0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : appext
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : rpo6
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 $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n127.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:39:09 CST 2018
0.00/0.23	% done 11 iterations in 0.025s
0.00/0.23	% SZS status Theorem for 'stdin'
0.00/0.23	% SZS output start Refutation
0.00/0.24	tff(zf_stmt_15, axiom,
0.00/0.24	  (![A:$tType,B:$tType,A0:app_encode_fun(B,app_encode_fun(B,B))]:
0.00/0.24	     (app_encode_app(app_encode_fun(B,app_encode_fun(B,B)),$o,
0.00/0.24	                     'const/iterate/monoidal'(B),A0) =>
0.00/0.24	      (![A1:app_encode_fun(A,B),A2:app_encode_fun(A,$o),
0.00/0.24	         A3:app_encode_fun(A,$o)]:
0.00/0.24	         ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A2) & 
0.00/0.24	           app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A3) & 
0.00/0.24	           (![A4:A]:
0.00/0.24	              (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.24	                              app_encode_app(A,
0.00/0.24	                                             app_encode_fun(app_encode_fun(
0.00/0.24	                                                            A,$o),$o),
0.00/0.24	                                             'const/sets/IN'(A),A4),
0.00/0.24	                              app_encode_app(app_encode_fun(A,$o),
0.00/0.24	                                             app_encode_fun(A,$o),
0.00/0.24	                                             app_encode_app(app_encode_fun(
0.00/0.24	                                                            A,$o),
0.00/0.24	                                                            app_encode_fun(
0.00/0.24	                                                            app_encode_fun(
0.00/0.24	                                                            A,$o),
0.00/0.24	                                                            app_encode_fun(
0.00/0.24	                                                            A,$o)),
0.00/0.24	                                                            'const/sets/INTER'(
0.00/0.24	                                                            A),A2),
0.00/0.24	                                             A3)) =>
0.00/0.24	               (app_encode_app(A,B,A1,A4) =
0.00/0.24	                app_encode_app(app_encode_fun(B,app_encode_fun(B,B)),B,
0.00/0.24	                               'const/iterate/neutral'(B),A0))))) =>
0.00/0.24	          (app_encode_app(app_encode_fun(A,B),B,
0.00/0.24	                          app_encode_app(app_encode_fun(A,$o),
0.00/0.24	                                         app_encode_fun(app_encode_fun(A,B),B),
0.00/0.24	                                         app_encode_app(app_encode_fun(
0.00/0.24	                                                        B,app_encode_fun(B,B)),
0.00/0.24	                                                        app_encode_fun(
0.00/0.24	                                                        app_encode_fun(A,$o),
0.00/0.24	                                                        app_encode_fun(
0.00/0.24	                                                        app_encode_fun(A,B),B)),
0.00/0.24	                                                        'const/iterate/iterate'(
0.00/0.24	                                                        A,B),A0),
0.00/0.24	                                         app_encode_app(app_encode_fun(A,$o),
0.00/0.24	                                                        app_encode_fun(A,$o),
0.00/0.24	                                                        app_encode_app(
0.00/0.24	                                                        app_encode_fun(A,$o),
0.00/0.24	                                                        app_encode_fun(
0.00/0.24	                                                        app_encode_fun(A,$o),
0.00/0.24	                                                        app_encode_fun(A,$o)),
0.00/0.24	                                                        'const/sets/UNION'(A),
0.00/0.24	                                                        A2),A3)),
0.00/0.24	                          A1) =
0.00/0.24	           app_encode_app(B,B,
0.00/0.24	                          app_encode_app(B,app_encode_fun(B,B),A0,
0.00/0.24	                                         app_encode_app(app_encode_fun(A,B),
0.00/0.24	                                                        B,
0.00/0.24	                                                        app_encode_app(
0.00/0.24	                                                        app_encode_fun(A,$o),
0.00/0.24	                                                        app_encode_fun(
0.00/0.24	                                                        app_encode_fun(A,B),B),
0.00/0.24	                                                        app_encode_app(
0.00/0.24	                                                        app_encode_fun(
0.00/0.24	                                                        B,app_encode_fun(B,B)),
0.00/0.24	                                                        app_encode_fun(
0.00/0.24	                                                        app_encode_fun(A,$o),
0.00/0.24	                                                        app_encode_fun(
0.00/0.24	                                                        app_encode_fun(A,B),B)),
0.00/0.24	                                                        'const/iterate/iterate'(
0.00/0.24	                                                        A,B),A0),A2),A1)),
0.00/0.24	                          app_encode_app(app_encode_fun(A,B),B,
0.00/0.24	                                         app_encode_app(app_encode_fun(A,$o),
0.00/0.24	                                                        app_encode_fun(
0.00/0.24	                                                        app_encode_fun(A,B),B),
0.00/0.24	                                                        app_encode_app(
0.00/0.24	                                                        app_encode_fun(
0.00/0.24	                                                        B,app_encode_fun(B,B)),
0.00/0.24	                                                        app_encode_fun(
0.00/0.24	                                                        app_encode_fun(A,$o),
0.00/0.24	                                                        app_encode_fun(
0.00/0.24	                                                        app_encode_fun(A,B),B)),
0.00/0.24	                                                        'const/iterate/iterate'(
0.00/0.24	                                                        A,B),A0),A3),
0.00/0.24	                                         A1)))))))).
0.00/0.24	tff('0', plain,
0.00/0.24	    ![X4 : $tType, X5 : app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.00/0.24	      X6 : $tType, X7 : app_encode_fun(X6, $o), X8 : app_encode_fun(X6, X4), 
0.00/0.24	      X9 : app_encode_fun(X6, $o)]:
0.00/0.24	      (app_encode_app(app_encode_fun(X6, X4), X4, 
0.00/0.24	         app_encode_app(app_encode_fun(X6, $o), 
0.00/0.24	           app_encode_fun(app_encode_fun(X6, X4), X4), 
0.00/0.24	           app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.00/0.24	             app_encode_fun(app_encode_fun(X6, $o), 
0.00/0.24	               app_encode_fun(app_encode_fun(X6, X4), X4)), 
0.00/0.24	             'const/iterate/iterate'(X6, X4), X5), 
0.00/0.24	           app_encode_app(app_encode_fun(X6, $o), app_encode_fun(X6, $o), 
0.00/0.24	             app_encode_app(app_encode_fun(X6, $o), 
0.00/0.24	               app_encode_fun(app_encode_fun(X6, $o), app_encode_fun(X6, $o)), 
0.00/0.24	               'const/sets/UNION'(X6), X7), X9)), X8)
0.00/0.24	        = app_encode_app(X4, X4, 
0.00/0.24	            app_encode_app(X4, app_encode_fun(X4, X4), X5, 
0.00/0.24	              app_encode_app(app_encode_fun(X6, X4), X4, 
0.00/0.24	                app_encode_app(app_encode_fun(X6, $o), 
0.00/0.24	                  app_encode_fun(app_encode_fun(X6, X4), X4), 
0.00/0.24	                  app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.00/0.24	                    app_encode_fun(app_encode_fun(X6, $o), 
0.00/0.24	                      app_encode_fun(app_encode_fun(X6, X4), X4)), 
0.00/0.24	                    'const/iterate/iterate'(X6, X4), X5), X7), X8)), 
0.00/0.24	            app_encode_app(app_encode_fun(X6, X4), X4, 
0.00/0.24	              app_encode_app(app_encode_fun(X6, $o), 
0.00/0.24	                app_encode_fun(app_encode_fun(X6, X4), X4), 
0.00/0.24	                app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.00/0.24	                  app_encode_fun(app_encode_fun(X6, $o), 
0.00/0.24	                    app_encode_fun(app_encode_fun(X6, X4), X4)), 
0.00/0.24	                  'const/iterate/iterate'(X6, X4), X5), X9), X8))
0.00/0.24	       | app_encode_app(app_encode_fun(X6, $o), $o, 
0.00/0.24	           app_encode_app(X6, app_encode_fun(app_encode_fun(X6, $o), $o), 
0.00/0.24	             'const/sets/IN'(X6), sk_A4(X4, X6, X9, X7, X8, X5)), 
0.00/0.24	           app_encode_app(app_encode_fun(X6, $o), app_encode_fun(X6, $o), 
0.00/0.24	             app_encode_app(app_encode_fun(X6, $o), 
0.00/0.24	               app_encode_fun(app_encode_fun(X6, $o), app_encode_fun(X6, $o)), 
0.00/0.24	               'const/sets/INTER'(X6), X7), X9))
0.00/0.24	       | ~ app_encode_app(app_encode_fun(X6, $o), $o, 
0.00/0.24	             'const/sets/FINITE'(X6), X9)
0.00/0.24	       | ~ app_encode_app(app_encode_fun(X6, $o), $o, 
0.00/0.24	             'const/sets/FINITE'(X6), X7)
0.00/0.24	       | ~ app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), $o, 
0.00/0.24	             'const/iterate/monoidal'(X4), X5)),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_15])).
0.00/0.24	tff(zf_stmt_19, conjecture,
0.00/0.24	  (![A:$tType,A0:app_encode_fun(A,'type/nums/num'),A1:app_encode_fun(A,$o),
0.00/0.24	     A2:app_encode_fun(A,$o)]:
0.00/0.24	     ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A1) & 
0.00/0.24	       app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A2) & 
0.00/0.24	       (![A3:A]:
0.00/0.24	          (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.24	                          app_encode_app(A,
0.00/0.24	                                         app_encode_fun(app_encode_fun(A,$o),
0.00/0.24	                                                        $o),
0.00/0.24	                                         'const/sets/IN'(A),A3),
0.00/0.24	                          app_encode_app(app_encode_fun(A,$o),
0.00/0.24	                                         app_encode_fun(A,$o),
0.00/0.24	                                         app_encode_app(app_encode_fun(A,$o),
0.00/0.24	                                                        app_encode_fun(
0.00/0.24	                                                        app_encode_fun(A,$o),
0.00/0.24	                                                        app_encode_fun(A,$o)),
0.00/0.24	                                                        'const/sets/INTER'(A),
0.00/0.24	                                                        A1),
0.00/0.24	                                         A2)) =>
0.00/0.24	           (app_encode_app(A,'type/nums/num',A0,A3) =
0.00/0.24	            app_encode_app('type/nums/num','type/nums/num',
0.00/0.24	                           'const/nums/NUMERAL','const/nums/_0'))))) =>
0.00/0.24	      (app_encode_app(app_encode_fun(A,'type/nums/num'),'type/nums/num',
0.00/0.24	                      app_encode_app(app_encode_fun(A,$o),
0.00/0.24	                                     app_encode_fun(app_encode_fun(A,
0.00/0.24	                                                                   'type/nums/num'),
0.00/0.24	                                                    'type/nums/num'),
0.00/0.24	                                     'const/iterate/nsum'(A),
0.00/0.24	                                     app_encode_app(app_encode_fun(A,$o),
0.00/0.24	                                                    app_encode_fun(A,$o),
0.00/0.24	                                                    app_encode_app(app_encode_fun(
0.00/0.24	                                                                   A,$o),
0.00/0.24	                                                                   app_encode_fun(
0.00/0.24	                                                                   app_encode_fun(
0.00/0.24	                                                                   A,$o),
0.00/0.24	                                                                   app_encode_fun(
0.00/0.24	                                                                   A,$o)),
0.00/0.24	                                                                   'const/sets/UNION'(
0.00/0.24	                                                                   A),A1),
0.00/0.24	                                                    A2)),
0.00/0.24	                      A0) =
0.00/0.24	       app_encode_app('type/nums/num','type/nums/num',
0.00/0.24	                      app_encode_app('type/nums/num',
0.00/0.24	                                     app_encode_fun('type/nums/num',
0.00/0.24	                                                    'type/nums/num'),
0.00/0.24	                                     'const/arith/+',
0.00/0.24	                                     app_encode_app(app_encode_fun(A,
0.00/0.24	                                                                   'type/nums/num'),
0.00/0.24	                                                    'type/nums/num',
0.00/0.24	                                                    app_encode_app(app_encode_fun(
0.00/0.24	                                                                   A,$o),
0.00/0.24	                                                                   app_encode_fun(
0.00/0.24	                                                                   app_encode_fun(
0.00/0.24	                                                                   A,
0.00/0.24	                                                                   'type/nums/num'),
0.00/0.24	                                                                   'type/nums/num'),
0.00/0.24	                                                                   'const/iterate/nsum'(
0.00/0.24	                                                                   A),A1),
0.00/0.24	                                                    A0)),
0.00/0.24	                      app_encode_app(app_encode_fun(A,'type/nums/num'),
0.00/0.24	                                     'type/nums/num',
0.00/0.24	                                     app_encode_app(app_encode_fun(A,$o),
0.00/0.24	                                                    app_encode_fun(app_encode_fun(
0.00/0.24	                                                                   A,
0.00/0.24	                                                                   'type/nums/num'),
0.00/0.24	                                                                   'type/nums/num'),
0.00/0.24	                                                    'const/iterate/nsum'(A),
0.00/0.24	                                                    A2),
0.00/0.24	                                     A0)))))).
0.00/0.24	tff(zf_stmt_0, negated_conjecture,
0.00/0.24	  (~
0.00/0.24	    (![A:$tType,A0:app_encode_fun(A,'type/nums/num'),A1:app_encode_fun(A,$o),
0.00/0.24	       A2:app_encode_fun(A,$o)]:
0.00/0.24	       ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A1) & 
0.00/0.24	         app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A2) & 
0.00/0.24	         (![A3:A]:
0.00/0.24	            (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.24	                            app_encode_app(A,
0.00/0.24	                                           app_encode_fun(app_encode_fun(
0.00/0.24	                                                          A,$o),$o),
0.00/0.24	                                           'const/sets/IN'(A),A3),
0.00/0.24	                            app_encode_app(app_encode_fun(A,$o),
0.00/0.24	                                           app_encode_fun(A,$o),
0.00/0.24	                                           app_encode_app(app_encode_fun(
0.00/0.24	                                                          A,$o),
0.00/0.24	                                                          app_encode_fun(
0.00/0.24	                                                          app_encode_fun(
0.00/0.24	                                                          A,$o),
0.00/0.24	                                                          app_encode_fun(
0.00/0.24	                                                          A,$o)),
0.00/0.24	                                                          'const/sets/INTER'(
0.00/0.24	                                                          A),A1),
0.00/0.24	                                           A2)) =>
0.00/0.24	             (app_encode_app(A,'type/nums/num',A0,A3) =
0.00/0.24	              app_encode_app('type/nums/num','type/nums/num',
0.00/0.24	                             'const/nums/NUMERAL','const/nums/_0'))))) =>
0.00/0.24	        (app_encode_app(app_encode_fun(A,'type/nums/num'),'type/nums/num',
0.00/0.24	                        app_encode_app(app_encode_fun(A,$o),
0.00/0.24	                                       app_encode_fun(app_encode_fun(
0.00/0.24	                                                      A,'type/nums/num'),
0.00/0.24	                                                      'type/nums/num'),
0.00/0.24	                                       'const/iterate/nsum'(A),
0.00/0.24	                                       app_encode_app(app_encode_fun(A,$o),
0.00/0.24	                                                      app_encode_fun(A,$o),
0.00/0.24	                                                      app_encode_app(
0.00/0.24	                                                      app_encode_fun(A,$o),
0.00/0.24	                                                      app_encode_fun(
0.00/0.24	                                                      app_encode_fun(A,$o),
0.00/0.24	                                                      app_encode_fun(A,$o)),
0.00/0.24	                                                      'const/sets/UNION'(A),
0.00/0.24	                                                      A1),A2)),
0.00/0.24	                        A0) =
0.00/0.24	         app_encode_app('type/nums/num','type/nums/num',
0.00/0.24	                        app_encode_app('type/nums/num',
0.00/0.24	                                       app_encode_fun('type/nums/num',
0.00/0.24	                                                      'type/nums/num'),
0.00/0.24	                                       'const/arith/+',
0.00/0.24	                                       app_encode_app(app_encode_fun(
0.00/0.24	                                                      A,'type/nums/num'),
0.00/0.24	                                                      'type/nums/num',
0.00/0.24	                                                      app_encode_app(
0.00/0.24	                                                      app_encode_fun(A,$o),
0.00/0.24	                                                      app_encode_fun(
0.00/0.24	                                                      app_encode_fun(
0.00/0.24	                                                      A,'type/nums/num'),
0.00/0.24	                                                      'type/nums/num'),
0.00/0.24	                                                      'const/iterate/nsum'(A),
0.00/0.24	                                                      A1),A0)),
0.00/0.24	                        app_encode_app(app_encode_fun(A,'type/nums/num'),
0.00/0.24	                                       'type/nums/num',
0.00/0.24	                                       app_encode_app(app_encode_fun(A,$o),
0.00/0.24	                                                      app_encode_fun(
0.00/0.24	                                                      app_encode_fun(
0.00/0.24	                                                      A,'type/nums/num'),
0.00/0.24	                                                      'type/nums/num'),
0.00/0.24	                                                      'const/iterate/nsum'(A),
0.00/0.24	                                                      A2),
0.00/0.24	                                       A0))))))).
0.00/0.24	tff('1', plain,
0.00/0.24	    ![X11 : sk_A]:
0.00/0.24	      (app_encode_app(sk_A, 'type/nums/num', sk_A0, X11)
0.00/0.24	        = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.24	            'const/nums/NUMERAL', 'const/nums/_0')
0.00/0.24	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.24	             app_encode_app(sk_A, 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.24	               'const/sets/IN'(sk_A), X11), 
0.00/0.24	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                   app_encode_fun(sk_A, $o)), 'const/sets/INTER'(sk_A), 
0.00/0.24	                 sk_A1), sk_A2))),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.24	tff(zf_stmt_18, axiom,
0.00/0.24	  (app_encode_app(app_encode_fun('type/nums/num',
0.00/0.24	                                 app_encode_fun('type/nums/num',
0.00/0.24	                                                'type/nums/num')),
0.00/0.24	                  'type/nums/num','const/iterate/neutral'('type/nums/num'),
0.00/0.24	                  'const/arith/+') =
0.00/0.24	   app_encode_app('type/nums/num','type/nums/num','const/nums/NUMERAL',
0.00/0.24	                  'const/nums/_0'))).
0.00/0.24	tff('2', plain,
0.00/0.24	    app_encode_app(
0.00/0.24	      app_encode_fun('type/nums/num', 
0.00/0.24	        app_encode_fun('type/nums/num', 'type/nums/num')), 'type/nums/num', 
0.00/0.24	      'const/iterate/neutral'('type/nums/num'), 'const/arith/+')
0.00/0.24	     = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.24	         'const/nums/NUMERAL', 'const/nums/_0'),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_18])).
0.00/0.24	tff('3', plain,
0.00/0.24	    ![X11 : sk_A]:
0.00/0.24	      (app_encode_app(sk_A, 'type/nums/num', sk_A0, X11)
0.00/0.24	        = app_encode_app(
0.00/0.24	            app_encode_fun('type/nums/num', 
0.00/0.24	              app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	            'type/nums/num', 'const/iterate/neutral'('type/nums/num'), 
0.00/0.24	            'const/arith/+')
0.00/0.24	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.24	             app_encode_app(sk_A, 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.24	               'const/sets/IN'(sk_A), X11), 
0.00/0.24	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                   app_encode_fun(sk_A, $o)), 'const/sets/INTER'(sk_A), 
0.00/0.24	                 sk_A1), sk_A2))),
0.00/0.24	    inference('demod', [status(thm)], ['1', '2'])).
0.00/0.24	tff('4', plain,
0.00/0.24	    ![X0 : $tType, X1 : app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.24	      X2 : app_encode_fun(sk_A, X0)]:
0.00/0.24	      (~ $true
0.00/0.24	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.24	             'const/iterate/monoidal'(X0), X1)
0.00/0.24	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.24	             'const/sets/FINITE'(sk_A), sk_A1)
0.00/0.24	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.24	             'const/sets/FINITE'(sk_A), sk_A2)
0.00/0.24	       | app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.24	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	             app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.24	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.24	               'const/iterate/iterate'(sk_A, X0), X1), 
0.00/0.24	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                   app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), 
0.00/0.24	                 sk_A1), sk_A2)), X2)
0.00/0.24	          = app_encode_app(X0, X0, 
0.00/0.24	              app_encode_app(X0, app_encode_fun(X0, X0), X1, 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.24	                  app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.24	                    app_encode_app(
0.00/0.24	                      app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                        app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.24	                      'const/iterate/iterate'(sk_A, X0), X1), sk_A1), X2)), 
0.00/0.24	              app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                  app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.24	                  app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.24	                    'const/iterate/iterate'(sk_A, X0), X1), sk_A2), X2))
0.00/0.24	       | app_encode_app(sk_A, 'type/nums/num', sk_A0, 
0.00/0.24	           sk_A4(X0, sk_A, sk_A2, sk_A1, X2, X1))
0.00/0.24	          = app_encode_app(
0.00/0.24	              app_encode_fun('type/nums/num', 
0.00/0.24	                app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	              'type/nums/num', 'const/iterate/neutral'('type/nums/num'), 
0.00/0.24	              'const/arith/+')),
0.00/0.24	    inference('sup-', [status(thm)], ['0', '3'])).
0.00/0.24	tff('5', plain,
0.00/0.24	    app_encode_app(app_encode_fun(sk_A, $o), $o, 'const/sets/FINITE'(sk_A), 
0.00/0.24	      sk_A1),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.24	tff('6', plain,
0.00/0.24	    app_encode_app(app_encode_fun(sk_A, $o), $o, 'const/sets/FINITE'(sk_A), 
0.00/0.24	      sk_A2),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.24	tff('7', plain,
0.00/0.24	    ![X0 : $tType, X1 : app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.24	      X2 : app_encode_fun(sk_A, X0)]:
0.00/0.24	      (~ $true
0.00/0.24	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.24	             'const/iterate/monoidal'(X0), X1)
0.00/0.24	       | ~ $true
0.00/0.24	       | ~ $true
0.00/0.24	       | app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.24	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	             app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.24	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.24	               'const/iterate/iterate'(sk_A, X0), X1), 
0.00/0.24	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                   app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), 
0.00/0.24	                 sk_A1), sk_A2)), X2)
0.00/0.24	          = app_encode_app(X0, X0, 
0.00/0.24	              app_encode_app(X0, app_encode_fun(X0, X0), X1, 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.24	                  app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.24	                    app_encode_app(
0.00/0.24	                      app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                        app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.24	                      'const/iterate/iterate'(sk_A, X0), X1), sk_A1), X2)), 
0.00/0.24	              app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                  app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.24	                  app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.24	                    'const/iterate/iterate'(sk_A, X0), X1), sk_A2), X2))
0.00/0.24	       | app_encode_app(sk_A, 'type/nums/num', sk_A0, 
0.00/0.24	           sk_A4(X0, sk_A, sk_A2, sk_A1, X2, X1))
0.00/0.24	          = app_encode_app(
0.00/0.24	              app_encode_fun('type/nums/num', 
0.00/0.24	                app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	              'type/nums/num', 'const/iterate/neutral'('type/nums/num'), 
0.00/0.24	              'const/arith/+')),
0.00/0.24	    inference('demod', [status(thm)], ['4', '5', '6'])).
0.00/0.24	tff('8', plain,
0.00/0.24	    ![X0 : $tType, X1 : app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.24	      X2 : app_encode_fun(sk_A, X0)]:
0.00/0.24	      (app_encode_app(sk_A, 'type/nums/num', sk_A0, 
0.00/0.24	         sk_A4(X0, sk_A, sk_A2, sk_A1, X2, X1))
0.00/0.24	        = app_encode_app(
0.00/0.24	            app_encode_fun('type/nums/num', 
0.00/0.24	              app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	            'type/nums/num', 'const/iterate/neutral'('type/nums/num'), 
0.00/0.24	            'const/arith/+')
0.00/0.24	       | app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.24	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	             app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.24	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.24	               'const/iterate/iterate'(sk_A, X0), X1), 
0.00/0.24	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                   app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), 
0.00/0.24	                 sk_A1), sk_A2)), X2)
0.00/0.24	          = app_encode_app(X0, X0, 
0.00/0.24	              app_encode_app(X0, app_encode_fun(X0, X0), X1, 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.24	                  app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.24	                    app_encode_app(
0.00/0.24	                      app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                        app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.24	                      'const/iterate/iterate'(sk_A, X0), X1), sk_A1), X2)), 
0.00/0.24	              app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                  app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.24	                  app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.24	                    'const/iterate/iterate'(sk_A, X0), X1), sk_A2), X2))
0.00/0.24	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.24	             'const/iterate/monoidal'(X0), X1)),
0.00/0.24	    inference('simplify', [status(thm)], ['7'])).
0.00/0.24	tff('9', plain,
0.00/0.24	    ![X4 : $tType, X5 : app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.00/0.24	      X6 : $tType, X7 : app_encode_fun(X6, $o), X8 : app_encode_fun(X6, X4), 
0.00/0.24	      X9 : app_encode_fun(X6, $o)]:
0.00/0.24	      (app_encode_app(app_encode_fun(X6, X4), X4, 
0.00/0.24	         app_encode_app(app_encode_fun(X6, $o), 
0.00/0.24	           app_encode_fun(app_encode_fun(X6, X4), X4), 
0.00/0.24	           app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.00/0.24	             app_encode_fun(app_encode_fun(X6, $o), 
0.00/0.24	               app_encode_fun(app_encode_fun(X6, X4), X4)), 
0.00/0.24	             'const/iterate/iterate'(X6, X4), X5), 
0.00/0.24	           app_encode_app(app_encode_fun(X6, $o), app_encode_fun(X6, $o), 
0.00/0.24	             app_encode_app(app_encode_fun(X6, $o), 
0.00/0.24	               app_encode_fun(app_encode_fun(X6, $o), app_encode_fun(X6, $o)), 
0.00/0.24	               'const/sets/UNION'(X6), X7), X9)), X8)
0.00/0.24	        = app_encode_app(X4, X4, 
0.00/0.24	            app_encode_app(X4, app_encode_fun(X4, X4), X5, 
0.00/0.24	              app_encode_app(app_encode_fun(X6, X4), X4, 
0.00/0.24	                app_encode_app(app_encode_fun(X6, $o), 
0.00/0.24	                  app_encode_fun(app_encode_fun(X6, X4), X4), 
0.00/0.24	                  app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.00/0.24	                    app_encode_fun(app_encode_fun(X6, $o), 
0.00/0.24	                      app_encode_fun(app_encode_fun(X6, X4), X4)), 
0.00/0.24	                    'const/iterate/iterate'(X6, X4), X5), X7), X8)), 
0.00/0.24	            app_encode_app(app_encode_fun(X6, X4), X4, 
0.00/0.24	              app_encode_app(app_encode_fun(X6, $o), 
0.00/0.24	                app_encode_fun(app_encode_fun(X6, X4), X4), 
0.00/0.24	                app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.00/0.24	                  app_encode_fun(app_encode_fun(X6, $o), 
0.00/0.24	                    app_encode_fun(app_encode_fun(X6, X4), X4)), 
0.00/0.24	                  'const/iterate/iterate'(X6, X4), X5), X9), X8))
0.00/0.24	       | app_encode_app(X6, X4, X8, sk_A4(X4, X6, X9, X7, X8, X5))
0.00/0.24	          != app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), X4, 
0.00/0.24	               'const/iterate/neutral'(X4), X5)
0.00/0.24	       | ~ app_encode_app(app_encode_fun(X6, $o), $o, 
0.00/0.24	             'const/sets/FINITE'(X6), X9)
0.00/0.24	       | ~ app_encode_app(app_encode_fun(X6, $o), $o, 
0.00/0.24	             'const/sets/FINITE'(X6), X7)
0.00/0.24	       | ~ app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), $o, 
0.00/0.24	             'const/iterate/monoidal'(X4), X5)),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_15])).
0.00/0.24	tff('10', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/nums/num', 
0.00/0.24	             app_encode_fun('type/nums/num', 'type/nums/num'))]:
0.00/0.24	      (app_encode_app(
0.00/0.24	         app_encode_fun('type/nums/num', 
0.00/0.24	           app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	         'type/nums/num', 'const/iterate/neutral'('type/nums/num'), 
0.00/0.24	         'const/arith/+')
0.00/0.24	        != app_encode_app(
0.00/0.24	             app_encode_fun('type/nums/num', 
0.00/0.24	               app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	             'type/nums/num', 'const/iterate/neutral'('type/nums/num'), X0)
0.00/0.24	       | ~ app_encode_app(
0.00/0.24	             app_encode_fun('type/nums/num', 
0.00/0.24	               app_encode_fun('type/nums/num', 'type/nums/num')), $o, 
0.00/0.24	             'const/iterate/monoidal'('type/nums/num'), X0)
0.00/0.24	       | app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	           'type/nums/num', 
0.00/0.24	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	             app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	               'type/nums/num'), 
0.00/0.24	             app_encode_app(
0.00/0.24	               app_encode_fun('type/nums/num', 
0.00/0.24	                 app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                   'type/nums/num')), 
0.00/0.24	               'const/iterate/iterate'(sk_A, 'type/nums/num'), X0), 
0.00/0.24	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                   app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), 
0.00/0.24	                 sk_A1), sk_A2)), sk_A0)
0.00/0.24	          = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.24	              app_encode_app('type/nums/num', 
0.00/0.24	                app_encode_fun('type/nums/num', 'type/nums/num'), X0, 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                  'type/nums/num', 
0.00/0.24	                  app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                      'type/nums/num'), 
0.00/0.24	                    app_encode_app(
0.00/0.24	                      app_encode_fun('type/nums/num', 
0.00/0.24	                        app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                        app_encode_fun(
0.00/0.24	                          app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                          'type/nums/num')), 
0.00/0.24	                      'const/iterate/iterate'(sk_A, 'type/nums/num'), X0), 
0.00/0.24	                    sk_A1), sk_A0)), 
0.00/0.24	              app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                'type/nums/num', 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                  app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                    'type/nums/num'), 
0.00/0.24	                  app_encode_app(
0.00/0.24	                    app_encode_fun('type/nums/num', 
0.00/0.24	                      app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                        'type/nums/num')), 
0.00/0.24	                    'const/iterate/iterate'(sk_A, 'type/nums/num'), X0), 
0.00/0.24	                  sk_A2), sk_A0))
0.00/0.24	       | ~ app_encode_app(
0.00/0.24	             app_encode_fun('type/nums/num', 
0.00/0.24	               app_encode_fun('type/nums/num', 'type/nums/num')), $o, 
0.00/0.24	             'const/iterate/monoidal'('type/nums/num'), X0)
0.00/0.24	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.24	             'const/sets/FINITE'(sk_A), sk_A1)
0.00/0.24	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.24	             'const/sets/FINITE'(sk_A), sk_A2)
0.00/0.24	       | app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	           'type/nums/num', 
0.00/0.24	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	             app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	               'type/nums/num'), 
0.00/0.24	             app_encode_app(
0.00/0.24	               app_encode_fun('type/nums/num', 
0.00/0.24	                 app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                   'type/nums/num')), 
0.00/0.24	               'const/iterate/iterate'(sk_A, 'type/nums/num'), X0), 
0.00/0.24	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                   app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), 
0.00/0.24	                 sk_A1), sk_A2)), sk_A0)
0.00/0.24	          = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.24	              app_encode_app('type/nums/num', 
0.00/0.24	                app_encode_fun('type/nums/num', 'type/nums/num'), X0, 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                  'type/nums/num', 
0.00/0.24	                  app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                      'type/nums/num'), 
0.00/0.24	                    app_encode_app(
0.00/0.24	                      app_encode_fun('type/nums/num', 
0.00/0.24	                        app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                        app_encode_fun(
0.00/0.24	                          app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                          'type/nums/num')), 
0.00/0.24	                      'const/iterate/iterate'(sk_A, 'type/nums/num'), X0), 
0.00/0.24	                    sk_A1), sk_A0)), 
0.00/0.24	              app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                'type/nums/num', 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                  app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                    'type/nums/num'), 
0.00/0.24	                  app_encode_app(
0.00/0.24	                    app_encode_fun('type/nums/num', 
0.00/0.24	                      app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                        'type/nums/num')), 
0.00/0.24	                    'const/iterate/iterate'(sk_A, 'type/nums/num'), X0), 
0.00/0.24	                  sk_A2), sk_A0))),
0.00/0.24	    inference('sup-', [status(thm)], ['8', '9'])).
0.00/0.24	tff('11', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/nums/num', 
0.00/0.24	             app_encode_fun('type/nums/num', 'type/nums/num'))]:
0.00/0.24	      (app_encode_app(
0.00/0.24	         app_encode_fun('type/nums/num', 
0.00/0.24	           app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	         'type/nums/num', 'const/iterate/neutral'('type/nums/num'), 
0.00/0.24	         'const/arith/+')
0.00/0.24	        != app_encode_app(
0.00/0.24	             app_encode_fun('type/nums/num', 
0.00/0.24	               app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	             'type/nums/num', 'const/iterate/neutral'('type/nums/num'), X0)
0.00/0.24	       | ~ app_encode_app(
0.00/0.24	             app_encode_fun('type/nums/num', 
0.00/0.24	               app_encode_fun('type/nums/num', 'type/nums/num')), $o, 
0.00/0.24	             'const/iterate/monoidal'('type/nums/num'), X0)
0.00/0.24	       | app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	           'type/nums/num', 
0.00/0.24	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	             app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	               'type/nums/num'), 
0.00/0.24	             app_encode_app(
0.00/0.24	               app_encode_fun('type/nums/num', 
0.00/0.24	                 app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                   'type/nums/num')), 
0.00/0.24	               'const/iterate/iterate'(sk_A, 'type/nums/num'), X0), 
0.00/0.24	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                   app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), 
0.00/0.24	                 sk_A1), sk_A2)), sk_A0)
0.00/0.24	          = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.24	              app_encode_app('type/nums/num', 
0.00/0.24	                app_encode_fun('type/nums/num', 'type/nums/num'), X0, 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                  'type/nums/num', 
0.00/0.24	                  app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                      'type/nums/num'), 
0.00/0.24	                    app_encode_app(
0.00/0.24	                      app_encode_fun('type/nums/num', 
0.00/0.24	                        app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                        app_encode_fun(
0.00/0.24	                          app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                          'type/nums/num')), 
0.00/0.24	                      'const/iterate/iterate'(sk_A, 'type/nums/num'), X0), 
0.00/0.24	                    sk_A1), sk_A0)), 
0.00/0.24	              app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                'type/nums/num', 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                  app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                    'type/nums/num'), 
0.00/0.24	                  app_encode_app(
0.00/0.24	                    app_encode_fun('type/nums/num', 
0.00/0.24	                      app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                        'type/nums/num')), 
0.00/0.24	                    'const/iterate/iterate'(sk_A, 'type/nums/num'), X0), 
0.00/0.24	                  sk_A2), sk_A0))
0.00/0.24	       | ~ app_encode_app(
0.00/0.24	             app_encode_fun('type/nums/num', 
0.00/0.24	               app_encode_fun('type/nums/num', 'type/nums/num')), $o, 
0.00/0.24	             'const/iterate/monoidal'('type/nums/num'), X0)
0.00/0.24	       | ~ $true
0.00/0.24	       | ~ $true
0.00/0.24	       | app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	           'type/nums/num', 
0.00/0.24	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	             app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	               'type/nums/num'), 
0.00/0.24	             app_encode_app(
0.00/0.24	               app_encode_fun('type/nums/num', 
0.00/0.24	                 app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                   'type/nums/num')), 
0.00/0.24	               'const/iterate/iterate'(sk_A, 'type/nums/num'), X0), 
0.00/0.24	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                   app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), 
0.00/0.24	                 sk_A1), sk_A2)), sk_A0)
0.00/0.24	          = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.24	              app_encode_app('type/nums/num', 
0.00/0.24	                app_encode_fun('type/nums/num', 'type/nums/num'), X0, 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                  'type/nums/num', 
0.00/0.24	                  app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                      'type/nums/num'), 
0.00/0.24	                    app_encode_app(
0.00/0.24	                      app_encode_fun('type/nums/num', 
0.00/0.24	                        app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                        app_encode_fun(
0.00/0.24	                          app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                          'type/nums/num')), 
0.00/0.24	                      'const/iterate/iterate'(sk_A, 'type/nums/num'), X0), 
0.00/0.24	                    sk_A1), sk_A0)), 
0.00/0.24	              app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                'type/nums/num', 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                  app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                    'type/nums/num'), 
0.00/0.24	                  app_encode_app(
0.00/0.24	                    app_encode_fun('type/nums/num', 
0.00/0.24	                      app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                        'type/nums/num')), 
0.00/0.24	                    'const/iterate/iterate'(sk_A, 'type/nums/num'), X0), 
0.00/0.24	                  sk_A2), sk_A0))),
0.00/0.24	    inference('demod', [status(thm)], ['10', '5', '6'])).
0.00/0.24	tff('12', plain,
0.00/0.24	    ![X0 : app_encode_fun('type/nums/num', 
0.00/0.24	             app_encode_fun('type/nums/num', 'type/nums/num'))]:
0.00/0.24	      (app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	         'type/nums/num', 
0.00/0.24	         app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	           app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	             'type/nums/num'), 
0.00/0.24	           app_encode_app(
0.00/0.24	             app_encode_fun('type/nums/num', 
0.00/0.24	               app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                 'type/nums/num')), 
0.00/0.24	             'const/iterate/iterate'(sk_A, 'type/nums/num'), X0), 
0.00/0.24	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	             app_encode_fun(sk_A, $o), 
0.00/0.24	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), sk_A1), 
0.00/0.24	             sk_A2)), sk_A0)
0.00/0.24	        = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.24	            app_encode_app('type/nums/num', 
0.00/0.24	              app_encode_fun('type/nums/num', 'type/nums/num'), X0, 
0.00/0.24	              app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                'type/nums/num', 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                  app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                    'type/nums/num'), 
0.00/0.24	                  app_encode_app(
0.00/0.24	                    app_encode_fun('type/nums/num', 
0.00/0.24	                      app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                        'type/nums/num')), 
0.00/0.24	                    'const/iterate/iterate'(sk_A, 'type/nums/num'), X0), 
0.00/0.24	                  sk_A1), sk_A0)), 
0.00/0.24	            app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	              'type/nums/num', 
0.00/0.24	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                  'type/nums/num'), 
0.00/0.24	                app_encode_app(
0.00/0.24	                  app_encode_fun('type/nums/num', 
0.00/0.24	                    app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                      'type/nums/num')), 
0.00/0.24	                  'const/iterate/iterate'(sk_A, 'type/nums/num'), X0), sk_A2), 
0.00/0.24	              sk_A0))
0.00/0.24	       | ~ app_encode_app(
0.00/0.24	             app_encode_fun('type/nums/num', 
0.00/0.24	               app_encode_fun('type/nums/num', 'type/nums/num')), $o, 
0.00/0.24	             'const/iterate/monoidal'('type/nums/num'), X0)
0.00/0.24	       | app_encode_app(
0.00/0.24	           app_encode_fun('type/nums/num', 
0.00/0.24	             app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	           'type/nums/num', 'const/iterate/neutral'('type/nums/num'), 
0.00/0.24	           'const/arith/+')
0.00/0.24	          != app_encode_app(
0.00/0.24	               app_encode_fun('type/nums/num', 
0.00/0.24	                 app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	               'type/nums/num', 'const/iterate/neutral'('type/nums/num'), X0)),
0.00/0.24	    inference('simplify', [status(thm)], ['11'])).
0.00/0.24	tff('13', plain,
0.00/0.24	    (~ app_encode_app(
0.00/0.24	         app_encode_fun('type/nums/num', 
0.00/0.24	           app_encode_fun('type/nums/num', 'type/nums/num')), $o, 
0.00/0.24	         'const/iterate/monoidal'('type/nums/num'), 'const/arith/+')
0.00/0.24	     | app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	         'type/nums/num', 
0.00/0.24	         app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	           app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	             'type/nums/num'), 
0.00/0.24	           app_encode_app(
0.00/0.24	             app_encode_fun('type/nums/num', 
0.00/0.24	               app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                 'type/nums/num')), 
0.00/0.24	             'const/iterate/iterate'(sk_A, 'type/nums/num'), 'const/arith/+'), 
0.00/0.24	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	             app_encode_fun(sk_A, $o), 
0.00/0.24	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), sk_A1), 
0.00/0.24	             sk_A2)), sk_A0)
0.00/0.24	        = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.24	            app_encode_app('type/nums/num', 
0.00/0.24	              app_encode_fun('type/nums/num', 'type/nums/num'), 
0.00/0.24	              'const/arith/+', 
0.00/0.24	              app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                'type/nums/num', 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                  app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                    'type/nums/num'), 
0.00/0.24	                  app_encode_app(
0.00/0.24	                    app_encode_fun('type/nums/num', 
0.00/0.24	                      app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                        'type/nums/num')), 
0.00/0.24	                    'const/iterate/iterate'(sk_A, 'type/nums/num'), 
0.00/0.24	                    'const/arith/+'), sk_A1), sk_A0)), 
0.00/0.24	            app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	              'type/nums/num', 
0.00/0.24	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                  'type/nums/num'), 
0.00/0.24	                app_encode_app(
0.00/0.24	                  app_encode_fun('type/nums/num', 
0.00/0.24	                    app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                      'type/nums/num')), 
0.00/0.24	                  'const/iterate/iterate'(sk_A, 'type/nums/num'), 
0.00/0.24	                  'const/arith/+'), sk_A2), sk_A0))),
0.00/0.24	    inference('eq_res', [status(thm)], ['12'])).
0.00/0.24	tff(zf_stmt_16, axiom,
0.00/0.24	  (app_encode_app(app_encode_fun('type/nums/num',
0.00/0.24	                                 app_encode_fun('type/nums/num',
0.00/0.24	                                                'type/nums/num')),
0.00/0.24	                  $o,'const/iterate/monoidal'('type/nums/num'),
0.00/0.24	                  'const/arith/+'))).
0.00/0.24	tff('14', plain,
0.00/0.24	    app_encode_app(
0.00/0.24	      app_encode_fun('type/nums/num', 
0.00/0.24	        app_encode_fun('type/nums/num', 'type/nums/num')), $o, 
0.00/0.24	      'const/iterate/monoidal'('type/nums/num'), 'const/arith/+'),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_16])).
0.00/0.24	tff('15', plain,
0.00/0.24	    (~ $true
0.00/0.24	     | app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	         'type/nums/num', 
0.00/0.24	         app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	           app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	             'type/nums/num'), 
0.00/0.24	           app_encode_app(
0.00/0.24	             app_encode_fun('type/nums/num', 
0.00/0.24	               app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                 'type/nums/num')), 
0.00/0.24	             'const/iterate/iterate'(sk_A, 'type/nums/num'), 'const/arith/+'), 
0.00/0.24	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	             app_encode_fun(sk_A, $o), 
0.00/0.24	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), sk_A1), 
0.00/0.24	             sk_A2)), sk_A0)
0.00/0.24	        = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.24	            app_encode_app('type/nums/num', 
0.00/0.24	              app_encode_fun('type/nums/num', 'type/nums/num'), 
0.00/0.24	              'const/arith/+', 
0.00/0.24	              app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                'type/nums/num', 
0.00/0.24	                app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                  app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                    'type/nums/num'), 
0.00/0.24	                  app_encode_app(
0.00/0.24	                    app_encode_fun('type/nums/num', 
0.00/0.24	                      app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                      app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                        'type/nums/num')), 
0.00/0.24	                    'const/iterate/iterate'(sk_A, 'type/nums/num'), 
0.00/0.24	                    'const/arith/+'), sk_A1), sk_A0)), 
0.00/0.24	            app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	              'type/nums/num', 
0.00/0.24	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                  'type/nums/num'), 
0.00/0.24	                app_encode_app(
0.00/0.24	                  app_encode_fun('type/nums/num', 
0.00/0.24	                    app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                      'type/nums/num')), 
0.00/0.24	                  'const/iterate/iterate'(sk_A, 'type/nums/num'), 
0.00/0.24	                  'const/arith/+'), sk_A2), sk_A0))),
0.00/0.24	    inference('demod', [status(thm)], ['13', '14'])).
0.00/0.24	tff('16', plain,
0.00/0.24	    app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 'type/nums/num', 
0.00/0.24	      app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	        app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	          'type/nums/num'), 
0.00/0.24	        app_encode_app(
0.00/0.24	          app_encode_fun('type/nums/num', 
0.00/0.24	            app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	          app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	            app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	              'type/nums/num')), 
0.00/0.24	          'const/iterate/iterate'(sk_A, 'type/nums/num'), 'const/arith/+'), 
0.00/0.24	        app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A, $o), 
0.00/0.24	          app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	            app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	              app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), sk_A1), 
0.00/0.24	          sk_A2)), sk_A0)
0.00/0.24	     = app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.24	         app_encode_app('type/nums/num', 
0.00/0.24	           app_encode_fun('type/nums/num', 'type/nums/num'), 
0.00/0.24	           'const/arith/+', 
0.00/0.24	           app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	             'type/nums/num', 
0.00/0.24	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                 'type/nums/num'), 
0.00/0.24	               app_encode_app(
0.00/0.24	                 app_encode_fun('type/nums/num', 
0.00/0.24	                   app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                   app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                     'type/nums/num')), 
0.00/0.24	                 'const/iterate/iterate'(sk_A, 'type/nums/num'), 
0.00/0.24	                 'const/arith/+'), sk_A1), sk_A0)), 
0.00/0.24	         app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	           'type/nums/num', 
0.00/0.24	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	             app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	               'type/nums/num'), 
0.00/0.24	             app_encode_app(
0.00/0.24	               app_encode_fun('type/nums/num', 
0.00/0.24	                 app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                 app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                   'type/nums/num')), 
0.00/0.24	               'const/iterate/iterate'(sk_A, 'type/nums/num'), 
0.00/0.24	               'const/arith/+'), sk_A2), sk_A0)),
0.00/0.24	    inference('simplify', [status(thm)], ['15'])).
0.00/0.24	tff('17', plain,
0.00/0.24	    app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 'type/nums/num', 
0.00/0.24	      app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	        app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	          'type/nums/num'), 'const/iterate/nsum'(sk_A), 
0.00/0.24	        app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A, $o), 
0.00/0.24	          app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	            app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	              app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), sk_A1), 
0.00/0.24	          sk_A2)), sk_A0)
0.00/0.24	     != app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.24	          app_encode_app('type/nums/num', 
0.00/0.24	            app_encode_fun('type/nums/num', 'type/nums/num'), 
0.00/0.24	            'const/arith/+', 
0.00/0.24	            app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	              'type/nums/num', 
0.00/0.24	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                  'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A1), 
0.00/0.24	              sk_A0)), 
0.00/0.24	          app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	            'type/nums/num', 
0.00/0.24	            app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	              app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                'type/nums/num'), 'const/iterate/nsum'(sk_A), sk_A2), sk_A0)),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.24	tff(zf_stmt_17, axiom,
0.00/0.24	  (![A:$tType]:
0.00/0.24	     ('const/iterate/nsum'(A) =
0.00/0.24	      app_encode_app(app_encode_fun('type/nums/num',
0.00/0.24	                                    app_encode_fun('type/nums/num',
0.00/0.24	                                                   'type/nums/num')),
0.00/0.24	                     app_encode_fun(app_encode_fun(A,$o),
0.00/0.24	                                    app_encode_fun(app_encode_fun(A,
0.00/0.24	                                                                  'type/nums/num'),
0.00/0.24	                                                   'type/nums/num')),
0.00/0.24	                     'const/iterate/iterate'(A,'type/nums/num'),
0.00/0.24	                     'const/arith/+')))).
0.00/0.24	tff('18', plain,
0.00/0.24	    ![X10 : $tType]:
0.00/0.24	      'const/iterate/nsum'(X10)
0.00/0.24	       = app_encode_app(
0.00/0.24	           app_encode_fun('type/nums/num', 
0.00/0.24	             app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	           app_encode_fun(app_encode_fun(X10, $o), 
0.00/0.24	             app_encode_fun(app_encode_fun(X10, 'type/nums/num'), 
0.00/0.24	               'type/nums/num')), 
0.00/0.24	           'const/iterate/iterate'(X10, 'type/nums/num'), 'const/arith/+'),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_17])).
0.00/0.24	tff('19', plain,
0.00/0.24	    app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 'type/nums/num', 
0.00/0.24	      app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	        app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	          'type/nums/num'), 
0.00/0.24	        app_encode_app(
0.00/0.24	          app_encode_fun('type/nums/num', 
0.00/0.24	            app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	          app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	            app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	              'type/nums/num')), 
0.00/0.24	          'const/iterate/iterate'(sk_A, 'type/nums/num'), 'const/arith/+'), 
0.00/0.24	        app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_A, $o), 
0.00/0.24	          app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	            app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	              app_encode_fun(sk_A, $o)), 'const/sets/UNION'(sk_A), sk_A1), 
0.00/0.24	          sk_A2)), sk_A0)
0.00/0.24	     != app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.24	          app_encode_app('type/nums/num', 
0.00/0.24	            app_encode_fun('type/nums/num', 'type/nums/num'), 
0.00/0.24	            'const/arith/+', 
0.00/0.24	            app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	              'type/nums/num', 
0.00/0.24	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	                app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                  'type/nums/num'), 
0.00/0.24	                app_encode_app(
0.00/0.24	                  app_encode_fun('type/nums/num', 
0.00/0.24	                    app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                    app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                      'type/nums/num')), 
0.00/0.24	                  'const/iterate/iterate'(sk_A, 'type/nums/num'), 
0.00/0.24	                  'const/arith/+'), sk_A1), sk_A0)), 
0.00/0.24	          app_encode_app(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	            'type/nums/num', 
0.00/0.24	            app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.24	              app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                'type/nums/num'), 
0.00/0.24	              app_encode_app(
0.00/0.24	                app_encode_fun('type/nums/num', 
0.00/0.24	                  app_encode_fun('type/nums/num', 'type/nums/num')), 
0.00/0.24	                app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.24	                  app_encode_fun(app_encode_fun(sk_A, 'type/nums/num'), 
0.00/0.24	                    'type/nums/num')), 
0.00/0.24	                'const/iterate/iterate'(sk_A, 'type/nums/num'), 
0.00/0.24	                'const/arith/+'), sk_A2), sk_A0)),
0.00/0.24	    inference('demod', [status(thm)], ['17', '18', '18', '18'])).
0.00/0.24	tff('20', plain, $false,
0.00/0.24	    inference('simplify_reflect-', [status(thm)], ['16', '19'])).
0.00/0.24	
0.00/0.24	% SZS output end Refutation
0.00/0.24	EOF
