax/real'), X0), sk_A0)
0.00/0.28	       | app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             X0), sk_A)),
0.00/0.28	    inference('simplify_reflect-', [status(thm)], ['59', '13'])).
0.00/0.28	tff('61', plain,
0.00/0.28	    (~ $true
0.00/0.28	     | app_encode_app('type/realax/real', $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	           sk_A12), sk_A)),
0.00/0.28	    inference('sup-', [status(thm)], ['56', '60'])).
0.00/0.28	tff('62', plain,
0.00/0.28	    app_encode_app('type/realax/real', $o, 
0.00/0.28	      app_encode_app('type/realax/real', 
0.00/0.28	        app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	        sk_A12), sk_A),
0.00/0.28	    inference('simplify', [status(thm)], ['61'])).
0.00/0.28	tff('63', plain,
0.00/0.28	    (~ app_encode_app('type/realax/real', $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	           sk_A12), sk_A)
0.00/0.28	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	             'const/sets/IN'('type/realax/real'), sk_A), sk_A0)
0.00/0.28	     | app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.28	         'type/realax/real', 'const/sets/sup', sk_A0)
0.00/0.28	        != sk_A),
0.00/0.28	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.28	tff('64', plain,
0.00/0.28	    (~ app_encode_app('type/realax/real', $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	           sk_A12), sk_A)
0.00/0.28	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	             'const/sets/IN'('type/realax/real'), sk_A), sk_A0)
0.00/0.28	     | sk_A != sk_A),
0.00/0.28	    inference('demod', [status(thm)], ['63', '33'])).
0.00/0.28	tff('65', plain,
0.00/0.28	    (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.28	         app_encode_app('type/realax/real', 
0.00/0.28	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.28	           'const/sets/IN'('type/realax/real'), sk_A), sk_A0)
0.00/0.28	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             sk_A12), sk_A)),
0.00/0.28	    inference('simplify', [status(thm)], ['64'])).
0.00/0.28	tff('66', plain,
0.00/0.28	    (~ $true
0.00/0.28	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	           app_encode_app('type/realax/real', 
0.00/0.28	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	             sk_A12), sk_A)),
0.00/0.28	    inference('sup-', [status(thm)], ['54', '65'])).
0.00/0.28	tff('67', plain,
0.00/0.28	    ~ app_encode_app('type/realax/real', $o, 
0.00/0.28	        app_encode_app('type/realax/real', 
0.00/0.28	          app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.28	          sk_A12), sk_A),
0.00/0.28	    inference('simplify', [status(thm)], ['66'])).
0.00/0.28	tff('68', plain, ~ $true, inference('sup-', [status(thm)], ['62', '67'])).
0.00/0.28	tff('69', plain, $false, inference('simplify', [status(thm)], ['68'])).
0.00/0.28	
0.00/0.28	% SZS output end Refutation
0.00/0.28	EOF
