0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n132.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 18:43:09 CST 2018
0.61/0.86	% done 612 iterations in 0.658s
0.61/0.86	% SZS status Theorem for 'stdin'
0.61/0.86	% SZS output start Refutation
0.61/0.86	tff(zf_stmt_13, axiom,
0.61/0.86	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o)]:
0.61/0.86	     ((A0 = A1) <=>
0.61/0.86	      (![A2:A]:
0.61/0.86	         (app_encode_app(app_encode_fun(A,$o),$o,
0.61/0.86	                         app_encode_app(A,
0.61/0.86	                                        app_encode_fun(app_encode_fun(A,$o),
0.61/0.86	                                                       $o),
0.61/0.86	                                        'const/sets/IN'(A),A2),
0.61/0.86	                         A0) <=>
0.61/0.86	          app_encode_app(app_encode_fun(A,$o),$o,
0.61/0.86	                         app_encode_app(A,
0.61/0.86	                                        app_encode_fun(app_encode_fun(A,$o),
0.61/0.86	                                                       $o),
0.61/0.86	                                        'const/sets/IN'(A),A2),
0.61/0.86	                         A1)))))).
0.61/0.86	tff('0', plain,
0.61/0.86	    ![X10 : $tType, X13 : app_encode_fun(X10, $o), 
0.61/0.86	      X15 : app_encode_fun(X10, $o)]:
0.61/0.86	      (X13 = X15
0.61/0.86	       | app_encode_app(app_encode_fun(X10, $o), $o, 
0.61/0.86	           app_encode_app(X10, app_encode_fun(app_encode_fun(X10, $o), $o), 
0.61/0.86	             'const/sets/IN'(X10), sk_A2(X10, X15, X13)), X15)
0.61/0.86	       | app_encode_app(app_encode_fun(X10, $o), $o, 
0.61/0.86	           app_encode_app(X10, app_encode_fun(app_encode_fun(X10, $o), $o), 
0.61/0.86	             'const/sets/IN'(X10), sk_A2(X10, X15, X13)), X13)),
0.61/0.86	    inference('cnf', [status(esa)], [zf_stmt_13])).
0.61/0.86	tff(zf_stmt_12, axiom,
0.61/0.86	  (![A:$tType,A0:A]:
0.61/0.86	     (~
0.61/0.86	       app_encode_app(app_encode_fun(A,$o),$o,
0.61/0.86	                      app_encode_app(A,
0.61/0.86	                                     app_encode_fun(app_encode_fun(A,$o),$o),
0.61/0.86	                                     'const/sets/IN'(A),A0),
0.61/0.86	                      'const/sets/EMPTY'(A))))).
0.61/0.86	tff('1', plain,
0.61/0.86	    ![X8 : $tType, X9 : X8]:
0.61/0.86	      ~ app_encode_app(app_encode_fun(X8, $o), $o, 
0.61/0.86	          app_encode_app(X8, app_encode_fun(app_encode_fun(X8, $o), $o), 
0.61/0.86	            'const/sets/IN'(X8), X9), 'const/sets/EMPTY'(X8)),
0.61/0.86	    inference('cnf', [status(esa)], [zf_stmt_12])).
0.61/0.86	tff('2', plain,
0.61/0.86	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
0.61/0.86	      (~ $true
0.61/0.86	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.61/0.86	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.61/0.86	             'const/sets/IN'(X0), sk_A2(X0, X1, 'const/sets/EMPTY'(X0))), X1)
0.61/0.86	       | 'const/sets/EMPTY'(X0) = X1),
0.61/0.86	    inference('sup-', [status(thm)], ['0', '1'])).
0.61/0.86	tff('3', plain,
0.61/0.86	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
0.61/0.86	      ('const/sets/EMPTY'(X0) = X1
0.61/0.86	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.61/0.86	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.61/0.86	             'const/sets/IN'(X0), sk_A2(X0, X1, 'const/sets/EMPTY'(X0))), X1)),
0.61/0.86	    inference('simplify', [status(thm)], ['2'])).
0.61/0.86	tff(zf_stmt_11, axiom,
0.61/0.86	  (![A:$tType,P:app_encode_fun(A,$o),A0:A]:
0.61/0.86	     (app_encode_app(app_encode_fun(A,$o),$o,
0.61/0.86	                     app_encode_app(A,
0.61/0.86	                                    app_encode_fun(app_encode_fun(A,$o),$o),
0.61/0.86	                                    'const/sets/IN'(A),A0),
0.61/0.86	                     P) <=>
0.61/0.86	      app_encode_app(A,$o,P,A0)))).
0.61/0.86	tff('4', plain,
0.61/0.86	    ![X4 : $tType, X5 : app_encode_fun(X4, $o), X6 : X4]:
0.61/0.86	      (app_encode_app(X4, $o, X5, X6)
0.61/0.86	       | ~ app_encode_app(app_encode_fun(X4, $o), $o, 
0.61/0.86	             app_encode_app(X4, app_encode_fun(app_encode_fun(X4, $o), $o), 
0.61/0.86	               'const/sets/IN'(X4), X6), X5)),
0.61/0.86	    inference('cnf', [status(esa)], [zf_stmt_11])).
0.61/0.86	tff('5', plain,
0.61/0.86	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
0.61/0.86	      (~ $true
0.61/0.86	       | 'const/sets/EMPTY'(X0) = X1
0.61/0.86	       | app_encode_app(X0, $o, X1, sk_A2(X0, X1, 'const/sets/EMPTY'(X0)))),
0.61/0.86	    inference('sup-', [status(thm)], ['3', '4'])).
0.61/0.86	tff('6', plain,
0.61/0.86	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
0.61/0.86	      (app_encode_app(X0, $o, X1, sk_A2(X0, X1, 'const/sets/EMPTY'(X0)))
0.61/0.86	       | 'const/sets/EMPTY'(X0) = X1),
0.61/0.86	    inference('simplify', [status(thm)], ['5'])).
0.61/0.86	tff(zf_stmt_16, conjecture,
0.61/0.86	  (![A:app_encode_fun('type/realax/real',$o),
0.61/0.86	     A0:app_encode_fun('type/realax/real',$o)]:
0.61/0.86	     (((A0 != 'const/sets/EMPTY'('type/realax/real')) & 
0.61/0.86	       app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.61/0.86	                      app_encode_app(app_encode_fun('type/realax/real',$o),
0.61/0.86	                                     app_encode_fun(app_encode_fun('type/realax/real',
0.61/0.86	                                                                   $o),
0.61/0.86	                                                    $o),
0.61/0.86	                                     'const/sets/SUBSET'('type/realax/real'),
0.61/0.86	                                     A0),
0.61/0.86	                      A) & 
0.61/0.86	       (?[A1:'type/realax/real']:
0.61/0.86	          (![A2:'type/realax/real']:
0.61/0.86	             (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.61/0.86	                             app_encode_app('type/realax/real',
0.61/0.86	                                            app_encode_fun(app_encode_fun(
0.61/0.86	                                                           'type/realax/real',
0.61/0.86	                                                           $o),$o),
0.61/0.86	                                            'const/sets/IN'('type/realax/real'),
0.61/0.86	                                            A2),
0.61/0.86	                             A) =>
0.61/0.86	              app_encode_app('type/realax/real',$o,
0.61/0.86	                             app_encode_app('type/realax/real',
0.61/0.86	                                            app_encode_fun('type/realax/real',
0.61/0.86	                                                           $o),
0.61/0.86	                                            'const/realax/real_le',A1),
0.61/0.86	                             A2))))) =>
0.61/0.86	      app_encode_app('type/realax/real',$o,
0.61/0.86	                     app_encode_app('type/realax/real',
0.61/0.86	                                    app_encode_fun('type/realax/real',$o),
0.61/0.86	                                    'const/realax/real_le',
0.61/0.86	                                    app_encode_app(app_encode_fun('type/realax/real',
0.61/0.86	                                                                  $o),
0.61/0.86	                                                   'type/realax/real',
0.61/0.86	                                                   'const/sets/inf',A)),
0.61/0.86	                     app_encode_app(app_encode_fun('type/realax/real',$o),
0.61/0.86	                                    'type/realax/real','const/sets/inf',A0))))).
0.61/0.86	tff(zf_stmt_0, negated_conjecture,
0.61/0.86	  (~
0.61/0.86	    (![A:app_encode_fun('type/realax/real',$o),
0.61/0.86	       A0:app_encode_fun('type/realax/real',$o)]:
0.61/0.86	       (((A0 != 'const/sets/EMPTY'('type/realax/real')) & 
0.61/0.86	         app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.61/0.86	                        app_encode_app(app_encode_fun('type/realax/real',$o),
0.61/0.86	                                       app_encode_fun(app_encode_fun(
0.61/0.86	                                                      'type/realax/real',$o),
0.61/0.86	                                                      $o),
0.61/0.86	                                       'const/sets/SUBSET'('type/realax/real'),
0.61/0.86	                                       A0),
0.61/0.86	                        A) & 
0.61/0.86	         (?[A1:'type/realax/real']:
0.61/0.86	            (![A2:'type/realax/real']:
0.61/0.86	               (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.61/0.86	                               app_encode_app('type/realax/real',
0.61/0.86	                                              app_encode_fun(app_encode_fun(
0.61/0.86	                                                             'type/realax/real',
0.61/0.86	                                                             $o),$o),
0.61/0.86	                                              'const/sets/IN'('type/realax/real'),
0.61/0.86	                                              A2),
0.61/0.86	                               A) =>
0.61/0.86	                app_encode_app('type/realax/real',$o,
0.61/0.86	                               app_encode_app('type/realax/real',
0.61/0.86	                                              app_encode_fun('type/realax/real',
0.61/0.86	                                                             $o),
0.61/0.86	                                              'const/realax/real_le',A1),
0.61/0.86	                               A2))))) =>
0.61/0.86	        app_encode_app('type/realax/real',$o,
0.61/0.86	                       app_encode_app('type/realax/real',
0.61/0.86	                                      app_encode_fun('type/realax/real',$o),
0.61/0.86	                                      'const/realax/real_le',
0.61/0.86	                                      app_encode_app(app_encode_fun('type/realax/real',
0.61/0.86	                                                                    $o),
0.61/0.86	                                                     'type/realax/real',
0.61/0.86	                                                     'const/sets/inf',A)),
0.61/0.86	                       app_encode_app(app_encode_fun('type/realax/real',$o),
0.61/0.86	                                      'type/realax/real','const/sets/inf',A0)))))).
0.61/0.86	tff('7', plain,
0.61/0.86	    app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	      app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	        app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	        'const/sets/SUBSET'('type/realax/real'), sk_A0), sk_A),
0.61/0.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.61/0.86	tff('8', plain,
0.61/0.86	    ![X4 : $tType, X5 : app_encode_fun(X4, $o), X7 : X4]:
0.61/0.86	      (app_encode_app(app_encode_fun(X4, $o), $o, 
0.61/0.86	         app_encode_app(X4, app_encode_fun(app_encode_fun(X4, $o), $o), 
0.61/0.86	           'const/sets/IN'(X4), X7), X5)
0.61/0.86	       | ~ app_encode_app(X4, $o, X5, X7)),
0.61/0.86	    inference('cnf', [status(esa)], [zf_stmt_11])).
0.61/0.86	tff(zf_stmt_14, axiom,
0.61/0.86	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o)]:
0.61/0.86	     (app_encode_app(app_encode_fun(A,$o),$o,
0.61/0.86	                     app_encode_app(app_encode_fun(A,$o),
0.61/0.86	                                    app_encode_fun(app_encode_fun(A,$o),$o),
0.61/0.86	                                    'const/sets/SUBSET'(A),A0),
0.61/0.86	                     A1) <=>
0.61/0.86	      (![A2:A]:
0.61/0.86	         (app_encode_app(app_encode_fun(A,$o),$o,
0.61/0.86	                         app_encode_app(A,
0.61/0.86	                                        app_encode_fun(app_encode_fun(A,$o),
0.61/0.86	                                                       $o),
0.61/0.86	                                        'const/sets/IN'(A),A2),
0.61/0.86	                         A0) =>
0.61/0.86	          app_encode_app(app_encode_fun(A,$o),$o,
0.61/0.86	                         app_encode_app(A,
0.61/0.86	                                        app_encode_fun(app_encode_fun(A,$o),
0.61/0.86	                                                       $o),
0.61/0.86	                                        'const/sets/IN'(A),A2),
0.61/0.86	                         A1)))))).
0.61/0.86	tff('9', plain,
0.61/0.86	    ![X16 : $tType, X17 : X16, X18 : app_encode_fun(X16, $o), 
0.61/0.86	      X19 : app_encode_fun(X16, $o)]:
0.61/0.86	      (~ app_encode_app(app_encode_fun(X16, $o), $o, 
0.61/0.86	           app_encode_app(X16, app_encode_fun(app_encode_fun(X16, $o), $o), 
0.61/0.86	             'const/sets/IN'(X16), X17), X18)
0.61/0.86	       | app_encode_app(app_encode_fun(X16, $o), $o, 
0.61/0.86	           app_encode_app(X16, app_encode_fun(app_encode_fun(X16, $o), $o), 
0.61/0.86	             'const/sets/IN'(X16), X17), X19)
0.61/0.86	       | ~ app_encode_app(app_encode_fun(X16, $o), $o, 
0.61/0.86	             app_encode_app(app_encode_fun(X16, $o), 
0.61/0.86	               app_encode_fun(app_encode_fun(X16, $o), $o), 
0.61/0.86	               'const/sets/SUBSET'(X16), X18), X19)),
0.61/0.86	    inference('cnf', [status(esa)], [zf_stmt_14])).
0.61/0.86	tff('10', plain,
0.61/0.86	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0, 
0.61/0.86	      X3 : app_encode_fun(X0, $o)]:
0.61/0.86	      (~ $true
0.61/0.86	       | ~ app_encode_app(X0, $o, X1, X2)
0.61/0.86	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.61/0.86	             app_encode_app(app_encode_fun(X0, $o), 
0.61/0.86	               app_encode_fun(app_encode_fun(X0, $o), $o), 
0.61/0.86	               'const/sets/SUBSET'(X0), X1), X3)
0.61/0.86	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.61/0.86	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.61/0.86	             'const/sets/IN'(X0), X2), X3)),
0.61/0.86	    inference('sup-', [status(thm)], ['8', '9'])).
0.61/0.86	tff('11', plain,
0.61/0.86	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0, 
0.61/0.86	      X3 : app_encode_fun(X0, $o)]:
0.61/0.86	      (app_encode_app(app_encode_fun(X0, $o), $o, 
0.61/0.86	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.61/0.86	           'const/sets/IN'(X0), X2), X3)
0.61/0.86	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.61/0.86	             app_encode_app(app_encode_fun(X0, $o), 
0.61/0.86	               app_encode_fun(app_encode_fun(X0, $o), $o), 
0.61/0.86	               'const/sets/SUBSET'(X0), X1), X3)
0.61/0.86	       | ~ app_encode_app(X0, $o, X1, X2)),
0.61/0.86	    inference('simplify', [status(thm)], ['10'])).
0.61/0.86	tff('12', plain,
0.61/0.86	    ![X0 : 'type/realax/real']:
0.61/0.86	      (~ $true
0.61/0.86	       | ~ app_encode_app('type/realax/real', $o, sk_A0, X0)
0.61/0.86	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	             'const/sets/IN'('type/realax/real'), X0), sk_A)),
0.61/0.86	    inference('sup-', [status(thm)], ['7', '11'])).
0.61/0.86	tff('13', plain,
0.61/0.86	    ![X0 : 'type/realax/real']:
0.61/0.86	      (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	         app_encode_app('type/realax/real', 
0.61/0.86	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	           'const/sets/IN'('type/realax/real'), X0), sk_A)
0.61/0.86	       | ~ app_encode_app('type/realax/real', $o, sk_A0, X0)),
0.61/0.86	    inference('simplify', [status(thm)], ['12'])).
0.61/0.86	tff('14', plain,
0.61/0.86	    (~ $true
0.61/0.86	     | 'const/sets/EMPTY'('type/realax/real') = sk_A0
0.61/0.86	     | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	         app_encode_app('type/realax/real', 
0.61/0.86	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	           'const/sets/IN'('type/realax/real'), 
0.61/0.86	           sk_A2('type/realax/real', sk_A0, 
0.61/0.86	             'const/sets/EMPTY'('type/realax/real'))), sk_A)),
0.61/0.86	    inference('sup-', [status(thm)], ['6', '13'])).
0.61/0.86	tff('15', plain,
0.61/0.86	    (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	       app_encode_app('type/realax/real', 
0.61/0.86	         app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	         'const/sets/IN'('type/realax/real'), 
0.61/0.86	         sk_A2('type/realax/real', sk_A0, 
0.61/0.86	           'const/sets/EMPTY'('type/realax/real'))), sk_A)
0.61/0.86	     | 'const/sets/EMPTY'('type/realax/real') = sk_A0),
0.61/0.86	    inference('simplify', [status(thm)], ['14'])).
0.61/0.86	tff('16', plain, sk_A0 != 'const/sets/EMPTY'('type/realax/real'),
0.61/0.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.61/0.86	tff('17', plain,
0.61/0.86	    app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	      app_encode_app('type/realax/real', 
0.61/0.86	        app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	        'const/sets/IN'('type/realax/real'), 
0.61/0.86	        sk_A2('type/realax/real', sk_A0, 
0.61/0.86	          'const/sets/EMPTY'('type/realax/real'))), sk_A),
0.61/0.86	    inference('simplify_reflect-', [status(thm)], ['15', '16'])).
0.61/0.86	tff('18', plain,
0.61/0.86	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.61/0.86	      (~ $true
0.61/0.86	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	               'const/sets/SUBSET'('type/realax/real'), sk_A), X0)
0.61/0.86	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	             'const/sets/IN'('type/realax/real'), 
0.61/0.86	             sk_A2('type/realax/real', sk_A0, 
0.61/0.86	               'const/sets/EMPTY'('type/realax/real'))), X0)),
0.61/0.86	    inference('sup-', [status(thm)], ['17', '9'])).
0.61/0.86	tff('19', plain,
0.61/0.86	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.61/0.86	      (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	         app_encode_app('type/realax/real', 
0.61/0.86	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	           'const/sets/IN'('type/realax/real'), 
0.61/0.86	           sk_A2('type/realax/real', sk_A0, 
0.61/0.86	             'const/sets/EMPTY'('type/realax/real'))), X0)
0.61/0.86	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	               'const/sets/SUBSET'('type/realax/real'), sk_A), X0)),
0.61/0.86	    inference('simplify', [status(thm)], ['18'])).
0.61/0.86	tff('20', plain,
0.61/0.86	    (~ $true
0.61/0.86	     | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	             'const/sets/SUBSET'('type/realax/real'), sk_A), 
0.61/0.86	           'const/sets/EMPTY'('type/realax/real'))),
0.61/0.86	    inference('sup-', [status(thm)], ['19', '1'])).
0.61/0.86	tff('21', plain,
0.61/0.86	    ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	        app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	          app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	          'const/sets/SUBSET'('type/realax/real'), sk_A), 
0.61/0.86	        'const/sets/EMPTY'('type/realax/real')),
0.61/0.86	    inference('simplify', [status(thm)], ['20'])).
0.61/0.86	tff(zf_stmt_15, axiom,
0.61/0.86	  (![A:app_encode_fun('type/realax/real',$o)]:
0.61/0.86	     (((?[A0:'type/realax/real']:
0.61/0.86	          (![A1:'type/realax/real']:
0.61/0.86	             (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.61/0.86	                             app_encode_app('type/realax/real',
0.61/0.86	                                            app_encode_fun(app_encode_fun(
0.61/0.86	                                                           'type/realax/real',
0.61/0.86	                                                           $o),$o),
0.61/0.86	                                            'const/sets/IN'('type/realax/real'),
0.61/0.86	                                            A1),
0.61/0.86	                             A) =>
0.61/0.86	              app_encode_app('type/realax/real',$o,
0.61/0.86	                             app_encode_app('type/realax/real',
0.61/0.86	                                            app_encode_fun('type/realax/real',
0.61/0.86	                                                           $o),
0.61/0.86	                                            'const/realax/real_le',A0),
0.61/0.86	                             A1)))) & 
0.61/0.86	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
0.61/0.86	      ((![A0:'type/realax/real']:
0.61/0.86	          ((![A1:'type/realax/real']:
0.61/0.86	              (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.61/0.86	                              app_encode_app('type/realax/real',
0.61/0.86	                                             app_encode_fun(app_encode_fun(
0.61/0.86	                                                            'type/realax/real',
0.61/0.86	                                                            $o),$o),
0.61/0.86	                                             'const/sets/IN'('type/realax/real'),
0.61/0.86	                                             A1),
0.61/0.86	                              A) =>
0.61/0.86	               app_encode_app('type/realax/real',$o,
0.61/0.86	                              app_encode_app('type/realax/real',
0.61/0.86	                                             app_encode_fun('type/realax/real',
0.61/0.86	                                                            $o),
0.61/0.86	                                             'const/realax/real_le',A0),
0.61/0.86	                              A1))) =>
0.61/0.86	           app_encode_app('type/realax/real',$o,
0.61/0.86	                          app_encode_app('type/realax/real',
0.61/0.86	                                         app_encode_fun('type/realax/real',$o),
0.61/0.86	                                         'const/realax/real_le',A0),
0.61/0.86	                          app_encode_app(app_encode_fun('type/realax/real',$o),
0.61/0.86	                                         'type/realax/real','const/sets/inf',
0.61/0.86	                                         A)))) & 
0.61/0.86	       (![A0:'type/realax/real']:
0.61/0.86	          (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.61/0.86	                          app_encode_app('type/realax/real',
0.61/0.86	                                         app_encode_fun(app_encode_fun(
0.61/0.86	                                                        'type/realax/real',$o),
0.61/0.86	                                                        $o),
0.61/0.86	                                         'const/sets/IN'('type/realax/real'),
0.61/0.86	                                         A0),
0.61/0.86	                          A) =>
0.61/0.86	           app_encode_app('type/realax/real',$o,
0.61/0.86	                          app_encode_app('type/realax/real',
0.61/0.86	                                         app_encode_fun('type/realax/real',$o),
0.61/0.86	                                         'const/realax/real_le',
0.61/0.86	                                         app_encode_app(app_encode_fun(
0.61/0.86	                                                        'type/realax/real',$o),
0.61/0.86	                                                        'type/realax/real',
0.61/0.86	                                                        'const/sets/inf',A)),
0.61/0.86	                          A0))))))).
0.61/0.86	tff(zf_stmt_1, axiom,
0.61/0.86	  ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.61/0.86	                   app_encode_app('type/realax/real',
0.61/0.86	                                  app_encode_fun(app_encode_fun('type/realax/real',
0.61/0.86	                                                                $o),
0.61/0.86	                                                 $o),
0.61/0.86	                                  'const/sets/IN'('type/realax/real'),A1),
0.61/0.86	                   A) =>
0.61/0.86	    app_encode_app('type/realax/real',$o,
0.61/0.86	                   app_encode_app('type/realax/real',
0.61/0.86	                                  app_encode_fun('type/realax/real',$o),
0.61/0.86	                                  'const/realax/real_le',A0),
0.61/0.86	                   A1)) =>
0.61/0.86	   zip_tseitin0(A1,A0,A))).
0.61/0.86	tff('22', plain,
0.61/0.86	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
0.61/0.86	      X23 : app_encode_fun('type/realax/real', $o)]:
0.61/0.86	      (zip_tseitin0(X21, X22, X23)
0.61/0.86	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	             'const/sets/IN'('type/realax/real'), X21), X23)),
0.61/0.86	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.61/0.86	tff(zf_stmt_2, type, zip_tseitin2 :
0.61/0.86	    app_encode_fun('type/realax/real',$o) > $o).
0.61/0.86	tff(zf_stmt_3, axiom,
0.61/0.86	  (zip_tseitin2(A) =>
0.61/0.86	   ((![A0:'type/realax/real']:
0.61/0.86	       (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.61/0.86	                       app_encode_app('type/realax/real',
0.61/0.86	                                      app_encode_fun(app_encode_fun('type/realax/real',
0.61/0.86	                                                                    $o),
0.61/0.86	                                                     $o),
0.61/0.86	                                      'const/sets/IN'('type/realax/real'),A0),
0.61/0.86	                       A) =>
0.61/0.86	        app_encode_app('type/realax/real',$o,
0.61/0.86	                       app_encode_app('type/realax/real',
0.61/0.86	                                      app_encode_fun('type/realax/real',$o),
0.61/0.86	                                      'const/realax/real_le',
0.61/0.86	                                      app_encode_app(app_encode_fun('type/realax/real',
0.61/0.86	                                                                    $o),
0.61/0.86	                                                     'type/realax/real',
0.61/0.86	                                                     'const/sets/inf',A)),
0.61/0.86	                       A0))) & 
0.61/0.86	    (![A0:'type/realax/real']:
0.61/0.86	       ((![A1:'type/realax/real']: zip_tseitin1(A1,A0,A)) =>
0.61/0.86	        app_encode_app('type/realax/real',$o,
0.61/0.86	                       app_encode_app('type/realax/real',
0.61/0.86	                                      app_encode_fun('type/realax/real',$o),
0.61/0.86	                                      'const/realax/real_le',A0),
0.61/0.86	                       app_encode_app(app_encode_fun('type/realax/real',$o),
0.61/0.86	                                      'type/realax/real','const/sets/inf',A))))))).
0.61/0.86	tff(zf_stmt_4, type, zip_tseitin1 :
0.61/0.86	    ('type/realax/real' * 
0.61/0.86	     'type/realax/real' * 
0.61/0.86	     app_encode_fun('type/realax/real',$o)) > $o).
0.61/0.86	tff(zf_stmt_5, axiom,
0.61/0.86	  ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.61/0.86	                   app_encode_app('type/realax/real',
0.61/0.86	                                  app_encode_fun(app_encode_fun('type/realax/real',
0.61/0.86	                                                                $o),
0.61/0.86	                                                 $o),
0.61/0.86	                                  'const/sets/IN'('type/realax/real'),A1),
0.61/0.86	                   A) =>
0.61/0.86	    app_encode_app('type/realax/real',$o,
0.61/0.86	                   app_encode_app('type/realax/real',
0.61/0.86	                                  app_encode_fun('type/realax/real',$o),
0.61/0.86	                                  'const/realax/real_le',A0),
0.61/0.86	                   A1)) =>
0.61/0.86	   zip_tseitin1(A1,A0,A))).
0.61/0.86	tff(zf_stmt_6, type, zip_tseitin0 :
0.61/0.86	    ('type/realax/real' * 
0.61/0.86	     'type/realax/real' * 
0.61/0.86	     app_encode_fun('type/realax/real',$o)) > $o).
0.61/0.86	tff(zf_stmt_7, axiom,
0.61/0.86	  (![A:app_encode_fun('type/realax/real',$o)]:
0.61/0.86	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
0.61/0.86	       (?[A0:'type/realax/real']:
0.61/0.86	          (![A1:'type/realax/real']: zip_tseitin0(A1,A0,A)))) =>
0.61/0.86	      zip_tseitin2(A)))).
0.61/0.86	tff('23', plain,
0.61/0.86	    ![X28 : app_encode_fun('type/realax/real', $o), X29 : 'type/realax/real']:
0.61/0.86	      (zip_tseitin2(X28)
0.61/0.86	       | ~ zip_tseitin0(sk_A12(X29, X28), X29, X28)
0.61/0.86	       | X28 = 'const/sets/EMPTY'('type/realax/real')),
0.61/0.86	    inference('cnf', [status(esa)], [zf_stmt_7])).
0.61/0.86	tff('24', plain,
0.61/0.86	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.61/0.86	      (~ $true
0.61/0.86	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	             'const/sets/IN'('type/realax/real'), sk_A12(X1, X0)), X0)
0.61/0.86	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.61/0.86	       | zip_tseitin2(X0)),
0.61/0.86	    inference('sup-', [status(thm)], ['22', '23'])).
0.61/0.86	tff('25', plain,
0.61/0.86	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.61/0.86	      (zip_tseitin2(X0)
0.61/0.86	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.61/0.86	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	             'const/sets/IN'('type/realax/real'), sk_A12(X1, X0)), X0)),
0.61/0.86	    inference('simplify', [status(thm)], ['24'])).
0.61/0.86	tff('26', plain,
0.61/0.86	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.61/0.86	      (~ $true
0.61/0.86	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.61/0.86	       | zip_tseitin2(X0)
0.61/0.86	       | app_encode_app('type/realax/real', $o, X0, sk_A12(X1, X0))),
0.61/0.86	    inference('sup-', [status(thm)], ['25', '4'])).
0.61/0.86	tff('27', plain,
0.61/0.86	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.61/0.86	      (app_encode_app('type/realax/real', $o, X0, sk_A12(X1, X0))
0.61/0.86	       | zip_tseitin2(X0)
0.61/0.86	       | X0 = 'const/sets/EMPTY'('type/realax/real')),
0.61/0.86	    inference('simplify', [status(thm)], ['26'])).
0.61/0.86	tff('28', plain,
0.61/0.86	    ![X30 : 'type/realax/real']:
0.61/0.86	      (app_encode_app('type/realax/real', $o, 
0.61/0.86	         app_encode_app('type/realax/real', 
0.61/0.86	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	           sk_A13), X30)
0.61/0.86	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	             app_encode_app('type/realax/real', 
0.61/0.86	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	               'const/sets/IN'('type/realax/real'), X30), sk_A)),
0.61/0.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.61/0.86	tff('29', plain,
0.61/0.86	    ![X0 : 'type/realax/real']:
0.61/0.86	      (~ $true
0.61/0.86	       | ~ app_encode_app('type/realax/real', $o, sk_A, X0)
0.61/0.86	       | app_encode_app('type/realax/real', $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	             sk_A13), X0)),
0.61/0.86	    inference('sup-', [status(thm)], ['8', '28'])).
0.61/0.86	tff('30', plain,
0.61/0.86	    ![X0 : 'type/realax/real']:
0.61/0.86	      (app_encode_app('type/realax/real', $o, 
0.61/0.86	         app_encode_app('type/realax/real', 
0.61/0.86	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	           sk_A13), X0)
0.61/0.86	       | ~ app_encode_app('type/realax/real', $o, sk_A, X0)),
0.61/0.86	    inference('simplify', [status(thm)], ['29'])).
0.61/0.86	tff('31', plain,
0.61/0.86	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
0.61/0.86	      X23 : app_encode_fun('type/realax/real', $o)]:
0.61/0.86	      (zip_tseitin0(X21, X22, X23)
0.61/0.86	       | ~ app_encode_app('type/realax/real', $o, 
0.61/0.86	             app_encode_app('type/realax/real', 
0.61/0.86	               app_encode_fun('type/realax/real', $o), 
0.61/0.86	               'const/realax/real_le', X22), X21)),
0.61/0.86	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.61/0.86	tff('32', plain,
0.61/0.86	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.61/0.86	      (~ $true
0.61/0.86	       | ~ app_encode_app('type/realax/real', $o, 
0.61/0.86	             app_encode_app('type/realax/real', 
0.61/0.86	               app_encode_fun('type/realax/real', $o), 
0.61/0.86	               'const/realax/real_le', X1), sk_A12(X1, X0))
0.61/0.86	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.61/0.86	       | zip_tseitin2(X0)),
0.61/0.86	    inference('sup-', [status(thm)], ['31', '23'])).
0.61/0.86	tff('33', plain,
0.61/0.86	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.61/0.86	      (zip_tseitin2(X0)
0.61/0.86	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.61/0.86	       | ~ app_encode_app('type/realax/real', $o, 
0.61/0.86	             app_encode_app('type/realax/real', 
0.61/0.86	               app_encode_fun('type/realax/real', $o), 
0.61/0.86	               'const/realax/real_le', X1), sk_A12(X1, X0))),
0.61/0.86	    inference('simplify', [status(thm)], ['32'])).
0.61/0.86	tff('34', plain,
0.61/0.86	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.61/0.86	      (~ $true
0.61/0.86	       | ~ app_encode_app('type/realax/real', $o, sk_A, sk_A12(sk_A13, X0))
0.61/0.86	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.61/0.86	       | zip_tseitin2(X0)),
0.61/0.86	    inference('sup-', [status(thm)], ['30', '33'])).
0.61/0.86	tff('35', plain,
0.61/0.86	    ![X0 : app_encode_fun('type/realax/real', $o)]:
0.61/0.86	      (zip_tseitin2(X0)
0.61/0.86	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.61/0.86	       | ~ app_encode_app('type/realax/real', $o, sk_A, sk_A12(sk_A13, X0))),
0.61/0.86	    inference('simplify', [status(thm)], ['34'])).
0.61/0.86	tff('36', plain,
0.61/0.86	    (~ $true
0.61/0.86	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
0.61/0.86	     | zip_tseitin2(sk_A)
0.61/0.86	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
0.61/0.86	     | zip_tseitin2(sk_A)),
0.61/0.86	    inference('sup-', [status(thm)], ['27', '35'])).
0.61/0.86	tff('37', plain,
0.61/0.86	    (zip_tseitin2(sk_A) | sk_A = 'const/sets/EMPTY'('type/realax/real')),
0.61/0.86	    inference('simplify', [status(thm)], ['36'])).
0.61/0.86	tff(zf_stmt_9, axiom,
0.61/0.86	  (![A:app_encode_fun('type/realax/real',$o),A0:'type/realax/real']:
0.61/0.86	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
0.61/0.86	       (![A1:'type/realax/real']:
0.61/0.86	          (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.61/0.86	                          app_encode_app('type/realax/real',
0.61/0.86	                                         app_encode_fun(app_encode_fun(
0.61/0.86	                                                        'type/realax/real',$o),
0.61/0.86	                                                        $o),
0.61/0.86	                                         'const/sets/IN'('type/realax/real'),
0.61/0.86	                                         A1),
0.61/0.86	                          A) =>
0.61/0.86	           app_encode_app('type/realax/real',$o,
0.61/0.86	                          app_encode_app('type/realax/real',
0.61/0.86	                                         app_encode_fun('type/realax/real',$o),
0.61/0.86	                                         'const/realax/real_le',A0),
0.61/0.86	                          A1)))) =>
0.61/0.86	      app_encode_app('type/realax/real',$o,
0.61/0.86	                     app_encode_app('type/realax/real',
0.61/0.86	                                    app_encode_fun('type/realax/real',$o),
0.61/0.86	                                    'const/realax/real_le',A0),
0.61/0.86	                     app_encode_app(app_encode_fun('type/realax/real',$o),
0.61/0.86	                                    'type/realax/real','const/sets/inf',A))))).
0.61/0.86	tff('38', plain,
0.61/0.86	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.61/0.86	      (X0 = 'const/sets/EMPTY'('type/realax/real')
0.61/0.86	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	             'const/sets/IN'('type/realax/real'), sk_A1(X1, X0)), X0)
0.61/0.86	       | app_encode_app('type/realax/real', $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	             X1), 
0.61/0.86	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	             'type/realax/real', 'const/sets/inf', X0))),
0.61/0.86	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.61/0.86	tff('39', plain,
0.61/0.86	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.61/0.86	      (~ $true
0.61/0.86	       | app_encode_app('type/realax/real', $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	             X1), 
0.61/0.86	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	             'type/realax/real', 'const/sets/inf', X0))
0.61/0.86	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.61/0.86	       | app_encode_app('type/realax/real', $o, X0, sk_A1(X1, X0))),
0.61/0.86	    inference('sup-', [status(thm)], ['38', '4'])).
0.61/0.86	tff('40', plain,
0.61/0.86	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.61/0.86	      (app_encode_app('type/realax/real', $o, X0, sk_A1(X1, X0))
0.61/0.86	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.61/0.86	       | app_encode_app('type/realax/real', $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	             X1), 
0.61/0.86	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	             'type/realax/real', 'const/sets/inf', X0))),
0.61/0.86	    inference('simplify', [status(thm)], ['39'])).
0.61/0.86	tff('41', plain,
0.61/0.86	    ![X0 : 'type/realax/real']:
0.61/0.86	      (~ $true
0.61/0.86	       | app_encode_app('type/realax/real', $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	             X0), 
0.61/0.86	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	             'type/realax/real', 'const/sets/inf', sk_A0))
0.61/0.86	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.61/0.86	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	             'const/sets/IN'('type/realax/real'), sk_A1(X0, sk_A0)), sk_A)),
0.61/0.86	    inference('sup-', [status(thm)], ['40', '13'])).
0.61/0.86	tff('42', plain,
0.61/0.86	    ![X0 : 'type/realax/real']:
0.61/0.86	      (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	         app_encode_app('type/realax/real', 
0.61/0.86	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	           'const/sets/IN'('type/realax/real'), sk_A1(X0, sk_A0)), sk_A)
0.61/0.86	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.61/0.86	       | app_encode_app('type/realax/real', $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	             X0), 
0.61/0.86	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	             'type/realax/real', 'const/sets/inf', sk_A0))),
0.61/0.86	    inference('simplify', [status(thm)], ['41'])).
0.61/0.86	tff('43', plain,
0.61/0.86	    ![X0 : 'type/realax/real']:
0.61/0.86	      (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	         app_encode_app('type/realax/real', 
0.61/0.86	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	           'const/sets/IN'('type/realax/real'), sk_A1(X0, sk_A0)), sk_A)
0.61/0.86	       | app_encode_app('type/realax/real', $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	             X0), 
0.61/0.86	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	             'type/realax/real', 'const/sets/inf', sk_A0))),
0.61/0.86	    inference('simplify_reflect-', [status(thm)], ['42', '16'])).
0.61/0.86	tff('44', plain,
0.61/0.86	    ![X23 : app_encode_fun('type/realax/real', $o), X26 : 'type/realax/real']:
0.61/0.86	      (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.61/0.86	             'const/sets/IN'('type/realax/real'), X26), X23)
0.61/0.86	       | app_encode_app('type/realax/real', $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	               'type/realax/real', 'const/sets/inf', X23)), X26)
0.61/0.86	       | ~ zip_tseitin2(X23)),
0.61/0.86	    inference('cnf', [status(esa)], [zf_stmt_3])).
0.61/0.86	tff('45', plain,
0.61/0.86	    ![X0 : 'type/realax/real']:
0.61/0.86	      (~ $true
0.61/0.86	       | app_encode_app('type/realax/real', $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	             X0), 
0.61/0.86	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	             'type/realax/real', 'const/sets/inf', sk_A0))
0.61/0.86	       | ~ zip_tseitin2(sk_A)
0.61/0.86	       | app_encode_app('type/realax/real', $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	               'type/realax/real', 'const/sets/inf', sk_A)), 
0.61/0.86	           sk_A1(X0, sk_A0))),
0.61/0.86	    inference('sup-', [status(thm)], ['43', '44'])).
0.61/0.86	tff('46', plain,
0.61/0.86	    ![X0 : 'type/realax/real']:
0.61/0.86	      (app_encode_app('type/realax/real', $o, 
0.61/0.86	         app_encode_app('type/realax/real', 
0.61/0.86	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	             'type/realax/real', 'const/sets/inf', sk_A)), sk_A1(X0, sk_A0))
0.61/0.86	       | ~ zip_tseitin2(sk_A)
0.61/0.86	       | app_encode_app('type/realax/real', $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	             X0), 
0.61/0.86	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	             'type/realax/real', 'const/sets/inf', sk_A0))),
0.61/0.86	    inference('simplify', [status(thm)], ['45'])).
0.61/0.86	tff('47', plain,
0.61/0.86	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.61/0.86	      (X0 = 'const/sets/EMPTY'('type/realax/real')
0.61/0.86	       | ~ app_encode_app('type/realax/real', $o, 
0.61/0.86	             app_encode_app('type/realax/real', 
0.61/0.86	               app_encode_fun('type/realax/real', $o), 
0.61/0.86	               'const/realax/real_le', X1), sk_A1(X1, X0))
0.61/0.86	       | app_encode_app('type/realax/real', $o, 
0.61/0.86	           app_encode_app('type/realax/real', 
0.61/0.86	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	             X1), 
0.61/0.86	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	             'type/realax/real', 'const/sets/inf', X0))),
0.61/0.86	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.61/0.86	tff('48', plain,
0.61/0.86	    (~ $true
0.61/0.86	     | app_encode_app('type/realax/real', $o, 
0.61/0.86	         app_encode_app('type/realax/real', 
0.61/0.86	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	             'type/realax/real', 'const/sets/inf', sk_A)), 
0.61/0.86	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	           'type/realax/real', 'const/sets/inf', sk_A0))
0.61/0.86	     | ~ zip_tseitin2(sk_A)
0.61/0.86	     | app_encode_app('type/realax/real', $o, 
0.61/0.86	         app_encode_app('type/realax/real', 
0.61/0.86	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	             'type/realax/real', 'const/sets/inf', sk_A)), 
0.61/0.86	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	           'type/realax/real', 'const/sets/inf', sk_A0))
0.61/0.86	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.61/0.86	    inference('sup-', [status(thm)], ['46', '47'])).
0.61/0.86	tff('49', plain,
0.61/0.86	    (sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.61/0.86	     | ~ zip_tseitin2(sk_A)
0.61/0.86	     | app_encode_app('type/realax/real', $o, 
0.61/0.86	         app_encode_app('type/realax/real', 
0.61/0.86	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	             'type/realax/real', 'const/sets/inf', sk_A)), 
0.61/0.86	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	           'type/realax/real', 'const/sets/inf', sk_A0))),
0.61/0.86	    inference('simplify', [status(thm)], ['48'])).
0.61/0.86	tff('50', plain,
0.61/0.86	    (~ zip_tseitin2(sk_A)
0.61/0.86	     | app_encode_app('type/realax/real', $o, 
0.61/0.86	         app_encode_app('type/realax/real', 
0.61/0.86	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	             'type/realax/real', 'const/sets/inf', sk_A)), 
0.61/0.86	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	           'type/realax/real', 'const/sets/inf', sk_A0))),
0.61/0.86	    inference('simplify_reflect-', [status(thm)], ['49', '16'])).
0.61/0.86	tff('51', plain,
0.61/0.86	    ~ app_encode_app('type/realax/real', $o, 
0.61/0.86	        app_encode_app('type/realax/real', 
0.61/0.86	          app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.61/0.86	          app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	            'type/realax/real', 'const/sets/inf', sk_A)), 
0.61/0.86	        app_encode_app(app_encode_fun('type/realax/real', $o), 
0.61/0.86	          'type/realax/real', 'const/sets/inf', sk_A0)),
0.61/0.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.61/0.86	tff('52', plain, ~ zip_tseitin2(sk_A),
0.61/0.86	    inference('clc', [status(thm)], ['50', '51'])).
0.61/0.86	tff('53', plain, (~ $true | sk_A = 'const/sets/EMPTY'('type/realax/real')),
0.61/0.86	    inference('sup-', [status(thm)], ['37', '52'])).
0.61/0.86	tff('54', plain, sk_A = 'const/sets/EMPTY'('type/realax/real'),
0.61/0.86	    inference('simplify', [status(thm)], ['53'])).
0.61/0.86	tff('55', plain,
0.61/0.86	    ![X16 : $tType, X18 : app_encode_fun(X16, $o), 
0.61/0.86	      X20 : app_encode_fun(X16, $o)]:
0.61/0.86	      (app_encode_app(app_encode_fun(X16, $o), $o, 
0.61/0.86	         app_encode_app(app_encode_fun(X16, $o), 
0.61/0.86	           app_encode_fun(app_encode_fun(X16, $o), $o), 
0.61/0.86	           'const/sets/SUBSET'(X16), X18), X20)
0.61/0.86	       | app_encode_app(app_encode_fun(X16, $o), $o, 
0.61/0.86	           app_encode_app(X16, app_encode_fun(app_encode_fun(X16, $o), $o), 
0.61/0.86	             'const/sets/IN'(X16), sk_A21(X16, X20, X18)), X18)),
0.61/0.86	    inference('cnf', [status(esa)], [zf_stmt_14])).
0.61/0.86	tff('56', plain,
0.61/0.86	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
0.61/0.86	      (~ $true
0.61/0.86	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.61/0.86	           app_encode_app(app_encode_fun(X0, $o), 
0.61/0.86	             app_encode_fun(app_encode_fun(X0, $o), $o), 
0.61/0.86	             'const/sets/SUBSET'(X0), 'const/sets/EMPTY'(X0)), X1)),
0.61/0.86	    inference('sup-', [status(thm)], ['55', '1'])).
0.61/0.86	tff('57', plain,
0.61/0.86	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
0.61/0.86	      app_encode_app(app_encode_fun(X0, $o), $o, 
0.61/0.86	        app_encode_app(app_encode_fun(X0, $o), 
0.61/0.86	          app_encode_fun(app_encode_fun(X0, $o), $o), 
0.61/0.86	          'const/sets/SUBSET'(X0), 'const/sets/EMPTY'(X0)), X1),
0.61/0.86	    inference('simplify', [status(thm)], ['56'])).
0.61/0.86	tff('58', plain, ~ $true,
0.61/0.86	    inference('demod', [status(thm)], ['21', '54', '57'])).
0.61/0.86	tff('59', plain, $false, inference('simplify', [status(thm)], ['58'])).
0.61/0.86	
0.61/0.86	% SZS output end Refutation
0.61/0.86	EOF
