0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n066.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:40:24 CST 2018
0.91/1.11	% done 25 iterations in 0.904s
0.91/1.11	% SZS status Theorem for 'stdin'
0.91/1.11	% SZS output start Refutation
0.91/1.12	tff(zf_stmt_18, axiom,
0.91/1.12	  (![A:$tType]:
0.91/1.12	     ('const/iterate/sum'(A) =
0.91/1.12	      app_encode_app(app_encode_fun('type/realax/real',
0.91/1.12	                                    app_encode_fun('type/realax/real',
0.91/1.12	                                                   'type/realax/real')),
0.91/1.12	                     app_encode_fun(app_encode_fun(A,$o),
0.91/1.12	                                    app_encode_fun(app_encode_fun(A,
0.91/1.12	                                                                  'type/realax/real'),
0.91/1.12	                                                   'type/realax/real')),
0.91/1.12	                     'const/iterate/iterate'(A,'type/realax/real'),
0.91/1.12	                     'const/realax/real_add')))).
0.91/1.12	tff('0', plain,
0.91/1.12	    ![X7 : $tType]:
0.91/1.12	      'const/iterate/sum'(X7)
0.91/1.12	       = app_encode_app(
0.91/1.12	           app_encode_fun('type/realax/real', 
0.91/1.12	             app_encode_fun('type/realax/real', 'type/realax/real')), 
0.91/1.12	           app_encode_fun(app_encode_fun(X7, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(X7, 'type/realax/real'), 
0.91/1.12	               'type/realax/real')), 
0.91/1.12	           'const/iterate/iterate'(X7, 'type/realax/real'), 
0.91/1.12	           'const/realax/real_add'),
0.91/1.12	    inference('cnf', [status(esa)], [zf_stmt_18])).
0.91/1.12	tff(zf_stmt_16, axiom,
0.91/1.12	  (![C:$tType,A:$tType,B:$tType,A0:app_encode_fun(C,app_encode_fun(C,C))]:
0.91/1.12	     (app_encode_app(app_encode_fun(C,app_encode_fun(C,C)),$o,
0.91/1.12	                     'const/iterate/monoidal'(C),A0) =>
0.91/1.12	      (![A1:app_encode_fun(B,C),A2:app_encode_fun(A,B),
0.91/1.12	         A3:app_encode_fun(A,$o)]:
0.91/1.12	         ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A3) & 
0.91/1.12	           (![A4:A,A5:A]:
0.91/1.12	              ((app_encode_app(app_encode_fun(A,$o),$o,
0.91/1.12	                               app_encode_app(A,
0.91/1.12	                                              app_encode_fun(app_encode_fun(
0.91/1.12	                                                             A,$o),$o),
0.91/1.12	                                              'const/sets/IN'(A),A4),
0.91/1.12	                               A3) & 
0.91/1.12	                app_encode_app(app_encode_fun(A,$o),$o,
0.91/1.12	                               app_encode_app(A,
0.91/1.12	                                              app_encode_fun(app_encode_fun(
0.91/1.12	                                                             A,$o),$o),
0.91/1.12	                                              'const/sets/IN'(A),A5),
0.91/1.12	                               A3) & 
0.91/1.12	                (A4 != A5) & 
0.91/1.12	                (app_encode_app(A,B,A2,A4) = app_encode_app(A,B,A2,A5))) =>
0.91/1.12	               (app_encode_app(B,C,A1,app_encode_app(A,B,A2,A4)) =
0.91/1.12	                app_encode_app(app_encode_fun(C,app_encode_fun(C,C)),C,
0.91/1.12	                               'const/iterate/neutral'(C),A0))))) =>
0.91/1.12	          (app_encode_app(app_encode_fun(B,C),C,
0.91/1.12	                          app_encode_app(app_encode_fun(B,$o),
0.91/1.12	                                         app_encode_fun(app_encode_fun(B,C),C),
0.91/1.12	                                         app_encode_app(app_encode_fun(
0.91/1.12	                                                        C,app_encode_fun(C,C)),
0.91/1.12	                                                        app_encode_fun(
0.91/1.12	                                                        app_encode_fun(B,$o),
0.91/1.12	                                                        app_encode_fun(
0.91/1.12	                                                        app_encode_fun(B,C),C)),
0.91/1.12	                                                        'const/iterate/iterate'(
0.91/1.12	                                                        B,C),A0),
0.91/1.12	                                         app_encode_app(app_encode_fun(A,$o),
0.91/1.12	                                                        app_encode_fun(B,$o),
0.91/1.12	                                                        app_encode_app(
0.91/1.12	                                                        app_encode_fun(A,B),
0.91/1.12	                                                        app_encode_fun(
0.91/1.12	                                                        app_encode_fun(A,$o),
0.91/1.12	                                                        app_encode_fun(B,$o)),
0.91/1.12	                                                        'const/sets/IMAGE'(
0.91/1.12	                                                        A,B),A2),A3)),
0.91/1.12	                          A1) =
0.91/1.12	           app_encode_app(app_encode_fun(A,C),C,
0.91/1.12	                          app_encode_app(app_encode_fun(A,$o),
0.91/1.12	                                         app_encode_fun(app_encode_fun(A,C),C),
0.91/1.12	                                         app_encode_app(app_encode_fun(
0.91/1.12	                                                        C,app_encode_fun(C,C)),
0.91/1.12	                                                        app_encode_fun(
0.91/1.12	                                                        app_encode_fun(A,$o),
0.91/1.12	                                                        app_encode_fun(
0.91/1.12	                                                        app_encode_fun(A,C),C)),
0.91/1.12	                                                        'const/iterate/iterate'(
0.91/1.12	                                                        A,C),A0),
0.91/1.12	                                         A3),
0.91/1.12	                          app_encode_app(app_encode_fun(A,B),
0.91/1.12	                                         app_encode_fun(A,C),
0.91/1.12	                                         app_encode_app(app_encode_fun(B,C),
0.91/1.12	                                                        app_encode_fun(
0.91/1.12	                                                        app_encode_fun(A,B),
0.91/1.12	                                                        app_encode_fun(A,C)),
0.91/1.12	                                                        'const/trivia/o'(
0.91/1.12	                                                        B,A,C),A1),
0.91/1.12	                                         A2)))))))).
0.91/1.12	tff('1', plain,
0.91/1.12	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : $tType, 
0.91/1.12	      X3 : app_encode_fun(X0, X2), X4 : $tType, X5 : app_encode_fun(X2, X4), 
0.91/1.12	      X6 : app_encode_fun(X4, app_encode_fun(X4, X4))]:
0.91/1.12	      (~ app_encode_app(app_encode_fun(X0, $o), $o, 'const/sets/FINITE'(X0), 
0.91/1.12	           X1)
0.91/1.12	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.91/1.12	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.91/1.12	             'const/sets/IN'(X0), sk_A4(X2, X0, X4, X1, X3, X5, X6)), X1)
0.91/1.12	       | app_encode_app(app_encode_fun(X2, X4), X4, 
0.91/1.12	           app_encode_app(app_encode_fun(X2, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(X2, X4), X4), 
0.91/1.12	             app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.91/1.12	               app_encode_fun(app_encode_fun(X2, $o), 
0.91/1.12	                 app_encode_fun(app_encode_fun(X2, X4), X4)), 
0.91/1.12	               'const/iterate/iterate'(X2, X4), X6), 
0.91/1.12	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X2, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(X0, X2), 
0.91/1.12	                 app_encode_fun(app_encode_fun(X0, $o), 
0.91/1.12	                   app_encode_fun(X2, $o)), 'const/sets/IMAGE'(X0, X2), X3), 
0.91/1.12	               X1)), X5)
0.91/1.12	          = app_encode_app(app_encode_fun(X0, X4), X4, 
0.91/1.12	              app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	                app_encode_fun(app_encode_fun(X0, X4), X4), 
0.91/1.12	                app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X0, $o), 
0.91/1.12	                    app_encode_fun(app_encode_fun(X0, X4), X4)), 
0.91/1.12	                  'const/iterate/iterate'(X0, X4), X6), X1), 
0.91/1.12	              app_encode_app(app_encode_fun(X0, X2), app_encode_fun(X0, X4), 
0.91/1.12	                app_encode_app(app_encode_fun(X2, X4), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X0, X2), 
0.91/1.12	                    app_encode_fun(X0, X4)), 'const/trivia/o'(X2, X0, X4), 
0.91/1.12	                  X5), X3))
0.91/1.12	       | ~ app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), $o, 
0.91/1.12	             'const/iterate/monoidal'(X4), X6)),
0.91/1.12	    inference('cnf', [status(esa)], [zf_stmt_16])).
0.91/1.12	tff('2', plain,
0.91/1.12	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, X0), 
0.91/1.12	      X3 : app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	      X4 : app_encode_fun(X1, $o)]:
0.91/1.12	      (app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	         'type/realax/real', 
0.91/1.12	         app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	           app_encode_fun(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	             'type/realax/real'), 'const/iterate/sum'(X0), 
0.91/1.12	           app_encode_app(app_encode_fun(X1, $o), app_encode_fun(X0, $o), 
0.91/1.12	             app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	               app_encode_fun(app_encode_fun(X1, $o), app_encode_fun(X0, $o)), 
0.91/1.12	               'const/sets/IMAGE'(X1, X0), X2), X4)), X3)
0.91/1.12	        = app_encode_app(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	            'type/realax/real', 
0.91/1.12	            app_encode_app(app_encode_fun(X1, $o), 
0.91/1.12	              app_encode_fun(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                'type/realax/real'), 
0.91/1.12	              app_encode_app(
0.91/1.12	                app_encode_fun('type/realax/real', 
0.91/1.12	                  app_encode_fun('type/realax/real', 'type/realax/real')), 
0.91/1.12	                app_encode_fun(app_encode_fun(X1, $o), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                    'type/realax/real')), 
0.91/1.12	                'const/iterate/iterate'(X1, 'type/realax/real'), 
0.91/1.12	                'const/realax/real_add'), X4), 
0.91/1.12	            app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	              app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	              app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	                app_encode_fun(app_encode_fun(X1, X0), 
0.91/1.12	                  app_encode_fun(X1, 'type/realax/real')), 
0.91/1.12	                'const/trivia/o'(X0, X1, 'type/realax/real'), X3), X2))
0.91/1.12	       | ~ app_encode_app(
0.91/1.12	             app_encode_fun('type/realax/real', 
0.91/1.12	               app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.91/1.12	             'const/iterate/monoidal'('type/realax/real'), 
0.91/1.12	             'const/realax/real_add')
0.91/1.12	       | app_encode_app(app_encode_fun(X1, $o), $o, 
0.91/1.12	           app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
0.91/1.12	             'const/sets/IN'(X1), 
0.91/1.12	             sk_A4(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	               'const/realax/real_add')), X4)
0.91/1.12	       | ~ app_encode_app(app_encode_fun(X1, $o), $o, 
0.91/1.12	             'const/sets/FINITE'(X1), X4)),
0.91/1.12	    inference('sup+', [status(thm)], ['0', '1'])).
0.91/1.12	tff(zf_stmt_17, axiom,
0.91/1.12	  (app_encode_app(app_encode_fun('type/realax/real',
0.91/1.12	                                 app_encode_fun('type/realax/real',
0.91/1.12	                                                'type/realax/real')),
0.91/1.12	                  $o,'const/iterate/monoidal'('type/realax/real'),
0.91/1.12	                  'const/realax/real_add'))).
0.91/1.12	tff('3', plain,
0.91/1.12	    app_encode_app(
0.91/1.12	      app_encode_fun('type/realax/real', 
0.91/1.12	        app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.91/1.12	      'const/iterate/monoidal'('type/realax/real'), 'const/realax/real_add'),
0.91/1.12	    inference('cnf', [status(esa)], [zf_stmt_17])).
0.91/1.12	tff('4', plain,
0.91/1.12	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, X0), 
0.91/1.12	      X3 : app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	      X4 : app_encode_fun(X1, $o)]:
0.91/1.12	      (app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	         'type/realax/real', 
0.91/1.12	         app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	           app_encode_fun(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	             'type/realax/real'), 'const/iterate/sum'(X0), 
0.91/1.12	           app_encode_app(app_encode_fun(X1, $o), app_encode_fun(X0, $o), 
0.91/1.12	             app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	               app_encode_fun(app_encode_fun(X1, $o), app_encode_fun(X0, $o)), 
0.91/1.12	               'const/sets/IMAGE'(X1, X0), X2), X4)), X3)
0.91/1.12	        = app_encode_app(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	            'type/realax/real', 
0.91/1.12	            app_encode_app(app_encode_fun(X1, $o), 
0.91/1.12	              app_encode_fun(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                'type/realax/real'), 'const/iterate/sum'(X1), X4), 
0.91/1.12	            app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	              app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	              app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	                app_encode_fun(app_encode_fun(X1, X0), 
0.91/1.12	                  app_encode_fun(X1, 'type/realax/real')), 
0.91/1.12	                'const/trivia/o'(X0, X1, 'type/realax/real'), X3), X2))
0.91/1.12	       | ~ $true
0.91/1.12	       | app_encode_app(app_encode_fun(X1, $o), $o, 
0.91/1.12	           app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
0.91/1.12	             'const/sets/IN'(X1), 
0.91/1.12	             sk_A4(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	               'const/realax/real_add')), X4)
0.91/1.12	       | ~ app_encode_app(app_encode_fun(X1, $o), $o, 
0.91/1.12	             'const/sets/FINITE'(X1), X4)),
0.91/1.12	    inference('demod', [status(thm)], ['2', '0', '3'])).
0.91/1.12	tff('5', plain,
0.91/1.12	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, X0), 
0.91/1.12	      X3 : app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	      X4 : app_encode_fun(X1, $o)]:
0.91/1.12	      (~ app_encode_app(app_encode_fun(X1, $o), $o, 'const/sets/FINITE'(X1), 
0.91/1.12	           X4)
0.91/1.12	       | app_encode_app(app_encode_fun(X1, $o), $o, 
0.91/1.12	           app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
0.91/1.12	             'const/sets/IN'(X1), 
0.91/1.12	             sk_A4(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	               'const/realax/real_add')), X4)
0.91/1.12	       | app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	           'type/realax/real', 
0.91/1.12	           app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	               'type/realax/real'), 'const/iterate/sum'(X0), 
0.91/1.12	             app_encode_app(app_encode_fun(X1, $o), app_encode_fun(X0, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	                 app_encode_fun(app_encode_fun(X1, $o), 
0.91/1.12	                   app_encode_fun(X0, $o)), 'const/sets/IMAGE'(X1, X0), X2), 
0.91/1.12	               X4)), X3)
0.91/1.12	          = app_encode_app(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	              'type/realax/real', 
0.91/1.12	              app_encode_app(app_encode_fun(X1, $o), 
0.91/1.12	                app_encode_fun(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                  'type/realax/real'), 'const/iterate/sum'(X1), X4), 
0.91/1.12	              app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	                app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X1, X0), 
0.91/1.12	                    app_encode_fun(X1, 'type/realax/real')), 
0.91/1.12	                  'const/trivia/o'(X0, X1, 'type/realax/real'), X3), X2))),
0.91/1.12	    inference('simplify', [status(thm)], ['4'])).
0.91/1.12	tff(zf_stmt_20, conjecture,
0.91/1.12	  (![A:$tType,B:$tType,A0:app_encode_fun(B,'type/realax/real'),
0.91/1.12	     A1:app_encode_fun(A,B),A2:app_encode_fun(A,$o)]:
0.91/1.12	     ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A2) & 
0.91/1.12	       (![A3:A,A4:A]:
0.91/1.12	          ((app_encode_app(app_encode_fun(A,$o),$o,
0.91/1.12	                           app_encode_app(A,
0.91/1.12	                                          app_encode_fun(app_encode_fun(A,$o),
0.91/1.12	                                                         $o),
0.91/1.12	                                          'const/sets/IN'(A),A3),
0.91/1.12	                           A2) & 
0.91/1.12	            app_encode_app(app_encode_fun(A,$o),$o,
0.91/1.12	                           app_encode_app(A,
0.91/1.12	                                          app_encode_fun(app_encode_fun(A,$o),
0.91/1.12	                                                         $o),
0.91/1.12	                                          'const/sets/IN'(A),A4),
0.91/1.12	                           A2) & 
0.91/1.12	            (A3 != A4) & 
0.91/1.12	            (app_encode_app(A,B,A1,A3) = app_encode_app(A,B,A1,A4))) =>
0.91/1.12	           (app_encode_app(B,'type/realax/real',A0,app_encode_app(A,B,A1,A3)) =
0.91/1.12	            app_encode_app('type/nums/num','type/realax/real',
0.91/1.12	                           'const/realax/real_of_num',
0.91/1.12	                           app_encode_app('type/nums/num','type/nums/num',
0.91/1.12	                                          'const/nums/NUMERAL',
0.91/1.12	                                          'const/nums/_0')))))) =>
0.91/1.12	      (app_encode_app(app_encode_fun(B,'type/realax/real'),
0.91/1.12	                      'type/realax/real',
0.91/1.12	                      app_encode_app(app_encode_fun(B,$o),
0.91/1.12	                                     app_encode_fun(app_encode_fun(B,
0.91/1.12	                                                                   'type/realax/real'),
0.91/1.12	                                                    'type/realax/real'),
0.91/1.12	                                     'const/iterate/sum'(B),
0.91/1.12	                                     app_encode_app(app_encode_fun(A,$o),
0.91/1.12	                                                    app_encode_fun(B,$o),
0.91/1.12	                                                    app_encode_app(app_encode_fun(
0.91/1.12	                                                                   A,B),
0.91/1.12	                                                                   app_encode_fun(
0.91/1.12	                                                                   app_encode_fun(
0.91/1.12	                                                                   A,$o),
0.91/1.12	                                                                   app_encode_fun(
0.91/1.12	                                                                   B,$o)),
0.91/1.12	                                                                   'const/sets/IMAGE'(
0.91/1.12	                                                                   A,B),A1),
0.91/1.12	                                                    A2)),
0.91/1.12	                      A0) =
0.91/1.12	       app_encode_app(app_encode_fun(A,'type/realax/real'),
0.91/1.12	                      'type/realax/real',
0.91/1.12	                      app_encode_app(app_encode_fun(A,$o),
0.91/1.12	                                     app_encode_fun(app_encode_fun(A,
0.91/1.12	                                                                   'type/realax/real'),
0.91/1.12	                                                    'type/realax/real'),
0.91/1.12	                                     'const/iterate/sum'(A),A2),
0.91/1.12	                      app_encode_app(app_encode_fun(A,B),
0.91/1.12	                                     app_encode_fun(A,'type/realax/real'),
0.91/1.12	                                     app_encode_app(app_encode_fun(B,
0.91/1.12	                                                                   'type/realax/real'),
0.91/1.12	                                                    app_encode_fun(app_encode_fun(
0.91/1.12	                                                                   A,B),
0.91/1.12	                                                                   app_encode_fun(
0.91/1.12	                                                                   A,
0.91/1.12	                                                                   'type/realax/real')),
0.91/1.12	                                                    'const/trivia/o'(
0.91/1.12	                                                    B,A,'type/realax/real'),
0.91/1.12	                                                    A0),
0.91/1.12	                                     A1)))))).
0.91/1.12	tff(zf_stmt_0, negated_conjecture,
0.91/1.12	  (~
0.91/1.12	    (![A:$tType,B:$tType,A0:app_encode_fun(B,'type/realax/real'),
0.91/1.12	       A1:app_encode_fun(A,B),A2:app_encode_fun(A,$o)]:
0.91/1.12	       ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A2) & 
0.91/1.12	         (![A3:A,A4:A]:
0.91/1.12	            ((app_encode_app(app_encode_fun(A,$o),$o,
0.91/1.12	                             app_encode_app(A,
0.91/1.12	                                            app_encode_fun(app_encode_fun(
0.91/1.12	                                                           A,$o),$o),
0.91/1.12	                                            'const/sets/IN'(A),A3),
0.91/1.12	                             A2) & 
0.91/1.12	              app_encode_app(app_encode_fun(A,$o),$o,
0.91/1.12	                             app_encode_app(A,
0.91/1.12	                                            app_encode_fun(app_encode_fun(
0.91/1.12	                                                           A,$o),$o),
0.91/1.12	                                            'const/sets/IN'(A),A4),
0.91/1.12	                             A2) & 
0.91/1.12	              (A3 != A4) & 
0.91/1.12	              (app_encode_app(A,B,A1,A3) = app_encode_app(A,B,A1,A4))) =>
0.91/1.12	             (app_encode_app(B,'type/realax/real',A0,
0.91/1.12	                             app_encode_app(A,B,A1,A3)) =
0.91/1.12	              app_encode_app('type/nums/num','type/realax/real',
0.91/1.12	                             'const/realax/real_of_num',
0.91/1.12	                             app_encode_app('type/nums/num','type/nums/num',
0.91/1.12	                                            'const/nums/NUMERAL',
0.91/1.12	                                            'const/nums/_0')))))) =>
0.91/1.12	        (app_encode_app(app_encode_fun(B,'type/realax/real'),
0.91/1.12	                        'type/realax/real',
0.91/1.12	                        app_encode_app(app_encode_fun(B,$o),
0.91/1.12	                                       app_encode_fun(app_encode_fun(
0.91/1.12	                                                      B,'type/realax/real'),
0.91/1.12	                                                      'type/realax/real'),
0.91/1.12	                                       'const/iterate/sum'(B),
0.91/1.12	                                       app_encode_app(app_encode_fun(A,$o),
0.91/1.12	                                                      app_encode_fun(B,$o),
0.91/1.12	                                                      app_encode_app(
0.91/1.12	                                                      app_encode_fun(A,B),
0.91/1.12	                                                      app_encode_fun(
0.91/1.12	                                                      app_encode_fun(A,$o),
0.91/1.12	                                                      app_encode_fun(B,$o)),
0.91/1.12	                                                      'const/sets/IMAGE'(A,B),
0.91/1.12	                                                      A1),A2)),
0.91/1.12	                        A0) =
0.91/1.12	         app_encode_app(app_encode_fun(A,'type/realax/real'),
0.91/1.12	                        'type/realax/real',
0.91/1.12	                        app_encode_app(app_encode_fun(A,$o),
0.91/1.12	                                       app_encode_fun(app_encode_fun(
0.91/1.12	                                                      A,'type/realax/real'),
0.91/1.12	                                                      'type/realax/real'),
0.91/1.12	                                       'const/iterate/sum'(A),A2),
0.91/1.12	                        app_encode_app(app_encode_fun(A,B),
0.91/1.12	                                       app_encode_fun(A,'type/realax/real'),
0.91/1.12	                                       app_encode_app(app_encode_fun(
0.91/1.12	                                                      B,'type/realax/real'),
0.91/1.12	                                                      app_encode_fun(
0.91/1.12	                                                      app_encode_fun(A,B),
0.91/1.12	                                                      app_encode_fun(
0.91/1.12	                                                      A,'type/realax/real')),
0.91/1.12	                                                      'const/trivia/o'(
0.91/1.12	                                                      B,A,'type/realax/real'),
0.91/1.12	                                                      A0),
0.91/1.12	                                       A1))))))).
0.91/1.12	tff('6', plain,
0.91/1.12	    app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	      'type/realax/real', 
0.91/1.12	      app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	        app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	          'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	        app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_B, $o), 
0.91/1.12	          app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	            app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	              app_encode_fun(sk_B, $o)), 'const/sets/IMAGE'(sk_A, sk_B), 
0.91/1.12	            sk_A1), sk_A2)), sk_A0)
0.91/1.12	     != app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.91/1.12	          'type/realax/real', 
0.91/1.12	          app_encode_app(app_encode_fun(sk_A, $o), 
0.91/1.12	            app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.91/1.12	              'type/realax/real'), 'const/iterate/sum'(sk_A), sk_A2), 
0.91/1.12	          app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	            app_encode_fun(sk_A, 'type/realax/real'), 
0.91/1.12	            app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	              app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.91/1.12	                app_encode_fun(sk_A, 'type/realax/real')), 
0.91/1.12	              'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), 
0.91/1.12	            sk_A1)),
0.91/1.12	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.91/1.12	tff('7', plain,
0.91/1.12	    (app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	       'type/realax/real', 
0.91/1.12	       app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	         app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	           'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_B, $o), 
0.91/1.12	           app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	               app_encode_fun(sk_B, $o)), 'const/sets/IMAGE'(sk_A, sk_B), 
0.91/1.12	             sk_A1), sk_A2)), sk_A0)
0.91/1.12	      != app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	           'type/realax/real', 
0.91/1.12	           app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	               'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	             app_encode_app(app_encode_fun(sk_A, $o), 
0.91/1.12	               app_encode_fun(sk_B, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	                   app_encode_fun(sk_B, $o)), 
0.91/1.12	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.91/1.12	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.91/1.12	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.91/1.12	           'const/sets/IN'(sk_A), 
0.91/1.12	           sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	             'const/realax/real_add')), sk_A2)
0.91/1.12	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.91/1.12	           'const/sets/FINITE'(sk_A), sk_A2)),
0.91/1.12	    inference('sup-', [status(thm)], ['5', '6'])).
0.91/1.12	tff('8', plain,
0.91/1.12	    app_encode_app(app_encode_fun(sk_A, $o), $o, 'const/sets/FINITE'(sk_A), 
0.91/1.12	      sk_A2),
0.91/1.12	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.91/1.12	tff('9', plain,
0.91/1.12	    (app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	       'type/realax/real', 
0.91/1.12	       app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	         app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	           'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_B, $o), 
0.91/1.12	           app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	               app_encode_fun(sk_B, $o)), 'const/sets/IMAGE'(sk_A, sk_B), 
0.91/1.12	             sk_A1), sk_A2)), sk_A0)
0.91/1.12	      != app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	           'type/realax/real', 
0.91/1.12	           app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	               'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	             app_encode_app(app_encode_fun(sk_A, $o), 
0.91/1.12	               app_encode_fun(sk_B, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	                   app_encode_fun(sk_B, $o)), 
0.91/1.12	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.91/1.12	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.91/1.12	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.91/1.12	           'const/sets/IN'(sk_A), 
0.91/1.12	           sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	             'const/realax/real_add')), sk_A2)
0.91/1.12	     | ~ $true),
0.91/1.12	    inference('demod', [status(thm)], ['7', '8'])).
0.91/1.12	tff('10', plain,
0.91/1.12	    app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.91/1.12	      app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.91/1.12	        'const/sets/IN'(sk_A), 
0.91/1.12	        sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	          'const/realax/real_add')), sk_A2),
0.91/1.12	    inference('simplify', [status(thm)], ['9'])).
0.91/1.12	tff('11', plain,
0.91/1.12	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : $tType, 
0.91/1.12	      X3 : app_encode_fun(X0, X2), X4 : $tType, X5 : app_encode_fun(X2, X4), 
0.91/1.12	      X6 : app_encode_fun(X4, app_encode_fun(X4, X4))]:
0.91/1.12	      (~ app_encode_app(app_encode_fun(X0, $o), $o, 'const/sets/FINITE'(X0), 
0.91/1.12	           X1)
0.91/1.12	       | app_encode_app(app_encode_fun(X0, $o), $o, 
0.91/1.12	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
0.91/1.12	             'const/sets/IN'(X0), sk_A5(X2, X0, X4, X1, X3, X5, X6)), X1)
0.91/1.12	       | app_encode_app(app_encode_fun(X2, X4), X4, 
0.91/1.12	           app_encode_app(app_encode_fun(X2, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(X2, X4), X4), 
0.91/1.12	             app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.91/1.12	               app_encode_fun(app_encode_fun(X2, $o), 
0.91/1.12	                 app_encode_fun(app_encode_fun(X2, X4), X4)), 
0.91/1.12	               'const/iterate/iterate'(X2, X4), X6), 
0.91/1.12	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X2, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(X0, X2), 
0.91/1.12	                 app_encode_fun(app_encode_fun(X0, $o), 
0.91/1.12	                   app_encode_fun(X2, $o)), 'const/sets/IMAGE'(X0, X2), X3), 
0.91/1.12	               X1)), X5)
0.91/1.12	          = app_encode_app(app_encode_fun(X0, X4), X4, 
0.91/1.12	              app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	                app_encode_fun(app_encode_fun(X0, X4), X4), 
0.91/1.12	                app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X0, $o), 
0.91/1.12	                    app_encode_fun(app_encode_fun(X0, X4), X4)), 
0.91/1.12	                  'const/iterate/iterate'(X0, X4), X6), X1), 
0.91/1.12	              app_encode_app(app_encode_fun(X0, X2), app_encode_fun(X0, X4), 
0.91/1.12	                app_encode_app(app_encode_fun(X2, X4), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X0, X2), 
0.91/1.12	                    app_encode_fun(X0, X4)), 'const/trivia/o'(X2, X0, X4), 
0.91/1.12	                  X5), X3))
0.91/1.12	       | ~ app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), $o, 
0.91/1.12	             'const/iterate/monoidal'(X4), X6)),
0.91/1.12	    inference('cnf', [status(esa)], [zf_stmt_16])).
0.91/1.12	tff('12', plain,
0.91/1.12	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, X0), 
0.91/1.12	      X3 : app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	      X4 : app_encode_fun(X1, $o)]:
0.91/1.12	      (app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	         'type/realax/real', 
0.91/1.12	         app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	           app_encode_fun(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	             'type/realax/real'), 'const/iterate/sum'(X0), 
0.91/1.12	           app_encode_app(app_encode_fun(X1, $o), app_encode_fun(X0, $o), 
0.91/1.12	             app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	               app_encode_fun(app_encode_fun(X1, $o), app_encode_fun(X0, $o)), 
0.91/1.12	               'const/sets/IMAGE'(X1, X0), X2), X4)), X3)
0.91/1.12	        = app_encode_app(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	            'type/realax/real', 
0.91/1.12	            app_encode_app(app_encode_fun(X1, $o), 
0.91/1.12	              app_encode_fun(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                'type/realax/real'), 
0.91/1.12	              app_encode_app(
0.91/1.12	                app_encode_fun('type/realax/real', 
0.91/1.12	                  app_encode_fun('type/realax/real', 'type/realax/real')), 
0.91/1.12	                app_encode_fun(app_encode_fun(X1, $o), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                    'type/realax/real')), 
0.91/1.12	                'const/iterate/iterate'(X1, 'type/realax/real'), 
0.91/1.12	                'const/realax/real_add'), X4), 
0.91/1.12	            app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	              app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	              app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	                app_encode_fun(app_encode_fun(X1, X0), 
0.91/1.12	                  app_encode_fun(X1, 'type/realax/real')), 
0.91/1.12	                'const/trivia/o'(X0, X1, 'type/realax/real'), X3), X2))
0.91/1.12	       | ~ app_encode_app(
0.91/1.12	             app_encode_fun('type/realax/real', 
0.91/1.12	               app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.91/1.12	             'const/iterate/monoidal'('type/realax/real'), 
0.91/1.12	             'const/realax/real_add')
0.91/1.12	       | app_encode_app(app_encode_fun(X1, $o), $o, 
0.91/1.12	           app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
0.91/1.12	             'const/sets/IN'(X1), 
0.91/1.12	             sk_A5(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	               'const/realax/real_add')), X4)
0.91/1.12	       | ~ app_encode_app(app_encode_fun(X1, $o), $o, 
0.91/1.12	             'const/sets/FINITE'(X1), X4)),
0.91/1.12	    inference('sup+', [status(thm)], ['0', '11'])).
0.91/1.12	tff('13', plain,
0.91/1.12	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, X0), 
0.91/1.12	      X3 : app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	      X4 : app_encode_fun(X1, $o)]:
0.91/1.12	      (app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	         'type/realax/real', 
0.91/1.12	         app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	           app_encode_fun(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	             'type/realax/real'), 'const/iterate/sum'(X0), 
0.91/1.12	           app_encode_app(app_encode_fun(X1, $o), app_encode_fun(X0, $o), 
0.91/1.12	             app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	               app_encode_fun(app_encode_fun(X1, $o), app_encode_fun(X0, $o)), 
0.91/1.12	               'const/sets/IMAGE'(X1, X0), X2), X4)), X3)
0.91/1.12	        = app_encode_app(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	            'type/realax/real', 
0.91/1.12	            app_encode_app(app_encode_fun(X1, $o), 
0.91/1.12	              app_encode_fun(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                'type/realax/real'), 'const/iterate/sum'(X1), X4), 
0.91/1.12	            app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	              app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	              app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	                app_encode_fun(app_encode_fun(X1, X0), 
0.91/1.12	                  app_encode_fun(X1, 'type/realax/real')), 
0.91/1.12	                'const/trivia/o'(X0, X1, 'type/realax/real'), X3), X2))
0.91/1.12	       | ~ $true
0.91/1.12	       | app_encode_app(app_encode_fun(X1, $o), $o, 
0.91/1.12	           app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
0.91/1.12	             'const/sets/IN'(X1), 
0.91/1.12	             sk_A5(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	               'const/realax/real_add')), X4)
0.91/1.12	       | ~ app_encode_app(app_encode_fun(X1, $o), $o, 
0.91/1.12	             'const/sets/FINITE'(X1), X4)),
0.91/1.12	    inference('demod', [status(thm)], ['12', '0', '3'])).
0.91/1.12	tff('14', plain,
0.91/1.12	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, X0), 
0.91/1.12	      X3 : app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	      X4 : app_encode_fun(X1, $o)]:
0.91/1.12	      (~ app_encode_app(app_encode_fun(X1, $o), $o, 'const/sets/FINITE'(X1), 
0.91/1.12	           X4)
0.91/1.12	       | app_encode_app(app_encode_fun(X1, $o), $o, 
0.91/1.12	           app_encode_app(X1, app_encode_fun(app_encode_fun(X1, $o), $o), 
0.91/1.12	             'const/sets/IN'(X1), 
0.91/1.12	             sk_A5(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	               'const/realax/real_add')), X4)
0.91/1.12	       | app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	           'type/realax/real', 
0.91/1.12	           app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	               'type/realax/real'), 'const/iterate/sum'(X0), 
0.91/1.12	             app_encode_app(app_encode_fun(X1, $o), app_encode_fun(X0, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	                 app_encode_fun(app_encode_fun(X1, $o), 
0.91/1.12	                   app_encode_fun(X0, $o)), 'const/sets/IMAGE'(X1, X0), X2), 
0.91/1.12	               X4)), X3)
0.91/1.12	          = app_encode_app(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	              'type/realax/real', 
0.91/1.12	              app_encode_app(app_encode_fun(X1, $o), 
0.91/1.12	                app_encode_fun(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                  'type/realax/real'), 'const/iterate/sum'(X1), X4), 
0.91/1.12	              app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	                app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X1, X0), 
0.91/1.12	                    app_encode_fun(X1, 'type/realax/real')), 
0.91/1.12	                  'const/trivia/o'(X0, X1, 'type/realax/real'), X3), X2))),
0.91/1.12	    inference('simplify', [status(thm)], ['13'])).
0.91/1.12	tff('15', plain,
0.91/1.12	    (app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	       'type/realax/real', 
0.91/1.12	       app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	         app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	           'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_B, $o), 
0.91/1.12	           app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	               app_encode_fun(sk_B, $o)), 'const/sets/IMAGE'(sk_A, sk_B), 
0.91/1.12	             sk_A1), sk_A2)), sk_A0)
0.91/1.12	      != app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	           'type/realax/real', 
0.91/1.12	           app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	               'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	             app_encode_app(app_encode_fun(sk_A, $o), 
0.91/1.12	               app_encode_fun(sk_B, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	                   app_encode_fun(sk_B, $o)), 
0.91/1.12	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.91/1.12	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.91/1.12	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.91/1.12	           'const/sets/IN'(sk_A), 
0.91/1.12	           sk_A5(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	             'const/realax/real_add')), sk_A2)
0.91/1.12	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.91/1.12	           'const/sets/FINITE'(sk_A), sk_A2)),
0.91/1.12	    inference('sup-', [status(thm)], ['14', '6'])).
0.91/1.12	tff('16', plain,
0.91/1.12	    (app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	       'type/realax/real', 
0.91/1.12	       app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	         app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	           'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_B, $o), 
0.91/1.12	           app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	               app_encode_fun(sk_B, $o)), 'const/sets/IMAGE'(sk_A, sk_B), 
0.91/1.12	             sk_A1), sk_A2)), sk_A0)
0.91/1.12	      != app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	           'type/realax/real', 
0.91/1.12	           app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	               'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	             app_encode_app(app_encode_fun(sk_A, $o), 
0.91/1.12	               app_encode_fun(sk_B, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	                   app_encode_fun(sk_B, $o)), 
0.91/1.12	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.91/1.12	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.91/1.12	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.91/1.12	           'const/sets/IN'(sk_A), 
0.91/1.12	           sk_A5(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	             'const/realax/real_add')), sk_A2)
0.91/1.12	     | ~ $true),
0.91/1.12	    inference('demod', [status(thm)], ['15', '8'])).
0.91/1.12	tff('17', plain,
0.91/1.12	    app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.91/1.12	      app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.91/1.12	        'const/sets/IN'(sk_A), 
0.91/1.12	        sk_A5(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	          'const/realax/real_add')), sk_A2),
0.91/1.12	    inference('simplify', [status(thm)], ['16'])).
0.91/1.12	tff('18', plain,
0.91/1.12	    ![X8 : sk_A, X9 : sk_A]:
0.91/1.12	      (app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.91/1.12	         app_encode_app(sk_A, sk_B, sk_A1, X8))
0.91/1.12	        = app_encode_app('type/nums/num', 'type/realax/real', 
0.91/1.12	            'const/realax/real_of_num', 
0.91/1.12	            app_encode_app('type/nums/num', 'type/nums/num', 
0.91/1.12	              'const/nums/NUMERAL', 'const/nums/_0'))
0.91/1.12	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.91/1.12	             app_encode_app(sk_A, 
0.91/1.12	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.91/1.12	               'const/sets/IN'(sk_A), X8), sk_A2)
0.91/1.12	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.91/1.12	             app_encode_app(sk_A, 
0.91/1.12	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.91/1.12	               'const/sets/IN'(sk_A), X9), sk_A2)
0.91/1.12	       | X8 = X9
0.91/1.12	       | app_encode_app(sk_A, sk_B, sk_A1, X8)
0.91/1.12	          != app_encode_app(sk_A, sk_B, sk_A1, X9)),
0.91/1.12	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.91/1.12	tff('19', plain,
0.91/1.12	    ![X0 : sk_A]:
0.91/1.12	      (~ $true
0.91/1.12	       | app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	           sk_A5(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	             'const/realax/real_add'))
0.91/1.12	          != app_encode_app(sk_A, sk_B, sk_A1, X0)
0.91/1.12	       | sk_A5(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	           'const/realax/real_add')
0.91/1.12	          = X0
0.91/1.12	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.91/1.12	             app_encode_app(sk_A, 
0.91/1.12	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.91/1.12	               'const/sets/IN'(sk_A), X0), sk_A2)
0.91/1.12	       | app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.91/1.12	           app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	             sk_A5(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	               'const/realax/real_add')))
0.91/1.12	          = app_encode_app('type/nums/num', 'type/realax/real', 
0.91/1.12	              'const/realax/real_of_num', 
0.91/1.12	              app_encode_app('type/nums/num', 'type/nums/num', 
0.91/1.12	                'const/nums/NUMERAL', 'const/nums/_0'))),
0.91/1.12	    inference('sup-', [status(thm)], ['17', '18'])).
0.91/1.12	tff('20', plain,
0.91/1.12	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : $tType, 
0.91/1.12	      X3 : app_encode_fun(X0, X2), X4 : $tType, X5 : app_encode_fun(X2, X4), 
0.91/1.12	      X6 : app_encode_fun(X4, app_encode_fun(X4, X4))]:
0.91/1.12	      (~ app_encode_app(app_encode_fun(X0, $o), $o, 'const/sets/FINITE'(X0), 
0.91/1.12	           X1)
0.91/1.12	       | app_encode_app(X0, X2, X3, sk_A4(X2, X0, X4, X1, X3, X5, X6))
0.91/1.12	          = app_encode_app(X0, X2, X3, sk_A5(X2, X0, X4, X1, X3, X5, X6))
0.91/1.12	       | app_encode_app(app_encode_fun(X2, X4), X4, 
0.91/1.12	           app_encode_app(app_encode_fun(X2, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(X2, X4), X4), 
0.91/1.12	             app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.91/1.12	               app_encode_fun(app_encode_fun(X2, $o), 
0.91/1.12	                 app_encode_fun(app_encode_fun(X2, X4), X4)), 
0.91/1.12	               'const/iterate/iterate'(X2, X4), X6), 
0.91/1.12	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X2, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(X0, X2), 
0.91/1.12	                 app_encode_fun(app_encode_fun(X0, $o), 
0.91/1.12	                   app_encode_fun(X2, $o)), 'const/sets/IMAGE'(X0, X2), X3), 
0.91/1.12	               X1)), X5)
0.91/1.12	          = app_encode_app(app_encode_fun(X0, X4), X4, 
0.91/1.12	              app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	                app_encode_fun(app_encode_fun(X0, X4), X4), 
0.91/1.12	                app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X0, $o), 
0.91/1.12	                    app_encode_fun(app_encode_fun(X0, X4), X4)), 
0.91/1.12	                  'const/iterate/iterate'(X0, X4), X6), X1), 
0.91/1.12	              app_encode_app(app_encode_fun(X0, X2), app_encode_fun(X0, X4), 
0.91/1.12	                app_encode_app(app_encode_fun(X2, X4), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X0, X2), 
0.91/1.12	                    app_encode_fun(X0, X4)), 'const/trivia/o'(X2, X0, X4), 
0.91/1.12	                  X5), X3))
0.91/1.12	       | ~ app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), $o, 
0.91/1.12	             'const/iterate/monoidal'(X4), X6)),
0.91/1.12	    inference('cnf', [status(esa)], [zf_stmt_16])).
0.91/1.12	tff('21', plain,
0.91/1.12	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, X0), 
0.91/1.12	      X3 : app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	      X4 : app_encode_fun(X1, $o)]:
0.91/1.12	      (app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	         'type/realax/real', 
0.91/1.12	         app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	           app_encode_fun(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	             'type/realax/real'), 'const/iterate/sum'(X0), 
0.91/1.12	           app_encode_app(app_encode_fun(X1, $o), app_encode_fun(X0, $o), 
0.91/1.12	             app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	               app_encode_fun(app_encode_fun(X1, $o), app_encode_fun(X0, $o)), 
0.91/1.12	               'const/sets/IMAGE'(X1, X0), X2), X4)), X3)
0.91/1.12	        = app_encode_app(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	            'type/realax/real', 
0.91/1.12	            app_encode_app(app_encode_fun(X1, $o), 
0.91/1.12	              app_encode_fun(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                'type/realax/real'), 
0.91/1.12	              app_encode_app(
0.91/1.12	                app_encode_fun('type/realax/real', 
0.91/1.12	                  app_encode_fun('type/realax/real', 'type/realax/real')), 
0.91/1.12	                app_encode_fun(app_encode_fun(X1, $o), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                    'type/realax/real')), 
0.91/1.12	                'const/iterate/iterate'(X1, 'type/realax/real'), 
0.91/1.12	                'const/realax/real_add'), X4), 
0.91/1.12	            app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	              app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	              app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	                app_encode_fun(app_encode_fun(X1, X0), 
0.91/1.12	                  app_encode_fun(X1, 'type/realax/real')), 
0.91/1.12	                'const/trivia/o'(X0, X1, 'type/realax/real'), X3), X2))
0.91/1.12	       | ~ app_encode_app(
0.91/1.12	             app_encode_fun('type/realax/real', 
0.91/1.12	               app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.91/1.12	             'const/iterate/monoidal'('type/realax/real'), 
0.91/1.12	             'const/realax/real_add')
0.91/1.12	       | app_encode_app(X1, X0, X2, 
0.91/1.12	           sk_A4(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	             'const/realax/real_add'))
0.91/1.12	          = app_encode_app(X1, X0, X2, 
0.91/1.12	              sk_A5(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	                'const/realax/real_add'))
0.91/1.12	       | ~ app_encode_app(app_encode_fun(X1, $o), $o, 
0.91/1.12	             'const/sets/FINITE'(X1), X4)),
0.91/1.12	    inference('sup+', [status(thm)], ['0', '20'])).
0.91/1.12	tff('22', plain,
0.91/1.12	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, X0), 
0.91/1.12	      X3 : app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	      X4 : app_encode_fun(X1, $o)]:
0.91/1.12	      (app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	         'type/realax/real', 
0.91/1.12	         app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	           app_encode_fun(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	             'type/realax/real'), 'const/iterate/sum'(X0), 
0.91/1.12	           app_encode_app(app_encode_fun(X1, $o), app_encode_fun(X0, $o), 
0.91/1.12	             app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	               app_encode_fun(app_encode_fun(X1, $o), app_encode_fun(X0, $o)), 
0.91/1.12	               'const/sets/IMAGE'(X1, X0), X2), X4)), X3)
0.91/1.12	        = app_encode_app(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	            'type/realax/real', 
0.91/1.12	            app_encode_app(app_encode_fun(X1, $o), 
0.91/1.12	              app_encode_fun(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                'type/realax/real'), 'const/iterate/sum'(X1), X4), 
0.91/1.12	            app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	              app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	              app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	                app_encode_fun(app_encode_fun(X1, X0), 
0.91/1.12	                  app_encode_fun(X1, 'type/realax/real')), 
0.91/1.12	                'const/trivia/o'(X0, X1, 'type/realax/real'), X3), X2))
0.91/1.12	       | ~ $true
0.91/1.12	       | app_encode_app(X1, X0, X2, 
0.91/1.12	           sk_A4(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	             'const/realax/real_add'))
0.91/1.12	          = app_encode_app(X1, X0, X2, 
0.91/1.12	              sk_A5(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	                'const/realax/real_add'))
0.91/1.12	       | ~ app_encode_app(app_encode_fun(X1, $o), $o, 
0.91/1.12	             'const/sets/FINITE'(X1), X4)),
0.91/1.12	    inference('demod', [status(thm)], ['21', '0', '3'])).
0.91/1.12	tff('23', plain,
0.91/1.12	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, X0), 
0.91/1.12	      X3 : app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	      X4 : app_encode_fun(X1, $o)]:
0.91/1.12	      (~ app_encode_app(app_encode_fun(X1, $o), $o, 'const/sets/FINITE'(X1), 
0.91/1.12	           X4)
0.91/1.12	       | app_encode_app(X1, X0, X2, 
0.91/1.12	           sk_A4(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	             'const/realax/real_add'))
0.91/1.12	          = app_encode_app(X1, X0, X2, 
0.91/1.12	              sk_A5(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	                'const/realax/real_add'))
0.91/1.12	       | app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	           'type/realax/real', 
0.91/1.12	           app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	               'type/realax/real'), 'const/iterate/sum'(X0), 
0.91/1.12	             app_encode_app(app_encode_fun(X1, $o), app_encode_fun(X0, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	                 app_encode_fun(app_encode_fun(X1, $o), 
0.91/1.12	                   app_encode_fun(X0, $o)), 'const/sets/IMAGE'(X1, X0), X2), 
0.91/1.12	               X4)), X3)
0.91/1.12	          = app_encode_app(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	              'type/realax/real', 
0.91/1.12	              app_encode_app(app_encode_fun(X1, $o), 
0.91/1.12	                app_encode_fun(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                  'type/realax/real'), 'const/iterate/sum'(X1), X4), 
0.91/1.12	              app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	                app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X1, X0), 
0.91/1.12	                    app_encode_fun(X1, 'type/realax/real')), 
0.91/1.12	                  'const/trivia/o'(X0, X1, 'type/realax/real'), X3), X2))),
0.91/1.12	    inference('simplify', [status(thm)], ['22'])).
0.91/1.12	tff('24', plain,
0.91/1.12	    (app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	       'type/realax/real', 
0.91/1.12	       app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	         app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	           'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_B, $o), 
0.91/1.12	           app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	               app_encode_fun(sk_B, $o)), 'const/sets/IMAGE'(sk_A, sk_B), 
0.91/1.12	             sk_A1), sk_A2)), sk_A0)
0.91/1.12	      != app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	           'type/realax/real', 
0.91/1.12	           app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	               'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	             app_encode_app(app_encode_fun(sk_A, $o), 
0.91/1.12	               app_encode_fun(sk_B, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	                   app_encode_fun(sk_B, $o)), 
0.91/1.12	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.91/1.12	     | app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	         sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	           'const/realax/real_add'))
0.91/1.12	        = app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	            sk_A5(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	              'const/realax/real_add'))
0.91/1.12	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.91/1.12	           'const/sets/FINITE'(sk_A), sk_A2)),
0.91/1.12	    inference('sup-', [status(thm)], ['23', '6'])).
0.91/1.12	tff('25', plain,
0.91/1.12	    (app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	       'type/realax/real', 
0.91/1.12	       app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	         app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	           'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_B, $o), 
0.91/1.12	           app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	               app_encode_fun(sk_B, $o)), 'const/sets/IMAGE'(sk_A, sk_B), 
0.91/1.12	             sk_A1), sk_A2)), sk_A0)
0.91/1.12	      != app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	           'type/realax/real', 
0.91/1.12	           app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	               'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	             app_encode_app(app_encode_fun(sk_A, $o), 
0.91/1.12	               app_encode_fun(sk_B, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	                   app_encode_fun(sk_B, $o)), 
0.91/1.12	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.91/1.12	     | app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	         sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	           'const/realax/real_add'))
0.91/1.12	        = app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	            sk_A5(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	              'const/realax/real_add'))
0.91/1.12	     | ~ $true),
0.91/1.12	    inference('demod', [status(thm)], ['24', '8'])).
0.91/1.12	tff('26', plain,
0.91/1.12	    app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	      sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	        'const/realax/real_add'))
0.91/1.12	     = app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	         sk_A5(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	           'const/realax/real_add')),
0.91/1.12	    inference('simplify', [status(thm)], ['25'])).
0.91/1.12	tff('27', plain,
0.91/1.12	    ![X0 : sk_A]:
0.91/1.12	      (~ $true
0.91/1.12	       | app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	           sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	             'const/realax/real_add'))
0.91/1.12	          != app_encode_app(sk_A, sk_B, sk_A1, X0)
0.91/1.12	       | sk_A5(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	           'const/realax/real_add')
0.91/1.12	          = X0
0.91/1.12	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.91/1.12	             app_encode_app(sk_A, 
0.91/1.12	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.91/1.12	               'const/sets/IN'(sk_A), X0), sk_A2)
0.91/1.12	       | app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.91/1.12	           app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	             sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	               'const/realax/real_add')))
0.91/1.12	          = app_encode_app('type/nums/num', 'type/realax/real', 
0.91/1.12	              'const/realax/real_of_num', 
0.91/1.12	              app_encode_app('type/nums/num', 'type/nums/num', 
0.91/1.12	                'const/nums/NUMERAL', 'const/nums/_0'))),
0.91/1.12	    inference('demod', [status(thm)], ['19', '26', '26'])).
0.91/1.12	tff('28', plain,
0.91/1.12	    ![X0 : sk_A]:
0.91/1.12	      (app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.91/1.12	         app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	           sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	             'const/realax/real_add')))
0.91/1.12	        = app_encode_app('type/nums/num', 'type/realax/real', 
0.91/1.12	            'const/realax/real_of_num', 
0.91/1.12	            app_encode_app('type/nums/num', 'type/nums/num', 
0.91/1.12	              'const/nums/NUMERAL', 'const/nums/_0'))
0.91/1.12	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.91/1.12	             app_encode_app(sk_A, 
0.91/1.12	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.91/1.12	               'const/sets/IN'(sk_A), X0), sk_A2)
0.91/1.12	       | sk_A5(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	           'const/realax/real_add')
0.91/1.12	          = X0
0.91/1.12	       | app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	           sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	             'const/realax/real_add'))
0.91/1.12	          != app_encode_app(sk_A, sk_B, sk_A1, X0)),
0.91/1.12	    inference('simplify', [status(thm)], ['27'])).
0.91/1.12	tff('29', plain,
0.91/1.12	    (~ $true
0.91/1.12	     | app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	         sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	           'const/realax/real_add'))
0.91/1.12	        != app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	             sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	               'const/realax/real_add'))
0.91/1.12	     | sk_A5(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	         'const/realax/real_add')
0.91/1.12	        = sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	            'const/realax/real_add')
0.91/1.12	     | app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.91/1.12	         app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	           sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	             'const/realax/real_add')))
0.91/1.12	        = app_encode_app('type/nums/num', 'type/realax/real', 
0.91/1.12	            'const/realax/real_of_num', 
0.91/1.12	            app_encode_app('type/nums/num', 'type/nums/num', 
0.91/1.12	              'const/nums/NUMERAL', 'const/nums/_0'))),
0.91/1.12	    inference('sup-', [status(thm)], ['10', '28'])).
0.91/1.12	tff('30', plain,
0.91/1.12	    (app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.91/1.12	       app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	         sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	           'const/realax/real_add')))
0.91/1.12	      = app_encode_app('type/nums/num', 'type/realax/real', 
0.91/1.12	          'const/realax/real_of_num', 
0.91/1.12	          app_encode_app('type/nums/num', 'type/nums/num', 
0.91/1.12	            'const/nums/NUMERAL', 'const/nums/_0'))
0.91/1.12	     | sk_A5(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	         'const/realax/real_add')
0.91/1.12	        = sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	            'const/realax/real_add')),
0.91/1.12	    inference('simplify', [status(thm)], ['29'])).
0.91/1.12	tff('31', plain,
0.91/1.12	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : $tType, 
0.91/1.12	      X3 : app_encode_fun(X0, X2), X4 : $tType, X5 : app_encode_fun(X2, X4), 
0.91/1.12	      X6 : app_encode_fun(X4, app_encode_fun(X4, X4))]:
0.91/1.12	      (~ app_encode_app(app_encode_fun(X0, $o), $o, 'const/sets/FINITE'(X0), 
0.91/1.12	           X1)
0.91/1.12	       | sk_A4(X2, X0, X4, X1, X3, X5, X6)
0.91/1.12	          != sk_A5(X2, X0, X4, X1, X3, X5, X6)
0.91/1.12	       | app_encode_app(app_encode_fun(X2, X4), X4, 
0.91/1.12	           app_encode_app(app_encode_fun(X2, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(X2, X4), X4), 
0.91/1.12	             app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.91/1.12	               app_encode_fun(app_encode_fun(X2, $o), 
0.91/1.12	                 app_encode_fun(app_encode_fun(X2, X4), X4)), 
0.91/1.12	               'const/iterate/iterate'(X2, X4), X6), 
0.91/1.12	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X2, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(X0, X2), 
0.91/1.12	                 app_encode_fun(app_encode_fun(X0, $o), 
0.91/1.12	                   app_encode_fun(X2, $o)), 'const/sets/IMAGE'(X0, X2), X3), 
0.91/1.12	               X1)), X5)
0.91/1.12	          = app_encode_app(app_encode_fun(X0, X4), X4, 
0.91/1.12	              app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	                app_encode_fun(app_encode_fun(X0, X4), X4), 
0.91/1.12	                app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X0, $o), 
0.91/1.12	                    app_encode_fun(app_encode_fun(X0, X4), X4)), 
0.91/1.12	                  'const/iterate/iterate'(X0, X4), X6), X1), 
0.91/1.12	              app_encode_app(app_encode_fun(X0, X2), app_encode_fun(X0, X4), 
0.91/1.12	                app_encode_app(app_encode_fun(X2, X4), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X0, X2), 
0.91/1.12	                    app_encode_fun(X0, X4)), 'const/trivia/o'(X2, X0, X4), 
0.91/1.12	                  X5), X3))
0.91/1.12	       | ~ app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), $o, 
0.91/1.12	             'const/iterate/monoidal'(X4), X6)),
0.91/1.12	    inference('cnf', [status(esa)], [zf_stmt_16])).
0.91/1.12	tff('32', plain,
0.91/1.12	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, X0), 
0.91/1.12	      X3 : app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	      X4 : app_encode_fun(X1, $o)]:
0.91/1.12	      (app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	         'type/realax/real', 
0.91/1.12	         app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	           app_encode_fun(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	             'type/realax/real'), 'const/iterate/sum'(X0), 
0.91/1.12	           app_encode_app(app_encode_fun(X1, $o), app_encode_fun(X0, $o), 
0.91/1.12	             app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	               app_encode_fun(app_encode_fun(X1, $o), app_encode_fun(X0, $o)), 
0.91/1.12	               'const/sets/IMAGE'(X1, X0), X2), X4)), X3)
0.91/1.12	        = app_encode_app(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	            'type/realax/real', 
0.91/1.12	            app_encode_app(app_encode_fun(X1, $o), 
0.91/1.12	              app_encode_fun(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                'type/realax/real'), 
0.91/1.12	              app_encode_app(
0.91/1.12	                app_encode_fun('type/realax/real', 
0.91/1.12	                  app_encode_fun('type/realax/real', 'type/realax/real')), 
0.91/1.12	                app_encode_fun(app_encode_fun(X1, $o), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                    'type/realax/real')), 
0.91/1.12	                'const/iterate/iterate'(X1, 'type/realax/real'), 
0.91/1.12	                'const/realax/real_add'), X4), 
0.91/1.12	            app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	              app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	              app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	                app_encode_fun(app_encode_fun(X1, X0), 
0.91/1.12	                  app_encode_fun(X1, 'type/realax/real')), 
0.91/1.12	                'const/trivia/o'(X0, X1, 'type/realax/real'), X3), X2))
0.91/1.12	       | ~ app_encode_app(
0.91/1.12	             app_encode_fun('type/realax/real', 
0.91/1.12	               app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.91/1.12	             'const/iterate/monoidal'('type/realax/real'), 
0.91/1.12	             'const/realax/real_add')
0.91/1.12	       | sk_A4(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	           'const/realax/real_add')
0.91/1.12	          != sk_A5(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	               'const/realax/real_add')
0.91/1.12	       | ~ app_encode_app(app_encode_fun(X1, $o), $o, 
0.91/1.12	             'const/sets/FINITE'(X1), X4)),
0.91/1.12	    inference('sup+', [status(thm)], ['0', '31'])).
0.91/1.12	tff('33', plain,
0.91/1.12	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, X0), 
0.91/1.12	      X3 : app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	      X4 : app_encode_fun(X1, $o)]:
0.91/1.12	      (app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	         'type/realax/real', 
0.91/1.12	         app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	           app_encode_fun(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	             'type/realax/real'), 'const/iterate/sum'(X0), 
0.91/1.12	           app_encode_app(app_encode_fun(X1, $o), app_encode_fun(X0, $o), 
0.91/1.12	             app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	               app_encode_fun(app_encode_fun(X1, $o), app_encode_fun(X0, $o)), 
0.91/1.12	               'const/sets/IMAGE'(X1, X0), X2), X4)), X3)
0.91/1.12	        = app_encode_app(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	            'type/realax/real', 
0.91/1.12	            app_encode_app(app_encode_fun(X1, $o), 
0.91/1.12	              app_encode_fun(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                'type/realax/real'), 'const/iterate/sum'(X1), X4), 
0.91/1.12	            app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	              app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	              app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	                app_encode_fun(app_encode_fun(X1, X0), 
0.91/1.12	                  app_encode_fun(X1, 'type/realax/real')), 
0.91/1.12	                'const/trivia/o'(X0, X1, 'type/realax/real'), X3), X2))
0.91/1.12	       | ~ $true
0.91/1.12	       | sk_A4(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	           'const/realax/real_add')
0.91/1.12	          != sk_A5(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	               'const/realax/real_add')
0.91/1.12	       | ~ app_encode_app(app_encode_fun(X1, $o), $o, 
0.91/1.12	             'const/sets/FINITE'(X1), X4)),
0.91/1.12	    inference('demod', [status(thm)], ['32', '0', '3'])).
0.91/1.12	tff('34', plain,
0.91/1.12	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, X0), 
0.91/1.12	      X3 : app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	      X4 : app_encode_fun(X1, $o)]:
0.91/1.12	      (~ app_encode_app(app_encode_fun(X1, $o), $o, 'const/sets/FINITE'(X1), 
0.91/1.12	           X4)
0.91/1.12	       | sk_A4(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	           'const/realax/real_add')
0.91/1.12	          != sk_A5(X0, X1, 'type/realax/real', X4, X2, X3, 
0.91/1.12	               'const/realax/real_add')
0.91/1.12	       | app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	           'type/realax/real', 
0.91/1.12	           app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	               'type/realax/real'), 'const/iterate/sum'(X0), 
0.91/1.12	             app_encode_app(app_encode_fun(X1, $o), app_encode_fun(X0, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	                 app_encode_fun(app_encode_fun(X1, $o), 
0.91/1.12	                   app_encode_fun(X0, $o)), 'const/sets/IMAGE'(X1, X0), X2), 
0.91/1.12	               X4)), X3)
0.91/1.12	          = app_encode_app(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	              'type/realax/real', 
0.91/1.12	              app_encode_app(app_encode_fun(X1, $o), 
0.91/1.12	                app_encode_fun(app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                  'type/realax/real'), 'const/iterate/sum'(X1), X4), 
0.91/1.12	              app_encode_app(app_encode_fun(X1, X0), 
0.91/1.12	                app_encode_fun(X1, 'type/realax/real'), 
0.91/1.12	                app_encode_app(app_encode_fun(X0, 'type/realax/real'), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X1, X0), 
0.91/1.12	                    app_encode_fun(X1, 'type/realax/real')), 
0.91/1.12	                  'const/trivia/o'(X0, X1, 'type/realax/real'), X3), X2))),
0.91/1.12	    inference('simplify', [status(thm)], ['33'])).
0.91/1.12	tff('35', plain,
0.91/1.12	    (app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	       'type/realax/real', 
0.91/1.12	       app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	         app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	           'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_B, $o), 
0.91/1.12	           app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	               app_encode_fun(sk_B, $o)), 'const/sets/IMAGE'(sk_A, sk_B), 
0.91/1.12	             sk_A1), sk_A2)), sk_A0)
0.91/1.12	      != app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	           'type/realax/real', 
0.91/1.12	           app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	               'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	             app_encode_app(app_encode_fun(sk_A, $o), 
0.91/1.12	               app_encode_fun(sk_B, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	                   app_encode_fun(sk_B, $o)), 
0.91/1.12	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.91/1.12	     | sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	         'const/realax/real_add')
0.91/1.12	        != sk_A5(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	             'const/realax/real_add')
0.91/1.12	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.91/1.12	           'const/sets/FINITE'(sk_A), sk_A2)),
0.91/1.12	    inference('sup-', [status(thm)], ['34', '6'])).
0.91/1.12	tff('36', plain,
0.91/1.12	    (app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	       'type/realax/real', 
0.91/1.12	       app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	         app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	           'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	         app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_B, $o), 
0.91/1.12	           app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	               app_encode_fun(sk_B, $o)), 'const/sets/IMAGE'(sk_A, sk_B), 
0.91/1.12	             sk_A1), sk_A2)), sk_A0)
0.91/1.12	      != app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	           'type/realax/real', 
0.91/1.12	           app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	               'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	             app_encode_app(app_encode_fun(sk_A, $o), 
0.91/1.12	               app_encode_fun(sk_B, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	                   app_encode_fun(sk_B, $o)), 
0.91/1.12	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.91/1.12	     | sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	         'const/realax/real_add')
0.91/1.12	        != sk_A5(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	             'const/realax/real_add')
0.91/1.12	     | ~ $true),
0.91/1.12	    inference('demod', [status(thm)], ['35', '8'])).
0.91/1.12	tff('37', plain,
0.91/1.12	    sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	      'const/realax/real_add')
0.91/1.12	     != sk_A5(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	          'const/realax/real_add'),
0.91/1.12	    inference('simplify', [status(thm)], ['36'])).
0.91/1.12	tff('38', plain,
0.91/1.12	    app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.91/1.12	      app_encode_app(sk_A, sk_B, sk_A1, 
0.91/1.12	        sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, 
0.91/1.12	          'const/realax/real_add')))
0.91/1.12	     = app_encode_app('type/nums/num', 'type/realax/real', 
0.91/1.12	         'const/realax/real_of_num', 
0.91/1.12	         app_encode_app('type/nums/num', 'type/nums/num', 
0.91/1.12	           'const/nums/NUMERAL', 'const/nums/_0')),
0.91/1.12	    inference('simplify_reflect-', [status(thm)], ['30', '37'])).
0.91/1.12	tff('39', plain,
0.91/1.12	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : $tType, 
0.91/1.12	      X3 : app_encode_fun(X0, X2), X4 : $tType, X5 : app_encode_fun(X2, X4), 
0.91/1.12	      X6 : app_encode_fun(X4, app_encode_fun(X4, X4))]:
0.91/1.12	      (~ app_encode_app(app_encode_fun(X0, $o), $o, 'const/sets/FINITE'(X0), 
0.91/1.12	           X1)
0.91/1.12	       | app_encode_app(X2, X4, X5, 
0.91/1.12	           app_encode_app(X0, X2, X3, sk_A4(X2, X0, X4, X1, X3, X5, X6)))
0.91/1.12	          != app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), X4, 
0.91/1.12	               'const/iterate/neutral'(X4), X6)
0.91/1.12	       | app_encode_app(app_encode_fun(X2, X4), X4, 
0.91/1.12	           app_encode_app(app_encode_fun(X2, $o), 
0.91/1.12	             app_encode_fun(app_encode_fun(X2, X4), X4), 
0.91/1.12	             app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.91/1.12	               app_encode_fun(app_encode_fun(X2, $o), 
0.91/1.12	                 app_encode_fun(app_encode_fun(X2, X4), X4)), 
0.91/1.12	               'const/iterate/iterate'(X2, X4), X6), 
0.91/1.12	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X2, $o), 
0.91/1.12	               app_encode_app(app_encode_fun(X0, X2), 
0.91/1.12	                 app_encode_fun(app_encode_fun(X0, $o), 
0.91/1.12	                   app_encode_fun(X2, $o)), 'const/sets/IMAGE'(X0, X2), X3), 
0.91/1.12	               X1)), X5)
0.91/1.12	          = app_encode_app(app_encode_fun(X0, X4), X4, 
0.91/1.12	              app_encode_app(app_encode_fun(X0, $o), 
0.91/1.12	                app_encode_fun(app_encode_fun(X0, X4), X4), 
0.91/1.12	                app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X0, $o), 
0.91/1.12	                    app_encode_fun(app_encode_fun(X0, X4), X4)), 
0.91/1.12	                  'const/iterate/iterate'(X0, X4), X6), X1), 
0.91/1.12	              app_encode_app(app_encode_fun(X0, X2), app_encode_fun(X0, X4), 
0.91/1.12	                app_encode_app(app_encode_fun(X2, X4), 
0.91/1.12	                  app_encode_fun(app_encode_fun(X0, X2), 
0.91/1.12	                    app_encode_fun(X0, X4)), 'const/trivia/o'(X2, X0, X4), 
0.91/1.12	                  X5), X3))
0.91/1.12	       | ~ app_encode_app(app_encode_fun(X4, app_encode_fun(X4, X4)), $o, 
0.91/1.12	             'const/iterate/monoidal'(X4), X6)),
0.91/1.12	    inference('cnf', [status(esa)], [zf_stmt_16])).
0.91/1.12	tff('40', plain,
0.91/1.12	    (app_encode_app('type/nums/num', 'type/realax/real', 
0.91/1.12	       'const/realax/real_of_num', 
0.91/1.12	       app_encode_app('type/nums/num', 'type/nums/num', 
0.91/1.12	         'const/nums/NUMERAL', 'const/nums/_0'))
0.91/1.12	      != app_encode_app(
0.91/1.12	           app_encode_fun('type/realax/real', 
0.91/1.12	             app_encode_fun('type/realax/real', 'type/realax/real')), 
0.91/1.12	           'type/realax/real', 'const/iterate/neutral'('type/realax/real'), 
0.91/1.12	           'const/realax/real_add')
0.91/1.12	     | ~ app_encode_app(
0.91/1.12	           app_encode_fun('type/realax/real', 
0.91/1.12	             app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.91/1.12	           'const/iterate/monoidal'('type/realax/real'), 
0.91/1.12	           'const/realax/real_add')
0.91/1.12	     | app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	         'type/realax/real', 
0.91/1.12	         app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	           app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	             'type/realax/real'), 
0.91/1.12	           app_encode_app(
0.91/1.12	             app_encode_fun('type/realax/real', 
0.91/1.12	               app_encode_fun('type/realax/real', 'type/realax/real')), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_B, $o), 
0.91/1.12	               app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	                 'type/realax/real')), 
0.91/1.12	             'const/iterate/iterate'(sk_B, 'type/realax/real'), 
0.91/1.12	             'const/realax/real_add'), 
0.91/1.12	           app_encode_app(app_encode_fun(sk_A, $o), 
0.91/1.12	             app_encode_fun(sk_B, $o), 
0.91/1.12	             app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	                 app_encode_fun(sk_B, $o)), 'const/sets/IMAGE'(sk_A, sk_B), 
0.91/1.12	               sk_A1), sk_A2)), sk_A0)
0.91/1.12	        = app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.91/1.12	            'type/realax/real', 
0.91/1.12	            app_encode_app(app_encode_fun(sk_A, $o), 
0.91/1.12	              app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.91/1.12	                'type/realax/real'), 
0.91/1.12	              app_encode_app(
0.91/1.12	                app_encode_fun('type/realax/real', 
0.91/1.12	                  app_encode_fun('type/realax/real', 'type/realax/real')), 
0.91/1.12	                app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	                  app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.91/1.12	                    'type/realax/real')), 
0.91/1.12	                'const/iterate/iterate'(sk_A, 'type/realax/real'), 
0.91/1.12	                'const/realax/real_add'), sk_A2), 
0.91/1.12	            app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	              app_encode_fun(sk_A, 'type/realax/real'), 
0.91/1.12	              app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	                app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.91/1.12	                  app_encode_fun(sk_A, 'type/realax/real')), 
0.91/1.12	                'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), 
0.91/1.12	              sk_A1))
0.91/1.12	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.91/1.12	           'const/sets/FINITE'(sk_A), sk_A2)),
0.91/1.12	    inference('sup-', [status(thm)], ['38', '39'])).
0.91/1.12	tff(zf_stmt_19, axiom,
0.91/1.12	  (app_encode_app(app_encode_fun('type/realax/real',
0.91/1.12	                                 app_encode_fun('type/realax/real',
0.91/1.12	                                                'type/realax/real')),
0.91/1.12	                  'type/realax/real',
0.91/1.12	                  'const/iterate/neutral'('type/realax/real'),
0.91/1.12	                  'const/realax/real_add') =
0.91/1.12	   app_encode_app('type/nums/num','type/realax/real',
0.91/1.12	                  'const/realax/real_of_num',
0.91/1.12	                  app_encode_app('type/nums/num','type/nums/num',
0.91/1.12	                                 'const/nums/NUMERAL','const/nums/_0')))).
0.91/1.12	tff('41', plain,
0.91/1.12	    app_encode_app(
0.91/1.12	      app_encode_fun('type/realax/real', 
0.91/1.12	        app_encode_fun('type/realax/real', 'type/realax/real')), 
0.91/1.12	      'type/realax/real', 'const/iterate/neutral'('type/realax/real'), 
0.91/1.12	      'const/realax/real_add')
0.91/1.12	     = app_encode_app('type/nums/num', 'type/realax/real', 
0.91/1.12	         'const/realax/real_of_num', 
0.91/1.12	         app_encode_app('type/nums/num', 'type/nums/num', 
0.91/1.12	           'const/nums/NUMERAL', 'const/nums/_0')),
0.91/1.12	    inference('cnf', [status(esa)], [zf_stmt_19])).
0.91/1.12	tff('42', plain,
0.91/1.12	    (app_encode_app('type/nums/num', 'type/realax/real', 
0.91/1.12	       'const/realax/real_of_num', 
0.91/1.12	       app_encode_app('type/nums/num', 'type/nums/num', 
0.91/1.12	         'const/nums/NUMERAL', 'const/nums/_0'))
0.91/1.12	      != app_encode_app('type/nums/num', 'type/realax/real', 
0.91/1.12	           'const/realax/real_of_num', 
0.91/1.12	           app_encode_app('type/nums/num', 'type/nums/num', 
0.91/1.12	             'const/nums/NUMERAL', 'const/nums/_0'))
0.91/1.12	     | ~ $true
0.91/1.12	     | app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	         'type/realax/real', 
0.91/1.12	         app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	           app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	             'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	           app_encode_app(app_encode_fun(sk_A, $o), 
0.91/1.12	             app_encode_fun(sk_B, $o), 
0.91/1.12	             app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	                 app_encode_fun(sk_B, $o)), 'const/sets/IMAGE'(sk_A, sk_B), 
0.91/1.12	               sk_A1), sk_A2)), sk_A0)
0.91/1.12	        = app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.91/1.12	            'type/realax/real', 
0.91/1.12	            app_encode_app(app_encode_fun(sk_A, $o), 
0.91/1.12	              app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.91/1.12	                'type/realax/real'), 'const/iterate/sum'(sk_A), sk_A2), 
0.91/1.12	            app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	              app_encode_fun(sk_A, 'type/realax/real'), 
0.91/1.12	              app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	                app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.91/1.12	                  app_encode_fun(sk_A, 'type/realax/real')), 
0.91/1.12	                'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), 
0.91/1.12	              sk_A1))
0.91/1.12	     | ~ $true),
0.91/1.12	    inference('demod', [status(thm)], ['40', '41', '3', '0', '0', '8'])).
0.91/1.12	tff('43', plain,
0.91/1.12	    app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	      'type/realax/real', 
0.91/1.12	      app_encode_app(app_encode_fun(sk_B, $o), 
0.91/1.12	        app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	          'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.91/1.12	        app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_B, $o), 
0.91/1.12	          app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	            app_encode_fun(app_encode_fun(sk_A, $o), 
0.91/1.12	              app_encode_fun(sk_B, $o)), 'const/sets/IMAGE'(sk_A, sk_B), 
0.91/1.12	            sk_A1), sk_A2)), sk_A0)
0.91/1.12	     = app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.91/1.12	         'type/realax/real', 
0.91/1.12	         app_encode_app(app_encode_fun(sk_A, $o), 
0.91/1.12	           app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.91/1.12	             'type/realax/real'), 'const/iterate/sum'(sk_A), sk_A2), 
0.91/1.12	         app_encode_app(app_encode_fun(sk_A, sk_B), 
0.91/1.12	           app_encode_fun(sk_A, 'type/realax/real'), 
0.91/1.12	           app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.91/1.12	             app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.91/1.12	               app_encode_fun(sk_A, 'type/realax/real')), 
0.91/1.12	             'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), sk_A1)),
0.91/1.12	    inference('simplify', [status(thm)], ['42'])).
0.91/1.12	tff('44', plain, $false,
0.91/1.12	    inference('simplify_reflect-', [status(thm)], ['43', '6'])).
0.91/1.12	
0.91/1.12	% SZS output end Refutation
0.91/1.12	EOF
