0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : 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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n106.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 18:43:09 CST 2018
0.91/1.09	% done 949 iterations in 0.886s
0.91/1.09	% SZS status Theorem for 'stdin'
0.91/1.09	% SZS output start Refutation
0.91/1.09	tff(zf_stmt_10, axiom,
0.91/1.09	  (![A:app_encode_fun('type/realax/real',$o),A0:'type/realax/real']:
0.91/1.09	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
0.91/1.09	       (![A1:'type/realax/real']:
0.91/1.09	          (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.91/1.09	                          app_encode_app('type/realax/real',
0.91/1.09	                                         app_encode_fun(app_encode_fun(
0.91/1.09	                                                        'type/realax/real',$o),
0.91/1.09	                                                        $o),
0.91/1.09	                                         'const/sets/IN'('type/realax/real'),
0.91/1.09	                                         A1),
0.91/1.09	                          A) =>
0.91/1.09	           app_encode_app('type/realax/real',$o,
0.91/1.09	                          app_encode_app('type/realax/real',
0.91/1.09	                                         app_encode_fun('type/realax/real',$o),
0.91/1.09	                                         'const/realax/real_le',A0),
0.91/1.09	                          A1)))) =>
0.91/1.09	      app_encode_app('type/realax/real',$o,
0.91/1.09	                     app_encode_app('type/realax/real',
0.91/1.09	                                    app_encode_fun('type/realax/real',$o),
0.91/1.09	                                    'const/realax/real_le',A0),
0.91/1.09	                     app_encode_app(app_encode_fun('type/realax/real',$o),
0.91/1.09	                                    'type/realax/real','const/sets/inf',A))))).
0.91/1.09	tff('0', plain,
0.91/1.09	    ![X4 : app_encode_fun('type/realax/real', $o), X5 : 'type/realax/real']:
0.91/1.09	      (X4 = 'const/sets/EMPTY'('type/realax/real')
0.91/1.09	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.91/1.09	           app_encode_app('type/realax/real', 
0.91/1.09	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.91/1.09	             'const/sets/IN'('type/realax/real'), sk_A1(X5, X4)), X4)
0.91/1.09	       | app_encode_app('type/realax/real', $o, 
0.91/1.09	           app_encode_app('type/realax/real', 
0.91/1.09	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.91/1.09	             X5), 
0.91/1.09	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	             'type/realax/real', 'const/sets/inf', X4))),
0.91/1.09	    inference('cnf', [status(esa)], [zf_stmt_10])).
0.91/1.09	tff(zf_stmt_12, axiom,
0.91/1.09	  (![A:$tType,P:app_encode_fun(A,$o),A0:A]:
0.91/1.09	     (app_encode_app(app_encode_fun(A,$o),$o,
0.91/1.09	                     app_encode_app(A,
0.91/1.09	                                    app_encode_fun(app_encode_fun(A,$o),$o),
0.91/1.09	                                    'const/sets/IN'(A),A0),
0.91/1.09	                     P) <=>
0.91/1.09	      app_encode_app(A,$o,P,A0)))).
0.91/1.09	tff('1', plain,
0.91/1.09	    ![X8 : $tType, X9 : app_encode_fun(X8, $o), X10 : X8]:
0.91/1.09	      (app_encode_app(X8, $o, X9, X10)
0.91/1.09	       | ~ app_encode_app(app_encode_fun(X8, $o), $o, 
0.91/1.09	             app_encode_app(X8, app_encode_fun(app_encode_fun(X8, $o), $o), 
0.91/1.09	               'const/sets/IN'(X8), X10), X9)),
0.91/1.09	    inference('cnf', [status(esa)], [zf_stmt_12])).
0.91/1.09	tff('2', plain,
0.91/1.09	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.91/1.09	      (~ $true
0.91/1.09	       | app_encode_app('type/realax/real', $o, 
0.91/1.09	           app_encode_app('type/realax/real', 
0.91/1.09	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.91/1.09	             X1), 
0.91/1.09	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	             'type/realax/real', 'const/sets/inf', X0))
0.91/1.09	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.91/1.09	       | app_encode_app('type/realax/real', $o, X0, sk_A1(X1, X0))),
0.91/1.09	    inference('sup-', [status(thm)], ['0', '1'])).
0.91/1.09	tff('3', plain,
0.91/1.09	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.91/1.09	      (app_encode_app('type/realax/real', $o, X0, sk_A1(X1, X0))
0.91/1.09	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.91/1.09	       | app_encode_app('type/realax/real', $o, 
0.91/1.09	           app_encode_app('type/realax/real', 
0.91/1.09	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.91/1.09	             X1), 
0.91/1.09	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	             'type/realax/real', 'const/sets/inf', X0))),
0.91/1.09	    inference('simplify', [status(thm)], ['2'])).
0.91/1.09	tff(zf_stmt_17, conjecture,
0.91/1.09	  (![A:app_encode_fun('type/realax/real',$o),
0.91/1.09	     A0:app_encode_fun('type/realax/real',$o)]:
0.91/1.09	     (((A0 != 'const/sets/EMPTY'('type/realax/real')) & 
0.91/1.09	       app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.91/1.09	                      app_encode_app(app_encode_fun('type/realax/real',$o),
0.91/1.09	                                     app_encode_fun(app_encode_fun('type/realax/real',
0.91/1.09	                                                                   $o),
0.91/1.09	                                                    $o),
0.91/1.09	                                     'const/sets/SUBSET'('type/realax/real'),
0.91/1.09	                                     A0),
0.91/1.09	                      A) & 
0.91/1.09	       (?[A1:'type/realax/real']:
0.91/1.09	          (![A2:'type/realax/real']:
0.91/1.09	             (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.91/1.09	                             app_encode_app('type/realax/real',
0.91/1.09	                                            app_encode_fun(app_encode_fun(
0.91/1.09	                                                           'type/realax/real',
0.91/1.09	                                                           $o),$o),
0.91/1.09	                                            'const/sets/IN'('type/realax/real'),
0.91/1.09	                                            A2),
0.91/1.09	                             A) =>
0.91/1.09	              app_encode_app('type/realax/real',$o,
0.91/1.09	                             app_encode_app('type/realax/real',
0.91/1.09	                                            app_encode_fun('type/realax/real',
0.91/1.09	                                                           $o),
0.91/1.09	                                            'const/realax/real_le',A1),
0.91/1.09	                             A2))))) =>
0.91/1.09	      app_encode_app('type/realax/real',$o,
0.91/1.09	                     app_encode_app('type/realax/real',
0.91/1.09	                                    app_encode_fun('type/realax/real',$o),
0.91/1.09	                                    'const/realax/real_le',
0.91/1.09	                                    app_encode_app(app_encode_fun('type/realax/real',
0.91/1.09	                                                                  $o),
0.91/1.09	                                                   'type/realax/real',
0.91/1.09	                                                   'const/sets/inf',A)),
0.91/1.09	                     app_encode_app(app_encode_fun('type/realax/real',$o),
0.91/1.09	                                    'type/realax/real','const/sets/inf',A0))))).
0.91/1.09	tff(zf_stmt_0, negated_conjecture,
0.91/1.09	  (~
0.91/1.09	    (![A:app_encode_fun('type/realax/real',$o),
0.91/1.09	       A0:app_encode_fun('type/realax/real',$o)]:
0.91/1.09	       (((A0 != 'const/sets/EMPTY'('type/realax/real')) & 
0.91/1.09	         app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.91/1.09	                        app_encode_app(app_encode_fun('type/realax/real',$o),
0.91/1.09	                                       app_encode_fun(app_encode_fun(
0.91/1.09	                                                      'type/realax/real',$o),
0.91/1.09	                                                      $o),
0.91/1.09	                                       'const/sets/SUBSET'('type/realax/real'),
0.91/1.09	                                       A0),
0.91/1.09	                        A) & 
0.91/1.09	         (?[A1:'type/realax/real']:
0.91/1.09	            (![A2:'type/realax/real']:
0.91/1.09	               (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.91/1.09	                               app_encode_app('type/realax/real',
0.91/1.09	                                              app_encode_fun(app_encode_fun(
0.91/1.09	                                                             'type/realax/real',
0.91/1.09	                                                             $o),$o),
0.91/1.09	                                              'const/sets/IN'('type/realax/real'),
0.91/1.09	                                              A2),
0.91/1.09	                               A) =>
0.91/1.09	                app_encode_app('type/realax/real',$o,
0.91/1.09	                               app_encode_app('type/realax/real',
0.91/1.09	                                              app_encode_fun('type/realax/real',
0.91/1.09	                                                             $o),
0.91/1.09	                                              'const/realax/real_le',A1),
0.91/1.09	                               A2))))) =>
0.91/1.09	        app_encode_app('type/realax/real',$o,
0.91/1.09	                       app_encode_app('type/realax/real',
0.91/1.09	                                      app_encode_fun('type/realax/real',$o),
0.91/1.09	                                      'const/realax/real_le',
0.91/1.09	                                      app_encode_app(app_encode_fun('type/realax/real',
0.91/1.09	                                                                    $o),
0.91/1.09	                                                     'type/realax/real',
0.91/1.09	                                                     'const/sets/inf',A)),
0.91/1.09	                       app_encode_app(app_encode_fun('type/realax/real',$o),
0.91/1.09	                                      'type/realax/real','const/sets/inf',A0)))))).
0.91/1.09	tff('4', plain,
0.91/1.09	    ~ app_encode_app('type/realax/real', $o, 
0.91/1.09	        app_encode_app('type/realax/real', 
0.91/1.09	          app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.91/1.09	          app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	            'type/realax/real', 'const/sets/inf', sk_A)), 
0.91/1.09	        app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	          'type/realax/real', 'const/sets/inf', sk_A0)),
0.91/1.09	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.91/1.09	tff('5', plain,
0.91/1.09	    (~ $true
0.91/1.09	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.91/1.09	     | app_encode_app('type/realax/real', $o, sk_A0, 
0.91/1.09	         sk_A1(
0.91/1.09	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	             'type/realax/real', 'const/sets/inf', sk_A), sk_A0))),
0.91/1.09	    inference('sup-', [status(thm)], ['3', '4'])).
0.91/1.09	tff('6', plain,
0.91/1.09	    (app_encode_app('type/realax/real', $o, sk_A0, 
0.91/1.09	       sk_A1(
0.91/1.09	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	           'type/realax/real', 'const/sets/inf', sk_A), sk_A0))
0.91/1.09	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.91/1.09	    inference('simplify', [status(thm)], ['5'])).
0.91/1.09	tff('7', plain, sk_A0 != 'const/sets/EMPTY'('type/realax/real'),
0.91/1.09	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.91/1.09	tff('8', plain,
0.91/1.09	    app_encode_app('type/realax/real', $o, sk_A0, 
0.91/1.09	      sk_A1(
0.91/1.09	        app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	          'type/realax/real', 'const/sets/inf', sk_A), sk_A0)),
0.91/1.09	    inference('simplify_reflect-', [status(thm)], ['6', '7'])).
0.91/1.09	tff('9', plain,
0.91/1.09	    app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.91/1.09	      app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	        app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.91/1.09	        'const/sets/SUBSET'('type/realax/real'), sk_A0), sk_A),
0.91/1.09	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.91/1.09	tff('10', plain,
0.91/1.09	    ![X8 : $tType, X9 : app_encode_fun(X8, $o), X11 : X8]:
0.91/1.09	      (app_encode_app(app_encode_fun(X8, $o), $o, 
0.91/1.09	         app_encode_app(X8, app_encode_fun(app_encode_fun(X8, $o), $o), 
0.91/1.09	           'const/sets/IN'(X8), X11), X9)
0.91/1.09	       | ~ app_encode_app(X8, $o, X9, X11)),
0.91/1.09	    inference('cnf', [status(esa)], [zf_stmt_12])).
0.91/1.09	tff(zf_stmt_15, axiom,
0.91/1.09	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o)]:
0.91/1.09	     (app_encode_app(app_encode_fun(A,$o),$o,
0.91/1.09	                     app_encode_app(app_encode_fun(A,$o),
0.91/1.09	                                    app_encode_fun(app_encode_fun(A,$o),$o),
0.91/1.09	                                    'const/sets/SUBSET'(A),A0),
0.91/1.09	                     A1) <=>
0.91/1.09	      (![A2:A]:
0.91/1.09	         (app_encode_app(app_encode_fun(A,$o),$o,
0.91/1.09	                         app_encode_app(A,
0.91/1.09	                                        app_encode_fun(app_encode_fun(A,$o),
0.91/1.09	                                                       $o),
0.91/1.09	                                        'const/sets/IN'(A),A2),
0.91/1.09	                         A0) =>
0.91/1.09	          app_encode_app(app_encode_fun(A,$o),$o,
0.91/1.09	                         app_encode_app(A,
0.91/1.09	                                        app_encode_fun(app_encode_fun(A,$o),
0.91/1.09	                                                       $o),
0.91/1.09	                                        'const/sets/IN'(A),A2),
0.91/1.09	                         A1)))))).
0.91/1.09	tff('11', plain,
0.91/1.09	    ![X20 : $tType, X21 : X20, X22 : app_encode_fun(X20, $o), 
0.91/1.09	      X23 : app_encode_fun(X20, $o)]:
0.91/1.09	      (~ app_encode_app(app_encode_fun(X20, $o), $o, 
0.91/1.09	           app_encode_app(X20, app_encode_fun(app_encode_fun(X20, $o), $o), 
0.91/1.09	             'const/sets/IN'(X20), X21), X22)
0.91/1.09	       | app_encode_app(app_encode_fun(X20, $o), $o, 
0.91/1.09	           app_encode_app(X20, app_encode_fun(app_encode_fun(X20, $o), $o), 
0.91/1.09	             'const/sets/IN'(X20), X21), X23)
0.91/1.09	       | ~ app_encode_app(app_encode_fun(X20, $o), $o, 
0.91/1.09	             app_encode_app(app_encode_fun(X20, $o), 
0.91/1.09	               app_encode_fun(app_encode_fun(X20, $o), $o), 
0.91/1.09	               'const/sets/SUBSET'(X20), X22), X23)),
0.91/1.09	    inference('cnf', [status(esa)], [zf_stmt_15])).
0.91/1.09	tff('12', plain,
0.91/1.09	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0, 
0.91/1.09	      X3 : app_encode_fun(X0, $o)]:
0.91/1.09	      (~ $true
0.91/1.09	       | ~ app_encode_app(X0, $o, X1, X2)
0.91/1.09	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.91/1.09	             app_encode_app(app_encode_fun(X0, $o), 
0.91/1.09	               app_encode_fun(app_encode_fun(X0, $o), $o), 
0.91/1.09	               'const/sets/SUBSET'(X0), X1), X3)
0.91/1.09	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.91/1.09	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.91/1.09	             'const/sets/IN'(X0), X2), X3)),
0.91/1.09	    inference('sup-', [status(thm)], ['10', '11'])).
0.91/1.09	tff('13', plain,
0.91/1.09	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0, 
0.91/1.09	      X3 : app_encode_fun(X0, $o)]:
0.91/1.09	      (app_encode_app(app_encode_fun(X0, $o), $o, 
0.91/1.09	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.91/1.09	           'const/sets/IN'(X0), X2), X3)
0.91/1.09	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.91/1.09	             app_encode_app(app_encode_fun(X0, $o), 
0.91/1.09	               app_encode_fun(app_encode_fun(X0, $o), $o), 
0.91/1.09	               'const/sets/SUBSET'(X0), X1), X3)
0.91/1.09	       | ~ app_encode_app(X0, $o, X1, X2)),
0.91/1.09	    inference('simplify', [status(thm)], ['12'])).
0.91/1.09	tff('14', plain,
0.91/1.09	    ![X0 : 'type/realax/real']:
0.91/1.09	      (~ $true
0.91/1.09	       | ~ app_encode_app('type/realax/real', $o, sk_A0, X0)
0.91/1.09	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.91/1.09	           app_encode_app('type/realax/real', 
0.91/1.09	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.91/1.09	             'const/sets/IN'('type/realax/real'), X0), sk_A)),
0.91/1.09	    inference('sup-', [status(thm)], ['9', '13'])).
0.91/1.09	tff('15', plain,
0.91/1.09	    ![X0 : 'type/realax/real']:
0.91/1.09	      (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.91/1.09	         app_encode_app('type/realax/real', 
0.91/1.09	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.91/1.09	           'const/sets/IN'('type/realax/real'), X0), sk_A)
0.91/1.09	       | ~ app_encode_app('type/realax/real', $o, sk_A0, X0)),
0.91/1.09	    inference('simplify', [status(thm)], ['14'])).
0.91/1.09	tff('16', plain,
0.91/1.09	    ![X0 : 'type/realax/real']:
0.91/1.09	      (~ $true
0.91/1.09	       | ~ app_encode_app('type/realax/real', $o, sk_A0, X0)
0.91/1.09	       | app_encode_app('type/realax/real', $o, sk_A, X0)),
0.91/1.09	    inference('sup-', [status(thm)], ['15', '1'])).
0.91/1.09	tff('17', plain,
0.91/1.09	    ![X0 : 'type/realax/real']:
0.91/1.09	      (app_encode_app('type/realax/real', $o, sk_A, X0)
0.91/1.09	       | ~ app_encode_app('type/realax/real', $o, sk_A0, X0)),
0.91/1.09	    inference('simplify', [status(thm)], ['16'])).
0.91/1.09	tff('18', plain,
0.91/1.09	    (~ $true
0.91/1.09	     | app_encode_app('type/realax/real', $o, sk_A, 
0.91/1.09	         sk_A1(
0.91/1.09	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	             'type/realax/real', 'const/sets/inf', sk_A), sk_A0))),
0.91/1.09	    inference('sup-', [status(thm)], ['8', '17'])).
0.91/1.09	tff('19', plain,
0.91/1.09	    app_encode_app('type/realax/real', $o, sk_A, 
0.91/1.09	      sk_A1(
0.91/1.09	        app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	          'type/realax/real', 'const/sets/inf', sk_A), sk_A0)),
0.91/1.09	    inference('simplify', [status(thm)], ['18'])).
0.91/1.09	tff(zf_stmt_16, axiom,
0.91/1.09	  (![A:app_encode_fun('type/realax/real',$o)]:
0.91/1.09	     (((?[A0:'type/realax/real']:
0.91/1.09	          (![A1:'type/realax/real']:
0.91/1.09	             (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.91/1.09	                             app_encode_app('type/realax/real',
0.91/1.09	                                            app_encode_fun(app_encode_fun(
0.91/1.09	                                                           'type/realax/real',
0.91/1.09	                                                           $o),$o),
0.91/1.09	                                            'const/sets/IN'('type/realax/real'),
0.91/1.09	                                            A1),
0.91/1.09	                             A) =>
0.91/1.09	              app_encode_app('type/realax/real',$o,
0.91/1.09	                             app_encode_app('type/realax/real',
0.91/1.09	                                            app_encode_fun('type/realax/real',
0.91/1.09	                                                           $o),
0.91/1.09	                                            'const/realax/real_le',A0),
0.91/1.09	                             A1)))) & 
0.91/1.09	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
0.91/1.09	      ((![A0:'type/realax/real']:
0.91/1.09	          ((![A1:'type/realax/real']:
0.91/1.09	              (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.91/1.09	                              app_encode_app('type/realax/real',
0.91/1.09	                                             app_encode_fun(app_encode_fun(
0.91/1.09	                                                            'type/realax/real',
0.91/1.09	                                                            $o),$o),
0.91/1.09	                                             'const/sets/IN'('type/realax/real'),
0.91/1.09	                                             A1),
0.91/1.09	                              A) =>
0.91/1.09	               app_encode_app('type/realax/real',$o,
0.91/1.09	                              app_encode_app('type/realax/real',
0.91/1.09	                                             app_encode_fun('type/realax/real',
0.91/1.09	                                                            $o),
0.91/1.09	                                             'const/realax/real_le',A0),
0.91/1.09	                              A1))) =>
0.91/1.09	           app_encode_app('type/realax/real',$o,
0.91/1.09	                          app_encode_app('type/realax/real',
0.91/1.09	                                         app_encode_fun('type/realax/real',$o),
0.91/1.09	                                         'const/realax/real_le',A0),
0.91/1.09	                          app_encode_app(app_encode_fun('type/realax/real',$o),
0.91/1.09	                                         'type/realax/real','const/sets/inf',
0.91/1.09	                                         A)))) & 
0.91/1.09	       (![A0:'type/realax/real']:
0.91/1.09	          (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.91/1.09	                          app_encode_app('type/realax/real',
0.91/1.09	                                         app_encode_fun(app_encode_fun(
0.91/1.09	                                                        'type/realax/real',$o),
0.91/1.09	                                                        $o),
0.91/1.09	                                         'const/sets/IN'('type/realax/real'),
0.91/1.09	                                         A0),
0.91/1.09	                          A) =>
0.91/1.09	           app_encode_app('type/realax/real',$o,
0.91/1.09	                          app_encode_app('type/realax/real',
0.91/1.09	                                         app_encode_fun('type/realax/real',$o),
0.91/1.09	                                         'const/realax/real_le',
0.91/1.09	                                         app_encode_app(app_encode_fun(
0.91/1.09	                                                        'type/realax/real',$o),
0.91/1.09	                                                        'type/realax/real',
0.91/1.09	                                                        'const/sets/inf',A)),
0.91/1.09	                          A0))))))).
0.91/1.09	tff(zf_stmt_1, axiom,
0.91/1.09	  ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.91/1.09	                   app_encode_app('type/realax/real',
0.91/1.09	                                  app_encode_fun(app_encode_fun('type/realax/real',
0.91/1.09	                                                                $o),
0.91/1.09	                                                 $o),
0.91/1.09	                                  'const/sets/IN'('type/realax/real'),A1),
0.91/1.09	                   A) =>
0.91/1.09	    app_encode_app('type/realax/real',$o,
0.91/1.09	                   app_encode_app('type/realax/real',
0.91/1.09	                                  app_encode_fun('type/realax/real',$o),
0.91/1.09	                                  'const/realax/real_le',A0),
0.91/1.09	                   A1)) =>
0.91/1.09	   zip_tseitin0(A1,A0,A))).
0.91/1.09	tff('20', plain,
0.91/1.09	    ![X25 : 'type/realax/real', X26 : 'type/realax/real', 
0.91/1.09	      X27 : app_encode_fun('type/realax/real', $o)]:
0.91/1.09	      (zip_tseitin0(X25, X26, X27)
0.91/1.09	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.91/1.09	           app_encode_app('type/realax/real', 
0.91/1.09	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.91/1.09	             'const/sets/IN'('type/realax/real'), X25), X27)),
0.91/1.09	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.91/1.09	tff('21', plain,
0.91/1.09	    ![X34 : 'type/realax/real']:
0.91/1.09	      (app_encode_app('type/realax/real', $o, 
0.91/1.09	         app_encode_app('type/realax/real', 
0.91/1.09	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.91/1.09	           sk_A13), X34)
0.91/1.09	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.91/1.09	             app_encode_app('type/realax/real', 
0.91/1.09	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.91/1.09	               'const/sets/IN'('type/realax/real'), X34), sk_A)),
0.91/1.09	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.91/1.09	tff('22', plain,
0.91/1.09	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
0.91/1.09	      (~ $true
0.91/1.09	       | zip_tseitin0(X0, X1, sk_A)
0.91/1.09	       | app_encode_app('type/realax/real', $o, 
0.91/1.09	           app_encode_app('type/realax/real', 
0.91/1.09	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.91/1.09	             sk_A13), X0)),
0.91/1.09	    inference('sup-', [status(thm)], ['20', '21'])).
0.91/1.09	tff('23', plain,
0.91/1.09	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
0.91/1.09	      (app_encode_app('type/realax/real', $o, 
0.91/1.09	         app_encode_app('type/realax/real', 
0.91/1.09	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.91/1.09	           sk_A13), X0)
0.91/1.09	       | zip_tseitin0(X0, X1, sk_A)),
0.91/1.09	    inference('simplify', [status(thm)], ['22'])).
0.91/1.09	tff('24', plain,
0.91/1.09	    ![X25 : 'type/realax/real', X26 : 'type/realax/real', 
0.91/1.09	      X27 : app_encode_fun('type/realax/real', $o)]:
0.91/1.09	      (zip_tseitin0(X25, X26, X27)
0.91/1.09	       | ~ app_encode_app('type/realax/real', $o, 
0.91/1.09	             app_encode_app('type/realax/real', 
0.91/1.09	               app_encode_fun('type/realax/real', $o), 
0.91/1.09	               'const/realax/real_le', X26), X25)),
0.91/1.09	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.91/1.09	tff('25', plain,
0.91/1.09	    ![X0 : 'type/realax/real', X1 : app_encode_fun('type/realax/real', $o), 
0.91/1.09	      X2 : 'type/realax/real']:
0.91/1.09	      (~ $true | zip_tseitin0(X0, X2, sk_A) | zip_tseitin0(X0, sk_A13, X1)),
0.91/1.09	    inference('sup-', [status(thm)], ['23', '24'])).
0.91/1.09	tff('26', plain,
0.91/1.09	    ![X0 : 'type/realax/real', X1 : app_encode_fun('type/realax/real', $o), 
0.91/1.09	      X2 : 'type/realax/real']:
0.91/1.09	      (zip_tseitin0(X0, sk_A13, X1) | zip_tseitin0(X0, X2, sk_A)),
0.91/1.09	    inference('simplify', [status(thm)], ['25'])).
0.91/1.09	tff('27', plain,
0.91/1.09	    ![X0 : 'type/realax/real']: (~ $true | zip_tseitin0(X0, sk_A13, sk_A)),
0.91/1.09	    inference('eq_fact', [status(thm)], ['26'])).
0.91/1.09	tff('28', plain, ![X0 : 'type/realax/real']: zip_tseitin0(X0, sk_A13, sk_A),
0.91/1.09	    inference('simplify', [status(thm)], ['27'])).
0.91/1.09	tff(zf_stmt_2, type, zip_tseitin2 :
0.91/1.09	    app_encode_fun('type/realax/real',$o) > $o).
0.91/1.09	tff(zf_stmt_3, axiom,
0.91/1.09	  (zip_tseitin2(A) =>
0.91/1.09	   ((![A0:'type/realax/real']:
0.91/1.09	       (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.91/1.09	                       app_encode_app('type/realax/real',
0.91/1.09	                                      app_encode_fun(app_encode_fun('type/realax/real',
0.91/1.09	                                                                    $o),
0.91/1.09	                                                     $o),
0.91/1.09	                                      'const/sets/IN'('type/realax/real'),A0),
0.91/1.09	                       A) =>
0.91/1.09	        app_encode_app('type/realax/real',$o,
0.91/1.09	                       app_encode_app('type/realax/real',
0.91/1.09	                                      app_encode_fun('type/realax/real',$o),
0.91/1.09	                                      'const/realax/real_le',
0.91/1.09	                                      app_encode_app(app_encode_fun('type/realax/real',
0.91/1.09	                                                                    $o),
0.91/1.09	                                                     'type/realax/real',
0.91/1.09	                                                     'const/sets/inf',A)),
0.91/1.09	                       A0))) & 
0.91/1.09	    (![A0:'type/realax/real']:
0.91/1.09	       ((![A1:'type/realax/real']: zip_tseitin1(A1,A0,A)) =>
0.91/1.09	        app_encode_app('type/realax/real',$o,
0.91/1.09	                       app_encode_app('type/realax/real',
0.91/1.09	                                      app_encode_fun('type/realax/real',$o),
0.91/1.09	                                      'const/realax/real_le',A0),
0.91/1.09	                       app_encode_app(app_encode_fun('type/realax/real',$o),
0.91/1.09	                                      'type/realax/real','const/sets/inf',A))))))).
0.91/1.09	tff(zf_stmt_4, type, zip_tseitin1 :
0.91/1.09	    ('type/realax/real' * 
0.91/1.09	     'type/realax/real' * 
0.91/1.09	     app_encode_fun('type/realax/real',$o)) > $o).
0.91/1.09	tff(zf_stmt_5, axiom,
0.91/1.09	  ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.91/1.09	                   app_encode_app('type/realax/real',
0.91/1.09	                                  app_encode_fun(app_encode_fun('type/realax/real',
0.91/1.09	                                                                $o),
0.91/1.09	                                                 $o),
0.91/1.09	                                  'const/sets/IN'('type/realax/real'),A1),
0.91/1.09	                   A) =>
0.91/1.09	    app_encode_app('type/realax/real',$o,
0.91/1.09	                   app_encode_app('type/realax/real',
0.91/1.09	                                  app_encode_fun('type/realax/real',$o),
0.91/1.09	                                  'const/realax/real_le',A0),
0.91/1.09	                   A1)) =>
0.91/1.09	   zip_tseitin1(A1,A0,A))).
0.91/1.09	tff(zf_stmt_6, type, zip_tseitin0 :
0.91/1.09	    ('type/realax/real' * 
0.91/1.09	     'type/realax/real' * 
0.91/1.09	     app_encode_fun('type/realax/real',$o)) > $o).
0.91/1.09	tff(zf_stmt_7, axiom,
0.91/1.09	  (![A:app_encode_fun('type/realax/real',$o)]:
0.91/1.09	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
0.91/1.09	       (?[A0:'type/realax/real']:
0.91/1.09	          (![A1:'type/realax/real']: zip_tseitin0(A1,A0,A)))) =>
0.91/1.09	      zip_tseitin2(A)))).
0.91/1.09	tff('29', plain,
0.91/1.09	    ![X32 : app_encode_fun('type/realax/real', $o), X33 : 'type/realax/real']:
0.91/1.09	      (zip_tseitin2(X32)
0.91/1.09	       | ~ zip_tseitin0(sk_A12(X33, X32), X33, X32)
0.91/1.09	       | X32 = 'const/sets/EMPTY'('type/realax/real')),
0.91/1.09	    inference('cnf', [status(esa)], [zf_stmt_7])).
0.91/1.09	tff('30', plain,
0.91/1.09	    (~ $true
0.91/1.09	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
0.91/1.09	     | zip_tseitin2(sk_A)),
0.91/1.09	    inference('sup-', [status(thm)], ['28', '29'])).
0.91/1.09	tff('31', plain,
0.91/1.09	    (zip_tseitin2(sk_A) | sk_A = 'const/sets/EMPTY'('type/realax/real')),
0.91/1.09	    inference('simplify', [status(thm)], ['30'])).
0.91/1.09	tff('32', plain,
0.91/1.09	    ![X27 : app_encode_fun('type/realax/real', $o), 
0.91/1.09	      X28 : 'type/realax/real', X29 : 'type/realax/real']:
0.91/1.09	      (zip_tseitin1(X28, X29, X27)
0.91/1.09	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.91/1.09	           app_encode_app('type/realax/real', 
0.91/1.09	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.91/1.09	             'const/sets/IN'('type/realax/real'), X28), X27)),
0.91/1.09	    inference('cnf', [status(esa)], [zf_stmt_5])).
0.91/1.09	tff('33', plain,
0.91/1.09	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real', 
0.91/1.09	      X2 : app_encode_fun('type/realax/real', $o), X3 : 'type/realax/real']:
0.91/1.09	      (~ $true
0.91/1.09	       | zip_tseitin1(X1, X3, X0)
0.91/1.09	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.91/1.09	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.91/1.09	               'const/sets/SUBSET'('type/realax/real'), X0), X2)
0.91/1.09	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.91/1.09	           app_encode_app('type/realax/real', 
0.91/1.09	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.91/1.09	             'const/sets/IN'('type/realax/real'), X1), X2)),
0.91/1.09	    inference('sup-', [status(thm)], ['32', '11'])).
0.91/1.09	tff('34', plain,
0.91/1.09	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real', 
0.91/1.09	      X2 : app_encode_fun('type/realax/real', $o), X3 : 'type/realax/real']:
0.91/1.09	      (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.91/1.09	         app_encode_app('type/realax/real', 
0.91/1.09	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.91/1.09	           'const/sets/IN'('type/realax/real'), X1), X2)
0.91/1.09	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.91/1.09	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.91/1.09	               'const/sets/SUBSET'('type/realax/real'), X0), X2)
0.91/1.09	       | zip_tseitin1(X1, X3, X0)),
0.91/1.09	    inference('simplify', [status(thm)], ['33'])).
0.91/1.09	tff('35', plain,
0.91/1.09	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
0.91/1.09	      (~ $true
0.91/1.09	       | zip_tseitin1(X1, X0, sk_A0)
0.91/1.09	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.91/1.09	           app_encode_app('type/realax/real', 
0.91/1.09	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.91/1.09	             'const/sets/IN'('type/realax/real'), X1), sk_A)),
0.91/1.09	    inference('sup-', [status(thm)], ['9', '34'])).
0.91/1.09	tff('36', plain,
0.91/1.09	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
0.91/1.09	      (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.91/1.09	         app_encode_app('type/realax/real', 
0.91/1.09	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.91/1.09	           'const/sets/IN'('type/realax/real'), X1), sk_A)
0.91/1.09	       | zip_tseitin1(X1, X0, sk_A0)),
0.91/1.09	    inference('simplify', [status(thm)], ['35'])).
0.91/1.09	tff('37', plain,
0.91/1.09	    ![X27 : app_encode_fun('type/realax/real', $o), X30 : 'type/realax/real']:
0.91/1.09	      (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.91/1.09	           app_encode_app('type/realax/real', 
0.91/1.09	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.91/1.09	             'const/sets/IN'('type/realax/real'), X30), X27)
0.91/1.09	       | app_encode_app('type/realax/real', $o, 
0.91/1.09	           app_encode_app('type/realax/real', 
0.91/1.09	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.91/1.09	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	               'type/realax/real', 'const/sets/inf', X27)), X30)
0.91/1.09	       | ~ zip_tseitin2(X27)),
0.91/1.09	    inference('cnf', [status(esa)], [zf_stmt_3])).
0.91/1.09	tff('38', plain,
0.91/1.09	    ![X27 : app_encode_fun('type/realax/real', $o), 
0.91/1.09	      X28 : 'type/realax/real', X29 : 'type/realax/real']:
0.91/1.09	      (zip_tseitin1(X28, X29, X27)
0.91/1.09	       | ~ app_encode_app('type/realax/real', $o, 
0.91/1.09	             app_encode_app('type/realax/real', 
0.91/1.09	               app_encode_fun('type/realax/real', $o), 
0.91/1.09	               'const/realax/real_le', X29), X28)),
0.91/1.09	    inference('cnf', [status(esa)], [zf_stmt_5])).
0.91/1.09	tff('39', plain,
0.91/1.09	    ![X0 : 'type/realax/real', X1 : app_encode_fun('type/realax/real', $o), 
0.91/1.09	      X2 : app_encode_fun('type/realax/real', $o)]:
0.91/1.09	      (~ $true
0.91/1.09	       | ~ zip_tseitin2(X1)
0.91/1.09	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.91/1.09	             app_encode_app('type/realax/real', 
0.91/1.09	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.91/1.09	               'const/sets/IN'('type/realax/real'), X0), X1)
0.91/1.09	       | zip_tseitin1(X0, 
0.91/1.09	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	             'type/realax/real', 'const/sets/inf', X1), X2)),
0.91/1.09	    inference('sup-', [status(thm)], ['37', '38'])).
0.91/1.09	tff('40', plain,
0.91/1.09	    ![X0 : 'type/realax/real', X1 : app_encode_fun('type/realax/real', $o), 
0.91/1.09	      X2 : app_encode_fun('type/realax/real', $o)]:
0.91/1.09	      (zip_tseitin1(X0, 
0.91/1.09	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	           'type/realax/real', 'const/sets/inf', X1), X2)
0.91/1.09	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.91/1.09	             app_encode_app('type/realax/real', 
0.91/1.09	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.91/1.09	               'const/sets/IN'('type/realax/real'), X0), X1)
0.91/1.09	       | ~ zip_tseitin2(X1)),
0.91/1.09	    inference('simplify', [status(thm)], ['39'])).
0.91/1.09	tff('41', plain,
0.91/1.09	    ![X0 : 'type/realax/real', X1 : app_encode_fun('type/realax/real', $o), 
0.91/1.09	      X2 : 'type/realax/real']:
0.91/1.09	      (~ $true
0.91/1.09	       | zip_tseitin1(X0, X2, sk_A0)
0.91/1.09	       | ~ zip_tseitin2(sk_A)
0.91/1.09	       | zip_tseitin1(X0, 
0.91/1.09	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	             'type/realax/real', 'const/sets/inf', sk_A), X1)),
0.91/1.09	    inference('sup-', [status(thm)], ['36', '40'])).
0.91/1.09	tff('42', plain,
0.91/1.09	    ![X0 : 'type/realax/real', X1 : app_encode_fun('type/realax/real', $o), 
0.91/1.09	      X2 : 'type/realax/real']:
0.91/1.09	      (zip_tseitin1(X0, 
0.91/1.09	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	           'type/realax/real', 'const/sets/inf', sk_A), X1)
0.91/1.09	       | ~ zip_tseitin2(sk_A)
0.91/1.09	       | zip_tseitin1(X0, X2, sk_A0)),
0.91/1.09	    inference('simplify', [status(thm)], ['41'])).
0.91/1.09	tff('43', plain,
0.91/1.09	    ![X0 : 'type/realax/real']:
0.91/1.09	      (~ $true
0.91/1.09	       | zip_tseitin1(X0, 
0.91/1.09	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	             'type/realax/real', 'const/sets/inf', sk_A), sk_A0)
0.91/1.09	       | ~ zip_tseitin2(sk_A)),
0.91/1.09	    inference('eq_fact', [status(thm)], ['42'])).
0.91/1.09	tff('44', plain,
0.91/1.09	    ![X0 : 'type/realax/real']:
0.91/1.09	      (~ zip_tseitin2(sk_A)
0.91/1.09	       | zip_tseitin1(X0, 
0.91/1.09	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	             'type/realax/real', 'const/sets/inf', sk_A), sk_A0)),
0.91/1.09	    inference('simplify', [status(thm)], ['43'])).
0.91/1.09	tff('45', plain,
0.91/1.09	    ![X27 : app_encode_fun('type/realax/real', $o), X31 : 'type/realax/real']:
0.91/1.09	      (~ zip_tseitin1(sk_A11(X31, X27), X31, X27)
0.91/1.09	       | app_encode_app('type/realax/real', $o, 
0.91/1.09	           app_encode_app('type/realax/real', 
0.91/1.09	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.91/1.09	             X31), 
0.91/1.09	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	             'type/realax/real', 'const/sets/inf', X27))
0.91/1.09	       | ~ zip_tseitin2(X27)),
0.91/1.09	    inference('cnf', [status(esa)], [zf_stmt_3])).
0.91/1.09	tff('46', plain,
0.91/1.09	    (~ $true
0.91/1.09	     | ~ zip_tseitin2(sk_A)
0.91/1.09	     | ~ zip_tseitin2(sk_A0)
0.91/1.09	     | app_encode_app('type/realax/real', $o, 
0.91/1.09	         app_encode_app('type/realax/real', 
0.91/1.09	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.91/1.09	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	             'type/realax/real', 'const/sets/inf', sk_A)), 
0.91/1.09	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	           'type/realax/real', 'const/sets/inf', sk_A0))),
0.91/1.09	    inference('sup-', [status(thm)], ['44', '45'])).
0.91/1.09	tff('47', plain,
0.91/1.09	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real', 
0.91/1.09	      X2 : 'type/realax/real']:
0.91/1.09	      (~ $true
0.91/1.09	       | zip_tseitin0(X1, X2, X0)
0.91/1.09	       | app_encode_app('type/realax/real', $o, X0, X1)),
0.91/1.09	    inference('sup-', [status(thm)], ['20', '1'])).
0.91/1.09	tff('48', plain,
0.91/1.09	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real', 
0.91/1.09	      X2 : 'type/realax/real']:
0.91/1.09	      (app_encode_app('type/realax/real', $o, X0, X1)
0.91/1.09	       | zip_tseitin0(X1, X2, X0)),
0.91/1.09	    inference('simplify', [status(thm)], ['47'])).
0.91/1.09	tff('49', plain,
0.91/1.09	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.91/1.09	      (~ $true
0.91/1.09	       | app_encode_app('type/realax/real', $o, X0, sk_A12(X1, X0))
0.91/1.09	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.91/1.09	       | zip_tseitin2(X0)),
0.91/1.09	    inference('sup-', [status(thm)], ['48', '29'])).
0.91/1.09	tff('50', plain,
0.91/1.09	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.91/1.09	      (zip_tseitin2(X0)
0.91/1.09	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.91/1.09	       | app_encode_app('type/realax/real', $o, X0, sk_A12(X1, X0))),
0.91/1.09	    inference('simplify', [status(thm)], ['49'])).
0.91/1.09	tff('51', plain,
0.91/1.09	    ![X0 : 'type/realax/real']:
0.91/1.09	      (~ $true
0.91/1.09	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.91/1.09	       | zip_tseitin2(sk_A0)
0.91/1.09	       | app_encode_app('type/realax/real', $o, sk_A, sk_A12(X0, sk_A0))),
0.91/1.09	    inference('sup-', [status(thm)], ['50', '17'])).
0.91/1.09	tff('52', plain,
0.91/1.09	    ![X0 : 'type/realax/real']:
0.91/1.09	      (app_encode_app('type/realax/real', $o, sk_A, sk_A12(X0, sk_A0))
0.91/1.09	       | zip_tseitin2(sk_A0)
0.91/1.09	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.91/1.09	    inference('simplify', [status(thm)], ['51'])).
0.91/1.09	tff('53', plain,
0.91/1.09	    ![X0 : 'type/realax/real']:
0.91/1.09	      (app_encode_app('type/realax/real', $o, sk_A, sk_A12(X0, sk_A0))
0.91/1.09	       | zip_tseitin2(sk_A0)),
0.91/1.09	    inference('simplify_reflect-', [status(thm)], ['52', '7'])).
0.91/1.09	tff('54', plain,
0.91/1.09	    ![X0 : 'type/realax/real']:
0.91/1.09	      (~ $true
0.91/1.09	       | ~ app_encode_app('type/realax/real', $o, sk_A, X0)
0.91/1.09	       | app_encode_app('type/realax/real', $o, 
0.91/1.09	           app_encode_app('type/realax/real', 
0.91/1.09	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.91/1.09	             sk_A13), X0)),
0.91/1.09	    inference('sup-', [status(thm)], ['10', '21'])).
0.91/1.09	tff('55', plain,
0.91/1.09	    ![X0 : 'type/realax/real']:
0.91/1.09	      (app_encode_app('type/realax/real', $o, 
0.91/1.09	         app_encode_app('type/realax/real', 
0.91/1.09	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.91/1.09	           sk_A13), X0)
0.91/1.09	       | ~ app_encode_app('type/realax/real', $o, sk_A, X0)),
0.91/1.09	    inference('simplify', [status(thm)], ['54'])).
0.91/1.09	tff('56', plain,
0.91/1.09	    ![X0 : 'type/realax/real', X1 : app_encode_fun('type/realax/real', $o)]:
0.91/1.09	      (~ $true
0.91/1.09	       | ~ app_encode_app('type/realax/real', $o, sk_A, X0)
0.91/1.09	       | zip_tseitin0(X0, sk_A13, X1)),
0.91/1.09	    inference('sup-', [status(thm)], ['55', '24'])).
0.91/1.09	tff('57', plain,
0.91/1.09	    ![X0 : 'type/realax/real', X1 : app_encode_fun('type/realax/real', $o)]:
0.91/1.09	      (zip_tseitin0(X0, sk_A13, X1)
0.91/1.09	       | ~ app_encode_app('type/realax/real', $o, sk_A, X0)),
0.91/1.09	    inference('simplify', [status(thm)], ['56'])).
0.91/1.09	tff('58', plain,
0.91/1.09	    ![X0 : 'type/realax/real', X1 : app_encode_fun('type/realax/real', $o)]:
0.91/1.09	      (~ $true
0.91/1.09	       | zip_tseitin2(sk_A0)
0.91/1.09	       | zip_tseitin0(sk_A12(X0, sk_A0), sk_A13, X1)),
0.91/1.09	    inference('sup-', [status(thm)], ['53', '57'])).
0.91/1.09	tff('59', plain,
0.91/1.09	    ![X0 : 'type/realax/real', X1 : app_encode_fun('type/realax/real', $o)]:
0.91/1.09	      (zip_tseitin0(sk_A12(X0, sk_A0), sk_A13, X1) | zip_tseitin2(sk_A0)),
0.91/1.09	    inference('simplify', [status(thm)], ['58'])).
0.91/1.09	tff('60', plain,
0.91/1.09	    (~ $true
0.91/1.09	     | zip_tseitin2(sk_A0)
0.91/1.09	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.91/1.09	     | zip_tseitin2(sk_A0)),
0.91/1.09	    inference('sup-', [status(thm)], ['59', '29'])).
0.91/1.09	tff('61', plain,
0.91/1.09	    (sk_A0 = 'const/sets/EMPTY'('type/realax/real') | zip_tseitin2(sk_A0)),
0.91/1.09	    inference('simplify', [status(thm)], ['60'])).
0.91/1.09	tff('62', plain, zip_tseitin2(sk_A0),
0.91/1.09	    inference('simplify_reflect-', [status(thm)], ['61', '7'])).
0.91/1.09	tff('63', plain,
0.91/1.09	    (~ $true
0.91/1.09	     | ~ zip_tseitin2(sk_A)
0.91/1.09	     | ~ $true
0.91/1.09	     | app_encode_app('type/realax/real', $o, 
0.91/1.09	         app_encode_app('type/realax/real', 
0.91/1.09	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.91/1.09	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	             'type/realax/real', 'const/sets/inf', sk_A)), 
0.91/1.09	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	           'type/realax/real', 'const/sets/inf', sk_A0))),
0.91/1.09	    inference('demod', [status(thm)], ['46', '62'])).
0.91/1.09	tff('64', plain,
0.91/1.09	    (app_encode_app('type/realax/real', $o, 
0.91/1.09	       app_encode_app('type/realax/real', 
0.91/1.09	         app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.91/1.09	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	           'type/realax/real', 'const/sets/inf', sk_A)), 
0.91/1.09	       app_encode_app(app_encode_fun('type/realax/real', $o), 
0.91/1.09	         'type/realax/real', 'const/sets/inf', sk_A0))
0.91/1.09	     | ~ zip_tseitin2(sk_A)),
0.91/1.09	    inference('simplify', [status(thm)], ['63'])).
0.91/1.09	tff('65', plain, ~ zip_tseitin2(sk_A),
0.91/1.09	    inference('clc', [status(thm)], ['64', '4'])).
0.91/1.09	tff('66', plain, (~ $true | sk_A = 'const/sets/EMPTY'('type/realax/real')),
0.91/1.09	    inference('sup-', [status(thm)], ['31', '65'])).
0.91/1.09	tff('67', plain, sk_A = 'const/sets/EMPTY'('type/realax/real'),
0.91/1.09	    inference('simplify', [status(thm)], ['66'])).
0.91/1.09	tff(zf_stmt_13, axiom,
0.91/1.09	  (![A:$tType,A0:A]:
0.91/1.09	     (~
0.91/1.09	       app_encode_app(app_encode_fun(A,$o),$o,
0.91/1.09	                      app_encode_app(A,
0.91/1.09	                                     app_encode_fun(app_encode_fun(A,$o),$o),
0.91/1.09	                                     'const/sets/IN'(A),A0),
0.91/1.09	                      'const/sets/EMPTY'(A))))).
0.91/1.09	tff('68', plain,
0.91/1.09	    ![X12 : $tType, X13 : X12]:
0.91/1.09	      ~ app_encode_app(app_encode_fun(X12, $o), $o, 
0.91/1.09	          app_encode_app(X12, app_encode_fun(app_encode_fun(X12, $o), $o), 
0.91/1.09	            'const/sets/IN'(X12), X13), 'const/sets/EMPTY'(X12)),
0.91/1.09	    inference('cnf', [status(esa)], [zf_stmt_13])).
0.91/1.09	tff('69', plain,
0.91/1.09	    ![X0 : $tType, X1 : X0]:
0.91/1.09	      (~ $true | ~ app_encode_app(X0, $o, 'const/sets/EMPTY'(X0), X1)),
0.91/1.09	    inference('sup-', [status(thm)], ['10', '68'])).
0.91/1.09	tff('70', plain,
0.91/1.09	    ![X0 : $tType, X1 : X0]:
0.91/1.09	      ~ app_encode_app(X0, $o, 'const/sets/EMPTY'(X0), X1),
0.91/1.09	    inference('simplify', [status(thm)], ['69'])).
0.91/1.09	tff('71', plain,
0.91/1.09	    ![X0 : 'type/realax/real']:
0.91/1.09	      ~ app_encode_app('type/realax/real', $o, sk_A, X0),
0.91/1.09	    inference('sup-', [status(thm)], ['67', '70'])).
0.91/1.09	tff('72', plain, ~ $true, inference('sup-', [status(thm)], ['19', '71'])).
0.91/1.09	tff('73', plain, $false, inference('simplify', [status(thm)], ['72'])).
0.91/1.09	
0.91/1.09	% SZS output end Refutation
0.91/1.09	EOF
