0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n030.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 18:40:24 CST 2018
0.00/0.33	% done 18 iterations in 0.132s
0.00/0.33	% SZS status Theorem for 'stdin'
0.00/0.33	% SZS output start Refutation
0.00/0.34	tff(zf_stmt_17, axiom,
0.00/0.34	  (![C:$tType,A:$tType,B:$tType,A0:app_encode_fun(C,app_encode_fun(C,C))]:
0.00/0.34	     (app_encode_app(app_encode_fun(C,app_encode_fun(C,C)),$o,
0.00/0.34	                     'const/iterate/monoidal'(C),A0) =>
0.00/0.34	      (![A1:app_encode_fun(B,C),A2:app_encode_fun(A,B),
0.00/0.34	         A3:app_encode_fun(A,$o)]:
0.00/0.34	         ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A3) & 
0.00/0.34	           (![A4:A,A5:A]:
0.00/0.34	              ((app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.34	                               app_encode_app(A,
0.00/0.34	                                              app_encode_fun(app_encode_fun(
0.00/0.34	                                                             A,$o),$o),
0.00/0.34	                                              'const/sets/IN'(A),A4),
0.00/0.34	                               A3) & 
0.00/0.34	                app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.34	                               app_encode_app(A,
0.00/0.34	                                              app_encode_fun(app_encode_fun(
0.00/0.34	                                                             A,$o),$o),
0.00/0.34	                                              'const/sets/IN'(A),A5),
0.00/0.34	                               A3) & 
0.00/0.34	                (A4 != A5) & 
0.00/0.34	                (app_encode_app(A,B,A2,A4) = app_encode_app(A,B,A2,A5))) =>
0.00/0.34	               (app_encode_app(B,C,A1,app_encode_app(A,B,A2,A4)) =
0.00/0.34	                app_encode_app(app_encode_fun(C,app_encode_fun(C,C)),C,
0.00/0.34	                               'const/iterate/neutral'(C),A0))))) =>
0.00/0.34	          (app_encode_app(app_encode_fun(B,C),C,
0.00/0.34	                          app_encode_app(app_encode_fun(B,$o),
0.00/0.34	                                         app_encode_fun(app_encode_fun(B,C),C),
0.00/0.34	                                         app_encode_app(app_encode_fun(
0.00/0.34	                                                        C,app_encode_fun(C,C)),
0.00/0.34	                                                        app_encode_fun(
0.00/0.34	                                                        app_encode_fun(B,$o),
0.00/0.34	                                                        app_encode_fun(
0.00/0.34	                                                        app_encode_fun(B,C),C)),
0.00/0.34	                                                        'const/iterate/iterate'(
0.00/0.34	                                                        B,C),A0),
0.00/0.34	                                         app_encode_app(app_encode_fun(A,$o),
0.00/0.34	                                                        app_encode_fun(B,$o),
0.00/0.34	                                                        app_encode_app(
0.00/0.34	                                                        app_encode_fun(A,B),
0.00/0.34	                                                        app_encode_fun(
0.00/0.34	                                                        app_encode_fun(A,$o),
0.00/0.34	                                                        app_encode_fun(B,$o)),
0.00/0.34	                                                        'const/sets/IMAGE'(
0.00/0.34	                                                        A,B),A2),A3)),
0.00/0.34	                          A1) =
0.00/0.34	           app_encode_app(app_encode_fun(A,C),C,
0.00/0.34	                          app_encode_app(app_encode_fun(A,$o),
0.00/0.34	                                         app_encode_fun(app_encode_fun(A,C),C),
0.00/0.34	                                         app_encode_app(app_encode_fun(
0.00/0.34	                                                        C,app_encode_fun(C,C)),
0.00/0.34	                                                        app_encode_fun(
0.00/0.34	                                                        app_encode_fun(A,$o),
0.00/0.34	                                                        app_encode_fun(
0.00/0.34	                                                        app_encode_fun(A,C),C)),
0.00/0.34	                                                        'const/iterate/iterate'(
0.00/0.34	                                                        A,C),A0),
0.00/0.34	                                         A3),
0.00/0.34	                          app_encode_app(app_encode_fun(A,B),
0.00/0.34	                                         app_encode_fun(A,C),
0.00/0.34	                                         app_encode_app(app_encode_fun(B,C),
0.00/0.34	                                                        app_encode_fun(
0.00/0.34	                                                        app_encode_fun(A,B),
0.00/0.34	                                                        app_encode_fun(A,C)),
0.00/0.34	                                                        'const/trivia/o'(
0.00/0.34	                                                        B,A,C),A1),
0.00/0.34	                                         A2)))))))).
0.00/0.34	tff('0', plain,
0.00/0.34	    ![X4 : $tType, X5 : app_encode_fun(X4, $o), X6 : $tType, 
0.00/0.34	      X7 : app_encode_fun(X4, X6), X8 : $tType, X9 : app_encode_fun(X6, X8), 
0.00/0.34	      X10 : app_encode_fun(X8, app_encode_fun(X8, X8))]:
0.00/0.34	      (~ app_encode_app(app_encode_fun(X4, $o), $o, 'const/sets/FINITE'(X4), 
0.00/0.34	           X5)
0.00/0.34	       | app_encode_app(app_encode_fun(X4, $o), $o, 
0.00/0.34	           app_encode_app(X4, app_encode_fun(app_encode_fun(X4, $o), $o), 
0.00/0.34	             'const/sets/IN'(X4), sk_A4(X6, X4, X8, X5, X7, X9, X10)), X5)
0.00/0.34	       | app_encode_app(app_encode_fun(X6, X8), X8, 
0.00/0.34	           app_encode_app(app_encode_fun(X6, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(X6, X8), X8), 
0.00/0.34	             app_encode_app(app_encode_fun(X8, app_encode_fun(X8, X8)), 
0.00/0.34	               app_encode_fun(app_encode_fun(X6, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(X6, X8), X8)), 
0.00/0.34	               'const/iterate/iterate'(X6, X8), X10), 
0.00/0.34	             app_encode_app(app_encode_fun(X4, $o), app_encode_fun(X6, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(X4, X6), 
0.00/0.34	                 app_encode_fun(app_encode_fun(X4, $o), 
0.00/0.34	                   app_encode_fun(X6, $o)), 'const/sets/IMAGE'(X4, X6), X7), 
0.00/0.34	               X5)), X9)
0.00/0.34	          = app_encode_app(app_encode_fun(X4, X8), X8, 
0.00/0.34	              app_encode_app(app_encode_fun(X4, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(X4, X8), X8), 
0.00/0.34	                app_encode_app(app_encode_fun(X8, app_encode_fun(X8, X8)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(X4, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(X4, X8), X8)), 
0.00/0.34	                  'const/iterate/iterate'(X4, X8), X10), X5), 
0.00/0.34	              app_encode_app(app_encode_fun(X4, X6), app_encode_fun(X4, X8), 
0.00/0.34	                app_encode_app(app_encode_fun(X6, X8), 
0.00/0.34	                  app_encode_fun(app_encode_fun(X4, X6), 
0.00/0.34	                    app_encode_fun(X4, X8)), 'const/trivia/o'(X6, X4, X8), 
0.00/0.34	                  X9), X7))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X8, app_encode_fun(X8, X8)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X8), X10)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_17])).
0.00/0.34	tff('1', plain,
0.00/0.34	    ![X4 : $tType, X5 : app_encode_fun(X4, $o), X6 : $tType, 
0.00/0.34	      X7 : app_encode_fun(X4, X6), X8 : $tType, X9 : app_encode_fun(X6, X8), 
0.00/0.34	      X10 : app_encode_fun(X8, app_encode_fun(X8, X8))]:
0.00/0.34	      (~ app_encode_app(app_encode_fun(X4, $o), $o, 'const/sets/FINITE'(X4), 
0.00/0.34	           X5)
0.00/0.34	       | app_encode_app(X4, X6, X7, sk_A4(X6, X4, X8, X5, X7, X9, X10))
0.00/0.34	          = app_encode_app(X4, X6, X7, sk_A5(X6, X4, X8, X5, X7, X9, X10))
0.00/0.34	       | app_encode_app(app_encode_fun(X6, X8), X8, 
0.00/0.34	           app_encode_app(app_encode_fun(X6, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(X6, X8), X8), 
0.00/0.34	             app_encode_app(app_encode_fun(X8, app_encode_fun(X8, X8)), 
0.00/0.34	               app_encode_fun(app_encode_fun(X6, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(X6, X8), X8)), 
0.00/0.34	               'const/iterate/iterate'(X6, X8), X10), 
0.00/0.34	             app_encode_app(app_encode_fun(X4, $o), app_encode_fun(X6, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(X4, X6), 
0.00/0.34	                 app_encode_fun(app_encode_fun(X4, $o), 
0.00/0.34	                   app_encode_fun(X6, $o)), 'const/sets/IMAGE'(X4, X6), X7), 
0.00/0.34	               X5)), X9)
0.00/0.34	          = app_encode_app(app_encode_fun(X4, X8), X8, 
0.00/0.34	              app_encode_app(app_encode_fun(X4, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(X4, X8), X8), 
0.00/0.34	                app_encode_app(app_encode_fun(X8, app_encode_fun(X8, X8)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(X4, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(X4, X8), X8)), 
0.00/0.34	                  'const/iterate/iterate'(X4, X8), X10), X5), 
0.00/0.34	              app_encode_app(app_encode_fun(X4, X6), app_encode_fun(X4, X8), 
0.00/0.34	                app_encode_app(app_encode_fun(X6, X8), 
0.00/0.34	                  app_encode_fun(app_encode_fun(X4, X6), 
0.00/0.34	                    app_encode_fun(X4, X8)), 'const/trivia/o'(X6, X4, X8), 
0.00/0.34	                  X9), X7))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X8, app_encode_fun(X8, X8)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X8), X10)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_17])).
0.00/0.34	tff('2', plain,
0.00/0.34	    ![X4 : $tType, X5 : app_encode_fun(X4, $o), X6 : $tType, 
0.00/0.34	      X7 : app_encode_fun(X4, X6), X8 : $tType, X9 : app_encode_fun(X6, X8), 
0.00/0.34	      X10 : app_encode_fun(X8, app_encode_fun(X8, X8))]:
0.00/0.34	      (~ app_encode_app(app_encode_fun(X4, $o), $o, 'const/sets/FINITE'(X4), 
0.00/0.34	           X5)
0.00/0.34	       | app_encode_app(app_encode_fun(X4, $o), $o, 
0.00/0.34	           app_encode_app(X4, app_encode_fun(app_encode_fun(X4, $o), $o), 
0.00/0.34	             'const/sets/IN'(X4), sk_A5(X6, X4, X8, X5, X7, X9, X10)), X5)
0.00/0.34	       | app_encode_app(app_encode_fun(X6, X8), X8, 
0.00/0.34	           app_encode_app(app_encode_fun(X6, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(X6, X8), X8), 
0.00/0.34	             app_encode_app(app_encode_fun(X8, app_encode_fun(X8, X8)), 
0.00/0.34	               app_encode_fun(app_encode_fun(X6, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(X6, X8), X8)), 
0.00/0.34	               'const/iterate/iterate'(X6, X8), X10), 
0.00/0.34	             app_encode_app(app_encode_fun(X4, $o), app_encode_fun(X6, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(X4, X6), 
0.00/0.34	                 app_encode_fun(app_encode_fun(X4, $o), 
0.00/0.34	                   app_encode_fun(X6, $o)), 'const/sets/IMAGE'(X4, X6), X7), 
0.00/0.34	               X5)), X9)
0.00/0.34	          = app_encode_app(app_encode_fun(X4, X8), X8, 
0.00/0.34	              app_encode_app(app_encode_fun(X4, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(X4, X8), X8), 
0.00/0.34	                app_encode_app(app_encode_fun(X8, app_encode_fun(X8, X8)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(X4, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(X4, X8), X8)), 
0.00/0.34	                  'const/iterate/iterate'(X4, X8), X10), X5), 
0.00/0.34	              app_encode_app(app_encode_fun(X4, X6), app_encode_fun(X4, X8), 
0.00/0.34	                app_encode_app(app_encode_fun(X6, X8), 
0.00/0.34	                  app_encode_fun(app_encode_fun(X4, X6), 
0.00/0.34	                    app_encode_fun(X4, X8)), 'const/trivia/o'(X6, X4, X8), 
0.00/0.34	                  X9), X7))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X8, app_encode_fun(X8, X8)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X8), X10)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_17])).
0.00/0.34	tff(zf_stmt_21, conjecture,
0.00/0.34	  (![A:$tType,B:$tType,A0:app_encode_fun(B,'type/realax/real'),
0.00/0.34	     A1:app_encode_fun(A,B),A2:app_encode_fun(A,$o)]:
0.00/0.34	     ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A2) & 
0.00/0.34	       (![A3:A,A4:A]:
0.00/0.34	          ((app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.34	                           app_encode_app(A,
0.00/0.34	                                          app_encode_fun(app_encode_fun(A,$o),
0.00/0.34	                                                         $o),
0.00/0.34	                                          'const/sets/IN'(A),A3),
0.00/0.34	                           A2) & 
0.00/0.34	            app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.34	                           app_encode_app(A,
0.00/0.34	                                          app_encode_fun(app_encode_fun(A,$o),
0.00/0.34	                                                         $o),
0.00/0.34	                                          'const/sets/IN'(A),A4),
0.00/0.34	                           A2) & 
0.00/0.34	            (A3 != A4) & 
0.00/0.34	            (app_encode_app(A,B,A1,A3) = app_encode_app(A,B,A1,A4))) =>
0.00/0.34	           (app_encode_app(B,'type/realax/real',A0,app_encode_app(A,B,A1,A3)) =
0.00/0.34	            app_encode_app('type/nums/num','type/realax/real',
0.00/0.34	                           'const/realax/real_of_num',
0.00/0.34	                           app_encode_app('type/nums/num','type/nums/num',
0.00/0.34	                                          'const/nums/NUMERAL',
0.00/0.34	                                          'const/nums/_0')))))) =>
0.00/0.34	      (app_encode_app(app_encode_fun(B,'type/realax/real'),
0.00/0.34	                      'type/realax/real',
0.00/0.34	                      app_encode_app(app_encode_fun(B,$o),
0.00/0.34	                                     app_encode_fun(app_encode_fun(B,
0.00/0.34	                                                                   'type/realax/real'),
0.00/0.34	                                                    'type/realax/real'),
0.00/0.34	                                     'const/iterate/sum'(B),
0.00/0.34	                                     app_encode_app(app_encode_fun(A,$o),
0.00/0.34	                                                    app_encode_fun(B,$o),
0.00/0.34	                                                    app_encode_app(app_encode_fun(
0.00/0.34	                                                                   A,B),
0.00/0.34	                                                                   app_encode_fun(
0.00/0.34	                                                                   app_encode_fun(
0.00/0.34	                                                                   A,$o),
0.00/0.34	                                                                   app_encode_fun(
0.00/0.34	                                                                   B,$o)),
0.00/0.34	                                                                   'const/sets/IMAGE'(
0.00/0.34	                                                                   A,B),A1),
0.00/0.34	                                                    A2)),
0.00/0.34	                      A0) =
0.00/0.34	       app_encode_app(app_encode_fun(A,'type/realax/real'),
0.00/0.34	                      'type/realax/real',
0.00/0.34	                      app_encode_app(app_encode_fun(A,$o),
0.00/0.34	                                     app_encode_fun(app_encode_fun(A,
0.00/0.34	                                                                   'type/realax/real'),
0.00/0.34	                                                    'type/realax/real'),
0.00/0.34	                                     'const/iterate/sum'(A),A2),
0.00/0.34	                      app_encode_app(app_encode_fun(A,B),
0.00/0.34	                                     app_encode_fun(A,'type/realax/real'),
0.00/0.34	                                     app_encode_app(app_encode_fun(B,
0.00/0.34	                                                                   'type/realax/real'),
0.00/0.34	                                                    app_encode_fun(app_encode_fun(
0.00/0.34	                                                                   A,B),
0.00/0.34	                                                                   app_encode_fun(
0.00/0.34	                                                                   A,
0.00/0.34	                                                                   'type/realax/real')),
0.00/0.34	                                                    'const/trivia/o'(
0.00/0.34	                                                    B,A,'type/realax/real'),
0.00/0.34	                                                    A0),
0.00/0.34	                                     A1)))))).
0.00/0.34	tff(zf_stmt_0, negated_conjecture,
0.00/0.34	  (~
0.00/0.34	    (![A:$tType,B:$tType,A0:app_encode_fun(B,'type/realax/real'),
0.00/0.34	       A1:app_encode_fun(A,B),A2:app_encode_fun(A,$o)]:
0.00/0.34	       ((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A2) & 
0.00/0.34	         (![A3:A,A4:A]:
0.00/0.34	            ((app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.34	                             app_encode_app(A,
0.00/0.34	                                            app_encode_fun(app_encode_fun(
0.00/0.34	                                                           A,$o),$o),
0.00/0.34	                                            'const/sets/IN'(A),A3),
0.00/0.34	                             A2) & 
0.00/0.34	              app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.34	                             app_encode_app(A,
0.00/0.34	                                            app_encode_fun(app_encode_fun(
0.00/0.34	                                                           A,$o),$o),
0.00/0.34	                                            'const/sets/IN'(A),A4),
0.00/0.34	                             A2) & 
0.00/0.34	              (A3 != A4) & 
0.00/0.34	              (app_encode_app(A,B,A1,A3) = app_encode_app(A,B,A1,A4))) =>
0.00/0.34	             (app_encode_app(B,'type/realax/real',A0,
0.00/0.34	                             app_encode_app(A,B,A1,A3)) =
0.00/0.34	              app_encode_app('type/nums/num','type/realax/real',
0.00/0.34	                             'const/realax/real_of_num',
0.00/0.34	                             app_encode_app('type/nums/num','type/nums/num',
0.00/0.34	                                            'const/nums/NUMERAL',
0.00/0.34	                                            'const/nums/_0')))))) =>
0.00/0.34	        (app_encode_app(app_encode_fun(B,'type/realax/real'),
0.00/0.34	                        'type/realax/real',
0.00/0.34	                        app_encode_app(app_encode_fun(B,$o),
0.00/0.34	                                       app_encode_fun(app_encode_fun(
0.00/0.34	                                                      B,'type/realax/real'),
0.00/0.34	                                                      'type/realax/real'),
0.00/0.34	                                       'const/iterate/sum'(B),
0.00/0.34	                                       app_encode_app(app_encode_fun(A,$o),
0.00/0.34	                                                      app_encode_fun(B,$o),
0.00/0.34	                                                      app_encode_app(
0.00/0.34	                                                      app_encode_fun(A,B),
0.00/0.34	                                                      app_encode_fun(
0.00/0.34	                                                      app_encode_fun(A,$o),
0.00/0.34	                                                      app_encode_fun(B,$o)),
0.00/0.34	                                                      'const/sets/IMAGE'(A,B),
0.00/0.34	                                                      A1),A2)),
0.00/0.34	                        A0) =
0.00/0.34	         app_encode_app(app_encode_fun(A,'type/realax/real'),
0.00/0.34	                        'type/realax/real',
0.00/0.34	                        app_encode_app(app_encode_fun(A,$o),
0.00/0.34	                                       app_encode_fun(app_encode_fun(
0.00/0.34	                                                      A,'type/realax/real'),
0.00/0.34	                                                      'type/realax/real'),
0.00/0.34	                                       'const/iterate/sum'(A),A2),
0.00/0.34	                        app_encode_app(app_encode_fun(A,B),
0.00/0.34	                                       app_encode_fun(A,'type/realax/real'),
0.00/0.34	                                       app_encode_app(app_encode_fun(
0.00/0.34	                                                      B,'type/realax/real'),
0.00/0.34	                                                      app_encode_fun(
0.00/0.34	                                                      app_encode_fun(A,B),
0.00/0.34	                                                      app_encode_fun(
0.00/0.34	                                                      A,'type/realax/real')),
0.00/0.34	                                                      'const/trivia/o'(
0.00/0.34	                                                      B,A,'type/realax/real'),
0.00/0.34	                                                      A0),
0.00/0.34	                                       A1))))))).
0.00/0.34	tff('3', plain,
0.00/0.34	    ![X12 : sk_A, X13 : sk_A]:
0.00/0.34	      (app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.00/0.34	         app_encode_app(sk_A, sk_B, sk_A1, X12))
0.00/0.34	        = app_encode_app('type/nums/num', 'type/realax/real', 
0.00/0.34	            'const/realax/real_of_num', 
0.00/0.34	            app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.34	              'const/nums/NUMERAL', 'const/nums/_0'))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), X12), sk_A2)
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), X13), sk_A2)
0.00/0.34	       | X12 = X13
0.00/0.34	       | app_encode_app(sk_A, sk_B, sk_A1, X12)
0.00/0.34	          != app_encode_app(sk_A, sk_B, sk_A1, X13)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff(zf_stmt_20, axiom,
0.00/0.34	  (app_encode_app(app_encode_fun('type/realax/real',
0.00/0.34	                                 app_encode_fun('type/realax/real',
0.00/0.34	                                                'type/realax/real')),
0.00/0.34	                  'type/realax/real',
0.00/0.34	                  'const/iterate/neutral'('type/realax/real'),
0.00/0.34	                  'const/realax/real_add') =
0.00/0.34	   app_encode_app('type/nums/num','type/realax/real',
0.00/0.34	                  'const/realax/real_of_num',
0.00/0.34	                  app_encode_app('type/nums/num','type/nums/num',
0.00/0.34	                                 'const/nums/NUMERAL','const/nums/_0')))).
0.00/0.34	tff('4', plain,
0.00/0.34	    app_encode_app(
0.00/0.34	      app_encode_fun('type/realax/real', 
0.00/0.34	        app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	      'type/realax/real', 'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	      'const/realax/real_add')
0.00/0.34	     = app_encode_app('type/nums/num', 'type/realax/real', 
0.00/0.34	         'const/realax/real_of_num', 
0.00/0.34	         app_encode_app('type/nums/num', 'type/nums/num', 
0.00/0.34	           'const/nums/NUMERAL', 'const/nums/_0')),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_20])).
0.00/0.34	tff('5', plain,
0.00/0.34	    ![X12 : sk_A, X13 : sk_A]:
0.00/0.34	      (app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.00/0.34	         app_encode_app(sk_A, sk_B, sk_A1, X12))
0.00/0.34	        = app_encode_app(
0.00/0.34	            app_encode_fun('type/realax/real', 
0.00/0.34	              app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	            'type/realax/real', 'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	            'const/realax/real_add')
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), X12), sk_A2)
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), X13), sk_A2)
0.00/0.34	       | X12 = X13
0.00/0.34	       | app_encode_app(sk_A, sk_B, sk_A1, X12)
0.00/0.34	          != app_encode_app(sk_A, sk_B, sk_A1, X13)),
0.00/0.34	    inference('demod', [status(thm)], ['3', '4'])).
0.00/0.34	tff('6', plain,
0.00/0.34	    ![X0 : $tType, X1 : app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	      X2 : $tType, X3 : app_encode_fun(X2, X0), 
0.00/0.34	      X4 : app_encode_fun(sk_A, X2), X5 : sk_A]:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X0), X1)
0.00/0.34	       | app_encode_app(app_encode_fun(X2, X0), X0, 
0.00/0.34	           app_encode_app(app_encode_fun(X2, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(X2, X0), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	               app_encode_fun(app_encode_fun(X2, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(X2, X0), X0)), 
0.00/0.34	               'const/iterate/iterate'(X2, X0), X1), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(X2, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, X2), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(X2, $o)), 'const/sets/IMAGE'(sk_A, X2), X4), 
0.00/0.34	               sk_A2)), X3)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, X0), X1), sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, X2), 
0.00/0.34	                app_encode_fun(sk_A, X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X2, X0), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, X2), 
0.00/0.34	                    app_encode_fun(sk_A, X0)), 
0.00/0.34	                  'const/trivia/o'(X2, sk_A, X0), X3), X4))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             'const/sets/FINITE'(sk_A), sk_A2)
0.00/0.34	       | app_encode_app(sk_A, sk_B, sk_A1, X5)
0.00/0.34	          != app_encode_app(sk_A, sk_B, sk_A1, 
0.00/0.34	               sk_A5(X2, sk_A, X0, sk_A2, X4, X3, X1))
0.00/0.34	       | X5 = sk_A5(X2, sk_A, X0, sk_A2, X4, X3, X1)
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), X5), sk_A2)
0.00/0.34	       | app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.00/0.34	           app_encode_app(sk_A, sk_B, sk_A1, X5))
0.00/0.34	          = app_encode_app(
0.00/0.34	              app_encode_fun('type/realax/real', 
0.00/0.34	                app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	              'const/realax/real_add')),
0.00/0.34	    inference('sup-', [status(thm)], ['2', '5'])).
0.00/0.34	tff('7', plain,
0.00/0.34	    app_encode_app(app_encode_fun(sk_A, $o), $o, 'const/sets/FINITE'(sk_A), 
0.00/0.34	      sk_A2),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('8', plain,
0.00/0.34	    ![X0 : $tType, X1 : app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	      X2 : $tType, X3 : app_encode_fun(X2, X0), 
0.00/0.34	      X4 : app_encode_fun(sk_A, X2), X5 : sk_A]:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X0), X1)
0.00/0.34	       | app_encode_app(app_encode_fun(X2, X0), X0, 
0.00/0.34	           app_encode_app(app_encode_fun(X2, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(X2, X0), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	               app_encode_fun(app_encode_fun(X2, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(X2, X0), X0)), 
0.00/0.34	               'const/iterate/iterate'(X2, X0), X1), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(X2, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, X2), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(X2, $o)), 'const/sets/IMAGE'(sk_A, X2), X4), 
0.00/0.34	               sk_A2)), X3)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, X0), X1), sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, X2), 
0.00/0.34	                app_encode_fun(sk_A, X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X2, X0), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, X2), 
0.00/0.34	                    app_encode_fun(sk_A, X0)), 
0.00/0.34	                  'const/trivia/o'(X2, sk_A, X0), X3), X4))
0.00/0.34	       | ~ $true
0.00/0.34	       | app_encode_app(sk_A, sk_B, sk_A1, X5)
0.00/0.34	          != app_encode_app(sk_A, sk_B, sk_A1, 
0.00/0.34	               sk_A5(X2, sk_A, X0, sk_A2, X4, X3, X1))
0.00/0.34	       | X5 = sk_A5(X2, sk_A, X0, sk_A2, X4, X3, X1)
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), X5), sk_A2)
0.00/0.34	       | app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.00/0.34	           app_encode_app(sk_A, sk_B, sk_A1, X5))
0.00/0.34	          = app_encode_app(
0.00/0.34	              app_encode_fun('type/realax/real', 
0.00/0.34	                app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	              'const/realax/real_add')),
0.00/0.34	    inference('demod', [status(thm)], ['6', '7'])).
0.00/0.34	tff('9', plain,
0.00/0.34	    ![X0 : $tType, X1 : app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	      X2 : $tType, X3 : app_encode_fun(X2, X0), 
0.00/0.34	      X4 : app_encode_fun(sk_A, X2), X5 : sk_A]:
0.00/0.34	      (app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.00/0.34	         app_encode_app(sk_A, sk_B, sk_A1, X5))
0.00/0.34	        = app_encode_app(
0.00/0.34	            app_encode_fun('type/realax/real', 
0.00/0.34	              app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	            'type/realax/real', 'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	            'const/realax/real_add')
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), X5), sk_A2)
0.00/0.34	       | X5 = sk_A5(X2, sk_A, X0, sk_A2, X4, X3, X1)
0.00/0.34	       | app_encode_app(sk_A, sk_B, sk_A1, X5)
0.00/0.34	          != app_encode_app(sk_A, sk_B, sk_A1, 
0.00/0.34	               sk_A5(X2, sk_A, X0, sk_A2, X4, X3, X1))
0.00/0.34	       | app_encode_app(app_encode_fun(X2, X0), X0, 
0.00/0.34	           app_encode_app(app_encode_fun(X2, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(X2, X0), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	               app_encode_fun(app_encode_fun(X2, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(X2, X0), X0)), 
0.00/0.34	               'const/iterate/iterate'(X2, X0), X1), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(X2, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, X2), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(X2, $o)), 'const/sets/IMAGE'(sk_A, X2), X4), 
0.00/0.34	               sk_A2)), X3)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, X0), X1), sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, X2), 
0.00/0.34	                app_encode_fun(sk_A, X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X2, X0), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, X2), 
0.00/0.34	                    app_encode_fun(sk_A, X0)), 
0.00/0.34	                  'const/trivia/o'(X2, sk_A, X0), X3), X4))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X0), X1)),
0.00/0.34	    inference('simplify', [status(thm)], ['8'])).
0.00/0.34	tff('10', plain,
0.00/0.34	    ![X0 : $tType, X1 : app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	      X2 : app_encode_fun(sk_B, X0), X3 : sk_A]:
0.00/0.34	      (app_encode_app(sk_A, sk_B, sk_A1, X3)
0.00/0.34	        != app_encode_app(sk_A, sk_B, sk_A1, 
0.00/0.34	             sk_A4(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X0), X1)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, X0), X0, 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, X0), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, X0), X0)), 
0.00/0.34	               'const/iterate/iterate'(sk_B, X0), X1), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), X2)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, X0), X1), sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, X0), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, X0), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, X0)), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, X0), X2), sk_A1))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             'const/sets/FINITE'(sk_A), sk_A2)
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X0), X1)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, X0), X0, 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, X0), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, X0), X0)), 
0.00/0.34	               'const/iterate/iterate'(sk_B, X0), X1), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), X2)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, X0), X1), sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, X0), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, X0), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, X0)), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, X0), X2), sk_A1))
0.00/0.34	       | X3 = sk_A5(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), X3), sk_A2)
0.00/0.34	       | app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.00/0.34	           app_encode_app(sk_A, sk_B, sk_A1, X3))
0.00/0.34	          = app_encode_app(
0.00/0.34	              app_encode_fun('type/realax/real', 
0.00/0.34	                app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	              'const/realax/real_add')),
0.00/0.34	    inference('sup-', [status(thm)], ['1', '9'])).
0.00/0.34	tff('11', plain,
0.00/0.34	    ![X0 : $tType, X1 : app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	      X2 : app_encode_fun(sk_B, X0), X3 : sk_A]:
0.00/0.34	      (app_encode_app(sk_A, sk_B, sk_A1, X3)
0.00/0.34	        != app_encode_app(sk_A, sk_B, sk_A1, 
0.00/0.34	             sk_A4(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X0), X1)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, X0), X0, 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, X0), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, X0), X0)), 
0.00/0.34	               'const/iterate/iterate'(sk_B, X0), X1), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), X2)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, X0), X1), sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, X0), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, X0), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, X0)), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, X0), X2), sk_A1))
0.00/0.34	       | ~ $true
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X0), X1)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, X0), X0, 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, X0), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, X0), X0)), 
0.00/0.34	               'const/iterate/iterate'(sk_B, X0), X1), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), X2)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, X0), X1), sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, X0), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, X0), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, X0)), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, X0), X2), sk_A1))
0.00/0.34	       | X3 = sk_A5(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), X3), sk_A2)
0.00/0.34	       | app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.00/0.34	           app_encode_app(sk_A, sk_B, sk_A1, X3))
0.00/0.34	          = app_encode_app(
0.00/0.34	              app_encode_fun('type/realax/real', 
0.00/0.34	                app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	              'const/realax/real_add')),
0.00/0.34	    inference('demod', [status(thm)], ['10', '7'])).
0.00/0.34	tff('12', plain,
0.00/0.34	    ![X0 : $tType, X1 : app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	      X2 : app_encode_fun(sk_B, X0), X3 : sk_A]:
0.00/0.34	      (app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.00/0.34	         app_encode_app(sk_A, sk_B, sk_A1, X3))
0.00/0.34	        = app_encode_app(
0.00/0.34	            app_encode_fun('type/realax/real', 
0.00/0.34	              app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	            'type/realax/real', 'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	            'const/realax/real_add')
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), X3), sk_A2)
0.00/0.34	       | X3 = sk_A5(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, X0), X0, 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, X0), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, X0), X0)), 
0.00/0.34	               'const/iterate/iterate'(sk_B, X0), X1), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), X2)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, X0), X1), sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, X0), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, X0), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, X0)), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, X0), X2), sk_A1))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X0), X1)
0.00/0.34	       | app_encode_app(sk_A, sk_B, sk_A1, X3)
0.00/0.34	          != app_encode_app(sk_A, sk_B, sk_A1, 
0.00/0.34	               sk_A4(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1))),
0.00/0.34	    inference('simplify', [status(thm)], ['11'])).
0.00/0.34	tff('13', plain,
0.00/0.34	    ![X0 : $tType, X1 : app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	      X2 : app_encode_fun(sk_B, X0)]:
0.00/0.34	      (~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.34	           'const/iterate/monoidal'(X0), X1)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, X0), X0, 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, X0), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, X0), X0)), 
0.00/0.34	               'const/iterate/iterate'(sk_B, X0), X1), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), X2)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, X0), X1), sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, X0), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, X0), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, X0)), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, X0), X2), sk_A1))
0.00/0.34	       | sk_A4(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)
0.00/0.34	          = sk_A5(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), 
0.00/0.34	               sk_A4(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)), sk_A2)
0.00/0.34	       | app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.00/0.34	           app_encode_app(sk_A, sk_B, sk_A1, 
0.00/0.34	             sk_A4(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)))
0.00/0.34	          = app_encode_app(
0.00/0.34	              app_encode_fun('type/realax/real', 
0.00/0.34	                app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	              'const/realax/real_add')),
0.00/0.34	    inference('eq_res', [status(thm)], ['12'])).
0.00/0.34	tff('14', plain,
0.00/0.34	    ![X4 : $tType, X5 : app_encode_fun(X4, $o), X6 : $tType, 
0.00/0.34	      X7 : app_encode_fun(X4, X6), X8 : $tType, X9 : app_encode_fun(X6, X8), 
0.00/0.34	      X10 : app_encode_fun(X8, app_encode_fun(X8, X8))]:
0.00/0.34	      (~ app_encode_app(app_encode_fun(X4, $o), $o, 'const/sets/FINITE'(X4), 
0.00/0.34	           X5)
0.00/0.34	       | sk_A4(X6, X4, X8, X5, X7, X9, X10)
0.00/0.34	          != sk_A5(X6, X4, X8, X5, X7, X9, X10)
0.00/0.34	       | app_encode_app(app_encode_fun(X6, X8), X8, 
0.00/0.34	           app_encode_app(app_encode_fun(X6, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(X6, X8), X8), 
0.00/0.34	             app_encode_app(app_encode_fun(X8, app_encode_fun(X8, X8)), 
0.00/0.34	               app_encode_fun(app_encode_fun(X6, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(X6, X8), X8)), 
0.00/0.34	               'const/iterate/iterate'(X6, X8), X10), 
0.00/0.34	             app_encode_app(app_encode_fun(X4, $o), app_encode_fun(X6, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(X4, X6), 
0.00/0.34	                 app_encode_fun(app_encode_fun(X4, $o), 
0.00/0.34	                   app_encode_fun(X6, $o)), 'const/sets/IMAGE'(X4, X6), X7), 
0.00/0.34	               X5)), X9)
0.00/0.34	          = app_encode_app(app_encode_fun(X4, X8), X8, 
0.00/0.34	              app_encode_app(app_encode_fun(X4, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(X4, X8), X8), 
0.00/0.34	                app_encode_app(app_encode_fun(X8, app_encode_fun(X8, X8)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(X4, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(X4, X8), X8)), 
0.00/0.34	                  'const/iterate/iterate'(X4, X8), X10), X5), 
0.00/0.34	              app_encode_app(app_encode_fun(X4, X6), app_encode_fun(X4, X8), 
0.00/0.34	                app_encode_app(app_encode_fun(X6, X8), 
0.00/0.34	                  app_encode_fun(app_encode_fun(X4, X6), 
0.00/0.34	                    app_encode_fun(X4, X8)), 'const/trivia/o'(X6, X4, X8), 
0.00/0.34	                  X9), X7))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X8, app_encode_fun(X8, X8)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X8), X10)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_17])).
0.00/0.34	tff('15', plain,
0.00/0.34	    ![X0 : $tType, X1 : app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	      X2 : app_encode_fun(sk_B, X0)]:
0.00/0.34	      (sk_A4(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)
0.00/0.34	        != sk_A4(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)
0.00/0.34	       | app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.00/0.34	           app_encode_app(sk_A, sk_B, sk_A1, 
0.00/0.34	             sk_A4(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)))
0.00/0.34	          = app_encode_app(
0.00/0.34	              app_encode_fun('type/realax/real', 
0.00/0.34	                app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	              'const/realax/real_add')
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), 
0.00/0.34	               sk_A4(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)), sk_A2)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, X0), X0, 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, X0), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, X0), X0)), 
0.00/0.34	               'const/iterate/iterate'(sk_B, X0), X1), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), X2)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, X0), X1), sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, X0), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, X0), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, X0)), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, X0), X2), sk_A1))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X0), X1)
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X0), X1)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, X0), X0, 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, X0), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, X0), X0)), 
0.00/0.34	               'const/iterate/iterate'(sk_B, X0), X1), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), X2)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, X0), X1), sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, X0), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, X0), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, X0)), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, X0), X2), sk_A1))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             'const/sets/FINITE'(sk_A), sk_A2)),
0.00/0.34	    inference('sup-', [status(thm)], ['13', '14'])).
0.00/0.34	tff('16', plain,
0.00/0.34	    ![X0 : $tType, X1 : app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	      X2 : app_encode_fun(sk_B, X0)]:
0.00/0.34	      (sk_A4(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)
0.00/0.34	        != sk_A4(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)
0.00/0.34	       | app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.00/0.34	           app_encode_app(sk_A, sk_B, sk_A1, 
0.00/0.34	             sk_A4(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)))
0.00/0.34	          = app_encode_app(
0.00/0.34	              app_encode_fun('type/realax/real', 
0.00/0.34	                app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	              'const/realax/real_add')
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), 
0.00/0.34	               sk_A4(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)), sk_A2)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, X0), X0, 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, X0), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, X0), X0)), 
0.00/0.34	               'const/iterate/iterate'(sk_B, X0), X1), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), X2)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, X0), X1), sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, X0), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, X0), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, X0)), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, X0), X2), sk_A1))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X0), X1)
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X0), X1)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, X0), X0, 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, X0), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, X0), X0)), 
0.00/0.34	               'const/iterate/iterate'(sk_B, X0), X1), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), X2)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, X0), X1), sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, X0), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, X0), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, X0)), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, X0), X2), sk_A1))
0.00/0.34	       | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['15', '7'])).
0.00/0.34	tff('17', plain,
0.00/0.34	    ![X0 : $tType, X1 : app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	      X2 : app_encode_fun(sk_B, X0)]:
0.00/0.34	      (~ app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), $o, 
0.00/0.34	           'const/iterate/monoidal'(X0), X1)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, X0), X0, 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, X0), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, X0), X0)), 
0.00/0.34	               'const/iterate/iterate'(sk_B, X0), X1), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), X2)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, X0), X0, 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, X0), X0), 
0.00/0.34	                app_encode_app(app_encode_fun(X0, app_encode_fun(X0, X0)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, X0), X0)), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, X0), X1), sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, X0), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, X0), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, X0)), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, X0), X2), sk_A1))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), 
0.00/0.34	               sk_A4(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)), sk_A2)
0.00/0.34	       | app_encode_app(sk_B, 'type/realax/real', sk_A0, 
0.00/0.34	           app_encode_app(sk_A, sk_B, sk_A1, 
0.00/0.34	             sk_A4(sk_B, sk_A, X0, sk_A2, sk_A1, X2, X1)))
0.00/0.34	          = app_encode_app(
0.00/0.34	              app_encode_fun('type/realax/real', 
0.00/0.34	                app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	              'const/realax/real_add')),
0.00/0.34	    inference('simplify', [status(thm)], ['16'])).
0.00/0.34	tff('18', plain,
0.00/0.34	    ![X4 : $tType, X5 : app_encode_fun(X4, $o), X6 : $tType, 
0.00/0.34	      X7 : app_encode_fun(X4, X6), X8 : $tType, X9 : app_encode_fun(X6, X8), 
0.00/0.34	      X10 : app_encode_fun(X8, app_encode_fun(X8, X8))]:
0.00/0.34	      (~ app_encode_app(app_encode_fun(X4, $o), $o, 'const/sets/FINITE'(X4), 
0.00/0.34	           X5)
0.00/0.34	       | app_encode_app(X6, X8, X9, 
0.00/0.34	           app_encode_app(X4, X6, X7, sk_A4(X6, X4, X8, X5, X7, X9, X10)))
0.00/0.34	          != app_encode_app(app_encode_fun(X8, app_encode_fun(X8, X8)), X8, 
0.00/0.34	               'const/iterate/neutral'(X8), X10)
0.00/0.34	       | app_encode_app(app_encode_fun(X6, X8), X8, 
0.00/0.34	           app_encode_app(app_encode_fun(X6, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(X6, X8), X8), 
0.00/0.34	             app_encode_app(app_encode_fun(X8, app_encode_fun(X8, X8)), 
0.00/0.34	               app_encode_fun(app_encode_fun(X6, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(X6, X8), X8)), 
0.00/0.34	               'const/iterate/iterate'(X6, X8), X10), 
0.00/0.34	             app_encode_app(app_encode_fun(X4, $o), app_encode_fun(X6, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(X4, X6), 
0.00/0.34	                 app_encode_fun(app_encode_fun(X4, $o), 
0.00/0.34	                   app_encode_fun(X6, $o)), 'const/sets/IMAGE'(X4, X6), X7), 
0.00/0.34	               X5)), X9)
0.00/0.34	          = app_encode_app(app_encode_fun(X4, X8), X8, 
0.00/0.34	              app_encode_app(app_encode_fun(X4, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(X4, X8), X8), 
0.00/0.34	                app_encode_app(app_encode_fun(X8, app_encode_fun(X8, X8)), 
0.00/0.34	                  app_encode_fun(app_encode_fun(X4, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(X4, X8), X8)), 
0.00/0.34	                  'const/iterate/iterate'(X4, X8), X10), X5), 
0.00/0.34	              app_encode_app(app_encode_fun(X4, X6), app_encode_fun(X4, X8), 
0.00/0.34	                app_encode_app(app_encode_fun(X6, X8), 
0.00/0.34	                  app_encode_fun(app_encode_fun(X4, X6), 
0.00/0.34	                    app_encode_fun(X4, X8)), 'const/trivia/o'(X6, X4, X8), 
0.00/0.34	                  X9), X7))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(X8, app_encode_fun(X8, X8)), $o, 
0.00/0.34	             'const/iterate/monoidal'(X8), X10)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_17])).
0.00/0.34	tff('19', plain,
0.00/0.34	    ![X0 : app_encode_fun('type/realax/real', 
0.00/0.34	             app_encode_fun('type/realax/real', 'type/realax/real'))]:
0.00/0.34	      (app_encode_app(
0.00/0.34	         app_encode_fun('type/realax/real', 
0.00/0.34	           app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	         'type/realax/real', 'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	         'const/realax/real_add')
0.00/0.34	        != app_encode_app(
0.00/0.34	             app_encode_fun('type/realax/real', 
0.00/0.34	               app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	             'type/realax/real', 
0.00/0.34	             'const/iterate/neutral'('type/realax/real'), X0)
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), 
0.00/0.34	               sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, X0)), 
0.00/0.34	             sk_A2)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	           'type/realax/real', 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	               'type/realax/real'), 
0.00/0.34	             app_encode_app(
0.00/0.34	               app_encode_fun('type/realax/real', 
0.00/0.34	                 app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                   'type/realax/real')), 
0.00/0.34	               'const/iterate/iterate'(sk_B, 'type/realax/real'), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                  'type/realax/real'), 
0.00/0.34	                app_encode_app(
0.00/0.34	                  app_encode_fun('type/realax/real', 
0.00/0.34	                    app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                      'type/realax/real')), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, 'type/realax/real'), X0), 
0.00/0.34	                sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, 'type/realax/real')), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), 
0.00/0.34	                sk_A1))
0.00/0.34	       | ~ app_encode_app(
0.00/0.34	             app_encode_fun('type/realax/real', 
0.00/0.34	               app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.00/0.34	             'const/iterate/monoidal'('type/realax/real'), X0)
0.00/0.34	       | ~ app_encode_app(
0.00/0.34	             app_encode_fun('type/realax/real', 
0.00/0.34	               app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.00/0.34	             'const/iterate/monoidal'('type/realax/real'), X0)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	           'type/realax/real', 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	               'type/realax/real'), 
0.00/0.34	             app_encode_app(
0.00/0.34	               app_encode_fun('type/realax/real', 
0.00/0.34	                 app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                   'type/realax/real')), 
0.00/0.34	               'const/iterate/iterate'(sk_B, 'type/realax/real'), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                  'type/realax/real'), 
0.00/0.34	                app_encode_app(
0.00/0.34	                  app_encode_fun('type/realax/real', 
0.00/0.34	                    app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                      'type/realax/real')), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, 'type/realax/real'), X0), 
0.00/0.34	                sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, 'type/realax/real')), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), 
0.00/0.34	                sk_A1))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             'const/sets/FINITE'(sk_A), sk_A2)),
0.00/0.34	    inference('sup-', [status(thm)], ['17', '18'])).
0.00/0.34	tff('20', plain,
0.00/0.34	    ![X0 : app_encode_fun('type/realax/real', 
0.00/0.34	             app_encode_fun('type/realax/real', 'type/realax/real'))]:
0.00/0.34	      (app_encode_app(
0.00/0.34	         app_encode_fun('type/realax/real', 
0.00/0.34	           app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	         'type/realax/real', 'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	         'const/realax/real_add')
0.00/0.34	        != app_encode_app(
0.00/0.34	             app_encode_fun('type/realax/real', 
0.00/0.34	               app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	             'type/realax/real', 
0.00/0.34	             'const/iterate/neutral'('type/realax/real'), X0)
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), 
0.00/0.34	               sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, X0)), 
0.00/0.34	             sk_A2)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	           'type/realax/real', 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	               'type/realax/real'), 
0.00/0.34	             app_encode_app(
0.00/0.34	               app_encode_fun('type/realax/real', 
0.00/0.34	                 app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                   'type/realax/real')), 
0.00/0.34	               'const/iterate/iterate'(sk_B, 'type/realax/real'), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                  'type/realax/real'), 
0.00/0.34	                app_encode_app(
0.00/0.34	                  app_encode_fun('type/realax/real', 
0.00/0.34	                    app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                      'type/realax/real')), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, 'type/realax/real'), X0), 
0.00/0.34	                sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, 'type/realax/real')), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), 
0.00/0.34	                sk_A1))
0.00/0.34	       | ~ app_encode_app(
0.00/0.34	             app_encode_fun('type/realax/real', 
0.00/0.34	               app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.00/0.34	             'const/iterate/monoidal'('type/realax/real'), X0)
0.00/0.34	       | ~ app_encode_app(
0.00/0.34	             app_encode_fun('type/realax/real', 
0.00/0.34	               app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.00/0.34	             'const/iterate/monoidal'('type/realax/real'), X0)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	           'type/realax/real', 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	               'type/realax/real'), 
0.00/0.34	             app_encode_app(
0.00/0.34	               app_encode_fun('type/realax/real', 
0.00/0.34	                 app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                   'type/realax/real')), 
0.00/0.34	               'const/iterate/iterate'(sk_B, 'type/realax/real'), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                  'type/realax/real'), 
0.00/0.34	                app_encode_app(
0.00/0.34	                  app_encode_fun('type/realax/real', 
0.00/0.34	                    app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                      'type/realax/real')), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, 'type/realax/real'), X0), 
0.00/0.34	                sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, 'type/realax/real')), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), 
0.00/0.34	                sk_A1))
0.00/0.34	       | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['19', '7'])).
0.00/0.34	tff('21', plain,
0.00/0.34	    ![X0 : app_encode_fun('type/realax/real', 
0.00/0.34	             app_encode_fun('type/realax/real', 'type/realax/real'))]:
0.00/0.34	      (~ app_encode_app(
0.00/0.34	           app_encode_fun('type/realax/real', 
0.00/0.34	             app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.00/0.34	           'const/iterate/monoidal'('type/realax/real'), X0)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	           'type/realax/real', 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	               'type/realax/real'), 
0.00/0.34	             app_encode_app(
0.00/0.34	               app_encode_fun('type/realax/real', 
0.00/0.34	                 app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                   'type/realax/real')), 
0.00/0.34	               'const/iterate/iterate'(sk_B, 'type/realax/real'), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                  'type/realax/real'), 
0.00/0.34	                app_encode_app(
0.00/0.34	                  app_encode_fun('type/realax/real', 
0.00/0.34	                    app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                      'type/realax/real')), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, 'type/realax/real'), X0), 
0.00/0.34	                sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, 'type/realax/real')), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), 
0.00/0.34	                sk_A1))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             app_encode_app(sk_A, 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.34	               'const/sets/IN'(sk_A), 
0.00/0.34	               sk_A4(sk_B, sk_A, 'type/realax/real', sk_A2, sk_A1, sk_A0, X0)), 
0.00/0.34	             sk_A2)
0.00/0.34	       | app_encode_app(
0.00/0.34	           app_encode_fun('type/realax/real', 
0.00/0.34	             app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	           'type/realax/real', 'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	           'const/realax/real_add')
0.00/0.34	          != app_encode_app(
0.00/0.34	               app_encode_fun('type/realax/real', 
0.00/0.34	                 app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	               'type/realax/real', 
0.00/0.34	               'const/iterate/neutral'('type/realax/real'), X0)),
0.00/0.34	    inference('simplify', [status(thm)], ['20'])).
0.00/0.34	tff('22', plain,
0.00/0.34	    ![X0 : app_encode_fun('type/realax/real', 
0.00/0.34	             app_encode_fun('type/realax/real', 'type/realax/real'))]:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ app_encode_app(
0.00/0.34	             app_encode_fun('type/realax/real', 
0.00/0.34	               app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.00/0.34	             'const/iterate/monoidal'('type/realax/real'), X0)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	           'type/realax/real', 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	               'type/realax/real'), 
0.00/0.34	             app_encode_app(
0.00/0.34	               app_encode_fun('type/realax/real', 
0.00/0.34	                 app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                   'type/realax/real')), 
0.00/0.34	               'const/iterate/iterate'(sk_B, 'type/realax/real'), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                  'type/realax/real'), 
0.00/0.34	                app_encode_app(
0.00/0.34	                  app_encode_fun('type/realax/real', 
0.00/0.34	                    app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                      'type/realax/real')), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, 'type/realax/real'), X0), 
0.00/0.34	                sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, 'type/realax/real')), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), 
0.00/0.34	                sk_A1))
0.00/0.34	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.34	             'const/sets/FINITE'(sk_A), sk_A2)
0.00/0.34	       | app_encode_app(
0.00/0.34	           app_encode_fun('type/realax/real', 
0.00/0.34	             app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	           'type/realax/real', 'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	           'const/realax/real_add')
0.00/0.34	          != app_encode_app(
0.00/0.34	               app_encode_fun('type/realax/real', 
0.00/0.34	                 app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	               'type/realax/real', 
0.00/0.34	               'const/iterate/neutral'('type/realax/real'), X0)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	           'type/realax/real', 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	               'type/realax/real'), 
0.00/0.34	             app_encode_app(
0.00/0.34	               app_encode_fun('type/realax/real', 
0.00/0.34	                 app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                   'type/realax/real')), 
0.00/0.34	               'const/iterate/iterate'(sk_B, 'type/realax/real'), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                  'type/realax/real'), 
0.00/0.34	                app_encode_app(
0.00/0.34	                  app_encode_fun('type/realax/real', 
0.00/0.34	                    app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                      'type/realax/real')), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, 'type/realax/real'), X0), 
0.00/0.34	                sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, 'type/realax/real')), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), 
0.00/0.34	                sk_A1))
0.00/0.34	       | ~ app_encode_app(
0.00/0.34	             app_encode_fun('type/realax/real', 
0.00/0.34	               app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.00/0.34	             'const/iterate/monoidal'('type/realax/real'), X0)),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '21'])).
0.00/0.34	tff('23', plain,
0.00/0.34	    ![X0 : app_encode_fun('type/realax/real', 
0.00/0.34	             app_encode_fun('type/realax/real', 'type/realax/real'))]:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ app_encode_app(
0.00/0.34	             app_encode_fun('type/realax/real', 
0.00/0.34	               app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.00/0.34	             'const/iterate/monoidal'('type/realax/real'), X0)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	           'type/realax/real', 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	               'type/realax/real'), 
0.00/0.34	             app_encode_app(
0.00/0.34	               app_encode_fun('type/realax/real', 
0.00/0.34	                 app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                   'type/realax/real')), 
0.00/0.34	               'const/iterate/iterate'(sk_B, 'type/realax/real'), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                  'type/realax/real'), 
0.00/0.34	                app_encode_app(
0.00/0.34	                  app_encode_fun('type/realax/real', 
0.00/0.34	                    app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                      'type/realax/real')), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, 'type/realax/real'), X0), 
0.00/0.34	                sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, 'type/realax/real')), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), 
0.00/0.34	                sk_A1))
0.00/0.34	       | ~ $true
0.00/0.34	       | app_encode_app(
0.00/0.34	           app_encode_fun('type/realax/real', 
0.00/0.34	             app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	           'type/realax/real', 'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	           'const/realax/real_add')
0.00/0.34	          != app_encode_app(
0.00/0.34	               app_encode_fun('type/realax/real', 
0.00/0.34	                 app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	               'type/realax/real', 
0.00/0.34	               'const/iterate/neutral'('type/realax/real'), X0)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	           'type/realax/real', 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	               'type/realax/real'), 
0.00/0.34	             app_encode_app(
0.00/0.34	               app_encode_fun('type/realax/real', 
0.00/0.34	                 app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                   'type/realax/real')), 
0.00/0.34	               'const/iterate/iterate'(sk_B, 'type/realax/real'), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                  'type/realax/real'), 
0.00/0.34	                app_encode_app(
0.00/0.34	                  app_encode_fun('type/realax/real', 
0.00/0.34	                    app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                      'type/realax/real')), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, 'type/realax/real'), X0), 
0.00/0.34	                sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, 'type/realax/real')), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), 
0.00/0.34	                sk_A1))
0.00/0.34	       | ~ app_encode_app(
0.00/0.34	             app_encode_fun('type/realax/real', 
0.00/0.34	               app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.00/0.34	             'const/iterate/monoidal'('type/realax/real'), X0)),
0.00/0.34	    inference('demod', [status(thm)], ['22', '7'])).
0.00/0.34	tff('24', plain,
0.00/0.34	    ![X0 : app_encode_fun('type/realax/real', 
0.00/0.34	             app_encode_fun('type/realax/real', 'type/realax/real'))]:
0.00/0.34	      (app_encode_app(
0.00/0.34	         app_encode_fun('type/realax/real', 
0.00/0.34	           app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	         'type/realax/real', 'const/iterate/neutral'('type/realax/real'), 
0.00/0.34	         'const/realax/real_add')
0.00/0.34	        != app_encode_app(
0.00/0.34	             app_encode_fun('type/realax/real', 
0.00/0.34	               app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	             'type/realax/real', 
0.00/0.34	             'const/iterate/neutral'('type/realax/real'), X0)
0.00/0.34	       | app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	           'type/realax/real', 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	               'type/realax/real'), 
0.00/0.34	             app_encode_app(
0.00/0.34	               app_encode_fun('type/realax/real', 
0.00/0.34	                 app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                   'type/realax/real')), 
0.00/0.34	               'const/iterate/iterate'(sk_B, 'type/realax/real'), X0), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	               app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                 app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                   app_encode_fun(sk_B, $o)), 
0.00/0.34	                 'const/sets/IMAGE'(sk_A, sk_B), sk_A1), sk_A2)), sk_A0)
0.00/0.34	          = app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	              'type/realax/real', 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                  'type/realax/real'), 
0.00/0.34	                app_encode_app(
0.00/0.34	                  app_encode_fun('type/realax/real', 
0.00/0.34	                    app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                    app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                      'type/realax/real')), 
0.00/0.34	                  'const/iterate/iterate'(sk_A, 'type/realax/real'), X0), 
0.00/0.34	                sk_A2), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                    app_encode_fun(sk_A, 'type/realax/real')), 
0.00/0.34	                  'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), 
0.00/0.34	                sk_A1))
0.00/0.34	       | ~ app_encode_app(
0.00/0.34	             app_encode_fun('type/realax/real', 
0.00/0.34	               app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.00/0.34	             'const/iterate/monoidal'('type/realax/real'), X0)),
0.00/0.34	    inference('simplify', [status(thm)], ['23'])).
0.00/0.34	tff('25', plain,
0.00/0.34	    (~ app_encode_app(
0.00/0.34	         app_encode_fun('type/realax/real', 
0.00/0.34	           app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.00/0.34	         'const/iterate/monoidal'('type/realax/real'), 
0.00/0.34	         'const/realax/real_add')
0.00/0.34	     | app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	         'type/realax/real', 
0.00/0.34	         app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	           app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	             'type/realax/real'), 
0.00/0.34	           app_encode_app(
0.00/0.34	             app_encode_fun('type/realax/real', 
0.00/0.34	               app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_B, $o), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                 'type/realax/real')), 
0.00/0.34	             'const/iterate/iterate'(sk_B, 'type/realax/real'), 
0.00/0.34	             'const/realax/real_add'), 
0.00/0.34	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	             app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                 app_encode_fun(sk_B, $o)), 'const/sets/IMAGE'(sk_A, sk_B), 
0.00/0.34	               sk_A1), sk_A2)), sk_A0)
0.00/0.34	        = app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	            'type/realax/real', 
0.00/0.34	            app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	              app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                'type/realax/real'), 
0.00/0.34	              app_encode_app(
0.00/0.34	                app_encode_fun('type/realax/real', 
0.00/0.34	                  app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                  app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                    'type/realax/real')), 
0.00/0.34	                'const/iterate/iterate'(sk_A, 'type/realax/real'), 
0.00/0.34	                'const/realax/real_add'), sk_A2), 
0.00/0.34	            app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	              app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                  app_encode_fun(sk_A, 'type/realax/real')), 
0.00/0.34	                'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), 
0.00/0.34	              sk_A1))),
0.00/0.34	    inference('eq_res', [status(thm)], ['24'])).
0.00/0.34	tff(zf_stmt_18, axiom,
0.00/0.34	  (app_encode_app(app_encode_fun('type/realax/real',
0.00/0.34	                                 app_encode_fun('type/realax/real',
0.00/0.34	                                                'type/realax/real')),
0.00/0.34	                  $o,'const/iterate/monoidal'('type/realax/real'),
0.00/0.34	                  'const/realax/real_add'))).
0.00/0.34	tff('26', plain,
0.00/0.34	    app_encode_app(
0.00/0.34	      app_encode_fun('type/realax/real', 
0.00/0.34	        app_encode_fun('type/realax/real', 'type/realax/real')), $o, 
0.00/0.34	      'const/iterate/monoidal'('type/realax/real'), 'const/realax/real_add'),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_18])).
0.00/0.34	tff(zf_stmt_19, axiom,
0.00/0.34	  (![A:$tType]:
0.00/0.34	     ('const/iterate/sum'(A) =
0.00/0.34	      app_encode_app(app_encode_fun('type/realax/real',
0.00/0.34	                                    app_encode_fun('type/realax/real',
0.00/0.34	                                                   'type/realax/real')),
0.00/0.34	                     app_encode_fun(app_encode_fun(A,$o),
0.00/0.34	                                    app_encode_fun(app_encode_fun(A,
0.00/0.34	                                                                  'type/realax/real'),
0.00/0.34	                                                   'type/realax/real')),
0.00/0.34	                     'const/iterate/iterate'(A,'type/realax/real'),
0.00/0.34	                     'const/realax/real_add')))).
0.00/0.34	tff('27', plain,
0.00/0.34	    ![X11 : $tType]:
0.00/0.34	      'const/iterate/sum'(X11)
0.00/0.34	       = app_encode_app(
0.00/0.34	           app_encode_fun('type/realax/real', 
0.00/0.34	             app_encode_fun('type/realax/real', 'type/realax/real')), 
0.00/0.34	           app_encode_fun(app_encode_fun(X11, $o), 
0.00/0.34	             app_encode_fun(app_encode_fun(X11, 'type/realax/real'), 
0.00/0.34	               'type/realax/real')), 
0.00/0.34	           'const/iterate/iterate'(X11, 'type/realax/real'), 
0.00/0.34	           'const/realax/real_add'),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_19])).
0.00/0.34	tff('28', plain,
0.00/0.34	    (~ $true
0.00/0.34	     | app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	         'type/realax/real', 
0.00/0.34	         app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	           app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	             'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.00/0.34	           app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	             app_encode_fun(sk_B, $o), 
0.00/0.34	             app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	               app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	                 app_encode_fun(sk_B, $o)), 'const/sets/IMAGE'(sk_A, sk_B), 
0.00/0.34	               sk_A1), sk_A2)), sk_A0)
0.00/0.34	        = app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	            'type/realax/real', 
0.00/0.34	            app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	              app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	                'type/realax/real'), 'const/iterate/sum'(sk_A), sk_A2), 
0.00/0.34	            app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	              app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	              app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	                app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                  app_encode_fun(sk_A, 'type/realax/real')), 
0.00/0.34	                'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), 
0.00/0.34	              sk_A1))),
0.00/0.34	    inference('demod', [status(thm)], ['25', '26', '27', '27'])).
0.00/0.34	tff('29', plain,
0.00/0.34	    app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	      'type/realax/real', 
0.00/0.34	      app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	        app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	          'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.00/0.34	        app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_B, $o), 
0.00/0.34	          app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	            app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	              app_encode_fun(sk_B, $o)), 'const/sets/IMAGE'(sk_A, sk_B), 
0.00/0.34	            sk_A1), sk_A2)), sk_A0)
0.00/0.34	     = app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	         'type/realax/real', 
0.00/0.34	         app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	           app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	             'type/realax/real'), 'const/iterate/sum'(sk_A), sk_A2), 
0.00/0.34	         app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	           app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	           app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	             app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	               app_encode_fun(sk_A, 'type/realax/real')), 
0.00/0.34	             'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), sk_A1)),
0.00/0.34	    inference('simplify', [status(thm)], ['28'])).
0.00/0.34	tff('30', plain,
0.00/0.34	    app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	      'type/realax/real', 
0.00/0.34	      app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.34	        app_encode_fun(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	          'type/realax/real'), 'const/iterate/sum'(sk_B), 
0.00/0.34	        app_encode_app(app_encode_fun(sk_A, $o), app_encode_fun(sk_B, $o), 
0.00/0.34	          app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	            app_encode_fun(app_encode_fun(sk_A, $o), 
0.00/0.34	              app_encode_fun(sk_B, $o)), 'const/sets/IMAGE'(sk_A, sk_B), 
0.00/0.34	            sk_A1), sk_A2)), sk_A0)
0.00/0.34	     != app_encode_app(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	          'type/realax/real', 
0.00/0.34	          app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.34	            app_encode_fun(app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	              'type/realax/real'), 'const/iterate/sum'(sk_A), sk_A2), 
0.00/0.34	          app_encode_app(app_encode_fun(sk_A, sk_B), 
0.00/0.34	            app_encode_fun(sk_A, 'type/realax/real'), 
0.00/0.34	            app_encode_app(app_encode_fun(sk_B, 'type/realax/real'), 
0.00/0.34	              app_encode_fun(app_encode_fun(sk_A, sk_B), 
0.00/0.34	                app_encode_fun(sk_A, 'type/realax/real')), 
0.00/0.34	              'const/trivia/o'(sk_B, sk_A, 'type/realax/real'), sk_A0), 
0.00/0.34	            sk_A1)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('31', plain, $false,
0.00/0.34	    inference('simplify_reflect-', [status(thm)], ['29', '30'])).
0.00/0.34	
0.00/0.34	% SZS output end Refutation
0.00/0.34	EOF
