0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n065.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:41:38 CST 2018
0.00/0.39	% done 295 iterations in 0.182s
0.00/0.39	% SZS status Theorem for 'stdin'
0.00/0.39	% SZS output start Refutation
0.00/0.39	tff(zf_stmt_13, axiom,
0.00/0.39	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o)]:
0.00/0.39	     ((A0 = A1) <=>
0.00/0.39	      (![A2:A]:
0.00/0.39	         (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.39	                         app_encode_app(A,
0.00/0.39	                                        app_encode_fun(app_encode_fun(A,$o),
0.00/0.39	                                                       $o),
0.00/0.39	                                        'const/sets/IN'(A),A2),
0.00/0.39	                         A0) <=>
0.00/0.39	          app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.39	                         app_encode_app(A,
0.00/0.39	                                        app_encode_fun(app_encode_fun(A,$o),
0.00/0.39	                                                       $o),
0.00/0.39	                                        'const/sets/IN'(A),A2),
0.00/0.39	                         A1)))))).
0.00/0.39	tff('0', plain,
0.00/0.39	    ![X10 : $tType, X13 : app_encode_fun(X10, $o), 
0.00/0.39	      X15 : app_encode_fun(X10, $o)]:
0.00/0.39	      (X13 = X15
0.00/0.39	       | app_encode_app(app_encode_fun(X10, $o), $o, 
0.00/0.39	           app_encode_app(X10, app_encode_fun(app_encode_fun(X10, $o), $o), 
0.00/0.39	             'const/sets/IN'(X10), sk_A2(X10, X15, X13)), X15)
0.00/0.39	       | app_encode_app(app_encode_fun(X10, $o), $o, 
0.00/0.39	           app_encode_app(X10, app_encode_fun(app_encode_fun(X10, $o), $o), 
0.00/0.39	             'const/sets/IN'(X10), sk_A2(X10, X15, X13)), X13)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_13])).
0.00/0.39	tff(zf_stmt_12, axiom,
0.00/0.39	  (![A:$tType,A0:A]:
0.00/0.39	     (~
0.00/0.39	       app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.39	                      app_encode_app(A,
0.00/0.39	                                     app_encode_fun(app_encode_fun(A,$o),$o),
0.00/0.39	                                     'const/sets/IN'(A),A0),
0.00/0.39	                      'const/sets/EMPTY'(A))))).
0.00/0.39	tff('1', plain,
0.00/0.39	    ![X8 : $tType, X9 : X8]:
0.00/0.39	      ~ app_encode_app(app_encode_fun(X8, $o), $o, 
0.00/0.39	          app_encode_app(X8, app_encode_fun(app_encode_fun(X8, $o), $o), 
0.00/0.39	            'const/sets/IN'(X8), X9), 'const/sets/EMPTY'(X8)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_12])).
0.00/0.39	tff('2', plain,
0.00/0.39	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
0.00/0.39	      (~ $true
0.00/0.39	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.39	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.39	             'const/sets/IN'(X0), sk_A2(X0, X1, 'const/sets/EMPTY'(X0))), X1)
0.00/0.39	       | 'const/sets/EMPTY'(X0) = X1),
0.00/0.39	    inference('sup-', [status(thm)], ['0', '1'])).
0.00/0.39	tff('3', plain,
0.00/0.39	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
0.00/0.39	      ('const/sets/EMPTY'(X0) = X1
0.00/0.39	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.39	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.39	             'const/sets/IN'(X0), sk_A2(X0, X1, 'const/sets/EMPTY'(X0))), X1)),
0.00/0.39	    inference('simplify', [status(thm)], ['2'])).
0.00/0.39	tff(zf_stmt_11, axiom,
0.00/0.39	  (![A:$tType,P:app_encode_fun(A,$o),A0:A]:
0.00/0.39	     (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.39	                     app_encode_app(A,
0.00/0.39	                                    app_encode_fun(app_encode_fun(A,$o),$o),
0.00/0.39	                                    'const/sets/IN'(A),A0),
0.00/0.39	                     P) <=>
0.00/0.39	      app_encode_app(A,$o,P,A0)))).
0.00/0.39	tff('4', plain,
0.00/0.39	    ![X4 : $tType, X5 : app_encode_fun(X4, $o), X6 : X4]:
0.00/0.39	      (app_encode_app(X4, $o, X5, X6)
0.00/0.39	       | ~ app_encode_app(app_encode_fun(X4, $o), $o, 
0.00/0.39	             app_encode_app(X4, app_encode_fun(app_encode_fun(X4, $o), $o), 
0.00/0.39	               'const/sets/IN'(X4), X6), X5)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_11])).
0.00/0.39	tff('5', plain,
0.00/0.39	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
0.00/0.39	      (~ $true
0.00/0.39	       | 'const/sets/EMPTY'(X0) = X1
0.00/0.39	       | app_encode_app(X0, $o, X1, sk_A2(X0, X1, 'const/sets/EMPTY'(X0)))),
0.00/0.39	    inference('sup-', [status(thm)], ['3', '4'])).
0.00/0.39	tff('6', plain,
0.00/0.39	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
0.00/0.39	      (app_encode_app(X0, $o, X1, sk_A2(X0, X1, 'const/sets/EMPTY'(X0)))
0.00/0.39	       | 'const/sets/EMPTY'(X0) = X1),
0.00/0.39	    inference('simplify', [status(thm)], ['5'])).
0.00/0.39	tff(zf_stmt_16, conjecture,
0.00/0.39	  (![A:app_encode_fun('type/realax/real',$o),
0.00/0.39	     A0:app_encode_fun('type/realax/real',$o)]:
0.00/0.39	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
0.00/0.39	       app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.39	                      app_encode_app(app_encode_fun('type/realax/real',$o),
0.00/0.39	                                     app_encode_fun(app_encode_fun('type/realax/real',
0.00/0.39	                                                                   $o),
0.00/0.39	                                                    $o),
0.00/0.39	                                     'const/sets/SUBSET'('type/realax/real'),
0.00/0.39	                                     A),
0.00/0.39	                      A0) & 
0.00/0.39	       (?[A1:'type/realax/real']:
0.00/0.39	          (![A2:'type/realax/real']:
0.00/0.39	             (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.39	                             app_encode_app('type/realax/real',
0.00/0.39	                                            app_encode_fun(app_encode_fun(
0.00/0.39	                                                           'type/realax/real',
0.00/0.39	                                                           $o),$o),
0.00/0.39	                                            'const/sets/IN'('type/realax/real'),
0.00/0.39	                                            A2),
0.00/0.39	                             A0) =>
0.00/0.39	              app_encode_app('type/realax/real',$o,
0.00/0.39	                             app_encode_app('type/realax/real',
0.00/0.39	                                            app_encode_fun('type/realax/real',
0.00/0.39	                                                           $o),
0.00/0.39	                                            'const/realax/real_le',A2),
0.00/0.39	                             A1))))) =>
0.00/0.39	      app_encode_app('type/realax/real',$o,
0.00/0.39	                     app_encode_app('type/realax/real',
0.00/0.39	                                    app_encode_fun('type/realax/real',$o),
0.00/0.39	                                    'const/realax/real_le',
0.00/0.39	                                    app_encode_app(app_encode_fun('type/realax/real',
0.00/0.39	                                                                  $o),
0.00/0.39	                                                   'type/realax/real',
0.00/0.39	                                                   'const/sets/sup',A)),
0.00/0.39	                     app_encode_app(app_encode_fun('type/realax/real',$o),
0.00/0.39	                                    'type/realax/real','const/sets/sup',A0))))).
0.00/0.39	tff(zf_stmt_0, negated_conjecture,
0.00/0.39	  (~
0.00/0.39	    (![A:app_encode_fun('type/realax/real',$o),
0.00/0.39	       A0:app_encode_fun('type/realax/real',$o)]:
0.00/0.39	       (((A != 'const/sets/EMPTY'('type/realax/real')) & 
0.00/0.39	         app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.39	                        app_encode_app(app_encode_fun('type/realax/real',$o),
0.00/0.39	                                       app_encode_fun(app_encode_fun(
0.00/0.39	                                                      'type/realax/real',$o),
0.00/0.39	                                                      $o),
0.00/0.39	                                       'const/sets/SUBSET'('type/realax/real'),
0.00/0.39	                                       A),
0.00/0.39	                        A0) & 
0.00/0.39	         (?[A1:'type/realax/real']:
0.00/0.39	            (![A2:'type/realax/real']:
0.00/0.39	               (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.39	                               app_encode_app('type/realax/real',
0.00/0.39	                                              app_encode_fun(app_encode_fun(
0.00/0.39	                                                             'type/realax/real',
0.00/0.39	                                                             $o),$o),
0.00/0.39	                                              'const/sets/IN'('type/realax/real'),
0.00/0.39	                                              A2),
0.00/0.39	                               A0) =>
0.00/0.39	                app_encode_app('type/realax/real',$o,
0.00/0.39	                               app_encode_app('type/realax/real',
0.00/0.39	                                              app_encode_fun('type/realax/real',
0.00/0.39	                                                             $o),
0.00/0.39	                                              'const/realax/real_le',A2),
0.00/0.39	                               A1))))) =>
0.00/0.39	        app_encode_app('type/realax/real',$o,
0.00/0.39	                       app_encode_app('type/realax/real',
0.00/0.39	                                      app_encode_fun('type/realax/real',$o),
0.00/0.39	                                      'const/realax/real_le',
0.00/0.39	                                      app_encode_app(app_encode_fun('type/realax/real',
0.00/0.39	                                                                    $o),
0.00/0.39	                                                     'type/realax/real',
0.00/0.39	                                                     'const/sets/sup',A)),
0.00/0.39	                       app_encode_app(app_encode_fun('type/realax/real',$o),
0.00/0.39	                                      'type/realax/real','const/sets/sup',A0)))))).
0.00/0.39	tff('7', plain,
0.00/0.39	    app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.39	      app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	        app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.39	        'const/sets/SUBSET'('type/realax/real'), sk_A), sk_A0),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.39	tff('8', plain,
0.00/0.39	    ![X4 : $tType, X5 : app_encode_fun(X4, $o), X7 : X4]:
0.00/0.39	      (app_encode_app(app_encode_fun(X4, $o), $o, 
0.00/0.39	         app_encode_app(X4, app_encode_fun(app_encode_fun(X4, $o), $o), 
0.00/0.39	           'const/sets/IN'(X4), X7), X5)
0.00/0.39	       | ~ app_encode_app(X4, $o, X5, X7)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_11])).
0.00/0.39	tff(zf_stmt_14, axiom,
0.00/0.39	  (![A:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(A,$o)]:
0.00/0.39	     (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.39	                     app_encode_app(app_encode_fun(A,$o),
0.00/0.39	                                    app_encode_fun(app_encode_fun(A,$o),$o),
0.00/0.39	                                    'const/sets/SUBSET'(A),A0),
0.00/0.39	                     A1) <=>
0.00/0.39	      (![A2:A]:
0.00/0.39	         (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.39	                         app_encode_app(A,
0.00/0.39	                                        app_encode_fun(app_encode_fun(A,$o),
0.00/0.39	                                                       $o),
0.00/0.39	                                        'const/sets/IN'(A),A2),
0.00/0.39	                         A0) =>
0.00/0.39	          app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.39	                         app_encode_app(A,
0.00/0.39	                                        app_encode_fun(app_encode_fun(A,$o),
0.00/0.39	                                                       $o),
0.00/0.39	                                        'const/sets/IN'(A),A2),
0.00/0.39	                         A1)))))).
0.00/0.39	tff('9', plain,
0.00/0.39	    ![X16 : $tType, X17 : X16, X18 : app_encode_fun(X16, $o), 
0.00/0.39	      X19 : app_encode_fun(X16, $o)]:
0.00/0.39	      (~ app_encode_app(app_encode_fun(X16, $o), $o, 
0.00/0.39	           app_encode_app(X16, app_encode_fun(app_encode_fun(X16, $o), $o), 
0.00/0.39	             'const/sets/IN'(X16), X17), X18)
0.00/0.39	       | app_encode_app(app_encode_fun(X16, $o), $o, 
0.00/0.39	           app_encode_app(X16, app_encode_fun(app_encode_fun(X16, $o), $o), 
0.00/0.39	             'const/sets/IN'(X16), X17), X19)
0.00/0.39	       | ~ app_encode_app(app_encode_fun(X16, $o), $o, 
0.00/0.39	             app_encode_app(app_encode_fun(X16, $o), 
0.00/0.39	               app_encode_fun(app_encode_fun(X16, $o), $o), 
0.00/0.39	               'const/sets/SUBSET'(X16), X18), X19)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_14])).
0.00/0.39	tff('10', plain,
0.00/0.39	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0, 
0.00/0.39	      X3 : app_encode_fun(X0, $o)]:
0.00/0.39	      (~ $true
0.00/0.39	       | ~ app_encode_app(X0, $o, X1, X2)
0.00/0.39	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.39	             app_encode_app(app_encode_fun(X0, $o), 
0.00/0.39	               app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.39	               'const/sets/SUBSET'(X0), X1), X3)
0.00/0.39	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.39	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.39	             'const/sets/IN'(X0), X2), X3)),
0.00/0.39	    inference('sup-', [status(thm)], ['8', '9'])).
0.00/0.39	tff('11', plain,
0.00/0.39	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0, 
0.00/0.39	      X3 : app_encode_fun(X0, $o)]:
0.00/0.39	      (app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.39	         app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.39	           'const/sets/IN'(X0), X2), X3)
0.00/0.39	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.39	             app_encode_app(app_encode_fun(X0, $o), 
0.00/0.39	               app_encode_fun(app_encode_fun(X0, $o), $o), 
0.00/0.39	               'const/sets/SUBSET'(X0), X1), X3)
0.00/0.39	       | ~ app_encode_app(X0, $o, X1, X2)),
0.00/0.39	    inference('simplify', [status(thm)], ['10'])).
0.00/0.39	tff('12', plain,
0.00/0.39	    ![X0 : 'type/realax/real']:
0.00/0.39	      (~ $true
0.00/0.39	       | ~ app_encode_app('type/realax/real', $o, sk_A, X0)
0.00/0.39	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.39	             'const/sets/IN'('type/realax/real'), X0), sk_A0)),
0.00/0.39	    inference('sup-', [status(thm)], ['7', '11'])).
0.00/0.39	tff('13', plain,
0.00/0.39	    ![X0 : 'type/realax/real']:
0.00/0.39	      (app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.39	         app_encode_app('type/realax/real', 
0.00/0.39	           app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.39	           'const/sets/IN'('type/realax/real'), X0), sk_A0)
0.00/0.39	       | ~ app_encode_app('type/realax/real', $o, sk_A, X0)),
0.00/0.39	    inference('simplify', [status(thm)], ['12'])).
0.00/0.39	tff('14', plain,
0.00/0.39	    ![X0 : 'type/realax/real']:
0.00/0.39	      (~ $true
0.00/0.39	       | ~ app_encode_app('type/realax/real', $o, sk_A, X0)
0.00/0.39	       | app_encode_app('type/realax/real', $o, sk_A0, X0)),
0.00/0.39	    inference('sup-', [status(thm)], ['13', '4'])).
0.00/0.39	tff('15', plain,
0.00/0.39	    ![X0 : 'type/realax/real']:
0.00/0.39	      (app_encode_app('type/realax/real', $o, sk_A0, X0)
0.00/0.39	       | ~ app_encode_app('type/realax/real', $o, sk_A, X0)),
0.00/0.39	    inference('simplify', [status(thm)], ['14'])).
0.00/0.39	tff(zf_stmt_9, axiom,
0.00/0.39	  (![A:app_encode_fun('type/realax/real',$o),A0:'type/realax/real']:
0.00/0.39	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
0.00/0.39	       (![A1:'type/realax/real']:
0.00/0.39	          (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.39	                          app_encode_app('type/realax/real',
0.00/0.39	                                         app_encode_fun(app_encode_fun(
0.00/0.39	                                                        'type/realax/real',$o),
0.00/0.39	                                                        $o),
0.00/0.39	                                         'const/sets/IN'('type/realax/real'),
0.00/0.39	                                         A1),
0.00/0.39	                          A) =>
0.00/0.39	           app_encode_app('type/realax/real',$o,
0.00/0.39	                          app_encode_app('type/realax/real',
0.00/0.39	                                         app_encode_fun('type/realax/real',$o),
0.00/0.39	                                         'const/realax/real_le',A1),
0.00/0.39	                          A0)))) =>
0.00/0.39	      app_encode_app('type/realax/real',$o,
0.00/0.39	                     app_encode_app('type/realax/real',
0.00/0.39	                                    app_encode_fun('type/realax/real',$o),
0.00/0.39	                                    'const/realax/real_le',
0.00/0.39	                                    app_encode_app(app_encode_fun('type/realax/real',
0.00/0.39	                                                                  $o),
0.00/0.39	                                                   'type/realax/real',
0.00/0.39	                                                   'const/sets/sup',A)),
0.00/0.39	                     A0)))).
0.00/0.39	tff('16', plain,
0.00/0.39	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.39	      (X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.39	             'const/sets/IN'('type/realax/real'), sk_A1(X1, X0)), X0)
0.00/0.39	       | app_encode_app('type/realax/real', $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	               'type/realax/real', 'const/sets/sup', X0)), X1)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.00/0.39	tff('17', plain,
0.00/0.39	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.39	      (~ $true
0.00/0.39	       | app_encode_app('type/realax/real', $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	               'type/realax/real', 'const/sets/sup', X0)), X1)
0.00/0.39	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | app_encode_app('type/realax/real', $o, X0, sk_A1(X1, X0))),
0.00/0.39	    inference('sup-', [status(thm)], ['16', '4'])).
0.00/0.39	tff('18', plain,
0.00/0.39	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.39	      (app_encode_app('type/realax/real', $o, X0, sk_A1(X1, X0))
0.00/0.39	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | app_encode_app('type/realax/real', $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	               'type/realax/real', 'const/sets/sup', X0)), X1)),
0.00/0.39	    inference('simplify', [status(thm)], ['17'])).
0.00/0.39	tff(zf_stmt_15, axiom,
0.00/0.39	  (![A:app_encode_fun('type/realax/real',$o)]:
0.00/0.39	     (((?[A0:'type/realax/real']:
0.00/0.39	          (![A1:'type/realax/real']:
0.00/0.39	             (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.39	                             app_encode_app('type/realax/real',
0.00/0.39	                                            app_encode_fun(app_encode_fun(
0.00/0.39	                                                           'type/realax/real',
0.00/0.39	                                                           $o),$o),
0.00/0.39	                                            'const/sets/IN'('type/realax/real'),
0.00/0.39	                                            A1),
0.00/0.39	                             A) =>
0.00/0.39	              app_encode_app('type/realax/real',$o,
0.00/0.39	                             app_encode_app('type/realax/real',
0.00/0.39	                                            app_encode_fun('type/realax/real',
0.00/0.39	                                                           $o),
0.00/0.39	                                            'const/realax/real_le',A1),
0.00/0.39	                             A0)))) & 
0.00/0.39	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
0.00/0.39	      ((![A0:'type/realax/real']:
0.00/0.39	          ((![A1:'type/realax/real']:
0.00/0.39	              (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.39	                              app_encode_app('type/realax/real',
0.00/0.39	                                             app_encode_fun(app_encode_fun(
0.00/0.39	                                                            'type/realax/real',
0.00/0.39	                                                            $o),$o),
0.00/0.39	                                             'const/sets/IN'('type/realax/real'),
0.00/0.39	                                             A1),
0.00/0.39	                              A) =>
0.00/0.39	               app_encode_app('type/realax/real',$o,
0.00/0.39	                              app_encode_app('type/realax/real',
0.00/0.39	                                             app_encode_fun('type/realax/real',
0.00/0.39	                                                            $o),
0.00/0.39	                                             'const/realax/real_le',A1),
0.00/0.39	                              A0))) =>
0.00/0.39	           app_encode_app('type/realax/real',$o,
0.00/0.39	                          app_encode_app('type/realax/real',
0.00/0.39	                                         app_encode_fun('type/realax/real',$o),
0.00/0.39	                                         'const/realax/real_le',
0.00/0.39	                                         app_encode_app(app_encode_fun(
0.00/0.39	                                                        'type/realax/real',$o),
0.00/0.39	                                                        'type/realax/real',
0.00/0.39	                                                        'const/sets/sup',A)),
0.00/0.39	                          A0))) & 
0.00/0.39	       (![A0:'type/realax/real']:
0.00/0.39	          (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.39	                          app_encode_app('type/realax/real',
0.00/0.39	                                         app_encode_fun(app_encode_fun(
0.00/0.39	                                                        'type/realax/real',$o),
0.00/0.39	                                                        $o),
0.00/0.39	                                         'const/sets/IN'('type/realax/real'),
0.00/0.39	                                         A0),
0.00/0.39	                          A) =>
0.00/0.39	           app_encode_app('type/realax/real',$o,
0.00/0.39	                          app_encode_app('type/realax/real',
0.00/0.39	                                         app_encode_fun('type/realax/real',$o),
0.00/0.39	                                         'const/realax/real_le',A0),
0.00/0.39	                          app_encode_app(app_encode_fun('type/realax/real',$o),
0.00/0.39	                                         'type/realax/real','const/sets/sup',
0.00/0.39	                                         A)))))))).
0.00/0.39	tff(zf_stmt_1, axiom,
0.00/0.39	  ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.39	                   app_encode_app('type/realax/real',
0.00/0.39	                                  app_encode_fun(app_encode_fun('type/realax/real',
0.00/0.39	                                                                $o),
0.00/0.39	                                                 $o),
0.00/0.39	                                  'const/sets/IN'('type/realax/real'),A1),
0.00/0.39	                   A) =>
0.00/0.39	    app_encode_app('type/realax/real',$o,
0.00/0.39	                   app_encode_app('type/realax/real',
0.00/0.39	                                  app_encode_fun('type/realax/real',$o),
0.00/0.39	                                  'const/realax/real_le',A1),
0.00/0.39	                   A0)) =>
0.00/0.39	   zip_tseitin0(A1,A0,A))).
0.00/0.39	tff('19', plain,
0.00/0.39	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
0.00/0.39	      X23 : app_encode_fun('type/realax/real', $o)]:
0.00/0.39	      (zip_tseitin0(X21, X22, X23)
0.00/0.39	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.39	             'const/sets/IN'('type/realax/real'), X21), X23)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.00/0.39	tff(zf_stmt_2, type, zip_tseitin2 :
0.00/0.39	    app_encode_fun('type/realax/real',$o) > $o).
0.00/0.39	tff(zf_stmt_3, axiom,
0.00/0.39	  (zip_tseitin2(A) =>
0.00/0.39	   ((![A0:'type/realax/real']:
0.00/0.39	       (app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.39	                       app_encode_app('type/realax/real',
0.00/0.39	                                      app_encode_fun(app_encode_fun('type/realax/real',
0.00/0.39	                                                                    $o),
0.00/0.39	                                                     $o),
0.00/0.39	                                      'const/sets/IN'('type/realax/real'),A0),
0.00/0.39	                       A) =>
0.00/0.39	        app_encode_app('type/realax/real',$o,
0.00/0.39	                       app_encode_app('type/realax/real',
0.00/0.39	                                      app_encode_fun('type/realax/real',$o),
0.00/0.39	                                      'const/realax/real_le',A0),
0.00/0.39	                       app_encode_app(app_encode_fun('type/realax/real',$o),
0.00/0.39	                                      'type/realax/real','const/sets/sup',A)))) & 
0.00/0.39	    (![A0:'type/realax/real']:
0.00/0.39	       ((![A1:'type/realax/real']: zip_tseitin1(A1,A0,A)) =>
0.00/0.39	        app_encode_app('type/realax/real',$o,
0.00/0.39	                       app_encode_app('type/realax/real',
0.00/0.39	                                      app_encode_fun('type/realax/real',$o),
0.00/0.39	                                      'const/realax/real_le',
0.00/0.39	                                      app_encode_app(app_encode_fun('type/realax/real',
0.00/0.39	                                                                    $o),
0.00/0.39	                                                     'type/realax/real',
0.00/0.39	                                                     'const/sets/sup',A)),
0.00/0.39	                       A0)))))).
0.00/0.39	tff(zf_stmt_4, type, zip_tseitin1 :
0.00/0.39	    ('type/realax/real' * 
0.00/0.39	     'type/realax/real' * 
0.00/0.39	     app_encode_fun('type/realax/real',$o)) > $o).
0.00/0.39	tff(zf_stmt_5, axiom,
0.00/0.39	  ((app_encode_app(app_encode_fun('type/realax/real',$o),$o,
0.00/0.39	                   app_encode_app('type/realax/real',
0.00/0.39	                                  app_encode_fun(app_encode_fun('type/realax/real',
0.00/0.39	                                                                $o),
0.00/0.39	                                                 $o),
0.00/0.39	                                  'const/sets/IN'('type/realax/real'),A1),
0.00/0.39	                   A) =>
0.00/0.39	    app_encode_app('type/realax/real',$o,
0.00/0.39	                   app_encode_app('type/realax/real',
0.00/0.39	                                  app_encode_fun('type/realax/real',$o),
0.00/0.39	                                  'const/realax/real_le',A1),
0.00/0.39	                   A0)) =>
0.00/0.39	   zip_tseitin1(A1,A0,A))).
0.00/0.39	tff(zf_stmt_6, type, zip_tseitin0 :
0.00/0.39	    ('type/realax/real' * 
0.00/0.39	     'type/realax/real' * 
0.00/0.39	     app_encode_fun('type/realax/real',$o)) > $o).
0.00/0.39	tff(zf_stmt_7, axiom,
0.00/0.39	  (![A:app_encode_fun('type/realax/real',$o)]:
0.00/0.39	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
0.00/0.39	       (?[A0:'type/realax/real']:
0.00/0.39	          (![A1:'type/realax/real']: zip_tseitin0(A1,A0,A)))) =>
0.00/0.39	      zip_tseitin2(A)))).
0.00/0.39	tff('20', plain,
0.00/0.39	    ![X28 : app_encode_fun('type/realax/real', $o), X29 : 'type/realax/real']:
0.00/0.39	      (zip_tseitin2(X28)
0.00/0.39	       | ~ zip_tseitin0(sk_A12(X29, X28), X29, X28)
0.00/0.39	       | X28 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_7])).
0.00/0.39	tff('21', plain,
0.00/0.39	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.39	      (~ $true
0.00/0.39	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.39	             'const/sets/IN'('type/realax/real'), sk_A12(X1, X0)), X0)
0.00/0.39	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | zip_tseitin2(X0)),
0.00/0.39	    inference('sup-', [status(thm)], ['19', '20'])).
0.00/0.39	tff('22', plain,
0.00/0.39	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.39	      (zip_tseitin2(X0)
0.00/0.39	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.39	             'const/sets/IN'('type/realax/real'), sk_A12(X1, X0)), X0)),
0.00/0.39	    inference('simplify', [status(thm)], ['21'])).
0.00/0.39	tff('23', plain,
0.00/0.39	    ![X30 : 'type/realax/real']:
0.00/0.39	      (app_encode_app('type/realax/real', $o, 
0.00/0.39	         app_encode_app('type/realax/real', 
0.00/0.39	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	           X30), sk_A13)
0.00/0.39	       | ~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.39	             app_encode_app('type/realax/real', 
0.00/0.39	               app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.39	               'const/sets/IN'('type/realax/real'), X30), sk_A0)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.39	tff('24', plain,
0.00/0.39	    ![X0 : 'type/realax/real']:
0.00/0.39	      (~ $true
0.00/0.39	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | zip_tseitin2(sk_A0)
0.00/0.39	       | app_encode_app('type/realax/real', $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	             sk_A12(X0, sk_A0)), sk_A13)),
0.00/0.39	    inference('sup-', [status(thm)], ['22', '23'])).
0.00/0.39	tff('25', plain,
0.00/0.39	    ![X0 : 'type/realax/real']:
0.00/0.39	      (app_encode_app('type/realax/real', $o, 
0.00/0.39	         app_encode_app('type/realax/real', 
0.00/0.39	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	           sk_A12(X0, sk_A0)), sk_A13)
0.00/0.39	       | zip_tseitin2(sk_A0)
0.00/0.39	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.39	    inference('simplify', [status(thm)], ['24'])).
0.00/0.39	tff('26', plain,
0.00/0.39	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
0.00/0.39	      X23 : app_encode_fun('type/realax/real', $o)]:
0.00/0.39	      (zip_tseitin0(X21, X22, X23)
0.00/0.39	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.39	             app_encode_app('type/realax/real', 
0.00/0.39	               app_encode_fun('type/realax/real', $o), 
0.00/0.39	               'const/realax/real_le', X21), X22)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.00/0.39	tff('27', plain,
0.00/0.39	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.39	      (~ $true
0.00/0.39	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.39	             app_encode_app('type/realax/real', 
0.00/0.39	               app_encode_fun('type/realax/real', $o), 
0.00/0.39	               'const/realax/real_le', sk_A12(X1, X0)), X1)
0.00/0.39	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | zip_tseitin2(X0)),
0.00/0.39	    inference('sup-', [status(thm)], ['26', '20'])).
0.00/0.39	tff('28', plain,
0.00/0.39	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.39	      (zip_tseitin2(X0)
0.00/0.39	       | X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.39	             app_encode_app('type/realax/real', 
0.00/0.39	               app_encode_fun('type/realax/real', $o), 
0.00/0.39	               'const/realax/real_le', sk_A12(X1, X0)), X1)),
0.00/0.39	    inference('simplify', [status(thm)], ['27'])).
0.00/0.39	tff('29', plain,
0.00/0.39	    (~ $true
0.00/0.39	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	     | zip_tseitin2(sk_A0)
0.00/0.39	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	     | zip_tseitin2(sk_A0)),
0.00/0.39	    inference('sup-', [status(thm)], ['25', '28'])).
0.00/0.39	tff('30', plain,
0.00/0.39	    (zip_tseitin2(sk_A0) | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.39	    inference('simplify', [status(thm)], ['29'])).
0.00/0.39	tff('31', plain,
0.00/0.39	    ![X23 : app_encode_fun('type/realax/real', $o), X26 : 'type/realax/real']:
0.00/0.39	      (~ app_encode_app(app_encode_fun('type/realax/real', $o), $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun(app_encode_fun('type/realax/real', $o), $o), 
0.00/0.39	             'const/sets/IN'('type/realax/real'), X26), X23)
0.00/0.39	       | app_encode_app('type/realax/real', $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	             X26), 
0.00/0.39	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	             'type/realax/real', 'const/sets/sup', X23))
0.00/0.39	       | ~ zip_tseitin2(X23)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_3])).
0.00/0.39	tff('32', plain,
0.00/0.39	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.39	      (~ $true
0.00/0.39	       | ~ app_encode_app('type/realax/real', $o, X0, X1)
0.00/0.39	       | ~ zip_tseitin2(X0)
0.00/0.39	       | app_encode_app('type/realax/real', $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	             X1), 
0.00/0.39	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	             'type/realax/real', 'const/sets/sup', X0))),
0.00/0.39	    inference('sup-', [status(thm)], ['8', '31'])).
0.00/0.39	tff('33', plain,
0.00/0.39	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.39	      (app_encode_app('type/realax/real', $o, 
0.00/0.39	         app_encode_app('type/realax/real', 
0.00/0.39	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	           X1), 
0.00/0.39	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	           'type/realax/real', 'const/sets/sup', X0))
0.00/0.39	       | ~ zip_tseitin2(X0)
0.00/0.39	       | ~ app_encode_app('type/realax/real', $o, X0, X1)),
0.00/0.39	    inference('simplify', [status(thm)], ['32'])).
0.00/0.39	tff('34', plain,
0.00/0.39	    ![X0 : 'type/realax/real']:
0.00/0.39	      (~ $true
0.00/0.39	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | ~ app_encode_app('type/realax/real', $o, sk_A0, X0)
0.00/0.39	       | app_encode_app('type/realax/real', $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	             X0), 
0.00/0.39	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	             'type/realax/real', 'const/sets/sup', sk_A0))),
0.00/0.39	    inference('sup-', [status(thm)], ['30', '33'])).
0.00/0.39	tff('35', plain,
0.00/0.39	    ![X0 : 'type/realax/real']:
0.00/0.39	      (app_encode_app('type/realax/real', $o, 
0.00/0.39	         app_encode_app('type/realax/real', 
0.00/0.39	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	           X0), 
0.00/0.39	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	           'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.39	       | ~ app_encode_app('type/realax/real', $o, sk_A0, X0)
0.00/0.39	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.39	    inference('simplify', [status(thm)], ['34'])).
0.00/0.39	tff('36', plain,
0.00/0.39	    ![X0 : 'type/realax/real']:
0.00/0.39	      (~ $true
0.00/0.39	       | ~ app_encode_app('type/realax/real', $o, sk_A, X0)
0.00/0.39	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | app_encode_app('type/realax/real', $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	             X0), 
0.00/0.39	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	             'type/realax/real', 'const/sets/sup', sk_A0))),
0.00/0.39	    inference('sup-', [status(thm)], ['15', '35'])).
0.00/0.39	tff('37', plain,
0.00/0.39	    ![X0 : 'type/realax/real']:
0.00/0.39	      (app_encode_app('type/realax/real', $o, 
0.00/0.39	         app_encode_app('type/realax/real', 
0.00/0.39	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	           X0), 
0.00/0.39	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	           'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.39	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | ~ app_encode_app('type/realax/real', $o, sk_A, X0)),
0.00/0.39	    inference('simplify', [status(thm)], ['36'])).
0.00/0.39	tff('38', plain,
0.00/0.39	    ![X0 : 'type/realax/real']:
0.00/0.39	      (~ $true
0.00/0.39	       | app_encode_app('type/realax/real', $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	               'type/realax/real', 'const/sets/sup', sk_A)), X0)
0.00/0.39	       | sk_A = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | app_encode_app('type/realax/real', $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	             sk_A1(X0, sk_A)), 
0.00/0.39	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	             'type/realax/real', 'const/sets/sup', sk_A0))),
0.00/0.39	    inference('sup-', [status(thm)], ['18', '37'])).
0.00/0.39	tff('39', plain,
0.00/0.39	    ![X0 : 'type/realax/real']:
0.00/0.39	      (app_encode_app('type/realax/real', $o, 
0.00/0.39	         app_encode_app('type/realax/real', 
0.00/0.39	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	           sk_A1(X0, sk_A)), 
0.00/0.39	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	           'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.39	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | sk_A = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | app_encode_app('type/realax/real', $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	               'type/realax/real', 'const/sets/sup', sk_A)), X0)),
0.00/0.39	    inference('simplify', [status(thm)], ['38'])).
0.00/0.39	tff('40', plain, sk_A != 'const/sets/EMPTY'('type/realax/real'),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.39	tff('41', plain,
0.00/0.39	    ![X0 : 'type/realax/real']:
0.00/0.39	      (app_encode_app('type/realax/real', $o, 
0.00/0.39	         app_encode_app('type/realax/real', 
0.00/0.39	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	           sk_A1(X0, sk_A)), 
0.00/0.39	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	           'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.39	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | app_encode_app('type/realax/real', $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	               'type/realax/real', 'const/sets/sup', sk_A)), X0)),
0.00/0.39	    inference('simplify_reflect-', [status(thm)], ['39', '40'])).
0.00/0.39	tff('42', plain,
0.00/0.39	    ![X0 : app_encode_fun('type/realax/real', $o), X1 : 'type/realax/real']:
0.00/0.39	      (X0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.39	             app_encode_app('type/realax/real', 
0.00/0.39	               app_encode_fun('type/realax/real', $o), 
0.00/0.39	               'const/realax/real_le', sk_A1(X1, X0)), X1)
0.00/0.39	       | app_encode_app('type/realax/real', $o, 
0.00/0.39	           app_encode_app('type/realax/real', 
0.00/0.39	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	             app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	               'type/realax/real', 'const/sets/sup', X0)), X1)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_9])).
0.00/0.39	tff('43', plain,
0.00/0.39	    (~ $true
0.00/0.39	     | app_encode_app('type/realax/real', $o, 
0.00/0.39	         app_encode_app('type/realax/real', 
0.00/0.39	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	             'type/realax/real', 'const/sets/sup', sk_A)), 
0.00/0.39	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	           'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.39	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	     | app_encode_app('type/realax/real', $o, 
0.00/0.39	         app_encode_app('type/realax/real', 
0.00/0.39	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	             'type/realax/real', 'const/sets/sup', sk_A)), 
0.00/0.39	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	           'type/realax/real', 'const/sets/sup', sk_A0))
0.00/0.39	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
0.00/0.39	    inference('sup-', [status(thm)], ['41', '42'])).
0.00/0.39	tff('44', plain,
0.00/0.39	    (sk_A = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	     | app_encode_app('type/realax/real', $o, 
0.00/0.39	         app_encode_app('type/realax/real', 
0.00/0.39	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	             'type/realax/real', 'const/sets/sup', sk_A)), 
0.00/0.39	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	           'type/realax/real', 'const/sets/sup', sk_A0))),
0.00/0.39	    inference('simplify', [status(thm)], ['43'])).
0.00/0.39	tff('45', plain,
0.00/0.39	    (sk_A0 = 'const/sets/EMPTY'('type/realax/real')
0.00/0.39	     | app_encode_app('type/realax/real', $o, 
0.00/0.39	         app_encode_app('type/realax/real', 
0.00/0.39	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	           app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	             'type/realax/real', 'const/sets/sup', sk_A)), 
0.00/0.39	         app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	           'type/realax/real', 'const/sets/sup', sk_A0))),
0.00/0.39	    inference('simplify_reflect-', [status(thm)], ['44', '40'])).
0.00/0.39	tff('46', plain,
0.00/0.39	    ~ app_encode_app('type/realax/real', $o, 
0.00/0.39	        app_encode_app('type/realax/real', 
0.00/0.39	          app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.39	          app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	            'type/realax/real', 'const/sets/sup', sk_A)), 
0.00/0.39	        app_encode_app(app_encode_fun('type/realax/real', $o), 
0.00/0.39	          'type/realax/real', 'const/sets/sup', sk_A0)),
0.00/0.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.39	tff('47', plain, sk_A0 = 'const/sets/EMPTY'('type/realax/real'),
0.00/0.39	    inference('clc', [status(thm)], ['45', '46'])).
0.00/0.39	tff('48', plain,
0.00/0.39	    ![X0 : 'type/realax/real']:
0.00/0.39	      (app_encode_app('type/realax/real', $o, 
0.00/0.39	         'const/sets/EMPTY'('type/realax/real'), X0)
0.00/0.39	       | ~ app_encode_app('type/realax/real', $o, sk_A, X0)),
0.00/0.39	    inference('demod', [status(thm)], ['15', '47'])).
0.00/0.39	tff('49', plain,
0.00/0.39	    ![X0 : $tType, X1 : X0]:
0.00/0.39	      (~ $true | ~ app_encode_app(X0, $o, 'const/sets/EMPTY'(X0), X1)),
0.00/0.39	    inference('sup-', [status(thm)], ['8', '1'])).
0.00/0.39	tff('50', plain,
0.00/0.39	    ![X0 : $tType, X1 : X0]:
0.00/0.39	      ~ app_encode_app(X0, $o, 'const/sets/EMPTY'(X0), X1),
0.00/0.39	    inference('simplify', [status(thm)], ['49'])).
0.00/0.39	tff('51', plain,
0.00/0.39	    ![X0 : 'type/realax/real']:
0.00/0.39	      ~ app_encode_app('type/realax/real', $o, sk_A, X0),
0.00/0.39	    inference('clc', [status(thm)], ['48', '50'])).
0.00/0.39	tff('52', plain, (~ $true | 'const/sets/EMPTY'('type/realax/real') = sk_A),
0.00/0.39	    inference('sup-', [status(thm)], ['6', '51'])).
0.00/0.39	tff('53', plain, 'const/sets/EMPTY'('type/realax/real') = sk_A,
0.00/0.39	    inference('simplify', [status(thm)], ['52'])).
0.00/0.39	tff('54', plain, $false,
0.00/0.39	    inference('simplify_reflect-', [status(thm)], ['53', '40'])).
0.00/0.39	
0.00/0.39	% SZS output end Refutation
0.00/0.39	EOF
