0.00/0.01	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : appext
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : kbo
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n075.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:39:24 CST 2018
0.00/0.26	% done 31 iterations in 0.056s
0.00/0.26	% SZS status Theorem for 'stdin'
0.00/0.26	% SZS output start Refutation
0.00/0.27	tff(zf_stmt_14, axiom,
0.00/0.27	  (![A:$tType,A0:app_encode_fun(A,$o)]:
0.00/0.27	     ((?[A1:A]:
0.00/0.27	         app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.27	                        app_encode_app(A,
0.00/0.27	                                       app_encode_fun(app_encode_fun(A,$o),$o),
0.00/0.27	                                       'const/sets/IN'(A),A1),
0.00/0.27	                        A0)) <=>
0.00/0.27	      (A0 != 'const/sets/EMPTY'(A))))).
0.00/0.27	tff('0', plain,
0.00/0.27	    ![X13 : $tType, X16 : app_encode_fun(X13, $o)]:
0.00/0.27	      (app_encode_app(app_encode_fun(X13, $o), $o, 
0.00/0.27	         app_encode_app(X13, app_encode_fun(app_encode_fun(X13, $o), $o), 
0.00/0.27	           'const/sets/IN'(X13), sk_A1(X13, X16)), X16)
0.00/0.27	       | X16 = 'const/sets/EMPTY'(X13)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_14])).
0.00/0.27	tff(zf_stmt_15, conjecture,
0.00/0.27	  (![A:$tType,A0:app_encode_fun(A,'type/realax/real'),
0.00/0.27	     A1:app_encode_fun(A,'type/realax/real'),A2:app_encode_fun(A,$o)]:
0.00/0.27	     ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A2) & 
0.00/0.27	       (A2 != 'const/sets/EMPTY'(A)) & 
0.00/0.27	       (![A3:A]:
0.00/0.27	          (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.27	                          app_encode_app(A,
0.00/0.27	                                         app_encode_fun(app_encode_fun(A,$o),
0.00/0.27	                                                        $o),
0.00/0.27	                                         'const/sets/IN'(A),A3),
0.00/0.27	                          A2) =>
0.00/0.27	           app_encode_app('type/realax/real',$o,
0.00/0.27	                          app_encode_app('type/realax/real',
0.00/0.27	                                         app_encode_fun('type/realax/real',$o),
0.00/0.27	                                         'const/realax/real_lt',
0.00/0.27	                                         app_encode_app(A,'type/realax/real',
0.00/0.27	                                                        A0,A3)),
0.00/0.27	                          app_encode_app(A,'type/realax/real',A1,A3))))) =>
0.00/0.27	      app_encode_app('type/realax/real',$o,
0.00/0.27	                     app_encode_app('type/realax/real',
0.00/0.27	                                    app_encode_fun('type/realax/real',$o),
0.00/0.27	                                    'const/realax/real_lt',
0.00/0.27	                                    app_encode_app(app_encode_fun(A,
0.00/0.27	                                                                  'type/realax/real'),
0.00/0.27	                                                   'type/realax/real',
0.00/0.27	                                                   app_encode_app(app_encode_fun(
0.00/0.27	                                                                  A,$o),
0.00/0.27	                                                                  app_encode_fun(
0.00/0.27	                                                                  app_encode_fun(
0.00/0.27	                                                                  A,
0.00/0.27	                                                                  'type/realax/real'),
0.00/0.27	                                                                  'type/realax/real'),
0.00/0.27	                                                                  'const/iterate/sum'(
0.00/0.27	                                                                  A),A2),
0.00/0.27	                                                   A0)),
0.00/0.27	                     app_encode_app(app_encode_fun(A,'type/realax/real'),
0.00/0.27	                                    'type/realax/real',
0.00/0.27	                                    app_encode_app(app_encode_fun(A,$o),
0.00/0.27	                                                   app_encode_fun(app_encode_fun(
0.00/0.27	                                                                  A,
0.00/0.27	                                                                  'type/realax/real'),
0.00/0.27	                                                                  'type/realax/real'),
0.00/0.27	                                                   'const/iterate/sum'(A),A2),
0.00/0.27	                                    A1))))).
0.00/0.27	tff(zf_stmt_0, negated_conjecture,
0.00/0.27	  (~
0.00/0.27	    (![A:$tType,A0:app_encode_fun(A,'type/realax/real'),
0.00/0.27	       A1:app_encode_fun(A,'type/realax/real'),A2:app_encode_fun(A,$o)]:
0.00/0.27	       ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A2) & 
0.00/0.27	         (A2 != 'const/sets/EMPTY'(A)) & 
0.00/0.27	         (![A3:A]:
0.00/0.27	            (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.27	                            app_encode_app(A,
0.00/0.27	                                           app_encode_fun(app_encode_fun(
0.00/0.27	                                                          A,$o),$o),
0.00/0.27	                                           'const/sets/IN'(A),A3),
0.00/0.27	                            A2) =>
0.00/0.27	             app_encode_app('type/realax/real',$o,
0.00/0.27	                            app_encode_app('type/realax/real',
0.00/0.27	                                           app_encode_fun('type/realax/real',
0.00/0.27	                                                          $o),
0.00/0.27	                                           'const/realax/real_lt',
0.00/0.27	                                           app_encode_app(A,
0.00/0.27	                                                          'type/realax/real',
0.00/0.27	                                                          A0,A3)),
0.00/0.27	                            app_encode_app(A,'type/realax/real',A1,A3))))) =>
0.00/0.27	        app_encode_app('type/realax/real',$o,
0.00/0.27	                       app_encode_app('type/realax/real',
0.00/0.27	                                      app_encode_fun('type/realax/real',$o),
0.00/0.27	                                      'const/realax/real_lt',
0.00/0.27	                                      app_encode_app(app_encode_fun(A,
0.00/0.27	                                                                    'type/realax/real'),
0.00/0.27	                                                     'type/realax/real',
0.00/0.27	                                                     app_encode_app(app_encode_fun(
0.00/0.27	                                                                    A,$o),
0.00/0.27	                                                                    app_encode_fun(
0.00/0.27	                                                                    app_encode_fun(
0.00/0.27	                                                                    A,
0.00/0.27	                                                                    'type/realax/real'),
0.00/0.27	                                                                    'type/realax/real'),
0.00/0.27	                                                                    'const/iterate/sum'(
0.00/0.27	                                                                    A),A2),
0.00/0.27	                                                     A0)),
0.00/0.27	                       app_encode_app(app_encode_fun(A,'type/realax/real'),
0.00/0.27	                                      'type/realax/real',
0.00/0.27	                                      app_encode_app(app_encode_fun(A,$o),
0.00/0.27	                                                     app_encode_fun(app_encode_fun(
0.00/0.27	                                                                    A,
0.00/0.27	                                                                    'type/realax/real'),
0.00/0.27	                                                                    'type/realax/real'),
0.00/0.27	                                                     'const/iterate/sum'(A),
0.00/0.27	                                                     A2),
0.00/0.27	                                      A1)))))).
0.00/0.27	tff('1', plain,
0.00/0.27	    ![X17 : sk_A]:
0.00/0.27	      (app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_lt', 
0.00/0.27	           app_encode_app(sk_A, 'type/realax/real', sk_A0, X17)), 
0.00/0.27	         app_encode_app(sk_A, 'type/realax/real', sk_A11, X17))
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), X17), sk_A2)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.27	tff(zf_stmt_13, axiom,
0.00/0.27	  (![A:'type/realax/real',A0:'type/realax/real']:
0.00/0.27	     (app_encode_app('type/realax/real',$o,
0.00/0.27	                     app_encode_app('type/realax/real',
0.00/0.27	                                    app_encode_fun('type/realax/real',$o),
0.00/0.27	                                    'const/realax/real_lt',A),
0.00/0.27	                     A0) =>
0.00/0.27	      app_encode_app('type/realax/real',$o,
0.00/0.27	                     app_encode_app('type/realax/real',
0.00/0.27	                                    app_encode_fun('type/realax/real',$o),
0.00/0.27	                                    'const/realax/real_le',A),
0.00/0.27	                     A0)))).
0.00/0.27	tff('2', plain,
0.00/0.27	    ![X11 : 'type/realax/real', X12 : 'type/realax/real']:
0.00/0.27	      (app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           X11), X12)
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_lt', X11), X12)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_13])).
0.00/0.27	tff(zf_stmt_12, axiom,
0.00/0.27	  (![A:$tType,A0:app_encode_fun(A,'type/realax/real'),
0.00/0.27	     A1:app_encode_fun(A,'type/realax/real'),A2:app_encode_fun(A,$o)]:
0.00/0.27	     ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A2) & 
0.00/0.27	       (![A3:A]:
0.00/0.27	          (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.27	                          app_encode_app(A,
0.00/0.27	                                         app_encode_fun(app_encode_fun(A,$o),
0.00/0.27	                                                        $o),
0.00/0.27	                                         'const/sets/IN'(A),A3),
0.00/0.27	                          A2) =>
0.00/0.27	           app_encode_app('type/realax/real',$o,
0.00/0.27	                          app_encode_app('type/realax/real',
0.00/0.27	                                         app_encode_fun('type/realax/real',$o),
0.00/0.27	                                         'const/realax/real_le',
0.00/0.27	                                         app_encode_app(A,'type/realax/real',
0.00/0.27	                                                        A0,A3)),
0.00/0.27	                          app_encode_app(A,'type/realax/real',A1,A3)))) & 
0.00/0.27	       (?[A3:A]:
0.00/0.27	          (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.27	                          app_encode_app(A,
0.00/0.27	                                         app_encode_fun(app_encode_fun(A,$o),
0.00/0.27	                                                        $o),
0.00/0.27	                                         'const/sets/IN'(A),A3),
0.00/0.27	                          A2) & 
0.00/0.27	           app_encode_app('type/realax/real',$o,
0.00/0.27	                          app_encode_app('type/realax/real',
0.00/0.27	                                         app_encode_fun('type/realax/real',$o),
0.00/0.27	                                         'const/realax/real_lt',
0.00/0.27	                                         app_encode_app(A,'type/realax/real',
0.00/0.27	                                                        A0,A3)),
0.00/0.27	                          app_encode_app(A,'type/realax/real',A1,A3))))) =>
0.00/0.27	      app_encode_app('type/realax/real',$o,
0.00/0.27	                     app_encode_app('type/realax/real',
0.00/0.27	                                    app_encode_fun('type/realax/real',$o),
0.00/0.27	                                    'const/realax/real_lt',
0.00/0.27	                                    app_encode_app(app_encode_fun(A,
0.00/0.27	                                                                  'type/realax/real'),
0.00/0.27	                                                   'type/realax/real',
0.00/0.27	                                                   app_encode_app(app_encode_fun(
0.00/0.27	                                                                  A,$o),
0.00/0.27	                                                                  app_encode_fun(
0.00/0.27	                                                                  app_encode_fun(
0.00/0.27	                                                                  A,
0.00/0.27	                                                                  'type/realax/real'),
0.00/0.27	                                                                  'type/realax/real'),
0.00/0.27	                                                                  'const/iterate/sum'(
0.00/0.27	                                                                  A),A2),
0.00/0.27	                                                   A0)),
0.00/0.27	                     app_encode_app(app_encode_fun(A,'type/realax/real'),
0.00/0.27	                                    'type/realax/real',
0.00/0.27	                                    app_encode_app(app_encode_fun(A,$o),
0.00/0.27	                                                   app_encode_fun(app_encode_fun(
0.00/0.27	                                                                  A,
0.00/0.27	                                                                  'type/realax/real'),
0.00/0.27	                                                                  'type/realax/real'),
0.00/0.27	                                                   'const/iterate/sum'(A),A2),
0.00/0.27	                                    A1))))).
0.00/0.27	tff('3', plain,
0.00/0.27	    ![X6 : $tType, X7 : app_encode_fun(X6, $o), 
0.00/0.27	      X8 : app_encode_fun(X6, 'type/realax/real'), 
0.00/0.27	      X9 : app_encode_fun(X6, 'type/realax/real'), X10 : X6]:
0.00/0.27	      (app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_lt', 
0.00/0.27	           app_encode_app(app_encode_fun(X6, 'type/realax/real'), 
0.00/0.27	             'type/realax/real', 
0.00/0.27	             app_encode_app(app_encode_fun(X6, $o), 
0.00/0.27	               app_encode_fun(app_encode_fun(X6, 'type/realax/real'), 
0.00/0.27	                 'type/realax/real'), 'const/iterate/sum'(X6), X7), X8)), 
0.00/0.27	         app_encode_app(app_encode_fun(X6, 'type/realax/real'), 
0.00/0.27	           'type/realax/real', 
0.00/0.27	           app_encode_app(app_encode_fun(X6, $o), 
0.00/0.27	             app_encode_fun(app_encode_fun(X6, 'type/realax/real'), 
0.00/0.27	               'type/realax/real'), 'const/iterate/sum'(X6), X7), X9))
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_lt', 
0.00/0.27	               app_encode_app(X6, 'type/realax/real', X8, X10)), 
0.00/0.27	             app_encode_app(X6, 'type/realax/real', X9, X10))
0.00/0.27	       | ~ app_encode_app(app_encode_fun(X6, $o), $o, 
0.00/0.27	             app_encode_app(X6, app_encode_fun(app_encode_fun(X6, $o), $o), 
0.00/0.27	               'const/sets/IN'(X6), X10), X7)
0.00/0.27	       | app_encode_app(app_encode_fun(X6, $o), $o, 
0.00/0.27	           app_encode_app(X6, app_encode_fun(app_encode_fun(X6, $o), $o), 
0.00/0.27	             'const/sets/IN'(X6), sk_A3(X6, X7, X9, X8)), X7)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(X6, $o), $o, 
0.00/0.27	             'const/sets/FINITE'(X6), X7)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_12])).
0.00/0.27	tff('4', plain,
0.00/0.27	    ![X0 : sk_A, X1 : app_encode_fun(sk_A, $o)]:
0.00/0.27	      (~ $true
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), X0), sk_A2)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             'const/sets/FINITE'(sk_A), X1)
0.00/0.27	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A3(sk_A, X1, sk_A11, sk_A0)), X1)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), X0), X1)
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_lt', 
0.00/0.27	             app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	               'type/realax/real', 
0.00/0.27	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	                 app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	                   'type/realax/real'), 'const/iterate/sum'(sk_A), X1), 
0.00/0.27	               sk_A0)), 
0.00/0.27	           app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	             'type/realax/real', 
0.00/0.27	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	                 'type/realax/real'), 'const/iterate/sum'(sk_A), X1), sk_A11))),
0.00/0.27	    inference('sup-', [status(thm)], ['1', '3'])).
0.00/0.27	tff('5', plain,
0.00/0.27	    ![X0 : sk_A, X1 : app_encode_fun(sk_A, $o)]:
0.00/0.27	      (app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_lt', 
0.00/0.27	           app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	             'type/realax/real', 
0.00/0.27	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	                 'type/realax/real'), 'const/iterate/sum'(sk_A), X1), sk_A0)), 
0.00/0.27	         app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	           'type/realax/real', 
0.00/0.27	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	               'type/realax/real'), 'const/iterate/sum'(sk_A), X1), sk_A11))
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), X0), X1)
0.00/0.27	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A3(sk_A, X1, sk_A11, sk_A0)), X1)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             'const/sets/FINITE'(sk_A), X1)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), X0), sk_A2)),
0.00/0.27	    inference('simplify', [status(thm)], ['4'])).
0.00/0.27	tff('6', plain,
0.00/0.27	    ![X0 : app_encode_fun(sk_A, $o)]:
0.00/0.27	      (~ $true
0.00/0.27	       | X0 = 'const/sets/EMPTY'(sk_A)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), sk_A1(sk_A, X0)), sk_A2)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             'const/sets/FINITE'(sk_A), X0)
0.00/0.27	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A3(sk_A, X0, sk_A11, sk_A0)), X0)
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_lt', 
0.00/0.27	             app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	               'type/realax/real', 
0.00/0.27	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	                 app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	                   'type/realax/real'), 'const/iterate/sum'(sk_A), X0), 
0.00/0.27	               sk_A0)), 
0.00/0.27	           app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	             'type/realax/real', 
0.00/0.27	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	                 'type/realax/real'), 'const/iterate/sum'(sk_A), X0), sk_A11))),
0.00/0.27	    inference('sup-', [status(thm)], ['0', '5'])).
0.00/0.27	tff('7', plain,
0.00/0.27	    ![X0 : app_encode_fun(sk_A, $o)]:
0.00/0.27	      (app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_lt', 
0.00/0.27	           app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	             'type/realax/real', 
0.00/0.27	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	                 'type/realax/real'), 'const/iterate/sum'(sk_A), X0), sk_A0)), 
0.00/0.27	         app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	           'type/realax/real', 
0.00/0.27	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	               'type/realax/real'), 'const/iterate/sum'(sk_A), X0), sk_A11))
0.00/0.27	       | app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A3(sk_A, X0, sk_A11, sk_A0)), X0)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             'const/sets/FINITE'(sk_A), X0)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), sk_A1(sk_A, X0)), sk_A2)
0.00/0.27	       | X0 = 'const/sets/EMPTY'(sk_A)),
0.00/0.27	    inference('simplify', [status(thm)], ['6'])).
0.00/0.27	tff('8', plain,
0.00/0.27	    ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	        app_encode_app('type/realax/real', 
0.00/0.27	          app_encode_fun('type/realax/real', $o), 'const/realax/real_lt', 
0.00/0.27	          app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	            'type/realax/real', 
0.00/0.27	            app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	              app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	                'type/realax/real'), 'const/iterate/sum'(sk_A), sk_A2), 
0.00/0.27	            sk_A0)), 
0.00/0.27	        app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	          'type/realax/real', 
0.00/0.27	          app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	            app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	              'type/realax/real'), 'const/iterate/sum'(sk_A), sk_A2), sk_A11)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.27	tff('9', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | sk_A2 = 'const/sets/EMPTY'(sk_A)
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A1(sk_A, sk_A2)), sk_A2)
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           'const/sets/FINITE'(sk_A), sk_A2)
0.00/0.27	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	           'const/sets/IN'(sk_A), sk_A3(sk_A, sk_A2, sk_A11, sk_A0)), sk_A2)),
0.00/0.27	    inference('sup-', [status(thm)], ['7', '8'])).
0.00/0.27	tff('10', plain,
0.00/0.27	    app_encode_app(app_encode_fun(sk_A, $o), $o, 'const/sets/FINITE'(sk_A), 
0.00/0.27	      sk_A2),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.27	tff('11', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | sk_A2 = 'const/sets/EMPTY'(sk_A)
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A1(sk_A, sk_A2)), sk_A2)
0.00/0.27	     | ~ $true
0.00/0.27	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	           'const/sets/IN'(sk_A), sk_A3(sk_A, sk_A2, sk_A11, sk_A0)), sk_A2)),
0.00/0.27	    inference('demod', [status(thm)], ['9', '10'])).
0.00/0.27	tff('12', plain,
0.00/0.27	    (app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	       app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	         'const/sets/IN'(sk_A), sk_A3(sk_A, sk_A2, sk_A11, sk_A0)), sk_A2)
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A1(sk_A, sk_A2)), sk_A2)
0.00/0.27	     | sk_A2 = 'const/sets/EMPTY'(sk_A)),
0.00/0.27	    inference('simplify', [status(thm)], ['11'])).
0.00/0.27	tff('13', plain, sk_A2 != 'const/sets/EMPTY'(sk_A),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.27	tff('14', plain,
0.00/0.27	    (app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	       app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	         'const/sets/IN'(sk_A), sk_A3(sk_A, sk_A2, sk_A11, sk_A0)), sk_A2)
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A1(sk_A, sk_A2)), sk_A2)),
0.00/0.27	    inference('simplify_reflect-', [status(thm)], ['12', '13'])).
0.00/0.27	tff('15', plain,
0.00/0.27	    ![X6 : $tType, X7 : app_encode_fun(X6, $o), 
0.00/0.27	      X8 : app_encode_fun(X6, 'type/realax/real'), 
0.00/0.27	      X9 : app_encode_fun(X6, 'type/realax/real'), X10 : X6]:
0.00/0.27	      (app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_lt', 
0.00/0.27	           app_encode_app(app_encode_fun(X6, 'type/realax/real'), 
0.00/0.27	             'type/realax/real', 
0.00/0.27	             app_encode_app(app_encode_fun(X6, $o), 
0.00/0.27	               app_encode_fun(app_encode_fun(X6, 'type/realax/real'), 
0.00/0.27	                 'type/realax/real'), 'const/iterate/sum'(X6), X7), X8)), 
0.00/0.27	         app_encode_app(app_encode_fun(X6, 'type/realax/real'), 
0.00/0.27	           'type/realax/real', 
0.00/0.27	           app_encode_app(app_encode_fun(X6, $o), 
0.00/0.27	             app_encode_fun(app_encode_fun(X6, 'type/realax/real'), 
0.00/0.27	               'type/realax/real'), 'const/iterate/sum'(X6), X7), X9))
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_lt', 
0.00/0.27	               app_encode_app(X6, 'type/realax/real', X8, X10)), 
0.00/0.27	             app_encode_app(X6, 'type/realax/real', X9, X10))
0.00/0.27	       | ~ app_encode_app(app_encode_fun(X6, $o), $o, 
0.00/0.27	             app_encode_app(X6, app_encode_fun(app_encode_fun(X6, $o), $o), 
0.00/0.27	               'const/sets/IN'(X6), X10), X7)
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', 
0.00/0.27	               app_encode_app(X6, 'type/realax/real', X8, 
0.00/0.27	                 sk_A3(X6, X7, X9, X8))), 
0.00/0.27	             app_encode_app(X6, 'type/realax/real', X9, 
0.00/0.27	               sk_A3(X6, X7, X9, X8)))
0.00/0.27	       | ~ app_encode_app(app_encode_fun(X6, $o), $o, 
0.00/0.27	             'const/sets/FINITE'(X6), X7)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_12])).
0.00/0.27	tff('16', plain,
0.00/0.27	    ![X0 : sk_A, X1 : app_encode_fun(sk_A, $o)]:
0.00/0.27	      (~ $true
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), X0), sk_A2)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             'const/sets/FINITE'(sk_A), X1)
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', 
0.00/0.27	               app_encode_app(sk_A, 'type/realax/real', sk_A0, 
0.00/0.27	                 sk_A3(sk_A, X1, sk_A11, sk_A0))), 
0.00/0.27	             app_encode_app(sk_A, 'type/realax/real', sk_A11, 
0.00/0.27	               sk_A3(sk_A, X1, sk_A11, sk_A0)))
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), X0), X1)
0.00/0.27	       | app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_lt', 
0.00/0.27	             app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	               'type/realax/real', 
0.00/0.27	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	                 app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	                   'type/realax/real'), 'const/iterate/sum'(sk_A), X1), 
0.00/0.27	               sk_A0)), 
0.00/0.27	           app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	             'type/realax/real', 
0.00/0.27	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	                 'type/realax/real'), 'const/iterate/sum'(sk_A), X1), sk_A11))),
0.00/0.27	    inference('sup-', [status(thm)], ['1', '15'])).
0.00/0.27	tff('17', plain,
0.00/0.27	    ![X0 : sk_A, X1 : app_encode_fun(sk_A, $o)]:
0.00/0.27	      (app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_lt', 
0.00/0.27	           app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	             'type/realax/real', 
0.00/0.27	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	                 'type/realax/real'), 'const/iterate/sum'(sk_A), X1), sk_A0)), 
0.00/0.27	         app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	           'type/realax/real', 
0.00/0.27	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	               'type/realax/real'), 'const/iterate/sum'(sk_A), X1), sk_A11))
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), X0), X1)
0.00/0.27	       | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	             app_encode_app('type/realax/real', 
0.00/0.27	               app_encode_fun('type/realax/real', $o), 
0.00/0.27	               'const/realax/real_le', 
0.00/0.27	               app_encode_app(sk_A, 'type/realax/real', sk_A0, 
0.00/0.27	                 sk_A3(sk_A, X1, sk_A11, sk_A0))), 
0.00/0.27	             app_encode_app(sk_A, 'type/realax/real', sk_A11, 
0.00/0.27	               sk_A3(sk_A, X1, sk_A11, sk_A0)))
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             'const/sets/FINITE'(sk_A), X1)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), X0), sk_A2)),
0.00/0.27	    inference('simplify', [status(thm)], ['16'])).
0.00/0.27	tff('18', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A1(sk_A, sk_A2)), sk_A2)
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A3(sk_A, sk_A2, sk_A11, sk_A0)), 
0.00/0.27	           sk_A2)
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           'const/sets/FINITE'(sk_A), sk_A2)
0.00/0.27	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             app_encode_app(sk_A, 'type/realax/real', sk_A0, 
0.00/0.27	               sk_A3(sk_A, sk_A2, sk_A11, sk_A0))), 
0.00/0.27	           app_encode_app(sk_A, 'type/realax/real', sk_A11, 
0.00/0.27	             sk_A3(sk_A, sk_A2, sk_A11, sk_A0)))
0.00/0.27	     | app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_lt', 
0.00/0.27	           app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	             'type/realax/real', 
0.00/0.27	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	                 'type/realax/real'), 'const/iterate/sum'(sk_A), sk_A2), 
0.00/0.27	             sk_A0)), 
0.00/0.27	         app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	           'type/realax/real', 
0.00/0.27	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	               'type/realax/real'), 'const/iterate/sum'(sk_A), sk_A2), 
0.00/0.27	           sk_A11))),
0.00/0.27	    inference('sup-', [status(thm)], ['14', '17'])).
0.00/0.27	tff('19', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A1(sk_A, sk_A2)), sk_A2)
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A3(sk_A, sk_A2, sk_A11, sk_A0)), 
0.00/0.27	           sk_A2)
0.00/0.27	     | ~ $true
0.00/0.27	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             app_encode_app(sk_A, 'type/realax/real', sk_A0, 
0.00/0.27	               sk_A3(sk_A, sk_A2, sk_A11, sk_A0))), 
0.00/0.27	           app_encode_app(sk_A, 'type/realax/real', sk_A11, 
0.00/0.27	             sk_A3(sk_A, sk_A2, sk_A11, sk_A0)))
0.00/0.27	     | app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_lt', 
0.00/0.27	           app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	             'type/realax/real', 
0.00/0.27	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	                 'type/realax/real'), 'const/iterate/sum'(sk_A), sk_A2), 
0.00/0.27	             sk_A0)), 
0.00/0.27	         app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	           'type/realax/real', 
0.00/0.27	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	               'type/realax/real'), 'const/iterate/sum'(sk_A), sk_A2), 
0.00/0.27	           sk_A11))),
0.00/0.27	    inference('demod', [status(thm)], ['18', '10'])).
0.00/0.27	tff('20', plain,
0.00/0.27	    (app_encode_app('type/realax/real', $o, 
0.00/0.27	       app_encode_app('type/realax/real', 
0.00/0.27	         app_encode_fun('type/realax/real', $o), 'const/realax/real_lt', 
0.00/0.27	         app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	           'type/realax/real', 
0.00/0.27	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	               'type/realax/real'), 'const/iterate/sum'(sk_A), sk_A2), sk_A0)), 
0.00/0.27	       app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	         'type/realax/real', 
0.00/0.27	         app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	           app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.27	             'type/realax/real'), 'const/iterate/sum'(sk_A), sk_A2), sk_A11))
0.00/0.27	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             app_encode_app(sk_A, 'type/realax/real', sk_A0, 
0.00/0.27	               sk_A3(sk_A, sk_A2, sk_A11, sk_A0))), 
0.00/0.27	           app_encode_app(sk_A, 'type/realax/real', sk_A11, 
0.00/0.27	             sk_A3(sk_A, sk_A2, sk_A11, sk_A0)))
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A3(sk_A, sk_A2, sk_A11, sk_A0)), 
0.00/0.27	           sk_A2)
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A1(sk_A, sk_A2)), sk_A2)),
0.00/0.27	    inference('simplify', [status(thm)], ['19'])).
0.00/0.27	tff('21', plain,
0.00/0.27	    (~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	           'const/sets/IN'(sk_A), sk_A1(sk_A, sk_A2)), sk_A2)
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A3(sk_A, sk_A2, sk_A11, sk_A0)), 
0.00/0.27	           sk_A2)
0.00/0.27	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	             app_encode_app(sk_A, 'type/realax/real', sk_A0, 
0.00/0.27	               sk_A3(sk_A, sk_A2, sk_A11, sk_A0))), 
0.00/0.27	           app_encode_app(sk_A, 'type/realax/real', sk_A11, 
0.00/0.27	             sk_A3(sk_A, sk_A2, sk_A11, sk_A0)))),
0.00/0.27	    inference('clc', [status(thm)], ['20', '8'])).
0.00/0.27	tff('22', plain,
0.00/0.27	    (~ app_encode_app('type/realax/real', $o, 
0.00/0.27	         app_encode_app('type/realax/real', 
0.00/0.27	           app_encode_fun('type/realax/real', $o), 'const/realax/real_le', 
0.00/0.27	           app_encode_app(sk_A, 'type/realax/real', sk_A0, 
0.00/0.27	             sk_A3(sk_A, sk_A2, sk_A11, sk_A0))), 
0.00/0.27	         app_encode_app(sk_A, 'type/realax/real', sk_A11, 
0.00/0.27	           sk_A3(sk_A, sk_A2, sk_A11, sk_A0)))
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A1(sk_A, sk_A2)), sk_A2)),
0.00/0.27	    inference('clc', [status(thm)], ['21', '14'])).
0.00/0.27	tff('23', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_lt', 
0.00/0.27	             app_encode_app(sk_A, 'type/realax/real', sk_A0, 
0.00/0.27	               sk_A3(sk_A, sk_A2, sk_A11, sk_A0))), 
0.00/0.27	           app_encode_app(sk_A, 'type/realax/real', sk_A11, 
0.00/0.27	             sk_A3(sk_A, sk_A2, sk_A11, sk_A0)))
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A1(sk_A, sk_A2)), sk_A2)),
0.00/0.27	    inference('sup-', [status(thm)], ['2', '22'])).
0.00/0.27	tff('24', plain,
0.00/0.27	    (~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	           'const/sets/IN'(sk_A), sk_A1(sk_A, sk_A2)), sk_A2)
0.00/0.27	     | ~ app_encode_app('type/realax/real', $o, 
0.00/0.27	           app_encode_app('type/realax/real', 
0.00/0.27	             app_encode_fun('type/realax/real', $o), 'const/realax/real_lt', 
0.00/0.27	             app_encode_app(sk_A, 'type/realax/real', sk_A0, 
0.00/0.27	               sk_A3(sk_A, sk_A2, sk_A11, sk_A0))), 
0.00/0.27	           app_encode_app(sk_A, 'type/realax/real', sk_A11, 
0.00/0.27	             sk_A3(sk_A, sk_A2, sk_A11, sk_A0)))),
0.00/0.27	    inference('simplify', [status(thm)], ['23'])).
0.00/0.27	tff('25', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A3(sk_A, sk_A2, sk_A11, sk_A0)), 
0.00/0.27	           sk_A2)
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A1(sk_A, sk_A2)), sk_A2)),
0.00/0.27	    inference('sup-', [status(thm)], ['1', '24'])).
0.00/0.27	tff('26', plain,
0.00/0.27	    (~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	           'const/sets/IN'(sk_A), sk_A1(sk_A, sk_A2)), sk_A2)
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           app_encode_app(sk_A, 
0.00/0.27	             app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	             'const/sets/IN'(sk_A), sk_A3(sk_A, sk_A2, sk_A11, sk_A0)), 
0.00/0.27	           sk_A2)),
0.00/0.27	    inference('simplify', [status(thm)], ['25'])).
0.00/0.27	tff('27', plain,
0.00/0.27	    ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	        app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	          'const/sets/IN'(sk_A), sk_A1(sk_A, sk_A2)), sk_A2),
0.00/0.27	    inference('clc', [status(thm)], ['26', '14'])).
0.00/0.27	tff('28', plain, (~ $true | sk_A2 = 'const/sets/EMPTY'(sk_A)),
0.00/0.27	    inference('sup-', [status(thm)], ['0', '27'])).
0.00/0.27	tff('29', plain, sk_A2 = 'const/sets/EMPTY'(sk_A),
0.00/0.27	    inference('simplify', [status(thm)], ['28'])).
0.00/0.27	tff('30', plain, $false,
0.00/0.27	    inference('simplify_reflect-', [status(thm)], ['29', '13'])).
0.00/0.27	
0.00/0.27	% SZS output end Refutation
0.00/0.27	EOF
