0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n162.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:36:54 CST 2018
0.35/0.55	% done 254 iterations in 0.346s
0.35/0.55	% SZS status Theorem for 'stdin'
0.35/0.55	% SZS output start Refutation
0.35/0.56	tff(zf_stmt_4, conjecture,
0.35/0.56	  (![Xp:app_encode_fun(a,$o),
0.35/0.56	     Xe:app_encode_fun(a,
0.35/0.56	                       app_encode_fun(app_encode_fun(a,b),
0.35/0.56	                                      app_encode_fun(app_encode_fun(a,b),$o)))]:
0.35/0.56	     ((![Xx:a]:
0.35/0.56	         (app_encode_app(a,$o,Xp,Xx) =>
0.35/0.56	          ((![Xx0:app_encode_fun(a,b)]:
0.35/0.56	              app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                             app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                            app_encode_fun(app_encode_fun(
0.35/0.56	                                                           a,b),$o),
0.35/0.56	                                            app_encode_app(a,
0.35/0.56	                                                           app_encode_fun(
0.35/0.56	                                                           app_encode_fun(
0.35/0.56	                                                           a,b),
0.35/0.56	                                                           app_encode_fun(
0.35/0.56	                                                           app_encode_fun(
0.35/0.56	                                                           a,b),$o)),Xe,Xx),
0.35/0.56	                                            Xx0),
0.35/0.56	                             Xx0)) & 
0.35/0.56	           (![Xx0:app_encode_fun(a,b),Xy:app_encode_fun(a,b)]:
0.35/0.56	              (app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                              app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                             app_encode_fun(app_encode_fun(
0.35/0.56	                                                            a,b),$o),
0.35/0.56	                                             app_encode_app(a,
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            a,b),
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            a,b),$o)),Xe,Xx),
0.35/0.56	                                             Xx0),
0.35/0.56	                              Xy) =>
0.35/0.56	               app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                              app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                             app_encode_fun(app_encode_fun(
0.35/0.56	                                                            a,b),$o),
0.35/0.56	                                             app_encode_app(a,
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            a,b),
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            a,b),$o)),Xe,Xx),
0.35/0.56	                                             Xy),
0.35/0.56	                              Xx0))) & 
0.35/0.56	           (![Xx0:app_encode_fun(a,b),Xy:app_encode_fun(a,b),
0.35/0.56	              Xz:app_encode_fun(a,b)]:
0.35/0.56	              ((app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                               app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                              app_encode_fun(app_encode_fun(
0.35/0.56	                                                             a,b),$o),
0.35/0.56	                                              app_encode_app(a,
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             a,b),
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             a,b),$o)),Xe,Xx),
0.35/0.56	                                              Xx0),
0.35/0.56	                               Xy) & 
0.35/0.56	                app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                               app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                              app_encode_fun(app_encode_fun(
0.35/0.56	                                                             a,b),$o),
0.35/0.56	                                              app_encode_app(a,
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             a,b),
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             a,b),$o)),Xe,Xx),
0.35/0.56	                                              Xy),
0.35/0.56	                               Xz)) =>
0.35/0.56	               app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                              app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                             app_encode_fun(app_encode_fun(
0.35/0.56	                                                            a,b),$o),
0.35/0.56	                                             app_encode_app(a,
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            a,b),
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            a,b),$o)),Xe,Xx),
0.35/0.56	                                             Xx0),
0.35/0.56	                              Xz)))))) =>
0.35/0.56	      ((![Xx:app_encode_fun(a,b),Xx0:a]:
0.35/0.56	          (app_encode_app(a,$o,Xp,Xx0) =>
0.35/0.56	           app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                          app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                         app_encode_fun(app_encode_fun(a,b),
0.35/0.56	                                                        $o),
0.35/0.56	                                         app_encode_app(a,
0.35/0.56	                                                        app_encode_fun(
0.35/0.56	                                                        app_encode_fun(a,b),
0.35/0.56	                                                        app_encode_fun(
0.35/0.56	                                                        app_encode_fun(a,b),
0.35/0.56	                                                        $o)),Xe,Xx0),
0.35/0.56	                                         Xx),
0.35/0.56	                          Xx))) & 
0.35/0.56	       (![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b)]:
0.35/0.56	          ((![Xx0:a]:
0.35/0.56	              (app_encode_app(a,$o,Xp,Xx0) =>
0.35/0.56	               app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                              app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                             app_encode_fun(app_encode_fun(
0.35/0.56	                                                            a,b),$o),
0.35/0.56	                                             app_encode_app(a,
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            a,b),
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            a,b),$o)),Xe,Xx0),
0.35/0.56	                                             Xx),
0.35/0.56	                              Xy))) =>
0.35/0.56	           (![Xx0:a]:
0.35/0.56	              (app_encode_app(a,$o,Xp,Xx0) =>
0.35/0.56	               app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                              app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                             app_encode_fun(app_encode_fun(
0.35/0.56	                                                            a,b),$o),
0.35/0.56	                                             app_encode_app(a,
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            a,b),
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            a,b),$o)),Xe,Xx0),
0.35/0.56	                                             Xy),
0.35/0.56	                              Xx))))) & 
0.35/0.56	       (![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b),
0.35/0.56	          Xz:app_encode_fun(a,b)]:
0.35/0.56	          (((![Xx0:a]:
0.35/0.56	               (app_encode_app(a,$o,Xp,Xx0) =>
0.35/0.56	                app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                               app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                              app_encode_fun(app_encode_fun(
0.35/0.56	                                                             a,b),$o),
0.35/0.56	                                              app_encode_app(a,
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             a,b),
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             a,b),$o)),Xe,Xx0),
0.35/0.56	                                              Xx),
0.35/0.56	                               Xy))) & 
0.35/0.56	            (![Xx0:a]:
0.35/0.56	               (app_encode_app(a,$o,Xp,Xx0) =>
0.35/0.56	                app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                               app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                              app_encode_fun(app_encode_fun(
0.35/0.56	                                                             a,b),$o),
0.35/0.56	                                              app_encode_app(a,
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             a,b),
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             a,b),$o)),Xe,Xx0),
0.35/0.56	                                              Xy),
0.35/0.56	                               Xz)))) =>
0.35/0.56	           (![Xx0:a]:
0.35/0.56	              (app_encode_app(a,$o,Xp,Xx0) =>
0.35/0.56	               app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                              app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                             app_encode_fun(app_encode_fun(
0.35/0.56	                                                            a,b),$o),
0.35/0.56	                                             app_encode_app(a,
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            a,b),
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            app_encode_fun(
0.35/0.56	                                                            a,b),$o)),Xe,Xx0),
0.35/0.56	                                             Xx),
0.35/0.56	                              Xz))))))))).
0.35/0.56	tff(zf_stmt_0, negated_conjecture,
0.35/0.56	  (~
0.35/0.56	    (![Xp:app_encode_fun(a,$o),
0.35/0.56	       Xe:app_encode_fun(a,
0.35/0.56	                         app_encode_fun(app_encode_fun(a,b),
0.35/0.56	                                        app_encode_fun(app_encode_fun(a,b),$o)))]:
0.35/0.56	       ((![Xx:a]:
0.35/0.56	           (app_encode_app(a,$o,Xp,Xx) =>
0.35/0.56	            ((![Xx0:app_encode_fun(a,b)]:
0.35/0.56	                app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                               app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                              app_encode_fun(app_encode_fun(
0.35/0.56	                                                             a,b),$o),
0.35/0.56	                                              app_encode_app(a,
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             a,b),
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             app_encode_fun(
0.35/0.56	                                                             a,b),$o)),Xe,Xx),
0.35/0.56	                                              Xx0),
0.35/0.56	                               Xx0)) & 
0.35/0.56	             (![Xx0:app_encode_fun(a,b),Xy:app_encode_fun(a,b)]:
0.35/0.56	                (app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                                app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                               app_encode_fun(app_encode_fun(
0.35/0.56	                                                              a,b),$o),
0.35/0.56	                                               app_encode_app(a,
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              a,b),
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              a,b),$o)),Xe,Xx),
0.35/0.56	                                               Xx0),
0.35/0.56	                                Xy) =>
0.35/0.56	                 app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                                app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                               app_encode_fun(app_encode_fun(
0.35/0.56	                                                              a,b),$o),
0.35/0.56	                                               app_encode_app(a,
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              a,b),
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              a,b),$o)),Xe,Xx),
0.35/0.56	                                               Xy),
0.35/0.56	                                Xx0))) & 
0.35/0.56	             (![Xx0:app_encode_fun(a,b),Xy:app_encode_fun(a,b),
0.35/0.56	                Xz:app_encode_fun(a,b)]:
0.35/0.56	                ((app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                                 app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                                app_encode_fun(app_encode_fun(
0.35/0.56	                                                               a,b),$o),
0.35/0.56	                                                app_encode_app(a,
0.35/0.56	                                                               app_encode_fun(
0.35/0.56	                                                               app_encode_fun(
0.35/0.56	                                                               a,b),
0.35/0.56	                                                               app_encode_fun(
0.35/0.56	                                                               app_encode_fun(
0.35/0.56	                                                               a,b),$o)),Xe,
0.35/0.56	                                                               Xx),
0.35/0.56	                                                Xx0),
0.35/0.56	                                 Xy) & 
0.35/0.56	                  app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                                 app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                                app_encode_fun(app_encode_fun(
0.35/0.56	                                                               a,b),$o),
0.35/0.56	                                                app_encode_app(a,
0.35/0.56	                                                               app_encode_fun(
0.35/0.56	                                                               app_encode_fun(
0.35/0.56	                                                               a,b),
0.35/0.56	                                                               app_encode_fun(
0.35/0.56	                                                               app_encode_fun(
0.35/0.56	                                                               a,b),$o)),Xe,
0.35/0.56	                                                               Xx),
0.35/0.56	                                                Xy),
0.35/0.56	                                 Xz)) =>
0.35/0.56	                 app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                                app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                               app_encode_fun(app_encode_fun(
0.35/0.56	                                                              a,b),$o),
0.35/0.56	                                               app_encode_app(a,
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              a,b),
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              a,b),$o)),Xe,Xx),
0.35/0.56	                                               Xx0),
0.35/0.56	                                Xz)))))) =>
0.35/0.56	        ((![Xx:app_encode_fun(a,b),Xx0:a]:
0.35/0.56	            (app_encode_app(a,$o,Xp,Xx0) =>
0.35/0.56	             app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                            app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                           app_encode_fun(app_encode_fun(a,b),
0.35/0.56	                                                          $o),
0.35/0.56	                                           app_encode_app(a,
0.35/0.56	                                                          app_encode_fun(
0.35/0.56	                                                          app_encode_fun(a,b),
0.35/0.56	                                                          app_encode_fun(
0.35/0.56	                                                          app_encode_fun(a,b),
0.35/0.56	                                                          $o)),Xe,Xx0),
0.35/0.56	                                           Xx),
0.35/0.56	                            Xx))) & 
0.35/0.56	         (![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b)]:
0.35/0.56	            ((![Xx0:a]:
0.35/0.56	                (app_encode_app(a,$o,Xp,Xx0) =>
0.35/0.56	                 app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                                app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                               app_encode_fun(app_encode_fun(
0.35/0.56	                                                              a,b),$o),
0.35/0.56	                                               app_encode_app(a,
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              a,b),
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              a,b),$o)),Xe,
0.35/0.56	                                                              Xx0),
0.35/0.56	                                               Xx),
0.35/0.56	                                Xy))) =>
0.35/0.56	             (![Xx0:a]:
0.35/0.56	                (app_encode_app(a,$o,Xp,Xx0) =>
0.35/0.56	                 app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                                app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                               app_encode_fun(app_encode_fun(
0.35/0.56	                                                              a,b),$o),
0.35/0.56	                                               app_encode_app(a,
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              a,b),
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              a,b),$o)),Xe,
0.35/0.56	                                                              Xx0),
0.35/0.56	                                               Xy),
0.35/0.56	                                Xx))))) & 
0.35/0.56	         (![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b),
0.35/0.56	            Xz:app_encode_fun(a,b)]:
0.35/0.56	            (((![Xx0:a]:
0.35/0.56	                 (app_encode_app(a,$o,Xp,Xx0) =>
0.35/0.56	                  app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                                 app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                                app_encode_fun(app_encode_fun(
0.35/0.56	                                                               a,b),$o),
0.35/0.56	                                                app_encode_app(a,
0.35/0.56	                                                               app_encode_fun(
0.35/0.56	                                                               app_encode_fun(
0.35/0.56	                                                               a,b),
0.35/0.56	                                                               app_encode_fun(
0.35/0.56	                                                               app_encode_fun(
0.35/0.56	                                                               a,b),$o)),Xe,
0.35/0.56	                                                               Xx0),
0.35/0.56	                                                Xx),
0.35/0.56	                                 Xy))) & 
0.35/0.56	              (![Xx0:a]:
0.35/0.56	                 (app_encode_app(a,$o,Xp,Xx0) =>
0.35/0.56	                  app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                                 app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                                app_encode_fun(app_encode_fun(
0.35/0.56	                                                               a,b),$o),
0.35/0.56	                                                app_encode_app(a,
0.35/0.56	                                                               app_encode_fun(
0.35/0.56	                                                               app_encode_fun(
0.35/0.56	                                                               a,b),
0.35/0.56	                                                               app_encode_fun(
0.35/0.56	                                                               app_encode_fun(
0.35/0.56	                                                               a,b),$o)),Xe,
0.35/0.56	                                                               Xx0),
0.35/0.56	                                                Xy),
0.35/0.56	                                 Xz)))) =>
0.35/0.56	             (![Xx0:a]:
0.35/0.56	                (app_encode_app(a,$o,Xp,Xx0) =>
0.35/0.56	                 app_encode_app(app_encode_fun(a,b),$o,
0.35/0.56	                                app_encode_app(app_encode_fun(a,b),
0.35/0.56	                                               app_encode_fun(app_encode_fun(
0.35/0.56	                                                              a,b),$o),
0.35/0.56	                                               app_encode_app(a,
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              a,b),
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              app_encode_fun(
0.35/0.56	                                                              a,b),$o)),Xe,
0.35/0.56	                                                              Xx0),
0.35/0.56	                                               Xx),
0.35/0.56	                                Xz)))))))))).
0.35/0.56	tff('0', plain,
0.35/0.56	    ![X0 : a, X1 : app_encode_fun(a, b)]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
0.35/0.56	         X1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('1', plain,
0.35/0.56	    ![X7 : a, X9 : a]:
0.35/0.56	      (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X7)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X7), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X9), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X9)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('2', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)),
0.35/0.56	    inference('sup-', [status(thm)], ['0', '1'])).
0.35/0.56	tff('3', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('simplify', [status(thm)], ['2'])).
0.35/0.56	tff('4', plain,
0.35/0.56	    ![X7 : a, X9 : a]:
0.35/0.56	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X7)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X7), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X9), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X9)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('5', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)),
0.35/0.56	    inference('clc', [status(thm)], ['3', '4'])).
0.35/0.56	tff('6', plain,
0.35/0.56	    ![X0 : a, X2 : app_encode_fun(a, b), X3 : app_encode_fun(a, b)]:
0.35/0.56	      (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X2), 
0.35/0.56	           X3)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X3), 
0.35/0.56	           X2)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('7', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy), sk_Xx1)),
0.35/0.56	    inference('sup-', [status(thm)], ['5', '6'])).
0.35/0.56	tff('8', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy), 
0.35/0.56	         sk_Xx1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('simplify', [status(thm)], ['7'])).
0.35/0.56	tff('9', plain,
0.35/0.56	    ![X9 : a]:
0.35/0.56	      (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.56	               sk_Xy), sk_Xx1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X9), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X9)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('10', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	               sk_Xx), sk_Xx)),
0.35/0.56	    inference('sup-', [status(thm)], ['8', '9'])).
0.35/0.56	tff('11', plain,
0.35/0.56	    ![X9 : a]:
0.35/0.56	      (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X9), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X9)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('12', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
0.35/0.56	    inference('sup-', [status(thm)], ['0', '11'])).
0.35/0.56	tff('13', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('simplify', [status(thm)], ['12'])).
0.35/0.56	tff('14', plain,
0.35/0.56	    ![X9 : a]:
0.35/0.56	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X9), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X9)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('15', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
0.35/0.56	    inference('clc', [status(thm)], ['13', '14'])).
0.35/0.56	tff('16', plain,
0.35/0.56	    ![X8 : a]:
0.35/0.56	      (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X8), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X8)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('17', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
0.35/0.56	    inference('sup-', [status(thm)], ['0', '16'])).
0.35/0.56	tff('18', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('simplify', [status(thm)], ['17'])).
0.35/0.56	tff('19', plain,
0.35/0.56	    ![X8 : a]:
0.35/0.56	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X8), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X8)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('20', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
0.35/0.56	    inference('clc', [status(thm)], ['18', '19'])).
0.35/0.56	tff('21', plain,
0.35/0.56	    ![X0 : a, X4 : app_encode_fun(a, b), X5 : app_encode_fun(a, b), 
0.35/0.56	      X6 : app_encode_fun(a, b)]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X4), 
0.35/0.56	         X5)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X6), 
0.35/0.56	             X5)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X4), 
0.35/0.56	             X6)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('22', plain,
0.35/0.56	    ![X0 : a, X1 : app_encode_fun(a, b)]:
0.35/0.56	      (~ $true
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
0.35/0.56	             sk_Xy1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
0.35/0.56	           sk_Xz)),
0.35/0.56	    inference('sup-', [status(thm)], ['20', '21'])).
0.35/0.56	tff('23', plain,
0.35/0.56	    ![X0 : a, X1 : app_encode_fun(a, b)]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
0.35/0.56	         sk_Xz)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
0.35/0.56	             sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
0.35/0.56	    inference('simplify', [status(thm)], ['22'])).
0.35/0.56	tff('24', plain,
0.35/0.56	    (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	           sk_Xx), sk_Xx)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
0.35/0.56	             sk_Xx2), sk_Xz)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('25', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)),
0.35/0.56	    inference('sup-', [status(thm)], ['23', '24'])).
0.35/0.56	tff('26', plain,
0.35/0.56	    ![X7 : a]:
0.35/0.56	      (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X7)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X7), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('27', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('sup-', [status(thm)], ['0', '26'])).
0.35/0.56	tff('28', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('simplify', [status(thm)], ['27'])).
0.35/0.56	tff('29', plain,
0.35/0.56	    ![X7 : a]:
0.35/0.56	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X7)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X7), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('30', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy), sk_Xx1)),
0.35/0.56	    inference('sup-', [status(thm)], ['29', '6'])).
0.35/0.56	tff('31', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy), 
0.35/0.56	         sk_Xx1)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
0.35/0.56	    inference('simplify', [status(thm)], ['30'])).
0.35/0.56	tff('32', plain,
0.35/0.56	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.56	             sk_Xy), sk_Xx1)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('33', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('sup-', [status(thm)], ['31', '32'])).
0.35/0.56	tff('34', plain,
0.35/0.56	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
0.35/0.56	    inference('simplify', [status(thm)], ['33'])).
0.35/0.56	tff('35', plain,
0.35/0.56	    (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	           sk_Xx), sk_Xx)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('36', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
0.35/0.56	    inference('sup-', [status(thm)], ['0', '35'])).
0.35/0.56	tff('37', plain,
0.35/0.56	    (app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('simplify', [status(thm)], ['36'])).
0.35/0.56	tff('38', plain,
0.35/0.56	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('39', plain,
0.35/0.56	    (app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
0.35/0.56	    inference('clc', [status(thm)], ['37', '38'])).
0.35/0.56	tff('40', plain,
0.35/0.56	    (app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('clc', [status(thm)], ['34', '39'])).
0.35/0.56	tff('41', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('clc', [status(thm)], ['28', '40'])).
0.35/0.56	tff('42', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy), sk_Xx1)),
0.35/0.56	    inference('sup-', [status(thm)], ['41', '6'])).
0.35/0.56	tff('43', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy), 
0.35/0.56	         sk_Xx1)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('simplify', [status(thm)], ['42'])).
0.35/0.56	tff('44', plain,
0.35/0.56	    (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	           sk_Xx), sk_Xx)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.56	             sk_Xy), sk_Xx1)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('45', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)),
0.35/0.56	    inference('sup-', [status(thm)], ['43', '44'])).
0.35/0.56	tff('46', plain,
0.35/0.56	    (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	           sk_Xx), sk_Xx)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)),
0.35/0.56	    inference('simplify', [status(thm)], ['45'])).
0.35/0.56	tff('47', plain,
0.35/0.56	    (app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)),
0.35/0.56	    inference('clc', [status(thm)], ['46', '39'])).
0.35/0.56	tff('48', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx02)),
0.35/0.56	    inference('sup-', [status(thm)], ['0', '47'])).
0.35/0.56	tff('49', plain,
0.35/0.56	    (app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('simplify', [status(thm)], ['48'])).
0.35/0.56	tff('50', plain, app_encode_app(a, $o, sk_Xp, sk_Xx02),
0.35/0.56	    inference('clc', [status(thm)], ['49', '40'])).
0.35/0.56	tff('51', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | ~ $true
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)),
0.35/0.56	    inference('demod', [status(thm)], ['25', '50'])).
0.35/0.56	tff('52', plain,
0.35/0.56	    (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	           sk_Xx), sk_Xx)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
0.35/0.56	    inference('simplify', [status(thm)], ['51'])).
0.35/0.56	tff('53', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)),
0.35/0.56	    inference('sup-', [status(thm)], ['15', '52'])).
0.35/0.56	tff('54', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | ~ $true
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)),
0.35/0.56	    inference('demod', [status(thm)], ['53', '50'])).
0.35/0.56	tff('55', plain,
0.35/0.56	    (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	           sk_Xx), sk_Xx)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
0.35/0.56	    inference('simplify', [status(thm)], ['54'])).
0.35/0.56	tff('56', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
0.35/0.56	    inference('sup-', [status(thm)], ['0', '55'])).
0.35/0.56	tff('57', plain,
0.35/0.56	    (app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('simplify', [status(thm)], ['56'])).
0.35/0.56	tff('58', plain,
0.35/0.56	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
0.35/0.56	             sk_Xx2), sk_Xz)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('59', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('sup-', [status(thm)], ['23', '58'])).
0.35/0.56	tff('60', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | ~ $true
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('demod', [status(thm)], ['59', '50'])).
0.35/0.56	tff('61', plain,
0.35/0.56	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
0.35/0.56	    inference('simplify', [status(thm)], ['60'])).
0.35/0.56	tff('62', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('sup-', [status(thm)], ['15', '61'])).
0.35/0.56	tff('63', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | ~ $true
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('demod', [status(thm)], ['62', '50'])).
0.35/0.56	tff('64', plain,
0.35/0.56	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx01)),
0.35/0.56	    inference('simplify', [status(thm)], ['63'])).
0.35/0.56	tff('65', plain, app_encode_app(a, $o, sk_Xp, sk_Xx01),
0.35/0.56	    inference('clc', [status(thm)], ['57', '64'])).
0.35/0.56	tff('66', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ $true
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	               sk_Xx), sk_Xx)),
0.35/0.56	    inference('demod', [status(thm)], ['10', '65'])).
0.35/0.56	tff('67', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xx2), sk_Xy1)),
0.35/0.56	    inference('simplify', [status(thm)], ['66'])).
0.35/0.56	tff('68', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xx2), sk_Xy1)),
0.35/0.56	    inference('sup-', [status(thm)], ['0', '67'])).
0.35/0.56	tff('69', plain,
0.35/0.56	    ![X9 : a]:
0.35/0.56	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.56	               sk_Xy), sk_Xx1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X9), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X9)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('70', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('sup-', [status(thm)], ['8', '69'])).
0.35/0.56	tff('71', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ $true
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('demod', [status(thm)], ['70', '65'])).
0.35/0.56	tff('72', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xx2), sk_Xy1)),
0.35/0.56	    inference('simplify', [status(thm)], ['71'])).
0.35/0.56	tff('73', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('eq_fact', [status(thm)], ['72'])).
0.35/0.56	tff('74', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)),
0.35/0.56	    inference('simplify', [status(thm)], ['73'])).
0.35/0.56	tff('75', plain,
0.35/0.56	    ![X7 : a, X8 : a]:
0.35/0.56	      (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X7)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X7), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X8), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X8)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('76', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)),
0.35/0.56	    inference('sup-', [status(thm)], ['0', '75'])).
0.35/0.56	tff('77', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('simplify', [status(thm)], ['76'])).
0.35/0.56	tff('78', plain,
0.35/0.56	    ![X7 : a, X8 : a]:
0.35/0.56	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X7)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X7), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X8), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X8)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('79', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)),
0.35/0.56	    inference('clc', [status(thm)], ['77', '78'])).
0.35/0.56	tff('80', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy), sk_Xx1)),
0.35/0.56	    inference('sup-', [status(thm)], ['79', '6'])).
0.35/0.56	tff('81', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy), 
0.35/0.56	         sk_Xx1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('simplify', [status(thm)], ['80'])).
0.35/0.56	tff('82', plain,
0.35/0.56	    ![X8 : a]:
0.35/0.56	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.56	               sk_Xy), sk_Xx1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X8), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X8)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('83', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('sup-', [status(thm)], ['81', '82'])).
0.35/0.56	tff('84', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ $true
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('demod', [status(thm)], ['83', '65'])).
0.35/0.56	tff('85', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xy1), sk_Xz)),
0.35/0.56	    inference('simplify', [status(thm)], ['84'])).
0.35/0.56	tff('86', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('eq_fact', [status(thm)], ['85'])).
0.35/0.56	tff('87', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)),
0.35/0.56	    inference('simplify', [status(thm)], ['86'])).
0.35/0.56	tff('88', plain,
0.35/0.56	    ![X0 : a, X1 : app_encode_fun(a, b)]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
0.35/0.56	             sk_Xy1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
0.35/0.56	           sk_Xz)),
0.35/0.56	    inference('sup-', [status(thm)], ['87', '21'])).
0.35/0.56	tff('89', plain,
0.35/0.56	    ![X0 : a, X1 : app_encode_fun(a, b)]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
0.35/0.56	         sk_Xz)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
0.35/0.56	             sk_Xy1)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('simplify', [status(thm)], ['88'])).
0.35/0.56	tff('90', plain,
0.35/0.56	    ![X0 : app_encode_fun(a, b), X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
0.35/0.56	             sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xz), X0)),
0.35/0.56	    inference('sup-', [status(thm)], ['89', '6'])).
0.35/0.56	tff('91', plain,
0.35/0.56	    ![X0 : app_encode_fun(a, b), X1 : a]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), sk_Xz), 
0.35/0.56	         X0)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
0.35/0.56	             sk_Xy1)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)),
0.35/0.56	    inference('simplify', [status(thm)], ['90'])).
0.35/0.56	tff('92', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xz), sk_Xx2)),
0.35/0.56	    inference('sup-', [status(thm)], ['74', '91'])).
0.35/0.56	tff('93', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xz), 
0.35/0.56	         sk_Xx2)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('simplify', [status(thm)], ['92'])).
0.35/0.56	tff('94', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xz)),
0.35/0.56	    inference('sup-', [status(thm)], ['93', '6'])).
0.35/0.56	tff('95', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xx2), 
0.35/0.56	         sk_Xz)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('simplify', [status(thm)], ['94'])).
0.35/0.56	tff('96', plain,
0.35/0.56	    ![X7 : a]:
0.35/0.56	      (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X7)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X7), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
0.35/0.56	               sk_Xx2), sk_Xz)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('97', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('sup-', [status(thm)], ['95', '96'])).
0.35/0.56	tff('98', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ $true
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('demod', [status(thm)], ['97', '50'])).
0.35/0.56	tff('99', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('simplify', [status(thm)], ['98'])).
0.35/0.56	tff('100', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy), sk_Xx1)),
0.35/0.56	    inference('sup-', [status(thm)], ['99', '6'])).
0.35/0.56	tff('101', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy), 
0.35/0.56	         sk_Xx1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('simplify', [status(thm)], ['100'])).
0.35/0.56	tff('102', plain,
0.35/0.56	    (app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.56	             sk_Xy), sk_Xx1)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
0.35/0.56	             sk_Xx2), sk_Xz)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('103', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.56	             sk_Xy), sk_Xx1)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('sup-', [status(thm)], ['89', '102'])).
0.35/0.56	tff('104', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | ~ $true
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.56	             sk_Xy), sk_Xx1)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('demod', [status(thm)], ['103', '50'])).
0.35/0.56	tff('105', plain,
0.35/0.56	    (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.56	           sk_Xy), sk_Xx1)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('simplify', [status(thm)], ['104'])).
0.35/0.56	tff('106', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.56	             sk_Xy), sk_Xx1)),
0.35/0.56	    inference('sup-', [status(thm)], ['74', '105'])).
0.35/0.56	tff('107', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | ~ $true
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.56	             sk_Xy), sk_Xx1)),
0.35/0.56	    inference('demod', [status(thm)], ['106', '50'])).
0.35/0.56	tff('108', plain,
0.35/0.56	    (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.56	           sk_Xy), sk_Xx1)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('simplify', [status(thm)], ['107'])).
0.35/0.56	tff('109', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('sup-', [status(thm)], ['101', '108'])).
0.35/0.56	tff('110', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	     | ~ $true
0.35/0.56	     | app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.56	    inference('demod', [status(thm)], ['109', '65'])).
0.35/0.56	tff('111', plain, app_encode_app(a, $o, sk_Xp, sk_Xx0),
0.35/0.56	    inference('simplify', [status(thm)], ['110'])).
0.35/0.56	tff('112', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ $true
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xx2), sk_Xy1)),
0.35/0.56	    inference('demod', [status(thm)], ['68', '111'])).
0.35/0.56	tff('113', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), sk_Xx2), 
0.35/0.56	         sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)),
0.35/0.56	    inference('simplify', [status(thm)], ['112'])).
0.35/0.56	tff('114', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('eq_fact', [status(thm)], ['113'])).
0.35/0.56	tff('115', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xy1)),
0.35/0.56	    inference('simplify', [status(thm)], ['114'])).
0.35/0.56	tff('116', plain,
0.35/0.56	    ![X8 : a]:
0.35/0.56	      (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.56	               sk_Xy), sk_Xx1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X8), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X8)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('117', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	               sk_Xx), sk_Xx)),
0.35/0.56	    inference('sup-', [status(thm)], ['81', '116'])).
0.35/0.56	tff('118', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ $true
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	               sk_Xx), sk_Xx)),
0.35/0.56	    inference('demod', [status(thm)], ['117', '65'])).
0.35/0.56	tff('119', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xy1), sk_Xz)),
0.35/0.56	    inference('simplify', [status(thm)], ['118'])).
0.35/0.56	tff('120', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xy1), sk_Xz)),
0.35/0.56	    inference('sup-', [status(thm)], ['0', '119'])).
0.35/0.56	tff('121', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ $true
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xy1), sk_Xz)),
0.35/0.56	    inference('demod', [status(thm)], ['120', '111'])).
0.35/0.56	tff('122', plain,
0.35/0.56	    ![X0 : a, X1 : a]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), sk_Xy1), 
0.35/0.56	         sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)),
0.35/0.56	    inference('simplify', [status(thm)], ['121'])).
0.35/0.56	tff('123', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('eq_fact', [status(thm)], ['122'])).
0.35/0.56	tff('124', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy1), sk_Xz)),
0.35/0.56	    inference('simplify', [status(thm)], ['123'])).
0.35/0.56	tff('125', plain,
0.35/0.56	    ![X0 : a, X1 : app_encode_fun(a, b)]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
0.35/0.56	             sk_Xy1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
0.35/0.56	           sk_Xz)),
0.35/0.56	    inference('sup-', [status(thm)], ['124', '21'])).
0.35/0.56	tff('126', plain,
0.35/0.56	    ![X0 : a, X1 : app_encode_fun(a, b)]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
0.35/0.56	         sk_Xz)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), X1), 
0.35/0.56	             sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('simplify', [status(thm)], ['125'])).
0.35/0.56	tff('127', plain,
0.35/0.56	    ![X0 : app_encode_fun(a, b), X1 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
0.35/0.56	             sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), 
0.35/0.56	             sk_Xz), X0)),
0.35/0.56	    inference('sup-', [status(thm)], ['126', '6'])).
0.35/0.56	tff('128', plain,
0.35/0.56	    ![X0 : app_encode_fun(a, b), X1 : a]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), sk_Xz), 
0.35/0.56	         X0)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X1), X0), 
0.35/0.56	             sk_Xy1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X1)),
0.35/0.56	    inference('simplify', [status(thm)], ['127'])).
0.35/0.56	tff('129', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xz), sk_Xx2)),
0.35/0.56	    inference('sup-', [status(thm)], ['115', '128'])).
0.35/0.56	tff('130', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xz), 
0.35/0.56	         sk_Xx2)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('simplify', [status(thm)], ['129'])).
0.35/0.56	tff('131', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx2), sk_Xz)),
0.35/0.56	    inference('sup-', [status(thm)], ['130', '6'])).
0.35/0.56	tff('132', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xx2), 
0.35/0.56	         sk_Xz)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('simplify', [status(thm)], ['131'])).
0.35/0.56	tff('133', plain,
0.35/0.56	    ![X7 : a]:
0.35/0.56	      (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X7)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X7), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
0.35/0.56	               sk_Xx2), sk_Xz)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('134', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	               sk_Xx), sk_Xx)),
0.35/0.56	    inference('sup-', [status(thm)], ['132', '133'])).
0.35/0.56	tff('135', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ $true
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	             app_encode_app(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	               app_encode_app(a, 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                   app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	               sk_Xx), sk_Xx)),
0.35/0.56	    inference('demod', [status(thm)], ['134', '50'])).
0.35/0.56	tff('136', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx1), sk_Xy)),
0.35/0.56	    inference('simplify', [status(thm)], ['135'])).
0.35/0.56	tff('137', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('sup-', [status(thm)], ['0', '136'])).
0.35/0.56	tff('138', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ $true
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx1), sk_Xy)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('demod', [status(thm)], ['137', '111'])).
0.35/0.56	tff('139', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xx1), sk_Xy)),
0.35/0.56	    inference('simplify', [status(thm)], ['138'])).
0.35/0.56	tff('140', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (~ $true
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)
0.35/0.56	       | app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), 
0.35/0.56	             sk_Xy), sk_Xx1)),
0.35/0.56	    inference('sup-', [status(thm)], ['139', '6'])).
0.35/0.56	tff('141', plain,
0.35/0.56	    ![X0 : a]:
0.35/0.56	      (app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, X0), sk_Xy), 
0.35/0.56	         sk_Xx1)
0.35/0.56	       | ~ app_encode_app(a, $o, sk_Xp, X0)),
0.35/0.56	    inference('simplify', [status(thm)], ['140'])).
0.35/0.56	tff('142', plain,
0.35/0.56	    (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	           sk_Xx), sk_Xx)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.56	             sk_Xy), sk_Xx1)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx02), 
0.35/0.56	             sk_Xx2), sk_Xz)),
0.35/0.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.35/0.56	tff('143', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx02)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.56	             sk_Xy), sk_Xx1)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)),
0.35/0.56	    inference('sup-', [status(thm)], ['132', '142'])).
0.35/0.56	tff('144', plain,
0.35/0.56	    (~ $true
0.35/0.56	     | ~ $true
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.56	             sk_Xy), sk_Xx1)
0.35/0.56	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	           app_encode_app(app_encode_fun(a, b), 
0.35/0.56	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	             app_encode_app(a, 
0.35/0.56	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.56	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.56	             sk_Xx), sk_Xx)),
0.35/0.56	    inference('demod', [status(thm)], ['143', '50'])).
0.35/0.56	tff('145', plain,
0.35/0.56	    (~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.56	         app_encode_app(app_encode_fun(a, b), 
0.35/0.56	           app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.56	           app_encode_app(a, 
0.35/0.57	             app_encode_fun(app_encode_fun(a, b), 
0.35/0.57	               app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.57	           sk_Xx), sk_Xx)
0.35/0.57	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.57	           app_encode_app(app_encode_fun(a, b), 
0.35/0.57	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.57	             app_encode_app(a, 
0.35/0.57	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.57	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx01), 
0.35/0.57	             sk_Xy), sk_Xx1)),
0.35/0.57	    inference('simplify', [status(thm)], ['144'])).
0.35/0.57	tff('146', plain,
0.35/0.57	    (~ $true
0.35/0.57	     | ~ app_encode_app(a, $o, sk_Xp, sk_Xx01)
0.35/0.57	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.57	           app_encode_app(app_encode_fun(a, b), 
0.35/0.57	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.57	             app_encode_app(a, 
0.35/0.57	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.57	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.57	             sk_Xx), sk_Xx)),
0.35/0.57	    inference('sup-', [status(thm)], ['141', '145'])).
0.35/0.57	tff('147', plain,
0.35/0.57	    (~ $true
0.35/0.57	     | ~ $true
0.35/0.57	     | ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.57	           app_encode_app(app_encode_fun(a, b), 
0.35/0.57	             app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.57	             app_encode_app(a, 
0.35/0.57	               app_encode_fun(app_encode_fun(a, b), 
0.35/0.57	                 app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.57	             sk_Xx), sk_Xx)),
0.35/0.57	    inference('demod', [status(thm)], ['146', '65'])).
0.35/0.57	tff('148', plain,
0.35/0.57	    ~ app_encode_app(app_encode_fun(a, b), $o, 
0.35/0.57	        app_encode_app(app_encode_fun(a, b), 
0.35/0.57	          app_encode_fun(app_encode_fun(a, b), $o), 
0.35/0.57	          app_encode_app(a, 
0.35/0.57	            app_encode_fun(app_encode_fun(a, b), 
0.35/0.57	              app_encode_fun(app_encode_fun(a, b), $o)), sk_Xe, sk_Xx0), 
0.35/0.57	          sk_Xx), sk_Xx),
0.35/0.57	    inference('simplify', [status(thm)], ['147'])).
0.35/0.57	tff('149', plain, (~ $true | ~ app_encode_app(a, $o, sk_Xp, sk_Xx0)),
0.35/0.57	    inference('sup-', [status(thm)], ['0', '148'])).
0.35/0.57	tff('150', plain, (~ $true | ~ $true),
0.35/0.57	    inference('demod', [status(thm)], ['149', '111'])).
0.35/0.57	tff('151', plain, $false, inference('simplify', [status(thm)], ['150'])).
0.35/0.57	
0.35/0.57	% SZS output end Refutation
0.35/0.57	EOF
