0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n098.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:36:54 CST 2018
1.87/2.05	% done 1054 iterations in 1.845s
1.87/2.05	% SZS status Theorem for 'stdin'
1.87/2.05	% SZS output start Refutation
1.87/2.05	tff(zf_stmt_5, conjecture,
1.87/2.05	  (![Xp:app_encode_fun(a,$o),
1.87/2.05	     Xe:app_encode_fun(a,
1.87/2.05	                       app_encode_fun(app_encode_fun(a,b),
1.87/2.05	                                      app_encode_fun(app_encode_fun(a,b),$o)))]:
1.87/2.05	     ((![Xx:a]:
1.87/2.05	         (app_encode_app(a,$o,Xp,Xx) =>
1.87/2.05	          ((![Xx0:app_encode_fun(a,b)]:
1.87/2.05	              app_encode_app(app_encode_fun(a,b),$o,
1.87/2.05	                             app_encode_app(app_encode_fun(a,b),
1.87/2.05	                                            app_encode_fun(app_encode_fun(
1.87/2.05	                                                           a,b),$o),
1.87/2.05	                                            app_encode_app(a,
1.87/2.05	                                                           app_encode_fun(
1.87/2.05	                                                           app_encode_fun(
1.87/2.05	                                                           a,b),
1.87/2.05	                                                           app_encode_fun(
1.87/2.05	                                                           app_encode_fun(
1.87/2.05	                                                           a,b),$o)),Xe,Xx),
1.87/2.05	                                            Xx0),
1.87/2.05	                             Xx0)) & 
1.87/2.05	           (![Xx0:app_encode_fun(a,b),Xy:app_encode_fun(a,b)]:
1.87/2.05	              (app_encode_app(app_encode_fun(a,b),$o,
1.87/2.05	                              app_encode_app(app_encode_fun(a,b),
1.87/2.05	                                             app_encode_fun(app_encode_fun(
1.87/2.05	                                                            a,b),$o),
1.87/2.05	                                             app_encode_app(a,
1.87/2.05	                                                            app_encode_fun(
1.87/2.05	                                                            app_encode_fun(
1.87/2.05	                                                            a,b),
1.87/2.05	                                                            app_encode_fun(
1.87/2.05	                                                            app_encode_fun(
1.87/2.05	                                                            a,b),$o)),Xe,Xx),
1.87/2.05	                                             Xx0),
1.87/2.05	                              Xy) =>
1.87/2.05	               app_encode_app(app_encode_fun(a,b),$o,
1.87/2.05	                              app_encode_app(app_encode_fun(a,b),
1.87/2.05	                                             app_encode_fun(app_encode_fun(
1.87/2.05	                                                            a,b),$o),
1.87/2.05	                                             app_encode_app(a,
1.87/2.05	                                                            app_encode_fun(
1.87/2.05	                                                            app_encode_fun(
1.87/2.05	                                                            a,b),
1.87/2.05	                                                            app_encode_fun(
1.87/2.05	                                                            app_encode_fun(
1.87/2.05	                                                            a,b),$o)),Xe,Xx),
1.87/2.05	                                             Xy),
1.87/2.05	                              Xx0))) & 
1.87/2.05	           (![Xx0:app_encode_fun(a,b),Xy:app_encode_fun(a,b),
1.87/2.05	              Xz:app_encode_fun(a,b)]:
1.87/2.05	              ((app_encode_app(app_encode_fun(a,b),$o,
1.87/2.05	                               app_encode_app(app_encode_fun(a,b),
1.87/2.05	                                              app_encode_fun(app_encode_fun(
1.87/2.05	                                                             a,b),$o),
1.87/2.05	                                              app_encode_app(a,
1.87/2.05	                                                             app_encode_fun(
1.87/2.05	                                                             app_encode_fun(
1.87/2.05	                                                             a,b),
1.87/2.05	                                                             app_encode_fun(
1.87/2.05	                                                             app_encode_fun(
1.87/2.05	                                                             a,b),$o)),Xe,Xx),
1.87/2.05	                                              Xx0),
1.87/2.05	                               Xy) & 
1.87/2.05	                app_encode_app(app_encode_fun(a,b),$o,
1.87/2.05	                               app_encode_app(app_encode_fun(a,b),
1.87/2.05	                                              app_encode_fun(app_encode_fun(
1.87/2.05	                                                             a,b),$o),
1.87/2.05	                                              app_encode_app(a,
1.87/2.05	                                                             app_encode_fun(
1.87/2.05	                                                             app_encode_fun(
1.87/2.05	                                                             a,b),
1.87/2.05	                                                             app_encode_fun(
1.87/2.05	                                                             app_encode_fun(
1.87/2.05	                                                             a,b),$o)),Xe,Xx),
1.87/2.05	                                              Xy),
1.87/2.05	                               Xz)) =>
1.87/2.05	               app_encode_app(app_encode_fun(a,b),$o,
1.87/2.05	                              app_encode_app(app_encode_fun(a,b),
1.87/2.05	                                             app_encode_fun(app_encode_fun(
1.87/2.05	                                                            a,b),$o),
1.87/2.05	                                             app_encode_app(a,
1.87/2.06	                                                            app_encode_fun(
1.87/2.06	                                                            app_encode_fun(
1.87/2.06	                                                            a,b),
1.87/2.06	                                                            app_encode_fun(
1.87/2.06	                                                            app_encode_fun(
1.87/2.06	                                                            a,b),$o)),Xe,Xx),
1.87/2.06	                                             Xx0),
1.87/2.06	                              Xz)))))) =>
1.87/2.06	      ((![Xx:app_encode_fun(a,b),Xx0:a]:
1.87/2.06	          (app_encode_app(a,$o,Xp,Xx0) =>
1.87/2.06	           app_encode_app(app_encode_fun(a,b),$o,
1.87/2.06	                          app_encode_app(app_encode_fun(a,b),
1.87/2.06	                                         app_encode_fun(app_encode_fun(a,b),
1.87/2.06	                                                        $o),
1.87/2.06	                                         app_encode_app(a,
1.87/2.06	                                                        app_encode_fun(
1.87/2.06	                                                        app_encode_fun(a,b),
1.87/2.06	                                                        app_encode_fun(
1.87/2.06	                                                        app_encode_fun(a,b),
1.87/2.06	                                                        $o)),Xe,Xx0),
1.87/2.06	                                         Xx),
1.87/2.06	                          Xx))) & 
1.87/2.06	       (![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b)]:
1.87/2.06	          ((![Xx0:a]:
1.87/2.06	              (app_encode_app(a,$o,Xp,Xx0) =>
1.87/2.06	               app_encode_app(app_encode_fun(a,b),$o,
1.87/2.06	                              app_encode_app(app_encode_fun(a,b),
1.87/2.06	                                             app_encode_fun(app_encode_fun(
1.87/2.06	                                                            a,b),$o),
1.87/2.06	                                             app_encode_app(a,
1.87/2.06	                                                            app_encode_fun(
1.87/2.06	                                                            app_encode_fun(
1.87/2.06	                                                            a,b),
1.87/2.06	                                                            app_encode_fun(
1.87/2.06	                                                            app_encode_fun(
1.87/2.06	                                                            a,b),$o)),Xe,Xx0),
1.87/2.06	                                             Xx),
1.87/2.06	                              Xy))) =>
1.87/2.06	           (![Xx0:a]:
1.87/2.06	              (app_encode_app(a,$o,Xp,Xx0) =>
1.87/2.06	               app_encode_app(app_encode_fun(a,b),$o,
1.87/2.06	                              app_encode_app(app_encode_fun(a,b),
1.87/2.06	                                             app_encode_fun(app_encode_fun(
1.87/2.06	                                                            a,b),$o),
1.87/2.06	                                             app_encode_app(a,
1.87/2.06	                                                            app_encode_fun(
1.87/2.06	                                                            app_encode_fun(
1.87/2.06	                                                            a,b),
1.87/2.06	                                                            app_encode_fun(
1.87/2.06	                                                            app_encode_fun(
1.87/2.06	                                                            a,b),$o)),Xe,Xx0),
1.87/2.06	                                             Xy),
1.87/2.06	                              Xx))))) & 
1.87/2.06	       (![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b),
1.87/2.06	          Xz:app_encode_fun(a,b)]:
1.87/2.06	          (((![Xx0:a]:
1.87/2.06	               (app_encode_app(a,$o,Xp,Xx0) =>
1.87/2.06	                app_encode_app(app_encode_fun(a,b),$o,
1.87/2.06	                               app_encode_app(app_encode_fun(a,b),
1.87/2.06	                                              app_encode_fun(app_encode_fun(
1.87/2.06	                                                             a,b),$o),
1.87/2.06	                                              app_encode_app(a,
1.87/2.06	                                                             app_encode_fun(
1.87/2.06	                                                             app_encode_fun(
1.87/2.06	                                                             a,b),
1.87/2.06	                                                             app_encode_fun(
1.87/2.06	                                                             app_encode_fun(
1.87/2.06	                                                             a,b),$o)),Xe,Xx0),
1.87/2.06	                                              Xx),
1.87/2.06	                               Xy))) & 
1.87/2.06	            (![Xx0:a]:
1.87/2.06	               (app_encode_app(a,$o,Xp,Xx0) =>
1.87/2.06	                app_encode_app(app_encode_fun(a,b),$o,
1.87/2.06	                               app_encode_app(app_encode_fun(a,b),
1.87/2.06	                                              app_encode_fun(app_encode_fun(
1.87/2.06	                                                             a,b),$o),
1.87/2.06	                                              app_encode_app(a,
1.87/2.06	                                                             app_encode_fun(
1.87/2.06	                                                             app_encode_fun(
1.87/2.06	                                                             a,b),
1.87/2.06	                                                             app_encode_fun(
1.87/2.06	                                                             app_encode_fun(
1.87/2.06	                                                             a,b),$o)),Xe,Xx0),
1.87/2.06	                                              Xy),
1.87/2.06	                               Xz)))) =>
1.87/2.06	           (![Xx0:a]:
1.87/2.06	              (app_encode_app(a,$o,Xp,Xx0) =>
1.87/2.06	               app_encode_app(app_encode_fun(a,b),$o,
1.87/2.06	                              app_encode_app(app_encode_fun(a,b),
1.87/2.06	                                             app_encode_fun(app_encode_fun(
1.87/2.06	                                                            a,b),$o),
1.87/2.06	                                             app_encode_app(a,
1.87/2.06	                                                            app_encode_fun(
1.87/2.06	                                                            app_encode_fun(
1.87/2.06	                                                            a,b),
1.87/2.06	                                                            app_encode_fun(
1.87/2.06	                                                            app_encode_fun(
1.87/2.06	                                                            a,b),$o)),Xe,Xx0),
1.87/2.06	                                             Xx),
1.87/2.06	                              Xz))))))))).
1.87/2.06	tff(zf_stmt_0, negated_conjecture,
1.87/2.06	  (~
1.87/2.06	    (![Xp:app_encode_fun(a,$o),
1.87/2.06	       Xe:app_encode_fun(a,
1.87/2.06	                         app_encode_fun(app_encode_fun(a,b),
1.87/2.06	                                        app_encode_fun(app_encode_fun(a,b),$o)))]:
1.87/2.06	       ((![Xx:a]:
1.87/2.06	           (app_encode_app(a,$o,Xp,Xx) =>
1.87/2.06	            ((![Xx0:app_encode_fun(a,b)]:
1.87/2.06	                app_encode_app(app_encode_fun(a,b),$o,
1.87/2.06	                               app_encode_app(app_encode_fun(a,b),
1.87/2.06	                                              app_encode_fun(app_encode_fun(
1.87/2.06	                                                             a,b),$o),
1.87/2.06	                                              app_encode_app(a,
1.87/2.06	                                                             app_encode_fun(
1.87/2.06	                                                             app_encode_fun(
1.87/2.06	                                                             a,b),
1.87/2.06	                                                             app_encode_fun(
1.87/2.06	                                                             app_encode_fun(
1.87/2.06	                                                             a,b),$o)),Xe,Xx),
1.87/2.06	                                              Xx0),
1.87/2.06	                               Xx0)) & 
1.87/2.06	             (![Xx0:app_encode_fun(a,b),Xy:app_encode_fun(a,b)]:
1.87/2.06	                (app_encode_app(app_encode_fun(a,b),$o,
1.87/2.06	                                app_encode_app(app_encode_fun(a,b),
1.87/2.06	                                               app_encode_fun(app_encode_fun(
1.87/2.06	                                                              a,b),$o),
1.87/2.06	                                               app_encode_app(a,
1.87/2.06	                                                              app_encode_fun(
1.87/2.06	                                                              app_encode_fun(
1.87/2.06	                                                              a,b),
1.87/2.06	                                                              app_encode_fun(
1.87/2.06	                                                              app_encode_fun(
1.87/2.06	                                                              a,b),$o)),Xe,Xx),
1.87/2.06	                                               Xx0),
1.87/2.06	                                Xy) =>
1.87/2.06	                 app_encode_app(app_encode_fun(a,b),$o,
1.87/2.06	                                app_encode_app(app_encode_fun(a,b),
1.87/2.06	                                               app_encode_fun(app_encode_fun(
1.87/2.06	                                                              a,b),$o),
1.87/2.06	                                               app_encode_app(a,
1.87/2.06	                                                              app_encode_fun(
1.87/2.06	                                                              app_encode_fun(
1.87/2.06	                                                              a,b),
1.87/2.06	                                                              app_encode_fun(
1.87/2.06	                                                              app_encode_fun(
1.87/2.06	                                                              a,b),$o)),Xe,Xx),
1.87/2.06	                                               Xy),
1.87/2.06	                                Xx0))) & 
1.87/2.06	             (![Xx0:app_encode_fun(a,b),Xy:app_encode_fun(a,b),
1.87/2.06	                Xz:app_encode_fun(a,b)]:
1.87/2.06	                ((app_encode_app(app_encode_fun(a,b),$o,
1.87/2.06	                                 app_encode_app(app_encode_fun(a,b),
1.87/2.06	                                                app_encode_fun(app_encode_fun(
1.87/2.06	                                                               a,b),$o),
1.87/2.06	                                                app_encode_app(a,
1.87/2.06	                                                               app_encode_fun(
1.87/2.06	                                                               app_encode_fun(
1.87/2.06	                                                               a,b),
1.87/2.06	                                                               app_encode_fun(
1.87/2.06	                                                               app_encode_fun(
1.87/2.06	                                                               a,b),$o)),Xe,
1.87/2.06	                                                               Xx),
1.87/2.06	                                                Xx0),
1.87/2.06	                                 Xy) & 
1.87/2.06	                  app_encode_app(app_encode_fun(a,b),$o,
1.87/2.06	                                 app_encode_app(app_encode_fun(a,b),
1.87/2.06	                                                app_encode_fun(app_encode_fun(
1.87/2.06	                                                               a,b),$o),
1.87/2.06	                                                app_encode_app(a,
1.87/2.06	                                                               app_encode_fun(
1.87/2.06	                                                               app_encode_fun(
1.87/2.06	                                                               a,b),
1.87/2.06	                                                               app_encode_fun(
1.87/2.06	                                                               app_encode_fun(
1.87/2.06	                                                               a,b),$o)),Xe,
1.87/2.06	                                                               Xx),
1.87/2.06	                                                Xy),
1.87/2.06	                                 Xz)) =>
1.87/2.06	                 app_encode_app(app_encode_fun(a,b),$o,
1.87/2.06	                                app_encode_app(app_encode_fun(a,b),
1.87/2.06	                                               app_encode_fun(app_encode_fun(
1.87/2.06	                                                              a,b),$o),
1.87/2.06	                                               app_encode_app(a,
1.87/2.06	                                                              app_encode_fun(
1.87/2.06	                                                              app_encode_fun(
1.87/2.06	                                                              a,b),
1.87/2.06	                                                              app_encode_fun(
1.87/2.06	                                                              app_encode_fun(
1.87/2.06	                                                              a,b),$o)),Xe,Xx),
1.87/2.06	                                               Xx0),
1.87/2.06	                                Xz)))))) =>
1.87/2.06	        ((![Xx:app_encode_fun(a,b),Xx0:a]:
1.87/2.06	            (app_encode_app(a,$o,Xp,Xx0) =>
1.87/2.06	             app_encode_app(app_encode_fun(a,b),$o,
1.87/2.06	                            app_encode_app(app_encode_fun(a,b),
1.87/2.06	                                           app_encode_fun(app_encode_fun(a,b),
1.87/2.06	                                                          $o),
1.87/2.06	                                           app_encode_app(a,
1.87/2.06	                                                          app_encode_fun(
1.87/2.06	                                                          app_encode_fun(a,b),
1.87/2.06	                                                          app_encode_fun(
1.87/2.06	                                                          app_encode_fun(a,b),
1.87/2.06	                                                          $o)),Xe,Xx0),
1.87/2.06	                                           Xx),
1.87/2.06	                            Xx))) & 
1.87/2.06	         (![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b)]:
1.87/2.06	            ((![Xx0:a]:
1.87/2.06	                (app_encode_app(a,$o,Xp,Xx0) =>
1.87/2.06	                 app_encode_app(app_encode_fun(a,b),$o,
1.87/2.06	                                app_encode_app(app_encode_fun(a,b),
1.87/2.06	                                               app_encode_fun(app_encode_fun(
1.87/2.06	                                                              a,b),$o),
1.87/2.06	                                               app_encode_app(a,
1.87/2.06	                                                              app_encode_fun(
1.87/2.06	                                                              app_encode_fun(
1.87/2.06	                                                              a,b),
1.87/2.06	                                                              app_encode_fun(
1.87/2.06	                                                              app_encode_fun(
1.87/2.06	                                                              a,b),$o)),Xe,
1.87/2.06	                                                              Xx0),
1.87/2.06	                                               Xx),
1.87/2.06	                                Xy))) =>
1.87/2.06	             (![Xx0:a]:
1.87/2.06	                (app_encode_app(a,$o,Xp,Xx0) =>
1.87/2.06	                 app_encode_app(app_encode_fun(a,b),$o,
1.88/2.06	                                app_encode_app(app_encode_fun(a,b),
1.88/2.06	                                               app_encode_fun(app_encode_fun(
1.88/2.06	                                                              a,b),$o),
1.88/2.06	                                               app_encode_app(a,
1.88/2.06	                                                              app_encode_fun(
1.88/2.06	                                                              app_encode_fun(
1.88/2.06	                                                              a,b),
1.88/2.06	                                                              app_encode_fun(
1.88/2.06	                                                              app_encode_fun(
1.88/2.06	                                                              a,b),$o)),Xe,
1.88/2.06	                                                              Xx0),
1.88/2.06	                                               Xy),
1.88/2.06	                                Xx))))) & 
1.88/2.06	         (![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b),
1.88/2.06	            Xz:app_encode_fun(a,b)]:
1.88/2.06	            (((![Xx0:a]:
1.88/2.06	                 (app_encode_app(a,$o,Xp,Xx0) =>
1.88/2.06	                  app_encode_app(app_encode_fun(a,b),$o,
1.88/2.06	                                 app_encode_app(app_encode_fun(a,b),
1.88/2.06	                                                app_encode_fun(app_encode_fun(
1.88/2.06	                                                               a,b),$o),
1.88/2.06	                                                app_encode_app(a,
1.88/2.06	                                                               app_encode_fun(
1.88/2.06	                                                               app_encode_fun(
1.88/2.06	                                                               a,b),
1.88/2.06	                                                               app_encode_fun(
1.88/2.06	                                                               app_encode_fun(
1.88/2.06	                                                               a,b),$o)),Xe,
1.88/2.06	                                                               Xx0),
1.88/2.06	                                                Xx),
1.88/2.06	                                 Xy))) & 
1.88/2.06	              (![Xx0:a]:
1.88/2.06	                 (app_encode_app(a,$o,Xp,Xx0) =>
1.88/2.06	                  app_encode_app(app_encode_fun(a,b),$o,
1.88/2.06	                                 app_encode_app(app_encode_fun(a,b),
1.88/2.06	                                                app_encode_fun(app_encode_fun(
1.88/2.06	                                                               a,b),$o),
1.88/2.06	                                                app_encode_app(a,
1.88/2.06	                                                               app_encode_fun(
1.88/2.06	                                                               app_encode_fun(
1.88/2.06	                                                               a,b),
1.88/2.06	                                                               app_encode_fun(
1.88/2.06	                                                               app_encode_fun(
1.88/2.06	                                                               a,b),$o)),Xe,
1.88/2.06	                                                               Xx0),
1.88/2.06	                                                Xy),
1.88/2.06	                                 Xz)))) =>
1.88/2.06	             (![Xx0:a]:
1.88/2.06	                (app_encode_app(a,$o,Xp,Xx0) =>
1.88/2.06	                 app_encode_app(app_encode_fun(a,b),$o,
1.88/2.06	                                app_encode_app(app_encode_fun(a,b),
1.88/2.06	                                               app_encode_fun(app_encode_fun(
1.88/2.06	                                                              a,b),$o),
1.88/2.06	                                               app_encode_app(a,
1.88/2.06	                                                              app_encode_fun(
1.88/2.06	                                                              app_encode_fun(
1.88/2.06	                                                              a,b),
1.88/2.06	                                                              app_encode_fun(
1.88/2.06	                                                              app_encode_fun(
1.88/2.06	                                                              a,b),$o)),Xe,
1.88/2.06	                                                              Xx0),
1.88/2.06	                                               Xx),
1.88/2.06	                                Xz)))))))))).
1.88/2.06	tff('0', plain,
1.88/2.06	    ![X12 : a]:
1.88/2.06	      (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	             sk_Xx), sk_Xx)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X12), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X12)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('1', plain,
1.88/2.06	    ![X4 : a, X8 : app_encode_fun(a, b), X9 : app_encode_fun(a, b), 
1.88/2.06	      X10 : app_encode_fun(a, b)]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X4), X8), 
1.88/2.06	         X9)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X4), 
1.88/2.06	               X10), X9)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X4), X8), 
1.88/2.06	             X10)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X4)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('2', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b)]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	               sk_Xx), sk_Xx)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xy1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	           sk_Xz)),
1.88/2.06	    inference('sup-', [status(thm)], ['0', '1'])).
1.88/2.06	tff('3', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b)]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	         sk_Xz)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xy1)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	               sk_Xx), sk_Xx)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
1.88/2.06	    inference('simplify', [status(thm)], ['2'])).
1.88/2.06	tff('4', plain,
1.88/2.06	    (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	           sk_Xx), sk_Xx)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.06	             sk_Xx2), sk_Xz)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('5', plain,
1.88/2.06	    (~ $true
1.88/2.06	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	             sk_Xx), sk_Xx)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.06	             sk_Xx2), sk_Xy1)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	             sk_Xx), sk_Xx)),
1.88/2.06	    inference('sup-', [status(thm)], ['3', '4'])).
1.88/2.06	tff('6', plain,
1.88/2.06	    (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.06	           sk_Xx2), sk_Xy1)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	             sk_Xx), sk_Xx)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.06	    inference('simplify', [status(thm)], ['5'])).
1.88/2.06	tff('7', plain,
1.88/2.06	    ![X13 : a]:
1.88/2.06	      (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	             sk_Xx), sk_Xx)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X13), 
1.88/2.06	             sk_Xx2), sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X13)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('8', plain,
1.88/2.06	    (~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	             sk_Xx), sk_Xx)),
1.88/2.06	    inference('clc', [status(thm)], ['6', '7'])).
1.88/2.06	tff('9', plain,
1.88/2.06	    (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	           sk_Xx), sk_Xx)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('10', plain,
1.88/2.06	    (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	           sk_Xx), sk_Xx)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
1.88/2.06	    inference('clc', [status(thm)], ['8', '9'])).
1.88/2.06	tff('11', plain,
1.88/2.06	    ![X4 : a, X5 : app_encode_fun(a, b)]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X4), X5), 
1.88/2.06	         X5)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X4)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('12', plain,
1.88/2.06	    ![X0 : app_encode_fun(a, b)]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	               sk_Xx), sk_Xx)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             X0), X0)),
1.88/2.06	    inference('sup-', [status(thm)], ['10', '11'])).
1.88/2.06	tff('13', plain,
1.88/2.06	    ![X0 : app_encode_fun(a, b)]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	           X0), X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	               sk_Xx), sk_Xx)),
1.88/2.06	    inference('simplify', [status(thm)], ['12'])).
1.88/2.06	tff('14', plain,
1.88/2.06	    ![X11 : a]:
1.88/2.06	      (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	             sk_Xx), sk_Xx)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X11)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X11), 
1.88/2.06	             sk_Xx1), sk_Xy)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('15', plain,
1.88/2.06	    ![X4 : a, X6 : app_encode_fun(a, b), X7 : app_encode_fun(a, b)]:
1.88/2.06	      (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X4), X6), 
1.88/2.06	           X7)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X4), X7), 
1.88/2.06	           X6)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X4)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('16', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	               sk_Xx), sk_Xx)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xy), sk_Xx1)),
1.88/2.06	    inference('sup-', [status(thm)], ['14', '15'])).
1.88/2.06	tff('17', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy), 
1.88/2.06	         sk_Xx1)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	               sk_Xx), sk_Xx)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.06	    inference('simplify', [status(thm)], ['16'])).
1.88/2.06	tff('18', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b)]:
1.88/2.06	      (~ $true
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	               sk_Xx), sk_Xx)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xy)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	           sk_Xx1)),
1.88/2.06	    inference('sup-', [status(thm)], ['17', '1'])).
1.88/2.06	tff('19', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b)]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	         sk_Xx1)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xy)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	               sk_Xx), sk_Xx)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.06	    inference('simplify', [status(thm)], ['18'])).
1.88/2.06	tff('20', plain,
1.88/2.06	    (~ $true
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	             sk_Xx), sk_Xx)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	             sk_Xx), sk_Xx)
1.88/2.06	     | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	           sk_Xy), sk_Xx1)),
1.88/2.06	    inference('sup-', [status(thm)], ['13', '19'])).
1.88/2.06	tff('21', plain,
1.88/2.06	    (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	       app_encode_app(app_encode_fun(a, b), 
1.88/2.06	         app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	         app_encode_app(a, 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	         sk_Xy), sk_Xx1)
1.88/2.06	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	             sk_Xx), sk_Xx)),
1.88/2.06	    inference('simplify', [status(thm)], ['20'])).
1.88/2.06	tff('22', plain,
1.88/2.06	    (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	           sk_Xx), sk_Xx)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('23', plain,
1.88/2.06	    (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	           sk_Xx), sk_Xx)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
1.88/2.06	    inference('clc', [status(thm)], ['21', '22'])).
1.88/2.06	tff('24', plain,
1.88/2.06	    (app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	             sk_Xx), sk_Xx)),
1.88/2.06	    inference('clc', [status(thm)], ['23', '10'])).
1.88/2.06	tff('25', plain,
1.88/2.06	    ![X11 : a, X13 : a]:
1.88/2.06	      (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	             sk_Xx), sk_Xx)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X11)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X11), 
1.88/2.06	             sk_Xx1), sk_Xy)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X13), 
1.88/2.06	             sk_Xx2), sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X13)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('26', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X2)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
1.88/2.06	             sk_Xx2), sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	               sk_Xx), sk_Xx)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xx1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	           sk_Xy)),
1.88/2.06	    inference('sup-', [status(thm)], ['25', '1'])).
1.88/2.06	tff('27', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	         sk_Xy)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xx1)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	               sk_Xx), sk_Xx)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
1.88/2.06	             sk_Xx2), sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X2)),
1.88/2.06	    inference('simplify', [status(thm)], ['26'])).
1.88/2.06	tff('28', plain,
1.88/2.06	    ![X12 : a]:
1.88/2.06	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X12), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X12)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('29', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xz), sk_Xy1)),
1.88/2.06	    inference('sup-', [status(thm)], ['28', '15'])).
1.88/2.06	tff('30', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xz), 
1.88/2.06	         sk_Xy1)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
1.88/2.06	    inference('simplify', [status(thm)], ['29'])).
1.88/2.06	tff('31', plain,
1.88/2.06	    ![X13 : a]:
1.88/2.06	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X13), 
1.88/2.06	             sk_Xx2), sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X13)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('32', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xy1), sk_Xx2)),
1.88/2.06	    inference('sup-', [status(thm)], ['31', '15'])).
1.88/2.06	tff('33', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy1), 
1.88/2.06	         sk_Xx2)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
1.88/2.06	    inference('simplify', [status(thm)], ['32'])).
1.88/2.06	tff('34', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b)]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xy1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	           sk_Xx2)),
1.88/2.06	    inference('sup-', [status(thm)], ['33', '1'])).
1.88/2.06	tff('35', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b)]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	         sk_Xx2)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xy1)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
1.88/2.06	    inference('simplify', [status(thm)], ['34'])).
1.88/2.06	tff('36', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xz), sk_Xx2)),
1.88/2.06	    inference('sup-', [status(thm)], ['30', '35'])).
1.88/2.06	tff('37', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xz), 
1.88/2.06	         sk_Xx2)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
1.88/2.06	    inference('simplify', [status(thm)], ['36'])).
1.88/2.06	tff('38', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xx2), sk_Xz)),
1.88/2.06	    inference('sup-', [status(thm)], ['37', '15'])).
1.88/2.06	tff('39', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xx2), 
1.88/2.06	         sk_Xz)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
1.88/2.06	    inference('simplify', [status(thm)], ['38'])).
1.88/2.06	tff('40', plain,
1.88/2.06	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.06	             sk_Xx2), sk_Xz)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('41', plain,
1.88/2.06	    (~ $true
1.88/2.06	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
1.88/2.06	    inference('sup-', [status(thm)], ['39', '40'])).
1.88/2.06	tff('42', plain,
1.88/2.06	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.06	    inference('simplify', [status(thm)], ['41'])).
1.88/2.06	tff('43', plain,
1.88/2.06	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('44', plain,
1.88/2.06	    (app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
1.88/2.06	    inference('clc', [status(thm)], ['42', '43'])).
1.88/2.06	tff('45', plain,
1.88/2.06	    ![X0 : app_encode_fun(a, b)]:
1.88/2.06	      (~ $true
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             X0), X0)),
1.88/2.06	    inference('sup-', [status(thm)], ['44', '11'])).
1.88/2.06	tff('46', plain,
1.88/2.06	    ![X0 : app_encode_fun(a, b)]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	           X0), X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
1.88/2.06	    inference('simplify', [status(thm)], ['45'])).
1.88/2.06	tff('47', plain,
1.88/2.06	    ![X11 : a, X12 : a]:
1.88/2.06	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X11)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X11), 
1.88/2.06	             sk_Xx1), sk_Xy)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X12), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X12)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('48', plain,
1.88/2.06	    ![X0 : a, X1 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xy), sk_Xx1)),
1.88/2.06	    inference('sup-', [status(thm)], ['47', '15'])).
1.88/2.06	tff('49', plain,
1.88/2.06	    ![X0 : a, X1 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy), 
1.88/2.06	         sk_Xx1)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X1)),
1.88/2.06	    inference('simplify', [status(thm)], ['48'])).
1.88/2.06	tff('50', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X2)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xy)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	           sk_Xx1)),
1.88/2.06	    inference('sup-', [status(thm)], ['49', '1'])).
1.88/2.06	tff('51', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	         sk_Xx1)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xy)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X2)),
1.88/2.06	    inference('simplify', [status(thm)], ['50'])).
1.88/2.06	tff('52', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)),
1.88/2.06	    inference('sup-', [status(thm)], ['46', '51'])).
1.88/2.06	tff('53', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	           sk_Xy), sk_Xx1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
1.88/2.06	    inference('simplify', [status(thm)], ['52'])).
1.88/2.06	tff('54', plain,
1.88/2.06	    ![X12 : a]:
1.88/2.06	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	               sk_Xy), sk_Xx1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X12), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X12)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('55', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b)]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	               sk_Xy), sk_Xx1)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xy1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	           sk_Xz)),
1.88/2.06	    inference('sup-', [status(thm)], ['54', '1'])).
1.88/2.06	tff('56', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b)]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	         sk_Xz)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xy1)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	               sk_Xy), sk_Xx1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
1.88/2.06	    inference('simplify', [status(thm)], ['55'])).
1.88/2.06	tff('57', plain,
1.88/2.06	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.06	             sk_Xx2), sk_Xz)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('58', plain,
1.88/2.06	    (~ $true
1.88/2.06	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.06	             sk_Xx2), sk_Xy1)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
1.88/2.06	    inference('sup-', [status(thm)], ['56', '57'])).
1.88/2.06	tff('59', plain,
1.88/2.06	    (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.06	           sk_Xx2), sk_Xy1)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)
1.88/2.06	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.06	    inference('simplify', [status(thm)], ['58'])).
1.88/2.06	tff('60', plain,
1.88/2.06	    ![X13 : a]:
1.88/2.06	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	               sk_Xy), sk_Xx1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X13), 
1.88/2.06	             sk_Xx2), sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X13)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('61', plain,
1.88/2.06	    (~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
1.88/2.06	    inference('clc', [status(thm)], ['59', '60'])).
1.88/2.06	tff('62', plain,
1.88/2.06	    ![X11 : a]:
1.88/2.06	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X11)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X11), 
1.88/2.06	             sk_Xx1), sk_Xy)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('63', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xy), sk_Xx1)),
1.88/2.06	    inference('sup-', [status(thm)], ['62', '15'])).
1.88/2.06	tff('64', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy), 
1.88/2.06	         sk_Xx1)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.06	    inference('simplify', [status(thm)], ['63'])).
1.88/2.06	tff('65', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b)]:
1.88/2.06	      (~ $true
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xy)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	           sk_Xx1)),
1.88/2.06	    inference('sup-', [status(thm)], ['64', '1'])).
1.88/2.06	tff('66', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b)]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	         sk_Xx1)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xy)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.06	    inference('simplify', [status(thm)], ['65'])).
1.88/2.06	tff('67', plain,
1.88/2.06	    (~ $true
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	     | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	           sk_Xy), sk_Xx1)),
1.88/2.06	    inference('sup-', [status(thm)], ['46', '66'])).
1.88/2.06	tff('68', plain,
1.88/2.06	    (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	       app_encode_app(app_encode_fun(a, b), 
1.88/2.06	         app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	         app_encode_app(a, 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	         sk_Xy), sk_Xx1)
1.88/2.06	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
1.88/2.06	    inference('simplify', [status(thm)], ['67'])).
1.88/2.06	tff('69', plain,
1.88/2.06	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('70', plain,
1.88/2.06	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
1.88/2.06	    inference('clc', [status(thm)], ['68', '69'])).
1.88/2.06	tff('71', plain,
1.88/2.06	    (app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
1.88/2.06	    inference('clc', [status(thm)], ['70', '44'])).
1.88/2.06	tff('72', plain,
1.88/2.06	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)),
1.88/2.06	    inference('clc', [status(thm)], ['61', '71'])).
1.88/2.06	tff('73', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
1.88/2.06	    inference('clc', [status(thm)], ['53', '72'])).
1.88/2.06	tff('74', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy1), 
1.88/2.06	         sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
1.88/2.06	    inference('clc', [status(thm)], ['73', '44'])).
1.88/2.06	tff('75', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b)]:
1.88/2.06	      (~ $true
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xy1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	           sk_Xz)),
1.88/2.06	    inference('sup-', [status(thm)], ['74', '1'])).
1.88/2.06	tff('76', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b)]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	         sk_Xz)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
1.88/2.06	    inference('simplify', [status(thm)], ['75'])).
1.88/2.06	tff('77', plain,
1.88/2.06	    ![X11 : a]:
1.88/2.06	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X11)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X11), 
1.88/2.06	             sk_Xx1), sk_Xy)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.06	               sk_Xx2), sk_Xz)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('78', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.06	               sk_Xx2), sk_Xy1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xx1), sk_Xy)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
1.88/2.06	    inference('sup-', [status(thm)], ['76', '77'])).
1.88/2.06	tff('79', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xx1), sk_Xy)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.06	               sk_Xx2), sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
1.88/2.06	    inference('simplify', [status(thm)], ['78'])).
1.88/2.06	tff('80', plain,
1.88/2.06	    ![X11 : a, X13 : a]:
1.88/2.06	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X11)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X11), 
1.88/2.06	             sk_Xx1), sk_Xy)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X13), 
1.88/2.06	             sk_Xx2), sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X13)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('81', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xx1), sk_Xy)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
1.88/2.06	    inference('clc', [status(thm)], ['79', '80'])).
1.88/2.06	tff('82', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xx1), sk_Xy)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
1.88/2.06	    inference('clc', [status(thm)], ['81', '71'])).
1.88/2.06	tff('83', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xy), sk_Xx1)),
1.88/2.06	    inference('sup-', [status(thm)], ['82', '15'])).
1.88/2.06	tff('84', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy), 
1.88/2.06	         sk_Xx1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
1.88/2.06	    inference('simplify', [status(thm)], ['83'])).
1.88/2.06	tff('85', plain,
1.88/2.06	    (~ $true
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
1.88/2.06	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
1.88/2.06	    inference('sup-', [status(thm)], ['84', '72'])).
1.88/2.06	tff('86', plain,
1.88/2.06	    (~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
1.88/2.06	    inference('simplify', [status(thm)], ['85'])).
1.88/2.06	tff('87', plain, app_encode_app(a, $o, sk_Xp, sk_Xx0),
1.88/2.06	    inference('clc', [status(thm)], ['86', '44'])).
1.88/2.06	tff('88', plain,
1.88/2.06	    ![X0 : app_encode_fun(a, b)]:
1.88/2.06	      (~ $true
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	             X0), X0)),
1.88/2.06	    inference('sup-', [status(thm)], ['87', '11'])).
1.88/2.06	tff('89', plain,
1.88/2.06	    ![X0 : app_encode_fun(a, b)]:
1.88/2.06	      app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	        app_encode_app(app_encode_fun(a, b), 
1.88/2.06	          app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	          app_encode_app(a, 
1.88/2.06	            app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	              app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), X0), 
1.88/2.06	        X0),
1.88/2.06	    inference('simplify', [status(thm)], ['88'])).
1.88/2.06	tff('90', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	         sk_Xy)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xx1)
1.88/2.06	       | ~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
1.88/2.06	             sk_Xx2), sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X2)),
1.88/2.06	    inference('demod', [status(thm)], ['27', '89'])).
1.88/2.06	tff('91', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
1.88/2.06	      (~ app_encode_app(a, $o, sk_Xp, X2)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
1.88/2.06	             sk_Xx2), sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xx1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	           sk_Xy)),
1.88/2.06	    inference('simplify', [status(thm)], ['90'])).
1.88/2.06	tff('92', plain,
1.88/2.06	    ![X0 : app_encode_fun(a, b), X1 : a, X2 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
1.88/2.06	             sk_Xx1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
1.88/2.06	             sk_Xx2), sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X2)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
1.88/2.06	             sk_Xy), X0)),
1.88/2.06	    inference('sup-', [status(thm)], ['91', '15'])).
1.88/2.06	tff('93', plain,
1.88/2.06	    ![X0 : app_encode_fun(a, b), X1 : a, X2 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), sk_Xy), 
1.88/2.06	         X0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X2)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
1.88/2.06	             sk_Xx2), sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X1)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
1.88/2.06	             sk_Xx1)),
1.88/2.06	    inference('simplify', [status(thm)], ['92'])).
1.88/2.06	tff('94', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	               sk_Xx), sk_Xx)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xx2), sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)),
1.88/2.06	    inference('sup-', [status(thm)], ['13', '93'])).
1.88/2.06	tff('95', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xx2), sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)),
1.88/2.06	    inference('demod', [status(thm)], ['94', '89'])).
1.88/2.06	tff('96', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	           sk_Xy), sk_Xx1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xx2), sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
1.88/2.06	    inference('simplify', [status(thm)], ['95'])).
1.88/2.06	tff('97', plain,
1.88/2.06	    ![X11 : a, X12 : a]:
1.88/2.06	      (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	             sk_Xx), sk_Xx)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X11)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X11), 
1.88/2.06	             sk_Xx1), sk_Xy)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X12), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X12)),
1.88/2.06	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.06	tff('98', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X2)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	               sk_Xx), sk_Xx)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xx1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	           sk_Xy)),
1.88/2.06	    inference('sup-', [status(thm)], ['97', '1'])).
1.88/2.06	tff('99', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	         sk_Xy)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xx1)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	               sk_Xx), sk_Xx)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X2)),
1.88/2.06	    inference('simplify', [status(thm)], ['98'])).
1.88/2.06	tff('100', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	         sk_Xy)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xx1)
1.88/2.06	       | ~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X2)),
1.88/2.06	    inference('demod', [status(thm)], ['99', '89'])).
1.88/2.06	tff('101', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b), X2 : a]:
1.88/2.06	      (~ app_encode_app(a, $o, sk_Xp, X2)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xx1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	           sk_Xy)),
1.88/2.06	    inference('simplify', [status(thm)], ['100'])).
1.88/2.06	tff('102', plain,
1.88/2.06	    ![X0 : app_encode_fun(a, b), X1 : a, X2 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
1.88/2.06	             sk_Xx1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X2)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
1.88/2.06	             sk_Xy), X0)),
1.88/2.06	    inference('sup-', [status(thm)], ['101', '15'])).
1.88/2.06	tff('103', plain,
1.88/2.06	    ![X0 : app_encode_fun(a, b), X1 : a, X2 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), sk_Xy), 
1.88/2.06	         X0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X2)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X2), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X1)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
1.88/2.06	             sk_Xx1)),
1.88/2.06	    inference('simplify', [status(thm)], ['102'])).
1.88/2.06	tff('104', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.06	               sk_Xx), sk_Xx)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)),
1.88/2.06	    inference('sup-', [status(thm)], ['13', '103'])).
1.88/2.06	tff('105', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)),
1.88/2.06	    inference('demod', [status(thm)], ['104', '89'])).
1.88/2.06	tff('106', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	           sk_Xy), sk_Xx1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xy1), sk_Xz)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
1.88/2.06	    inference('simplify', [status(thm)], ['105'])).
1.88/2.06	tff('107', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b)]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xy1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	           sk_Xz)),
1.88/2.06	    inference('sup-', [status(thm)], ['106', '1'])).
1.88/2.06	tff('108', plain,
1.88/2.06	    ![X0 : a, X1 : app_encode_fun(a, b)]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	         sk_Xz)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.06	             sk_Xy1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
1.88/2.06	    inference('simplify', [status(thm)], ['107'])).
1.88/2.06	tff('109', plain,
1.88/2.06	    ![X0 : app_encode_fun(a, b), X1 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
1.88/2.06	             sk_Xy1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
1.88/2.06	             sk_Xz), X0)),
1.88/2.06	    inference('sup-', [status(thm)], ['108', '15'])).
1.88/2.06	tff('110', plain,
1.88/2.06	    ![X0 : app_encode_fun(a, b), X1 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), sk_Xz), 
1.88/2.06	         X0)
1.88/2.06	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	             app_encode_app(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	               app_encode_app(a, 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
1.88/2.06	             sk_Xy1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
1.88/2.06	    inference('simplify', [status(thm)], ['109'])).
1.88/2.06	tff('111', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xz), sk_Xx2)),
1.88/2.06	    inference('sup-', [status(thm)], ['96', '110'])).
1.88/2.06	tff('112', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xz), 
1.88/2.06	         sk_Xx2)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
1.88/2.06	    inference('simplify', [status(thm)], ['111'])).
1.88/2.06	tff('113', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (~ $true
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.06	             sk_Xx2), sk_Xz)),
1.88/2.06	    inference('sup-', [status(thm)], ['112', '15'])).
1.88/2.06	tff('114', plain,
1.88/2.06	    ![X0 : a]:
1.88/2.06	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	         app_encode_app(app_encode_fun(a, b), 
1.88/2.06	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	           app_encode_app(a, 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xx2), 
1.88/2.06	         sk_Xz)
1.88/2.06	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.06	           app_encode_app(app_encode_fun(a, b), 
1.88/2.06	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.06	             app_encode_app(a, 
1.88/2.06	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.06	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.06	             sk_Xy), sk_Xx1)
1.88/2.06	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
1.88/2.07	    inference('simplify', [status(thm)], ['113'])).
1.88/2.07	tff('115', plain,
1.88/2.07	    ![X11 : a]:
1.88/2.07	      (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	             sk_Xx), sk_Xx)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X11)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X11), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.07	               sk_Xx2), sk_Xz)),
1.88/2.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.07	tff('116', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (~ $true
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	             sk_Xy), sk_Xx1)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	               sk_Xx), sk_Xx)),
1.88/2.07	    inference('sup-', [status(thm)], ['114', '115'])).
1.88/2.07	tff('117', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (~ $true
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	             sk_Xy), sk_Xx1)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | ~ $true),
1.88/2.07	    inference('demod', [status(thm)], ['116', '89'])).
1.88/2.07	tff('118', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	             sk_Xy), sk_Xx1)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
1.88/2.07	    inference('simplify', [status(thm)], ['117'])).
1.88/2.07	tff('119', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (~ $true
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.07	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	               sk_Xx), sk_Xx)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.07	               sk_Xx2), sk_Xy1)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	               sk_Xx), sk_Xx)),
1.88/2.07	    inference('sup-', [status(thm)], ['3', '115'])).
1.88/2.07	tff('120', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.07	               sk_Xx2), sk_Xy1)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	               sk_Xx), sk_Xx)
1.88/2.07	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.07	    inference('simplify', [status(thm)], ['119'])).
1.88/2.07	tff('121', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.07	               sk_Xx2), sk_Xy1)
1.88/2.07	       | ~ $true
1.88/2.07	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.07	    inference('demod', [status(thm)], ['120', '89'])).
1.88/2.07	tff('122', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.07	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.07	               sk_Xx2), sk_Xy1)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
1.88/2.07	    inference('simplify', [status(thm)], ['121'])).
1.88/2.07	tff('123', plain,
1.88/2.07	    ![X0 : a, X1 : a]:
1.88/2.07	      (~ $true
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X1)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	               sk_Xx), sk_Xx)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.07	    inference('sup-', [status(thm)], ['25', '122'])).
1.88/2.07	tff('124', plain,
1.88/2.07	    ![X0 : a, X1 : a]:
1.88/2.07	      (~ $true
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X1)
1.88/2.07	       | ~ $true
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.07	    inference('demod', [status(thm)], ['123', '89'])).
1.88/2.07	tff('125', plain,
1.88/2.07	    ![X0 : a, X1 : a]:
1.88/2.07	      (app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X1)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.07	    inference('simplify', [status(thm)], ['124'])).
1.88/2.07	tff('126', plain,
1.88/2.07	    ![X0 : a, X1 : a]:
1.88/2.07	      (~ $true
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	               sk_Xx), sk_Xx)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X1)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
1.88/2.07	    inference('sup-', [status(thm)], ['24', '125'])).
1.88/2.07	tff('127', plain,
1.88/2.07	    ![X0 : a, X1 : a]:
1.88/2.07	      (~ $true
1.88/2.07	       | ~ $true
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X1)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
1.88/2.07	    inference('demod', [status(thm)], ['126', '89'])).
1.88/2.07	tff('128', plain,
1.88/2.07	    ![X0 : a, X1 : a]:
1.88/2.07	      (app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X1)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)),
1.88/2.07	    inference('simplify', [status(thm)], ['127'])).
1.88/2.07	tff('129', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (~ $true
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
1.88/2.07	    inference('eq_fact', [status(thm)], ['128'])).
1.88/2.07	tff('130', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)),
1.88/2.07	    inference('simplify', [status(thm)], ['129'])).
1.88/2.07	tff('131', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	             sk_Xy), sk_Xx1)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
1.88/2.07	    inference('clc', [status(thm)], ['118', '130'])).
1.88/2.07	tff('132', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (~ $true
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	               sk_Xx), sk_Xx)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	             sk_Xy), sk_Xx1)),
1.88/2.07	    inference('sup-', [status(thm)], ['24', '131'])).
1.88/2.07	tff('133', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (~ $true
1.88/2.07	       | ~ $true
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	             sk_Xy), sk_Xx1)),
1.88/2.07	    inference('demod', [status(thm)], ['132', '89'])).
1.88/2.07	tff('134', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	         app_encode_app(app_encode_fun(a, b), 
1.88/2.07	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	           app_encode_app(a, 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	           sk_Xy), sk_Xx1)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
1.88/2.07	    inference('simplify', [status(thm)], ['133'])).
1.88/2.07	tff('135', plain,
1.88/2.07	    ![X12 : a]:
1.88/2.07	      (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	             sk_Xx), sk_Xx)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	               sk_Xy), sk_Xx1)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X12), 
1.88/2.07	             sk_Xy1), sk_Xz)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X12)),
1.88/2.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.07	tff('136', plain,
1.88/2.07	    ![X0 : a, X1 : app_encode_fun(a, b)]:
1.88/2.07	      (~ $true
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	               sk_Xy), sk_Xx1)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	               sk_Xx), sk_Xx)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.07	             sk_Xy1)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.07	           sk_Xz)),
1.88/2.07	    inference('sup-', [status(thm)], ['135', '1'])).
1.88/2.07	tff('137', plain,
1.88/2.07	    ![X0 : a, X1 : app_encode_fun(a, b)]:
1.88/2.07	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	         app_encode_app(app_encode_fun(a, b), 
1.88/2.07	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	           app_encode_app(a, 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.07	         sk_Xz)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
1.88/2.07	             sk_Xy1)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	               sk_Xx), sk_Xx)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	               sk_Xy), sk_Xx1)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
1.88/2.07	    inference('simplify', [status(thm)], ['136'])).
1.88/2.07	tff('138', plain,
1.88/2.07	    (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	         app_encode_app(app_encode_fun(a, b), 
1.88/2.07	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	           app_encode_app(a, 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	           sk_Xx), sk_Xx)
1.88/2.07	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	             sk_Xy), sk_Xx1)
1.88/2.07	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.07	             sk_Xx2), sk_Xz)),
1.88/2.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.07	tff('139', plain,
1.88/2.07	    (~ $true
1.88/2.07	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.07	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	             sk_Xy), sk_Xx1)
1.88/2.07	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	             sk_Xx), sk_Xx)
1.88/2.07	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.07	             sk_Xx2), sk_Xy1)
1.88/2.07	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	             sk_Xy), sk_Xx1)
1.88/2.07	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	             sk_Xx), sk_Xx)),
1.88/2.07	    inference('sup-', [status(thm)], ['137', '138'])).
1.88/2.07	tff('140', plain,
1.88/2.07	    (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	         app_encode_app(app_encode_fun(a, b), 
1.88/2.07	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	           app_encode_app(a, 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
1.88/2.07	           sk_Xx2), sk_Xy1)
1.88/2.07	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	             sk_Xx), sk_Xx)
1.88/2.07	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	             sk_Xy), sk_Xx1)
1.88/2.07	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)),
1.88/2.07	    inference('simplify', [status(thm)], ['139'])).
1.88/2.07	tff('141', plain,
1.88/2.07	    ![X13 : a]:
1.88/2.07	      (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	             sk_Xx), sk_Xx)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	               sk_Xy), sk_Xx1)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X13), 
1.88/2.07	             sk_Xx2), sk_Xy1)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X13)),
1.88/2.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.88/2.07	tff('142', plain,
1.88/2.07	    (~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
1.88/2.07	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	             sk_Xy), sk_Xx1)
1.88/2.07	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	             sk_Xx), sk_Xx)),
1.88/2.07	    inference('clc', [status(thm)], ['140', '141'])).
1.88/2.07	tff('143', plain,
1.88/2.07	    (~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	         app_encode_app(app_encode_fun(a, b), 
1.88/2.07	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	           app_encode_app(a, 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	           sk_Xx), sk_Xx)
1.88/2.07	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
1.88/2.07	             sk_Xy), sk_Xx1)),
1.88/2.07	    inference('clc', [status(thm)], ['142', '24'])).
1.88/2.07	tff('144', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (~ $true
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	             app_encode_app(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	               app_encode_app(a, 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	               sk_Xx), sk_Xx)),
1.88/2.07	    inference('sup-', [status(thm)], ['134', '143'])).
1.88/2.07	tff('145', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (~ $true
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xx1), sk_Xy)
1.88/2.07	       | ~ $true),
1.88/2.07	    inference('demod', [status(thm)], ['144', '89'])).
1.88/2.07	tff('146', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	         app_encode_app(app_encode_fun(a, b), 
1.88/2.07	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	           app_encode_app(a, 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xx1), 
1.88/2.07	         sk_Xy)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
1.88/2.07	    inference('simplify', [status(thm)], ['145'])).
1.88/2.07	tff('147', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (~ $true
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)
1.88/2.07	       | app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
1.88/2.07	             sk_Xy), sk_Xx1)),
1.88/2.07	    inference('sup-', [status(thm)], ['146', '15'])).
1.88/2.07	tff('148', plain,
1.88/2.07	    ![X0 : a]:
1.88/2.07	      (app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	         app_encode_app(app_encode_fun(a, b), 
1.88/2.07	           app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	           app_encode_app(a, 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy), 
1.88/2.07	         sk_Xx1)
1.88/2.07	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
1.88/2.07	    inference('simplify', [status(thm)], ['147'])).
1.88/2.07	tff('149', plain,
1.88/2.07	    (~ $true
1.88/2.07	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
1.88/2.07	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	             sk_Xx), sk_Xx)),
1.88/2.07	    inference('sup-', [status(thm)], ['148', '143'])).
1.88/2.07	tff('150', plain,
1.88/2.07	    (~ $true | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01) | ~ $true),
1.88/2.07	    inference('demod', [status(thm)], ['149', '89'])).
1.88/2.07	tff('151', plain, ~ app_encode_app(a, $o, sk_Xp, sk_Xx01),
1.88/2.07	    inference('simplify', [status(thm)], ['150'])).
1.88/2.07	tff('152', plain,
1.88/2.07	    (~ $true
1.88/2.07	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
1.88/2.07	           app_encode_app(app_encode_fun(a, b), 
1.88/2.07	             app_encode_fun(app_encode_fun(a, b), $o), 
1.88/2.07	             app_encode_app(a, 
1.88/2.07	               app_encode_fun(app_encode_fun(a, b), 
1.88/2.07	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
1.88/2.07	             sk_Xx), sk_Xx)),
1.88/2.07	    inference('sup-', [status(thm)], ['10', '151'])).
1.88/2.07	tff('153', plain, (~ $true | ~ $true),
1.88/2.07	    inference('demod', [status(thm)], ['152', '89'])).
1.88/2.07	tff('154', plain, $false, inference('simplify', [status(thm)], ['153'])).
1.88/2.07	
1.88/2.07	% SZS output end Refutation
1.88/2.07	EOF
