0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : app
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : rpo6
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n091.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:36:54 CST 2018
6.38/6.57	% done 2853 iterations in 6.358s
6.38/6.57	% SZS status Theorem for 'stdin'
6.38/6.57	% SZS output start Refutation
6.38/6.58	tff(zf_stmt_4, conjecture,
6.38/6.58	  (![Xp:app_encode_fun(a,$o),
6.38/6.58	     Xe:app_encode_fun(a,
6.38/6.58	                       app_encode_fun(app_encode_fun(a,b),
6.38/6.58	                                      app_encode_fun(app_encode_fun(a,b),$o)))]:
6.38/6.58	     ((![Xx:a]:
6.38/6.58	         (app_encode_app(a,$o,Xp,Xx) =>
6.38/6.58	          ((![Xx0:app_encode_fun(a,b)]:
6.38/6.58	              app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                             app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                            app_encode_fun(app_encode_fun(
6.38/6.58	                                                           a,b),$o),
6.38/6.58	                                            app_encode_app(a,
6.38/6.58	                                                           app_encode_fun(
6.38/6.58	                                                           app_encode_fun(
6.38/6.58	                                                           a,b),
6.38/6.58	                                                           app_encode_fun(
6.38/6.58	                                                           app_encode_fun(
6.38/6.58	                                                           a,b),$o)),Xe,Xx),
6.38/6.58	                                            Xx0),
6.38/6.58	                             Xx0)) & 
6.38/6.58	           (![Xx0:app_encode_fun(a,b),Xy:app_encode_fun(a,b)]:
6.38/6.58	              (app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                              app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                             app_encode_fun(app_encode_fun(
6.38/6.58	                                                            a,b),$o),
6.38/6.58	                                             app_encode_app(a,
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            a,b),
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            a,b),$o)),Xe,Xx),
6.38/6.58	                                             Xx0),
6.38/6.58	                              Xy) =>
6.38/6.58	               app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                              app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                             app_encode_fun(app_encode_fun(
6.38/6.58	                                                            a,b),$o),
6.38/6.58	                                             app_encode_app(a,
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            a,b),
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            a,b),$o)),Xe,Xx),
6.38/6.58	                                             Xy),
6.38/6.58	                              Xx0))) & 
6.38/6.58	           (![Xx0:app_encode_fun(a,b),Xy:app_encode_fun(a,b),
6.38/6.58	              Xz:app_encode_fun(a,b)]:
6.38/6.58	              ((app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                               app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                              app_encode_fun(app_encode_fun(
6.38/6.58	                                                             a,b),$o),
6.38/6.58	                                              app_encode_app(a,
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             a,b),
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             a,b),$o)),Xe,Xx),
6.38/6.58	                                              Xx0),
6.38/6.58	                               Xy) & 
6.38/6.58	                app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                               app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                              app_encode_fun(app_encode_fun(
6.38/6.58	                                                             a,b),$o),
6.38/6.58	                                              app_encode_app(a,
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             a,b),
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             a,b),$o)),Xe,Xx),
6.38/6.58	                                              Xy),
6.38/6.58	                               Xz)) =>
6.38/6.58	               app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                              app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                             app_encode_fun(app_encode_fun(
6.38/6.58	                                                            a,b),$o),
6.38/6.58	                                             app_encode_app(a,
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            a,b),
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            a,b),$o)),Xe,Xx),
6.38/6.58	                                             Xx0),
6.38/6.58	                              Xz)))))) =>
6.38/6.58	      ((![Xx:app_encode_fun(a,b),Xx0:a]:
6.38/6.58	          (app_encode_app(a,$o,Xp,Xx0) =>
6.38/6.58	           app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                          app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                         app_encode_fun(app_encode_fun(a,b),
6.38/6.58	                                                        $o),
6.38/6.58	                                         app_encode_app(a,
6.38/6.58	                                                        app_encode_fun(
6.38/6.58	                                                        app_encode_fun(a,b),
6.38/6.58	                                                        app_encode_fun(
6.38/6.58	                                                        app_encode_fun(a,b),
6.38/6.58	                                                        $o)),Xe,Xx0),
6.38/6.58	                                         Xx),
6.38/6.58	                          Xx))) & 
6.38/6.58	       (![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b)]:
6.38/6.58	          ((![Xx0:a]:
6.38/6.58	              (app_encode_app(a,$o,Xp,Xx0) =>
6.38/6.58	               app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                              app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                             app_encode_fun(app_encode_fun(
6.38/6.58	                                                            a,b),$o),
6.38/6.58	                                             app_encode_app(a,
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            a,b),
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            a,b),$o)),Xe,Xx0),
6.38/6.58	                                             Xx),
6.38/6.58	                              Xy))) =>
6.38/6.58	           (![Xx0:a]:
6.38/6.58	              (app_encode_app(a,$o,Xp,Xx0) =>
6.38/6.58	               app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                              app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                             app_encode_fun(app_encode_fun(
6.38/6.58	                                                            a,b),$o),
6.38/6.58	                                             app_encode_app(a,
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            a,b),
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            a,b),$o)),Xe,Xx0),
6.38/6.58	                                             Xy),
6.38/6.58	                              Xx))))) & 
6.38/6.58	       (![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b),
6.38/6.58	          Xz:app_encode_fun(a,b)]:
6.38/6.58	          (((![Xx0:a]:
6.38/6.58	               (app_encode_app(a,$o,Xp,Xx0) =>
6.38/6.58	                app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                               app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                              app_encode_fun(app_encode_fun(
6.38/6.58	                                                             a,b),$o),
6.38/6.58	                                              app_encode_app(a,
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             a,b),
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             a,b),$o)),Xe,Xx0),
6.38/6.58	                                              Xx),
6.38/6.58	                               Xy))) & 
6.38/6.58	            (![Xx0:a]:
6.38/6.58	               (app_encode_app(a,$o,Xp,Xx0) =>
6.38/6.58	                app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                               app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                              app_encode_fun(app_encode_fun(
6.38/6.58	                                                             a,b),$o),
6.38/6.58	                                              app_encode_app(a,
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             a,b),
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             a,b),$o)),Xe,Xx0),
6.38/6.58	                                              Xy),
6.38/6.58	                               Xz)))) =>
6.38/6.58	           (![Xx0:a]:
6.38/6.58	              (app_encode_app(a,$o,Xp,Xx0) =>
6.38/6.58	               app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                              app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                             app_encode_fun(app_encode_fun(
6.38/6.58	                                                            a,b),$o),
6.38/6.58	                                             app_encode_app(a,
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            a,b),
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            app_encode_fun(
6.38/6.58	                                                            a,b),$o)),Xe,Xx0),
6.38/6.58	                                             Xx),
6.38/6.58	                              Xz))))))))).
6.38/6.58	tff(zf_stmt_0, negated_conjecture,
6.38/6.58	  (~
6.38/6.58	    (![Xp:app_encode_fun(a,$o),
6.38/6.58	       Xe:app_encode_fun(a,
6.38/6.58	                         app_encode_fun(app_encode_fun(a,b),
6.38/6.58	                                        app_encode_fun(app_encode_fun(a,b),$o)))]:
6.38/6.58	       ((![Xx:a]:
6.38/6.58	           (app_encode_app(a,$o,Xp,Xx) =>
6.38/6.58	            ((![Xx0:app_encode_fun(a,b)]:
6.38/6.58	                app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                               app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                              app_encode_fun(app_encode_fun(
6.38/6.58	                                                             a,b),$o),
6.38/6.58	                                              app_encode_app(a,
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             a,b),
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             app_encode_fun(
6.38/6.58	                                                             a,b),$o)),Xe,Xx),
6.38/6.58	                                              Xx0),
6.38/6.58	                               Xx0)) & 
6.38/6.58	             (![Xx0:app_encode_fun(a,b),Xy:app_encode_fun(a,b)]:
6.38/6.58	                (app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                                app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                               app_encode_fun(app_encode_fun(
6.38/6.58	                                                              a,b),$o),
6.38/6.58	                                               app_encode_app(a,
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              a,b),
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              a,b),$o)),Xe,Xx),
6.38/6.58	                                               Xx0),
6.38/6.58	                                Xy) =>
6.38/6.58	                 app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                                app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                               app_encode_fun(app_encode_fun(
6.38/6.58	                                                              a,b),$o),
6.38/6.58	                                               app_encode_app(a,
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              a,b),
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              a,b),$o)),Xe,Xx),
6.38/6.58	                                               Xy),
6.38/6.58	                                Xx0))) & 
6.38/6.58	             (![Xx0:app_encode_fun(a,b),Xy:app_encode_fun(a,b),
6.38/6.58	                Xz:app_encode_fun(a,b)]:
6.38/6.58	                ((app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                                 app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                                app_encode_fun(app_encode_fun(
6.38/6.58	                                                               a,b),$o),
6.38/6.58	                                                app_encode_app(a,
6.38/6.58	                                                               app_encode_fun(
6.38/6.58	                                                               app_encode_fun(
6.38/6.58	                                                               a,b),
6.38/6.58	                                                               app_encode_fun(
6.38/6.58	                                                               app_encode_fun(
6.38/6.58	                                                               a,b),$o)),Xe,
6.38/6.58	                                                               Xx),
6.38/6.58	                                                Xx0),
6.38/6.58	                                 Xy) & 
6.38/6.58	                  app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                                 app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                                app_encode_fun(app_encode_fun(
6.38/6.58	                                                               a,b),$o),
6.38/6.58	                                                app_encode_app(a,
6.38/6.58	                                                               app_encode_fun(
6.38/6.58	                                                               app_encode_fun(
6.38/6.58	                                                               a,b),
6.38/6.58	                                                               app_encode_fun(
6.38/6.58	                                                               app_encode_fun(
6.38/6.58	                                                               a,b),$o)),Xe,
6.38/6.58	                                                               Xx),
6.38/6.58	                                                Xy),
6.38/6.58	                                 Xz)) =>
6.38/6.58	                 app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                                app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                               app_encode_fun(app_encode_fun(
6.38/6.58	                                                              a,b),$o),
6.38/6.58	                                               app_encode_app(a,
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              a,b),
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              a,b),$o)),Xe,Xx),
6.38/6.58	                                               Xx0),
6.38/6.58	                                Xz)))))) =>
6.38/6.58	        ((![Xx:app_encode_fun(a,b),Xx0:a]:
6.38/6.58	            (app_encode_app(a,$o,Xp,Xx0) =>
6.38/6.58	             app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                            app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                           app_encode_fun(app_encode_fun(a,b),
6.38/6.58	                                                          $o),
6.38/6.58	                                           app_encode_app(a,
6.38/6.58	                                                          app_encode_fun(
6.38/6.58	                                                          app_encode_fun(a,b),
6.38/6.58	                                                          app_encode_fun(
6.38/6.58	                                                          app_encode_fun(a,b),
6.38/6.58	                                                          $o)),Xe,Xx0),
6.38/6.58	                                           Xx),
6.38/6.58	                            Xx))) & 
6.38/6.58	         (![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b)]:
6.38/6.58	            ((![Xx0:a]:
6.38/6.58	                (app_encode_app(a,$o,Xp,Xx0) =>
6.38/6.58	                 app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                                app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                               app_encode_fun(app_encode_fun(
6.38/6.58	                                                              a,b),$o),
6.38/6.58	                                               app_encode_app(a,
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              a,b),
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              a,b),$o)),Xe,
6.38/6.58	                                                              Xx0),
6.38/6.58	                                               Xx),
6.38/6.58	                                Xy))) =>
6.38/6.58	             (![Xx0:a]:
6.38/6.58	                (app_encode_app(a,$o,Xp,Xx0) =>
6.38/6.58	                 app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                                app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                               app_encode_fun(app_encode_fun(
6.38/6.58	                                                              a,b),$o),
6.38/6.58	                                               app_encode_app(a,
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              a,b),
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              a,b),$o)),Xe,
6.38/6.58	                                                              Xx0),
6.38/6.58	                                               Xy),
6.38/6.58	                                Xx))))) & 
6.38/6.58	         (![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b),
6.38/6.58	            Xz:app_encode_fun(a,b)]:
6.38/6.58	            (((![Xx0:a]:
6.38/6.58	                 (app_encode_app(a,$o,Xp,Xx0) =>
6.38/6.58	                  app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                                 app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                                app_encode_fun(app_encode_fun(
6.38/6.58	                                                               a,b),$o),
6.38/6.58	                                                app_encode_app(a,
6.38/6.58	                                                               app_encode_fun(
6.38/6.58	                                                               app_encode_fun(
6.38/6.58	                                                               a,b),
6.38/6.58	                                                               app_encode_fun(
6.38/6.58	                                                               app_encode_fun(
6.38/6.58	                                                               a,b),$o)),Xe,
6.38/6.58	                                                               Xx0),
6.38/6.58	                                                Xx),
6.38/6.58	                                 Xy))) & 
6.38/6.58	              (![Xx0:a]:
6.38/6.58	                 (app_encode_app(a,$o,Xp,Xx0) =>
6.38/6.58	                  app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                                 app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                                app_encode_fun(app_encode_fun(
6.38/6.58	                                                               a,b),$o),
6.38/6.58	                                                app_encode_app(a,
6.38/6.58	                                                               app_encode_fun(
6.38/6.58	                                                               app_encode_fun(
6.38/6.58	                                                               a,b),
6.38/6.58	                                                               app_encode_fun(
6.38/6.58	                                                               app_encode_fun(
6.38/6.58	                                                               a,b),$o)),Xe,
6.38/6.58	                                                               Xx0),
6.38/6.58	                                                Xy),
6.38/6.58	                                 Xz)))) =>
6.38/6.58	             (![Xx0:a]:
6.38/6.58	                (app_encode_app(a,$o,Xp,Xx0) =>
6.38/6.58	                 app_encode_app(app_encode_fun(a,b),$o,
6.38/6.58	                                app_encode_app(app_encode_fun(a,b),
6.38/6.58	                                               app_encode_fun(app_encode_fun(
6.38/6.58	                                                              a,b),$o),
6.38/6.58	                                               app_encode_app(a,
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              a,b),
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              app_encode_fun(
6.38/6.58	                                                              a,b),$o)),Xe,
6.38/6.58	                                                              Xx0),
6.38/6.58	                                               Xx),
6.38/6.58	                                Xz)))))))))).
6.38/6.58	tff('0', plain,
6.38/6.58	    ![X8 : a]:
6.38/6.58	      (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	             sk_Xx), sk_Xx)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X8), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X8)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('1', plain,
6.38/6.58	    ![X0 : a, X4 : app_encode_fun(a, b), X5 : app_encode_fun(a, b), 
6.38/6.58	      X6 : app_encode_fun(a, b)]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X4), 
6.38/6.58	         X5)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X6), 
6.38/6.58	             X5)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X4), 
6.38/6.58	             X6)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('2', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	               sk_Xx), sk_Xx)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	           sk_Xz)),
6.38/6.58	    inference('sup-', [status(thm)], ['0', '1'])).
6.38/6.58	tff('3', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	         sk_Xz)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy1)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	               sk_Xx), sk_Xx)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.58	    inference('simplify', [status(thm)], ['2'])).
6.38/6.58	tff('4', plain,
6.38/6.58	    (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	           sk_Xx), sk_Xx)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.58	             sk_Xx2), sk_Xz)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('5', plain,
6.38/6.58	    (~ $true
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	             sk_Xx), sk_Xx)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.58	             sk_Xx2), sk_Xy1)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	             sk_Xx), sk_Xx)),
6.38/6.58	    inference('sup-', [status(thm)], ['3', '4'])).
6.38/6.58	tff('6', plain,
6.38/6.58	    (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.58	           sk_Xx2), sk_Xy1)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	             sk_Xx), sk_Xx)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.58	    inference('simplify', [status(thm)], ['5'])).
6.38/6.58	tff('7', plain,
6.38/6.58	    ![X9 : a]:
6.38/6.58	      (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	             sk_Xx), sk_Xx)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X9), 
6.38/6.58	             sk_Xx2), sk_Xy1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X9)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('8', plain,
6.38/6.58	    (~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	             sk_Xx), sk_Xx)),
6.38/6.58	    inference('clc', [status(thm)], ['6', '7'])).
6.38/6.58	tff('9', plain,
6.38/6.58	    (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	           sk_Xx), sk_Xx)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('10', plain,
6.38/6.58	    (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	           sk_Xx), sk_Xx)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
6.38/6.58	    inference('clc', [status(thm)], ['8', '9'])).
6.38/6.58	tff('11', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	         X1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('12', plain,
6.38/6.58	    ![X0 : app_encode_fun(a, b)]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	               sk_Xx), sk_Xx)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             X0), X0)),
6.38/6.58	    inference('sup-', [status(thm)], ['10', '11'])).
6.38/6.58	tff('13', plain,
6.38/6.58	    ![X0 : app_encode_fun(a, b)]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	           X0), X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	               sk_Xx), sk_Xx)),
6.38/6.58	    inference('simplify', [status(thm)], ['12'])).
6.38/6.58	tff('14', plain,
6.38/6.58	    ![X7 : a]:
6.38/6.58	      (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	             sk_Xx), sk_Xx)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X7)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X7), 
6.38/6.58	             sk_Xx1), sk_Xy)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('15', plain,
6.38/6.58	    ![X0 : a, X2 : app_encode_fun(a, b), X3 : app_encode_fun(a, b)]:
6.38/6.58	      (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X2), 
6.38/6.58	           X3)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X3), 
6.38/6.58	           X2)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('16', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (~ $true
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	               sk_Xx), sk_Xx)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xy), sk_Xx1)),
6.38/6.58	    inference('sup-', [status(thm)], ['14', '15'])).
6.38/6.58	tff('17', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy), 
6.38/6.58	         sk_Xx1)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	               sk_Xx), sk_Xx)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.58	    inference('simplify', [status(thm)], ['16'])).
6.38/6.58	tff('18', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.58	      (~ $true
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	               sk_Xx), sk_Xx)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	           sk_Xx1)),
6.38/6.58	    inference('sup-', [status(thm)], ['17', '1'])).
6.38/6.58	tff('19', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	         sk_Xx1)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	               sk_Xx), sk_Xx)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.58	    inference('simplify', [status(thm)], ['18'])).
6.38/6.58	tff('20', plain,
6.38/6.58	    (~ $true
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	             sk_Xx), sk_Xx)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	             sk_Xx), sk_Xx)
6.38/6.58	     | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	           sk_Xy), sk_Xx1)),
6.38/6.58	    inference('sup-', [status(thm)], ['13', '19'])).
6.38/6.58	tff('21', plain,
6.38/6.58	    (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	       app_encode_app(app_encode_fun(a, b), 
6.38/6.58	         app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	         app_encode_app(a, 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	         sk_Xy), sk_Xx1)
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	             sk_Xx), sk_Xx)),
6.38/6.58	    inference('simplify', [status(thm)], ['20'])).
6.38/6.58	tff('22', plain,
6.38/6.58	    (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	           sk_Xx), sk_Xx)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             sk_Xy), sk_Xx1)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('23', plain,
6.38/6.58	    (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	           sk_Xx), sk_Xx)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
6.38/6.58	    inference('clc', [status(thm)], ['21', '22'])).
6.38/6.58	tff('24', plain,
6.38/6.58	    (app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	             sk_Xx), sk_Xx)),
6.38/6.58	    inference('clc', [status(thm)], ['23', '10'])).
6.38/6.58	tff('25', plain,
6.38/6.58	    ![X0 : app_encode_fun(a, b)]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	               sk_Xx), sk_Xx)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.58	             X0), X0)),
6.38/6.58	    inference('sup-', [status(thm)], ['24', '11'])).
6.38/6.58	tff('26', plain,
6.38/6.58	    ![X0 : app_encode_fun(a, b)]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.58	           X0), X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	               sk_Xx), sk_Xx)),
6.38/6.58	    inference('simplify', [status(thm)], ['25'])).
6.38/6.58	tff('27', plain,
6.38/6.58	    ![X7 : a, X8 : a]:
6.38/6.58	      (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	             sk_Xx), sk_Xx)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X7)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X7), 
6.38/6.58	             sk_Xx1), sk_Xy)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X8), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X8)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('28', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X2)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	               sk_Xx), sk_Xx)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xx1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	           sk_Xy)),
6.38/6.58	    inference('sup-', [status(thm)], ['27', '1'])).
6.38/6.58	tff('29', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	         sk_Xy)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xx1)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	               sk_Xx), sk_Xx)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X2)),
6.38/6.58	    inference('simplify', [status(thm)], ['28'])).
6.38/6.58	tff('30', plain,
6.38/6.58	    ![X8 : a]:
6.38/6.58	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X8), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X8)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('31', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xz), sk_Xy1)),
6.38/6.58	    inference('sup-', [status(thm)], ['30', '15'])).
6.38/6.58	tff('32', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xz), 
6.38/6.58	         sk_Xy1)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.58	    inference('simplify', [status(thm)], ['31'])).
6.38/6.58	tff('33', plain,
6.38/6.58	    ![X9 : a]:
6.38/6.58	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X9), 
6.38/6.58	             sk_Xx2), sk_Xy1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X9)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('34', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xy1), sk_Xx2)),
6.38/6.58	    inference('sup-', [status(thm)], ['33', '15'])).
6.38/6.58	tff('35', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy1), 
6.38/6.58	         sk_Xx2)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.58	    inference('simplify', [status(thm)], ['34'])).
6.38/6.58	tff('36', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	           sk_Xx2)),
6.38/6.58	    inference('sup-', [status(thm)], ['35', '1'])).
6.38/6.58	tff('37', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	         sk_Xx2)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy1)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.58	    inference('simplify', [status(thm)], ['36'])).
6.38/6.58	tff('38', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xz), sk_Xx2)),
6.38/6.58	    inference('sup-', [status(thm)], ['32', '37'])).
6.38/6.58	tff('39', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xz), 
6.38/6.58	         sk_Xx2)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.58	    inference('simplify', [status(thm)], ['38'])).
6.38/6.58	tff('40', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xx2), sk_Xz)),
6.38/6.58	    inference('sup-', [status(thm)], ['39', '15'])).
6.38/6.58	tff('41', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xx2), 
6.38/6.58	         sk_Xz)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.58	    inference('simplify', [status(thm)], ['40'])).
6.38/6.58	tff('42', plain,
6.38/6.58	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.58	             sk_Xx2), sk_Xz)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('43', plain,
6.38/6.58	    (~ $true
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
6.38/6.58	    inference('sup-', [status(thm)], ['41', '42'])).
6.38/6.58	tff('44', plain,
6.38/6.58	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.58	    inference('simplify', [status(thm)], ['43'])).
6.38/6.58	tff('45', plain,
6.38/6.58	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('46', plain,
6.38/6.58	    (app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
6.38/6.58	    inference('clc', [status(thm)], ['44', '45'])).
6.38/6.58	tff('47', plain,
6.38/6.58	    ![X0 : app_encode_fun(a, b)]:
6.38/6.58	      (~ $true
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             X0), X0)),
6.38/6.58	    inference('sup-', [status(thm)], ['46', '11'])).
6.38/6.58	tff('48', plain,
6.38/6.58	    ![X0 : app_encode_fun(a, b)]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	           X0), X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
6.38/6.58	    inference('simplify', [status(thm)], ['47'])).
6.38/6.58	tff('49', plain,
6.38/6.58	    ![X7 : a, X8 : a]:
6.38/6.58	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X7)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X7), 
6.38/6.58	             sk_Xx1), sk_Xy)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X8), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X8)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('50', plain,
6.38/6.58	    ![X0 : a, X1 : a]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xy), sk_Xx1)),
6.38/6.58	    inference('sup-', [status(thm)], ['49', '15'])).
6.38/6.58	tff('51', plain,
6.38/6.58	    ![X0 : a, X1 : a]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy), 
6.38/6.58	         sk_Xx1)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X1)),
6.38/6.58	    inference('simplify', [status(thm)], ['50'])).
6.38/6.58	tff('52', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X2)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	           sk_Xx1)),
6.38/6.58	    inference('sup-', [status(thm)], ['51', '1'])).
6.38/6.58	tff('53', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	         sk_Xx1)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X2)),
6.38/6.58	    inference('simplify', [status(thm)], ['52'])).
6.38/6.58	tff('54', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (~ $true
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             sk_Xy), sk_Xx1)),
6.38/6.58	    inference('sup-', [status(thm)], ['48', '53'])).
6.38/6.58	tff('55', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	           sk_Xy), sk_Xx1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
6.38/6.58	    inference('simplify', [status(thm)], ['54'])).
6.38/6.58	tff('56', plain,
6.38/6.58	    ![X8 : a]:
6.38/6.58	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	               sk_Xy), sk_Xx1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X8), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X8)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('57', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	               sk_Xy), sk_Xx1)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	           sk_Xz)),
6.38/6.58	    inference('sup-', [status(thm)], ['56', '1'])).
6.38/6.58	tff('58', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	         sk_Xz)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy1)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	               sk_Xy), sk_Xx1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.58	    inference('simplify', [status(thm)], ['57'])).
6.38/6.58	tff('59', plain,
6.38/6.58	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             sk_Xy), sk_Xx1)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.58	             sk_Xx2), sk_Xz)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('60', plain,
6.38/6.58	    (~ $true
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             sk_Xy), sk_Xx1)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.58	             sk_Xx2), sk_Xy1)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             sk_Xy), sk_Xx1)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
6.38/6.58	    inference('sup-', [status(thm)], ['58', '59'])).
6.38/6.58	tff('61', plain,
6.38/6.58	    (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.58	           sk_Xx2), sk_Xy1)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             sk_Xy), sk_Xx1)
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.58	    inference('simplify', [status(thm)], ['60'])).
6.38/6.58	tff('62', plain,
6.38/6.58	    ![X9 : a]:
6.38/6.58	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	               sk_Xy), sk_Xx1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X9), 
6.38/6.58	             sk_Xx2), sk_Xy1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X9)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('63', plain,
6.38/6.58	    (~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             sk_Xy), sk_Xx1)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
6.38/6.58	    inference('clc', [status(thm)], ['61', '62'])).
6.38/6.58	tff('64', plain,
6.38/6.58	    ![X7 : a]:
6.38/6.58	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X7)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X7), 
6.38/6.58	             sk_Xx1), sk_Xy)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('65', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (~ $true
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xy), sk_Xx1)),
6.38/6.58	    inference('sup-', [status(thm)], ['64', '15'])).
6.38/6.58	tff('66', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy), 
6.38/6.58	         sk_Xx1)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.58	    inference('simplify', [status(thm)], ['65'])).
6.38/6.58	tff('67', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.58	      (~ $true
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	           sk_Xx1)),
6.38/6.58	    inference('sup-', [status(thm)], ['66', '1'])).
6.38/6.58	tff('68', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	         sk_Xx1)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.58	    inference('simplify', [status(thm)], ['67'])).
6.38/6.58	tff('69', plain,
6.38/6.58	    (~ $true
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	     | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	           sk_Xy), sk_Xx1)),
6.38/6.58	    inference('sup-', [status(thm)], ['48', '68'])).
6.38/6.58	tff('70', plain,
6.38/6.58	    (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	       app_encode_app(app_encode_fun(a, b), 
6.38/6.58	         app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	         app_encode_app(a, 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	         sk_Xy), sk_Xx1)
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
6.38/6.58	    inference('simplify', [status(thm)], ['69'])).
6.38/6.58	tff('71', plain,
6.38/6.58	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             sk_Xy), sk_Xx1)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('72', plain,
6.38/6.58	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
6.38/6.58	    inference('clc', [status(thm)], ['70', '71'])).
6.38/6.58	tff('73', plain,
6.38/6.58	    (app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
6.38/6.58	    inference('clc', [status(thm)], ['72', '46'])).
6.38/6.58	tff('74', plain,
6.38/6.58	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             sk_Xy), sk_Xx1)),
6.38/6.58	    inference('clc', [status(thm)], ['63', '73'])).
6.38/6.58	tff('75', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
6.38/6.58	    inference('clc', [status(thm)], ['55', '74'])).
6.38/6.58	tff('76', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy1), 
6.38/6.58	         sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
6.38/6.58	    inference('clc', [status(thm)], ['75', '46'])).
6.38/6.58	tff('77', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.58	      (~ $true
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	           sk_Xz)),
6.38/6.58	    inference('sup-', [status(thm)], ['76', '1'])).
6.38/6.58	tff('78', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	         sk_Xz)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
6.38/6.58	    inference('simplify', [status(thm)], ['77'])).
6.38/6.58	tff('79', plain,
6.38/6.58	    ![X7 : a]:
6.38/6.58	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X7)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X7), 
6.38/6.58	             sk_Xx1), sk_Xy)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.58	               sk_Xx2), sk_Xz)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('80', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (~ $true
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.58	               sk_Xx2), sk_Xy1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xx1), sk_Xy)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
6.38/6.58	    inference('sup-', [status(thm)], ['78', '79'])).
6.38/6.58	tff('81', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xx1), sk_Xy)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.58	               sk_Xx2), sk_Xy1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
6.38/6.58	    inference('simplify', [status(thm)], ['80'])).
6.38/6.58	tff('82', plain,
6.38/6.58	    ![X7 : a, X9 : a]:
6.38/6.58	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X7)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X7), 
6.38/6.58	             sk_Xx1), sk_Xy)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X9), 
6.38/6.58	             sk_Xx2), sk_Xy1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X9)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('83', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xx1), sk_Xy)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.58	    inference('clc', [status(thm)], ['81', '82'])).
6.38/6.58	tff('84', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xx1), sk_Xy)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
6.38/6.58	    inference('clc', [status(thm)], ['83', '73'])).
6.38/6.58	tff('85', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (~ $true
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xy), sk_Xx1)),
6.38/6.58	    inference('sup-', [status(thm)], ['84', '15'])).
6.38/6.58	tff('86', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy), 
6.38/6.58	         sk_Xx1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
6.38/6.58	    inference('simplify', [status(thm)], ['85'])).
6.38/6.58	tff('87', plain,
6.38/6.58	    (~ $true
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
6.38/6.58	    inference('sup-', [status(thm)], ['86', '74'])).
6.38/6.58	tff('88', plain,
6.38/6.58	    (~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
6.38/6.58	    inference('simplify', [status(thm)], ['87'])).
6.38/6.58	tff('89', plain, app_encode_app(a, $o, sk_Xp, sk_Xx0),
6.38/6.58	    inference('clc', [status(thm)], ['88', '46'])).
6.38/6.58	tff('90', plain,
6.38/6.58	    ![X0 : app_encode_fun(a, b)]:
6.38/6.58	      (~ $true
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	             X0), X0)),
6.38/6.58	    inference('sup-', [status(thm)], ['89', '11'])).
6.38/6.58	tff('91', plain,
6.38/6.58	    ![X0 : app_encode_fun(a, b)]:
6.38/6.58	      app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	        app_encode_app(app_encode_fun(a, b), 
6.38/6.58	          app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	          app_encode_app(a, 
6.38/6.58	            app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	              app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), X0), 
6.38/6.58	        X0),
6.38/6.58	    inference('simplify', [status(thm)], ['90'])).
6.38/6.58	tff('92', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	         sk_Xy)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xx1)
6.38/6.58	       | ~ $true
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X2)),
6.38/6.58	    inference('demod', [status(thm)], ['29', '91'])).
6.38/6.58	tff('93', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
6.38/6.58	      (~ app_encode_app(a, $o, sk_Xp, X2)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xx1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	           sk_Xy)),
6.38/6.58	    inference('simplify', [status(thm)], ['92'])).
6.38/6.58	tff('94', plain,
6.38/6.58	    ![X0 : app_encode_fun(a, b), X1 : a, X2 : a]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
6.38/6.58	             sk_Xx1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X2)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
6.38/6.58	             sk_Xy), X0)),
6.38/6.58	    inference('sup-', [status(thm)], ['93', '15'])).
6.38/6.58	tff('95', plain,
6.38/6.58	    ![X0 : app_encode_fun(a, b), X1 : a, X2 : a]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), sk_Xy), 
6.38/6.58	         X0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X2)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X1)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
6.38/6.58	             sk_Xx1)),
6.38/6.58	    inference('simplify', [status(thm)], ['94'])).
6.38/6.58	tff('96', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	               sk_Xx), sk_Xx)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             sk_Xy), sk_Xx1)),
6.38/6.58	    inference('sup-', [status(thm)], ['13', '95'])).
6.38/6.58	tff('97', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ $true
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             sk_Xy), sk_Xx1)),
6.38/6.58	    inference('demod', [status(thm)], ['96', '91'])).
6.38/6.58	tff('98', plain,
6.38/6.58	    ![X0 : a]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	           sk_Xy), sk_Xx1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
6.38/6.58	    inference('simplify', [status(thm)], ['97'])).
6.38/6.58	tff('99', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             sk_Xy), sk_Xx1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	           sk_Xz)),
6.38/6.58	    inference('sup-', [status(thm)], ['98', '1'])).
6.38/6.58	tff('100', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	         sk_Xz)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             sk_Xy), sk_Xx1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
6.38/6.58	    inference('simplify', [status(thm)], ['99'])).
6.38/6.58	tff('101', plain,
6.38/6.58	    ![X0 : app_encode_fun(a, b), X1 : a]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             sk_Xy), sk_Xx1)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
6.38/6.58	             sk_Xy1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
6.38/6.58	             sk_Xz), X0)),
6.38/6.58	    inference('sup-', [status(thm)], ['100', '15'])).
6.38/6.58	tff('102', plain,
6.38/6.58	    ![X0 : app_encode_fun(a, b), X1 : a]:
6.38/6.58	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), sk_Xz), 
6.38/6.58	         X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
6.38/6.58	             sk_Xy1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	             sk_Xy), sk_Xx1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X1)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
6.38/6.58	    inference('simplify', [status(thm)], ['101'])).
6.38/6.58	tff('103', plain,
6.38/6.58	    (~ $true
6.38/6.58	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	             sk_Xx), sk_Xx)
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	     | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	           sk_Xy), sk_Xx1)
6.38/6.58	     | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.58	           sk_Xz), sk_Xy1)),
6.38/6.58	    inference('sup-', [status(thm)], ['26', '102'])).
6.38/6.58	tff('104', plain,
6.38/6.58	    (~ $true
6.38/6.58	     | ~ $true
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	     | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	           sk_Xy), sk_Xx1)
6.38/6.58	     | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.58	           sk_Xz), sk_Xy1)),
6.38/6.58	    inference('demod', [status(thm)], ['103', '91'])).
6.38/6.58	tff('105', plain,
6.38/6.58	    (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	       app_encode_app(app_encode_fun(a, b), 
6.38/6.58	         app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	         app_encode_app(a, 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.58	         sk_Xz), sk_Xy1)
6.38/6.58	     | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	         app_encode_app(app_encode_fun(a, b), 
6.38/6.58	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	           app_encode_app(a, 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	           sk_Xy), sk_Xx1)
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.58	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
6.38/6.58	    inference('simplify', [status(thm)], ['104'])).
6.38/6.58	tff('106', plain,
6.38/6.58	    ![X8 : a]:
6.38/6.58	      (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	             sk_Xx), sk_Xx)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	               sk_Xy), sk_Xx1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X8), 
6.38/6.58	             sk_Xy1), sk_Xz)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X8)),
6.38/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.58	tff('107', plain,
6.38/6.58	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.58	      (~ $true
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.58	               sk_Xy), sk_Xx1)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.58	               sk_Xx), sk_Xx)
6.38/6.58	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.58	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	             app_encode_app(app_encode_fun(a, b), 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	               app_encode_app(a, 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.58	             sk_Xy1)
6.38/6.58	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.58	           app_encode_app(app_encode_fun(a, b), 
6.38/6.58	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.58	             app_encode_app(a, 
6.38/6.58	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.58	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.59	           sk_Xz)),
6.38/6.59	    inference('sup-', [status(thm)], ['106', '1'])).
6.38/6.59	tff('108', plain,
6.38/6.59	    ![X0 : a, X1 : app_encode_fun(a, b)]:
6.38/6.59	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.59	         sk_Xz)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.59	             sk_Xy1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	               sk_Xx), sk_Xx)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	               sk_Xy), sk_Xx1)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.59	    inference('simplify', [status(thm)], ['107'])).
6.38/6.59	tff('109', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b), X1 : a, X2 : app_encode_fun(a, b)]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	               sk_Xy), sk_Xx1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	               sk_Xx), sk_Xx)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
6.38/6.59	             sk_Xy1)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X2), 
6.38/6.59	             X0)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X2), 
6.38/6.59	           sk_Xz)),
6.38/6.59	    inference('sup-', [status(thm)], ['108', '1'])).
6.38/6.59	tff('110', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b), X1 : a, X2 : app_encode_fun(a, b)]:
6.38/6.59	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X2), 
6.38/6.59	         sk_Xz)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X2), 
6.38/6.59	             X0)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
6.38/6.59	             sk_Xy1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	               sk_Xx), sk_Xx)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	               sk_Xy), sk_Xx1)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X1)),
6.38/6.59	    inference('simplify', [status(thm)], ['109'])).
6.38/6.59	tff('111', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b), X1 : a, X2 : app_encode_fun(a, b)]:
6.38/6.59	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X2), 
6.38/6.59	         sk_Xz)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X2), 
6.38/6.59	             X0)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
6.38/6.59	             sk_Xy1)
6.38/6.59	       | ~ $true
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	               sk_Xy), sk_Xx1)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X1)),
6.38/6.59	    inference('demod', [status(thm)], ['110', '91'])).
6.38/6.59	tff('112', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b), X1 : a, X2 : app_encode_fun(a, b)]:
6.38/6.59	      (~ app_encode_app(a, $o, sk_Xp, X1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	               sk_Xy), sk_Xx1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
6.38/6.59	             sk_Xy1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X2), 
6.38/6.59	             X0)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X2), 
6.38/6.59	           sk_Xz)),
6.38/6.59	    inference('simplify', [status(thm)], ['111'])).
6.38/6.59	tff('113', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b)]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	               sk_Xx), sk_Xx)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	             X0), sk_Xz)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	               X0), sk_Xy1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	               sk_Xy), sk_Xx1)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.59	    inference('sup-', [status(thm)], ['26', '112'])).
6.38/6.59	tff('114', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b)]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ $true
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	             X0), sk_Xz)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	               X0), sk_Xy1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	               sk_Xy), sk_Xx1)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.59	    inference('demod', [status(thm)], ['113', '91'])).
6.38/6.59	tff('115', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b)]:
6.38/6.59	      (~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	               sk_Xy), sk_Xx1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	               X0), sk_Xy1)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	             X0), sk_Xz)),
6.38/6.59	    inference('simplify', [status(thm)], ['114'])).
6.38/6.59	tff('116', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b)]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	               X0), sk_Xy1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	               sk_Xy), sk_Xx1)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	             sk_Xz), X0)),
6.38/6.59	    inference('sup-', [status(thm)], ['115', '15'])).
6.38/6.59	tff('117', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b)]:
6.38/6.59	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	           sk_Xz), X0)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	               sk_Xy), sk_Xx1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	               X0), sk_Xy1)),
6.38/6.59	    inference('simplify', [status(thm)], ['116'])).
6.38/6.59	tff('118', plain,
6.38/6.59	    (~ $true
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	             sk_Xx), sk_Xx)
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	             sk_Xy), sk_Xx1)
6.38/6.59	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	     | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	           sk_Xz), sk_Xy1)),
6.38/6.59	    inference('sup-', [status(thm)], ['26', '117'])).
6.38/6.59	tff('119', plain,
6.38/6.59	    (~ $true
6.38/6.59	     | ~ $true
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	             sk_Xy), sk_Xx1)
6.38/6.59	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	     | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	           sk_Xz), sk_Xy1)),
6.38/6.59	    inference('demod', [status(thm)], ['118', '91'])).
6.38/6.59	tff('120', plain,
6.38/6.59	    (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	       app_encode_app(app_encode_fun(a, b), 
6.38/6.59	         app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	         app_encode_app(a, 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	         sk_Xz), sk_Xy1)
6.38/6.59	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	             sk_Xy), sk_Xx1)),
6.38/6.59	    inference('simplify', [status(thm)], ['119'])).
6.38/6.59	tff('121', plain,
6.38/6.59	    (~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.59	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	     | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	           sk_Xz), sk_Xy1)),
6.38/6.59	    inference('clc', [status(thm)], ['105', '120'])).
6.38/6.59	tff('122', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b), X1 : a, X2 : app_encode_fun(a, b)]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X1)
6.38/6.59	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	               sk_Xx), sk_Xx)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
6.38/6.59	             sk_Xy1)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X2), 
6.38/6.59	             X0)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X2), 
6.38/6.59	           sk_Xz)),
6.38/6.59	    inference('sup-', [status(thm)], ['3', '1'])).
6.38/6.59	tff('123', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b), X1 : a, X2 : app_encode_fun(a, b)]:
6.38/6.59	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X2), 
6.38/6.59	         sk_Xz)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X2), 
6.38/6.59	             X0)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
6.38/6.59	             sk_Xy1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	               sk_Xx), sk_Xx)
6.38/6.59	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X1)),
6.38/6.59	    inference('simplify', [status(thm)], ['122'])).
6.38/6.59	tff('124', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b), X1 : a, X2 : app_encode_fun(a, b)]:
6.38/6.59	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X2), 
6.38/6.59	         sk_Xz)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X2), 
6.38/6.59	             X0)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
6.38/6.59	             sk_Xy1)
6.38/6.59	       | ~ $true
6.38/6.59	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X1)),
6.38/6.59	    inference('demod', [status(thm)], ['123', '91'])).
6.38/6.59	tff('125', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b), X1 : a, X2 : app_encode_fun(a, b)]:
6.38/6.59	      (~ app_encode_app(a, $o, sk_Xp, X1)
6.38/6.59	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
6.38/6.59	             sk_Xy1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X2), 
6.38/6.59	             X0)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X2), 
6.38/6.59	           sk_Xz)),
6.38/6.59	    inference('simplify', [status(thm)], ['124'])).
6.38/6.59	tff('126', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b)]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	               sk_Xx), sk_Xx)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	             X0), sk_Xz)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	               X0), sk_Xy1)
6.38/6.59	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.59	    inference('sup-', [status(thm)], ['26', '125'])).
6.38/6.59	tff('127', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b)]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ $true
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	             X0), sk_Xz)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	               X0), sk_Xy1)
6.38/6.59	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.59	    inference('demod', [status(thm)], ['126', '91'])).
6.38/6.59	tff('128', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b)]:
6.38/6.59	      (~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	               X0), sk_Xy1)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	             X0), sk_Xz)),
6.38/6.59	    inference('simplify', [status(thm)], ['127'])).
6.38/6.59	tff('129', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b)]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	               X0), sk_Xy1)
6.38/6.59	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	             sk_Xz), X0)),
6.38/6.59	    inference('sup-', [status(thm)], ['128', '15'])).
6.38/6.59	tff('130', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b)]:
6.38/6.59	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	           sk_Xz), X0)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	               X0), sk_Xy1)),
6.38/6.59	    inference('simplify', [status(thm)], ['129'])).
6.38/6.59	tff('131', plain,
6.38/6.59	    (~ $true
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	             sk_Xx), sk_Xx)
6.38/6.59	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.59	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	     | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	           sk_Xz), sk_Xy1)),
6.38/6.59	    inference('sup-', [status(thm)], ['26', '130'])).
6.38/6.59	tff('132', plain,
6.38/6.59	    (~ $true
6.38/6.59	     | ~ $true
6.38/6.59	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.59	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	     | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	           sk_Xz), sk_Xy1)),
6.38/6.59	    inference('demod', [status(thm)], ['131', '91'])).
6.38/6.59	tff('133', plain,
6.38/6.59	    (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	       app_encode_app(app_encode_fun(a, b), 
6.38/6.59	         app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	         app_encode_app(a, 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	         sk_Xz), sk_Xy1)
6.38/6.59	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
6.38/6.59	    inference('simplify', [status(thm)], ['132'])).
6.38/6.59	tff('134', plain,
6.38/6.59	    (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	       app_encode_app(app_encode_fun(a, b), 
6.38/6.59	         app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	         app_encode_app(a, 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	         sk_Xz), sk_Xy1)
6.38/6.59	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.59	    inference('clc', [status(thm)], ['121', '133'])).
6.38/6.59	tff('135', plain,
6.38/6.59	    (~ $true
6.38/6.59	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	     | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	           sk_Xy1), sk_Xz)),
6.38/6.59	    inference('sup-', [status(thm)], ['134', '15'])).
6.38/6.59	tff('136', plain,
6.38/6.59	    (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	       app_encode_app(app_encode_fun(a, b), 
6.38/6.59	         app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	         app_encode_app(a, 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	         sk_Xy1), sk_Xz)
6.38/6.59	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.59	    inference('simplify', [status(thm)], ['135'])).
6.38/6.59	tff('137', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b)]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	               X0), sk_Xy1)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	             X0), sk_Xz)),
6.38/6.59	    inference('sup-', [status(thm)], ['136', '1'])).
6.38/6.59	tff('138', plain,
6.38/6.59	    ![X0 : app_encode_fun(a, b)]:
6.38/6.59	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	           X0), sk_Xz)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	               X0), sk_Xy1)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.59	    inference('simplify', [status(thm)], ['137'])).
6.38/6.59	tff('139', plain,
6.38/6.59	    ![X7 : a]:
6.38/6.59	      (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	             sk_Xx), sk_Xx)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X7)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X7), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	               sk_Xx2), sk_Xz)),
6.38/6.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.59	tff('140', plain,
6.38/6.59	    ![X0 : a]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	               sk_Xx2), sk_Xy1)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	               sk_Xx), sk_Xx)),
6.38/6.59	    inference('sup-', [status(thm)], ['138', '139'])).
6.38/6.59	tff('141', plain,
6.38/6.59	    ![X0 : a]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	               sk_Xx2), sk_Xy1)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.59	       | ~ $true),
6.38/6.59	    inference('demod', [status(thm)], ['140', '91'])).
6.38/6.59	tff('142', plain,
6.38/6.59	    ![X0 : a]:
6.38/6.59	      (~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	               sk_Xx2), sk_Xy1)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.59	    inference('simplify', [status(thm)], ['141'])).
6.38/6.59	tff('143', plain,
6.38/6.59	    ![X7 : a, X9 : a]:
6.38/6.59	      (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	             sk_Xx), sk_Xx)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X7)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X7), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X9), 
6.38/6.59	             sk_Xx2), sk_Xy1)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X9)),
6.38/6.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.59	tff('144', plain,
6.38/6.59	    ![X0 : a, X1 : a]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	               sk_Xx), sk_Xx)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.59	             sk_Xy1), sk_Xx2)),
6.38/6.59	    inference('sup-', [status(thm)], ['143', '15'])).
6.38/6.59	tff('145', plain,
6.38/6.59	    ![X0 : a, X1 : a]:
6.38/6.59	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy1), 
6.38/6.59	         sk_Xx2)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	               sk_Xx), sk_Xx)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X1)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.59	    inference('simplify', [status(thm)], ['144'])).
6.38/6.59	tff('146', plain,
6.38/6.59	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X2)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	               sk_Xx), sk_Xx)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.59	             sk_Xy1)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.59	           sk_Xx2)),
6.38/6.59	    inference('sup-', [status(thm)], ['145', '1'])).
6.38/6.59	tff('147', plain,
6.38/6.59	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
6.38/6.59	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.59	         sk_Xx2)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.59	             sk_Xy1)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	               sk_Xx), sk_Xx)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X2)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.59	    inference('simplify', [status(thm)], ['146'])).
6.38/6.59	tff('148', plain,
6.38/6.59	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
6.38/6.59	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.59	         sk_Xx2)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.59	             sk_Xy1)
6.38/6.59	       | ~ $true
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X2)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.59	    inference('demod', [status(thm)], ['147', '91'])).
6.38/6.59	tff('149', plain,
6.38/6.59	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
6.38/6.59	      (~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X2)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.59	             sk_Xy1)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
6.38/6.59	           sk_Xx2)),
6.38/6.59	    inference('simplify', [status(thm)], ['148'])).
6.38/6.59	tff('150', plain,
6.38/6.59	    ![X0 : a]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	               sk_Xx), sk_Xx)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	             sk_Xy1), sk_Xx2)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.59	    inference('sup-', [status(thm)], ['26', '149'])).
6.38/6.59	tff('151', plain,
6.38/6.59	    ![X0 : a]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ $true
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	             sk_Xy1), sk_Xx2)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.59	    inference('demod', [status(thm)], ['150', '91'])).
6.38/6.59	tff('152', plain,
6.38/6.59	    ![X0 : a]:
6.38/6.59	      (~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	             sk_Xy1), sk_Xx2)),
6.38/6.59	    inference('simplify', [status(thm)], ['151'])).
6.38/6.59	tff('153', plain,
6.38/6.59	    ![X0 : a]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	             sk_Xx2), sk_Xy1)),
6.38/6.59	    inference('sup-', [status(thm)], ['152', '15'])).
6.38/6.59	tff('154', plain,
6.38/6.59	    ![X0 : a]:
6.38/6.59	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	           sk_Xx2), sk_Xy1)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.59	    inference('simplify', [status(thm)], ['153'])).
6.38/6.59	tff('155', plain,
6.38/6.59	    ![X0 : a]:
6.38/6.59	      (~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.59	             sk_Xx1), sk_Xy)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.59	    inference('clc', [status(thm)], ['142', '154'])).
6.38/6.59	tff('156', plain,
6.38/6.59	    ![X0 : a]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	               sk_Xx), sk_Xx)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.59	             sk_Xx1), sk_Xy)),
6.38/6.59	    inference('sup-', [status(thm)], ['24', '155'])).
6.38/6.59	tff('157', plain,
6.38/6.59	    ![X0 : a]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ $true
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.59	             sk_Xx1), sk_Xy)),
6.38/6.59	    inference('demod', [status(thm)], ['156', '91'])).
6.38/6.59	tff('158', plain,
6.38/6.59	    ![X0 : a]:
6.38/6.59	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xx1), 
6.38/6.59	         sk_Xy)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.59	    inference('simplify', [status(thm)], ['157'])).
6.38/6.59	tff('159', plain,
6.38/6.59	    ![X0 : a]:
6.38/6.59	      (~ $true
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
6.38/6.59	             sk_Xy), sk_Xx1)),
6.38/6.59	    inference('sup-', [status(thm)], ['158', '15'])).
6.38/6.59	tff('160', plain,
6.38/6.59	    ![X0 : a]:
6.38/6.59	      (app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy), 
6.38/6.59	         sk_Xx1)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
6.38/6.59	    inference('simplify', [status(thm)], ['159'])).
6.38/6.59	tff('161', plain,
6.38/6.59	    (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	           sk_Xx), sk_Xx)
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	             sk_Xy), sk_Xx1)
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	             sk_Xx2), sk_Xz)),
6.38/6.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.59	tff('162', plain,
6.38/6.59	    (~ $true
6.38/6.59	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	             sk_Xy), sk_Xx1)
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	             sk_Xx), sk_Xx)
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	             sk_Xx2), sk_Xy1)
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	             sk_Xy), sk_Xx1)
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	             sk_Xx), sk_Xx)),
6.38/6.59	    inference('sup-', [status(thm)], ['108', '161'])).
6.38/6.59	tff('163', plain,
6.38/6.59	    (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
6.38/6.59	           sk_Xx2), sk_Xy1)
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	             sk_Xx), sk_Xx)
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	             sk_Xy), sk_Xx1)
6.38/6.59	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
6.38/6.59	    inference('simplify', [status(thm)], ['162'])).
6.38/6.59	tff('164', plain,
6.38/6.59	    ![X9 : a]:
6.38/6.59	      (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	             sk_Xx), sk_Xx)
6.38/6.59	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	             app_encode_app(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	               app_encode_app(a, 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	               sk_Xy), sk_Xx1)
6.38/6.59	       | app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X9), 
6.38/6.59	             sk_Xx2), sk_Xy1)
6.38/6.59	       | ~ app_encode_app(a, $o, sk_Xp, X9)),
6.38/6.59	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.38/6.59	tff('165', plain,
6.38/6.59	    (~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	             sk_Xy), sk_Xx1)
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	             sk_Xx), sk_Xx)),
6.38/6.59	    inference('clc', [status(thm)], ['163', '164'])).
6.38/6.59	tff('166', plain,
6.38/6.59	    (~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	         app_encode_app(app_encode_fun(a, b), 
6.38/6.59	           app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	           app_encode_app(a, 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	           sk_Xx), sk_Xx)
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
6.38/6.59	             sk_Xy), sk_Xx1)),
6.38/6.59	    inference('clc', [status(thm)], ['165', '24'])).
6.38/6.59	tff('167', plain,
6.38/6.59	    (~ $true
6.38/6.59	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	             sk_Xx), sk_Xx)),
6.38/6.59	    inference('sup-', [status(thm)], ['160', '166'])).
6.38/6.59	tff('168', plain,
6.38/6.59	    (~ $true | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01) | ~ $true),
6.38/6.59	    inference('demod', [status(thm)], ['167', '91'])).
6.38/6.59	tff('169', plain, ~ app_encode_app(a, $o, sk_Xp, sk_Xx01),
6.38/6.59	    inference('simplify', [status(thm)], ['168'])).
6.38/6.59	tff('170', plain,
6.38/6.59	    (~ $true
6.38/6.59	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
6.38/6.59	           app_encode_app(app_encode_fun(a, b), 
6.38/6.59	             app_encode_fun(app_encode_fun(a, b), $o), 
6.38/6.59	             app_encode_app(a, 
6.38/6.59	               app_encode_fun(app_encode_fun(a, b), 
6.38/6.59	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
6.38/6.59	             sk_Xx), sk_Xx)),
6.38/6.59	    inference('sup-', [status(thm)], ['10', '169'])).
6.38/6.59	tff('171', plain, (~ $true | ~ $true),
6.38/6.59	    inference('demod', [status(thm)], ['170', '91'])).
6.38/6.59	tff('172', plain, $false, inference('simplify', [status(thm)], ['171'])).
6.38/6.59	
6.38/6.59	% SZS output end Refutation
6.38/6.59	EOF
